Cover page

Image Name: Glow Window Tetra:Known as ‘glow widow tetra’, ‘glow skirt tetra’, ‘colour widow tetra’ in the

ornamental ﬁsh industry, a genetically modiﬁed variety of the black widow tetra Gymnocorymbus ternetzi is the

most favoured by aquarium ﬁsh hobbyists in West Bengal. Stunning and sparkling red, blue, yellow, green, pink,

orange, and purple bodied colour variations of this tetra have been developed through gene transfer or transgenic

technology. Photo: Geetha Paul

Managing Editor Chief Editor Editorial Board Correspondence

Ninan Sajeeth Philip Abraham Mulamoottil K Babu Joseph The Chief Editor

Ajit K Kembhavi airis4D

Geetha Paul Thelliyoor - 689544

Arun Kumar Aniyan India

Sindhu G

Journal Publisher Details

Publisher : airis4D, Thelliyoor 689544, India

Website : www.airis4d.com

Email : nsp@airis4d.com

Phone : +919497552476

Editorial

by Fr Dr Abraham Mulamoottil

airis4D, Vol.3, No.7, 2025

www.airis4d.com

This edition starts with the article “Entropy in

Natural Language Processing: Structure in Seeming

Chaos” by Jinsu Ann Mathew. The author explores

how entropy—a concept from physics and information

theory—is used in Natural Language Processing (NLP)

to uncover structure in language that often appears

random. The article introduces lexical entropy to

measure the unpredictability of words or characters

in a text, highlighting how repetition leads to lower

entropy and greater variety indicates higher entropy. It

then explains n-gram entropy, which examines patterns

in sequences of language units (like word pairs or trios),

providing deeper insights into syntax and style. Cross-

entropy, a metric used to evaluate how well language

models predict upcoming words, is discussed as both

a performance measure and an indicator of linguistic

complexity. Together, these entropy measures reveal

that beneath the surface of human language lies an

underlying structure that can be analyzed and modeled,

making entropy a powerful tool in computational

linguistics.

The article “Nonlinear Waves in Plasma Physics”

by Abishek P S explores the crucial role of nonlinear

wave phenomena in understanding and harnessing the

behavior of plasma—the fourth state of matter that

dominates the universe. Unlike linear waves, nonlinear

plasma waves give rise to complex structures like shock

waves, solitons, and double layers, which govern energy

transport, particle acceleration, and self-organization

across a range of environments from space to laboratory

settings. These structures are central to astrophysical

phenomena such as supernova explosions and solar

ﬂares, and are also vital in applied ﬁelds like fusion

energy, plasma-based propulsion, and advanced particle

accelerators. The article emphasizes that linear theories

fall short in capturing the richness of plasma dynamics,

and advanced simulations and diagnostics are essential

for studying these nonlinear eﬀects. Understanding

these waves not only enhances predictive capabilities

in space weather and fusion stability but also opens

avenues for transformative technologies. Ultimately,

the study of nonlinear waves bridges theoretical insight

with practical impact, oﬀering tools to decode and

control the dynamic nature of plasma across scales.

In the article Black Hole Stories-19, Professor Ajit

Kembhavi explores how gravitational waves—ripples in

the fabric of four-dimensional space-time—aﬀect matter

and how their presence can be experimentally detected.

Unlike electromagnetic waves that exert noticeable

forces on charged particles, gravitational waves cause

minute changes in spatial geometry, subtly stretching

and compressing distances. When such a wave passes

through a circle of free particles, it deforms the circle

into an ellipse in a periodic fashion, with the direction

of deformation depending on the wave’s polarization.

Early attempts to detect these waves included bar

detectors, notably constructed by physicist Joseph

Weber in the 1960s. Although Weber’s experiments

with large aluminium cylinders aimed to detect wave-

induced vibrations, his ﬁndings were ultimately not

conﬁrmed by others. However, his pioneering work

paved the way for more advanced detection methods.

The article then introduces interferometric detectors,

particularly a simpliﬁed Michelson interferometer,

where laser beams reﬂect oﬀ mirrors placed at equal

distances. The passage of a gravitational wave

alters the distances between mirrors, changing the

interference pattern of the light. These ﬂuctuations in

the interference pattern serve as a detectable signature

of a gravitational wave. The story sets the stage for

the next article, which will describe how this principle

is applied in the large-scale LIGO experiment that

successfully detected gravitational waves in 2015.

The article X-ray Astronomy: Through Missions

by Aromal P discusses key X-ray astronomy missions

launched in the 2010s, focusing on three signiﬁcant

satellites: NuSTAR, AstroSat, and Hitomi. NuSTAR,

launched in 2012 by NASA, is the ﬁrst focusing

high-energy X-ray telescope in orbit and has enabled

groundbreaking studies of supermassive black holes,

neutron stars, and supernova remnants. AstroSat,

India’s ﬁrst multi-wavelength space observatory

launched in 2015, carries ﬁve co-aligned instruments

covering UV to hard X-rays. It has advanced studies in

gamma-ray bursts, neutron stars, and stellar evolution.

Hitomi, a Japanese mission launched in 2016, was

designed for high-resolution spectroscopy across a

wide energy range but was unfortunately lost shortly

after beginning operations. Each mission signiﬁcantly

expanded our understanding of the high-energy universe

through improved instrumentation and observational

capabilities.

The article “The Bright Centers of Galaxies:

A Peek into Active Galactic Nuclei (AGN)” by Dr.

Savithri H. Ezhikode explores the nature, structure, and

history of active galactic nuclei—extremely luminous

regions at the centers of some galaxies powered

by supermassive black holes (SMBHs). While

most SMBHs are dormant, those actively accreting

matter form AGN, which emit vast energy across

the electromagnetic spectrum and can outshine entire

galaxies. Historical observations dating back to the early

20th century laid the groundwork for identifying AGN

subclasses such as Seyfert galaxies and quasars. AGN

exhibit distinctive features including high luminosity,

broadband emission, rapid variability, emission lines,

and powerful relativistic jets. Their core engine

consists of an SMBH surrounded by an accretion disk,

a hot corona, and various emission regions like the

broad and narrow line regions. A dusty torus further

inﬂuences the AGN’s appearance depending on viewing

angle. The article highlights the multi-component

and highly energetic nature of AGN and emphasizes

their importance in understanding cosmic evolution,

with future studies promising deeper insight into their

dynamic processes.

Sindhu G’s article, T Coronae Borealis (T CrB)

describes a rare and fascinating recurrent nova located

in the constellation Corona Borealis, poised for a

spectacular eruption in 2025 after previous outbursts

in 1866 and 1946. This binary system, consisting

of a white dwarf and a red giant, undergoes nova

eruptions when hydrogen transferred from the red giant

accumulates on the white dwarf and ignites in a surface

thermonuclear explosion. Unlike most novae, T CrB

erupts roughly every 80 years, oﬀering scientists a

unique chance to observe and study the full nova cycle.

Since 2023, the system has shown pre-eruption signs

such as optical brightening and increased X-ray activity,

strongly indicating an imminent explosion. When it

erupts, T CrB is expected to become visible to the

naked eye and oﬀer a rare celestial spectacle. Beyond

the visual awe, the event will help astronomers reﬁne

nova prediction models, explore binary star evolution,

and assess whether the system could one day become a

Type Ia supernova.

This article ”Decoding DNA’s Secrets: How

Sequence Shapes Life” by Geetha Paul explores the

intricate language of DNA and how its sequence of four

chemical bases—adenine (A), thymine (T), cytosine

(C), and guanine (G)—encodes the instructions for life.

It explains how DNA’s double-helix structure enables

the storage and transmission of genetic information,

with genes acting as functional units that dictate

protein synthesis. The genetic code is read in triplets

(codons), each representing a speciﬁc amino acid

or signaling function. Through transcription and

translation, these codes are converted into proteins

essential for cellular functions. The article also

examines the roles of regulatory DNA in controlling

gene expression and highlights real-world implications

of DNA sequence changes, such as in sickle cell

anemia, lactose intolerance, and eye color variation.

Emphasizing the near-universality of the genetic code,

iii

it discusses its signiﬁcance in biotechnology and

medicine, illustrating that DNA is not just a molecular

blueprint but the very narrative of life.

The article “Understanding Performance

Metrics in Parallel Computing” by Dr. Ajay

Vibhute explores essential metrics used to evaluate the

eﬀectiveness of parallel algorithms. It emphasizes that

designing parallel programs is only half the challenge;

assessing their performance is equally critical. Key

metrics discussed include speedup, which measures

how much faster a task runs on multiple processors;

eﬃciency, which gauges how well processor resources

are utilized; and scalability, which evaluates how

performance evolves as more processors or larger

problems are introduced. The article also covers

Amdahl’s Law, highlighting the theoretical limits of

speedup imposed by the non-parallelizable portions

of code. Through examples and analysis, it shows

how performance bottlenecks, overheads, and design

limitations impact real-world outcomes. Ultimately, the

article underscores the need for thoughtful, iterative

optimization and early integration of performance

evaluation to develop scalable, high-performance

software for modern multicore and distributed systems.

Contents

Editorial ii

I Artiﬁcial Intelligence and Machine Learning 1

1 Entropy in Natural Language Processing: Structure in Seeming Chaos 2

1.1 Lexical Entropy: Quantifying Uncertainty in Text . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 N-Gram Entropy: Capturing Sequence Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Language Models and Cross-Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

II Astronomy and Astrophysics 5

1 Nonlinear Waves in Plasma Physics 6

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2 Nonlinear Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Types of Nonlinear Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Signiﬁcance of Studying Nonlinear Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Black Hole Stories-19

The Detection of Gravitational Waves 12

2.1 Eﬀects Produced by Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Bar Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Interferometric Detectors for Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 X-ray Astronomy: Through Missions 16

3.1 Satellites in 2010s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 NuSTAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3 AstroSat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.4 HITOMI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4 The Bright Centers of Galaxies: A Peek into Active Galactic Nuclei 20

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.2 Observational Signatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.3 The AGN Central Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.4 Components of AGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5 T Coronae Borealis: A Recurrent Nova on the Verge of Eruption 24

5.1 Introduction: The Sleeping Star in Corona Borealis . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.2 Past Eruptions and Their Signiﬁcance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

CONTENTS

5.3 The Science Behind a Nova Eruption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.4 Current Observations and Signs of Imminent Eruption . . . . . . . . . . . . . . . . . . . . . . . . 25

5.5 The Anticipated Nova Event and Its Scientiﬁc Impact . . . . . . . . . . . . . . . . . . . . . . . . 26

5.6 Conclusion: Awaiting a Celestial Spectacle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

III Biosciences 28

1 Decoding DNA’s Secrets: How Sequence Shapes Life 29

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1.2 The Structure of DNA: The Blueprint of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1.3 Genes: The Units of Heredity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

1.4 The Genetic Code: Triplets and Codons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

1.5 From DNA Sequence to Biological Message . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

1.6 Protein Folding and Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

1.7 Real-World Examples of DNA Messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

1.8 The Universality and Flexibility of the Genetic Code . . . . . . . . . . . . . . . . . . . . . . . . . 33

1.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

IV Computer Programming 34

1 Understanding Performance Metrics in Parallel Computing 35

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

1.2 Speedup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

1.3 Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

1.4 Scalability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

1.5 Amdahl’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

vii

Part I

Artiﬁcial Intelligence and Machine Learning

Entropy in Natural Language Processing:

Structure in Seeming Chaos

by Jinsu Ann Mathew

airis4D, Vol.3, No.7, 2025

www.airis4d.com

Language might seem unpredictable at

times—with new words, diﬀerent writing styles,

and sentences that don’t always follow clear rules. But

when we look closely, there is a hidden structure behind

the way we speak and write. One useful way to study

this structure is through a concept called entropy.

Originally used in physics and information theory,

entropy is a way to measure uncertainty or randomness.

In Natural Language Processing (NLP), we use entropy

to understand how ordered or chaotic a piece of text is.

For example, we can measure how predictable certain

words or letters are in a sentence or how much variety

there is in the way language is used.

In this article, we’ll explore how entropy helps

us analyze text using simple tools like n-grams and

language models. We’ll also see how it can reveal

interesting patterns in how language works—even when

it seems random.

1.1 Lexical Entropy: Quantifying

Uncertainty in Text

Lexical entropy is a way of measuring how

unpredictable or random the characters or words in a

piece of text are. In simple terms, it helps us understand

how much variety exists in the language being used. If

a text is highly repetitive, it has low entropy, meaning it

is more predictable. On the other hand, if a text uses a

wide range of words or characters in an unpredictable

way, it has high entropy. This makes lexical entropy a

useful tool for examining the complexity and structure

of language.

At the character level, consider a string like

’aaaaaa’. It contains only one character repeated several

times, making it extremely predictable. The lexical

entropy here is low, possibly even zero. Now compare

that to a string like ’abcdef’, which contains six diﬀerent

letters with no repetition. Each character is equally

likely and gives us new information, making the string

less predictable and the entropy higher. This kind of

calculation helps quantify the randomness in a sequence

of letters.

The same idea applies at the word level. For

example, a simple sentence like “The cat sat on the

mat” repeats common words and follows a familiar

pattern, leading to lower entropy. In contrast, a complex

sentence from a scientiﬁc paper or literary text might

contain rare or specialized words, used less frequently

and less predictably, resulting in higher entropy. By

measuring how often each word appears and calculating

their probabilities, we can compute the lexical entropy

of the text.

Understanding lexical entropy helps us make useful

observations. Low entropy often suggests structured

or constrained language—such as in children’s books,

instructions, or poetry—where repetition and patterns

are common. High entropy indicates greater diversity

or randomness, which can be seen in academic texts,

stream-of-consciousness writing, or even randomly

generated strings of text. Each case tells us something

about how the text is constructed and what kind of

1.2 N-Gram Entropy: Capturing Sequence Patterns

cognitive load it may carry for the reader.

Lexical entropy has practical applications in many

areas of Natural Language Processing. It can be used

to compare writing styles, estimate the richness or

simplicity of a document, or detect changes in language

use over time. It also plays a role in stylometry (the

study of writing style), language development research,

and text classiﬁcation. In essence, lexical entropy gives

us a way to measure the invisible patterns that shape

our communication.

1.2 N-Gram Entropy: Capturing

Sequence Patterns

While lexical entropy looks at the unpredictability

of individual characters or words, n-gram entropy

focuses on the patterns formed by sequences of these

elements. An n-gram is a group of ’n’ items taken from

a sequence of text—these items could be characters

or words. For example, in the phrase “the cat,” the

character bigrams (n = 2) are “th,” “he,” “e,” “ c,” “ca,”

and “at.” Similarly, word bigrams are “the cat.” By

analyzing how frequently these n-grams occur in a text,

we can calculate the entropy of these sequences and

gain insights into the structure of the language.

N-gram entropy helps us understand how

predictable these short sequences are. If a certain

bigram appears very often—like “th” in English—it

contributes less to the overall entropy. In contrast,

if a wide variety of bigrams are used with roughly

equal frequency, the entropy increases, reﬂecting greater

diversity and less predictability. For example, a tightly

structured text such as a legal document may repeat

speciﬁc phrases and word combinations, leading to

low n-gram entropy. Meanwhile, creative writing or

spontaneous speech often contains a much broader

and less predictable set of n-grams, resulting in higher

entropy.

The level of n (i.e., how many items are grouped

together) matters signiﬁcantly. Unigram entropy gives

a basic sense of variation among individual items, like

letters or words. Bigram and trigram entropy go a step

further by capturing how elements combine, oﬀering

Figure 1: Sequences of n language units.

(image courtesy:https://www.pykonik.org/media/slides/tech-talks-49-statistical-language-modeling-

with-n-grams-in-python.pdf)

a better view of language patterns such as grammar,

syntax, or common phraseology (Fig 1). Higher-order

n-grams (like 4-grams or 5-grams) can capture more

complex patterns, but they also require more data to be

reliable.

In practical applications, n-gram entropy is used

in tasks like language modeling, authorship analysis,

and stylistic comparison. It can reveal how formulaic or

expressive a text is, and it plays a crucial role in machine

learning models that predict text, such as predictive

keyboards or speech recognition systems. By analyzing

how predictable a sequence is, these systems can better

guess what comes next in a sentence.

Ultimately, n-gram entropy allows us to move

beyond looking at individual words and begin analyzing

the structure and rhythm of language. It shows how

pieces of language are put together and gives us a way to

quantify how tightly or loosely a text follows common

patterns.

1.3 Language Models and

Cross-Entropy

In Natural Language Processing, a language model

is a tool that learns the structure of a language by

analyzing large amounts of text. Its main job is to predict

the next word (or character) in a sentence, given the

words that came before. For example, given the phrase

“The sky is,” a good language model might predict that

the next word is “blue” with a high probability. To

do this well, the model must learn which sequences of

words are common and which are not.

As language models make predictions, they assign

probabilities to all the possible next words. Some

1.4 Conclusion

words are more likely than others based on context. For

instance, after the word “peanut,” the word “butter”

is more probable than “car” in most contexts. The

model’s accuracy depends on how closely its predicted

probabilities match the actual words that appear in the

text.

This is where cross-entropy comes in. Cross-

entropy is a way to measure how well a language model

predicts the next word. It calculates the diﬀerence

between the model’s predicted probability distribution

and the actual outcome. If the model is conﬁdent and

correct, the cross-entropy will be low. But if it assigns

low probability to the actual word that appears, the cross-

entropy will be high. In other words, low cross-entropy

means better predictions and more understanding of

language structure.

Cross-entropy is not just a performance metric—it

also reﬂects the complexity of the text being modeled.

Text that follows common patterns or contains repeated

phrases will be easier for the model to predict, resulting

in lower cross-entropy. On the other hand, texts with

rare words, creative language, or unusual grammar

will confuse the model more and produce higher cross-

entropy values. This makes cross-entropy a useful tool

for evaluating both the model and the text itself.

In practical terms, cross-entropy is used during

the training and evaluation of language models like

n-gram models, recurrent neural networks (RNNs), and

transformers. It helps determine how well the model

has learned and how it might perform on unseen data.

Researchers and developers use cross-entropy loss to

guide the learning process, reducing it over time to

improve accuracy.

1.4 Conclusion

Entropy, though rooted in physics and mathematics,

proves to be an incredibly insightful tool for

understanding the complexity of human language.

Through lexical entropy, we can measure how

predictable individual characters or words are in a text,

revealing the richness or simplicity of its vocabulary.

With n-gram entropy, we dive deeper into the structure

of language, uncovering patterns in sequences of words

or letters that reﬂect grammar, style, and coherence.

Finally, cross-entropy allows us to assess how well

predictive models capture the underlying structure of

language, giving us a way to evaluate both text and

model performance.

Each of these forms of entropy sheds light on

diﬀerent aspects of linguistic order and variation.

Together, they demonstrate that language—though

it may often appear chaotic—is shaped by subtle,

measurable regularities. By using entropy-based

approaches, we gain not only a better understanding

of how language works but also powerful tools for

analyzing, modeling, and processing it more eﬀectively.

References

Entropy of natural languages: Theory and

experiment

The Word Entropy of Natural Languages

Entropy increasing for NLP: Understanding its

impact

Entropy Rate Estimates for Natural Language—A

New Extrapolation of Compressed Large-Scale

Corpora

EDT: Improving Large Language Models’

Generation by Entropy-based Dynamic

Temperature Sampling

Excess entropy in natural language: Present state

and perspectives

Entropy analysis of natural language written texts

About the Author

Jinsu Ann Mathew is a research scholar

in Natural Language Processing and Chemical

Informatics. Her interests include applying basic

scientiﬁc research on computational linguistics,

practical applications of human language technology,

and interdisciplinary work in computational physics.

Part II

Astronomy and Astrophysics

Nonlinear Waves in Plasma Physics

by Abishek P S

airis4D, Vol.3, No.7, 2025

www.airis4d.com

1.1 Introduction

Plasma, often hailed as the fourth state of matter,

is a highly energetic and conductive medium composed

of freely moving ions and electrons. It constitutes over

99% of the visible universe, from the blazing interiors

of stars and solar ﬂares to the vast interstellar and

intergalactic mediums. Unlike solids, liquids, or gases,

plasma is intrinsically collective in its behavior—its

charged particles respond not only to local forces but

also to long-range electromagnetic ﬁelds, giving rise

to a fascinating array of instabilities, turbulence, and

wave phenomena[1,2].

Among these, nonlinear plasma waves occupy a

particularly important niche. Unlike linear waves, which

obey simple superposition principles, nonlinear waves

exhibit complex interactions, amplitude-dependent

propagation speeds, and can form persistent structures

such as solitons, shocks, and double layers. These

structures are not mere curiosities; they encapsulate

deep physical principles and serve as signatures of

plasma’s intricate internal dynamics.

The study of these nonlinear phenomena is

pivotal—not just to decode the universe’s grand

mechanisms, but also to push the boundaries of human

achievement in applied technologies. In fusion energy

research, for example, understanding how nonlinear

waves transport energy and particles helps us ﬁne-

tune conﬁnement strategies in magnetic and inertial

fusion devices. In space and astrophysical plasmas,

these waves govern critical processes like particle

acceleration in the magnetosphere, shock formation

in supernova remnants, and even the modulation of

cosmic rays. They also play a subtle yet vital role in

next-generation communication systems, where space

plasma interactions can aﬀect signal propagation in

satellite and deep-space missions.

Thus, delving into the world of nonlinear plasma

waves is not merely a theoretical endeavour—it is a

key to unlocking transformative capabilities in science,

technology, and our understanding of the cosmos.

1.2 Nonlinear Waves

Linear wave theory, while foundational to classical

plasma physics, provides only a limited lens through

which to view the vibrant, often chaotic dynamics

of real plasma systems. At its core, linear analysis

assumes small amplitude perturbations and neglects

feedback mechanisms and intermodal interactions. As

a result, it falters when applied to scenarios marked

by strong ﬂuctuations, steep gradients, or long-range

electromagnetic coupling—conditions that are not

only common but fundamental in both laboratory and

astrophysical plasmas.

Under such circumstances, nonlinear eﬀects

emerge as the primary architects of plasma behaviour.

These eﬀects give rise to a remarkable array of

phenomena that cannot be understood as mere

sums of simpler waveforms. Instead, the plasma

reorganises itself into structures characterised by

stability, resilience, and complex interactions[3].

Solitary waves, for example, maintain their integrity

through a precise balance between nonlinearity and

dispersion[4]. Shock waves propagate with abrupt

discontinuities, often associated with irreversible

1.3 Types of Nonlinear Waves

processes like heating or particle acceleration[5].

Double layers act as microscopic particle accelerators,

embedding signiﬁcant potential drops across narrow

spatial regions[6].

Importantly, these nonlinear structures are not

just academic curiosities—they are powerful agents of

transport, energy conversion, and self-regulation. In

the realm of controlled fusion, they can either hinder

conﬁnement through enhanced transport or facilitate

heating mechanisms such as nonlinear wave-particle

interactions. In space plasmas, from the solar wind to

planetary magnetospheres, nonlinear wave phenomena

govern everything from auroral substorms to cosmic ray

modulation. They are also instrumental in mediating

magnetic reconnection, a process central to explosive

energy release events like solar ﬂares and geomagnetic

storms.

Capturing these rich behaviours demands a

departure from purely analytic approaches toward

advanced numerical simulations, where the full

nonlinearity of Maxwell’s equations and the Vlasov or

ﬂuid equations can be incorporated. These models are

essential for predicting the onset of instabilities, the

evolution of coherent structures, and the thresholds at

which linear theory ceases to apply.

In this broader light, the study of nonlinear waves

is not just a deeper layer of theory—it is the essential

framework for making sense of the dynamic tapestry

that deﬁnes plasma as a state of matter.

1.3 Types of Nonlinear Waves

1.3.1 Shock Waves

Shock waves in plasma represent a class of

nonlinear structures that arise when disturbances

propagate faster than the characteristic wave speeds

(see Fig.1) —such as the ion acoustic or magnetosonic

speed—of the ambient medium. These waves

produce abrupt, irreversible changes in plasma

parameters including density, temperature, velocity,

and electromagnetic ﬁelds, acting as key sites for

energy dissipation, particle acceleration, and entropy

generation. Their formation mechanisms diﬀer

Figure 1: Formation of Shock Wave.

Image courtesy : https://www.kindpng.com/imgv/Twwhoib show-more-plots- debye-shielding-in-p

lasma-physics/

signiﬁcantly between collisional and collisionless

regimes. In collisional plasmas, inter-particle

collisions provide the requisite dissipation, whereas

in collisionless systems—prevalent in astrophysical and

space environments—energy is redistributed through

wave-particle interactions, kinetic instabilities, and

electromagnetic ﬁelds. These collisionless shocks

exhibit layered internal structures, including a foot,

ramp, and overshoot, which encapsulate ion reﬂection,

electron heating, and self-generated turbulence. Earth’s

bow shock, resulting from the interaction between

the supersonic solar wind and the geomagnetic

ﬁeld[7], serves as a benchmark example and has been

extensively studied through high-resolution satellite

missions like MMS, Cluster, and THEMIS. These

missions have revealed the spatial and temporal

intricacies of shock fronts, including shock reformation,

electron-scale dissipation, and anisotropic pressure

eﬀects. Beyond the geospace context, shock waves

are fundamental to numerous astrophysical phenomena

such as supernova remnant expansion, cosmic ray

acceleration through diﬀusive mechanisms, and energy

transport in relativistic jets from active galactic nuclei.

In all cases, the inherently nonlinear and dissipative

nature of shocks underscores their central role in

mediating energy ﬂow and structuring plasma behavior

across vastly diﬀerent scales and environments.

1.3.2 SOLITONS

Solitons are a class of nonlinear wave structures

that exhibit remarkable stability and coherence,

maintaining their shape and speed over extended

distances and through mutual interactions. Unlike

ordinary wave packets that disperse due to the medium’s

1.4 Signiﬁcance of Studying Nonlinear Waves

Figure 2: Shape of Soliton Wave.

Image courtesy : https://www.kindpng.com/imgv/Twwhoib show-more-plots- debye-shielding- in-p

lasma-physics/

natural dispersion, solitons emerge from a precise

balance between nonlinear steepening and dispersive

spreading. This balance is governed by integrable

systems—such as those described by the Korteweg–de

Vries (KdV) equation or its variants—making solitons

exact solutions within certain mathematical frameworks.

In plasma environments, ion-acoustic solitons are

among the most commonly observed, particularly in

low-temperature, collisionless, and weakly magnetized

plasmas where ion inertia and electron pressure eﬀects

are dominant. These structures appear as localized

density enhancements or depletions and can be either

compressive or rarefactive, depending on the electron-

to-ion temperature ratio and the presence of additional

plasma species such as dust grains, negative ions, or

energetic electrons.

One of the most intriguing features of solitons

is their particle-like behaviour: they can propagate

long distances without attenuation and interact non-

destructively. When two solitons “collide,” they may

temporarily distort, but afterwards each reemerges with

its original shape and velocity—a property unique to

integrable systems. This has profound implications

not only for plasma theory but also for communication

systems, optical ﬁbre technologies, and quantum ﬁeld

analogues, where soliton dynamics oﬀer robust modes

of signal transmission and energy localisation.

In laboratory and space plasmas, soliton detection

and modelling often rely on nonlinear ﬂuid models,

Vlasov simulations, and Langmuir probe diagnostics,

providing insights into nonlinear energy transport

and wave-particle interactions. Understanding soliton

behaviour in multi-component or magnetised plasmas

is also critical in reﬁning models of space weather

phenomena, dusty plasma dynamics, and even early-

universe cosmology.

1.3.3 Double Layers

Double layers (DLs) are highly localised, non-

neutral plasma structures characterised by a sharp

electric potential drop across a narrow spatial region,

typically spanning just a few Debye lengths. This

abrupt potential gradient arises from the juxtaposition

of two thin layers of net positive and negative space

charge, resulting in an intense electrostatic ﬁeld that

can accelerate charged particles to high energies over

very short distances. From a dynamical standpoint,

DLs function as microscopic electrostatic barriers,

often forming spontaneously in regions with current-

driven instabilities, charge separation, or boundary

interactions. Their capacitive-like nature—in which

the adjacent space-charge layers mimic the plates

of a capacitor—makes them uniquely eﬃcient at

concentrating and directing electrical energy into

kinetic energy. In space plasmas, double layers are

frequently observed in auroral acceleration zones,

where they are implicated in generating bursts of

suprathermal electrons responsible for discrete auroral

arcs. In laboratory environments, particularly in

glow discharges, plasma thrusters, and double plasma

devices, DLs manifest during transitions between

diﬀerent plasma regimes, often serving as diagnostic

indicators of nonequilibrium conditions. Theoretical

models such as the Bernstein–Greene–Kruskal (BGK)

approach and Sagdeev pseudopotential analysis are

commonly employed to study their formation and

stability. Understanding double layers is therefore

critical not only to unravelling the microphysics of

space weather phenomena but also to optimising plasma

propulsion systems and advancing high-voltage plasma

applications.

1.4 Signiﬁcance of Studying Nonlinear Waves

Figure 3: Formation of Double Layer.

Image courtesy: https://www.kindpng.com/imgv/Twwhoib show-more-plots-debye-shielding- in-p

lasma-physics/

1.4 Signiﬁcance of Studying

Nonlinear Waves

1.4.1 Predicting and Controlling Instabilities

in Fusion Devices such as Tokamaks

In magnetic conﬁnement fusion devices,

maintaining plasma stability is paramount to achieving

sustained thermonuclear reactions. Nonlinear

wave theory plays a pivotal role in deciphering

how microturbulence, drift-wave instabilities, and

magnetohydrodynamic (MHD) modes evolve and

interact[8]. Researchers analyze nonlinear couplings,

saturation mechanisms, and energy cascades to model

how coherent structures such as zonal ﬂows and

blobs inﬂuence cross-ﬁeld transport. A deeper

understanding of these phenomena is instrumental for

devising real-time control schemes, including resonant

magnetic perturbations (RMPs) and feedback-driven

current proﬁle shaping, ultimately enhancing plasma

performance and preventing disruptions.

Figure 4: Tokamak.

Image courtesy: https://www.kindpng.com/imgv/Twwhoib show-more-plots-debye-shielding- in-p

lasma-physics/

1.4.2 Interpreting Satellite Observations of a

Planet’s Magnetosphere and Solar Wind

Space-borne missions continuously detect

signatures of nonlinear plasma processes, particularly

during events such as magnetic reconnection, bow

shock formation, or auroral acceleration. Researchers

leverage these observations to identify nonlinear solitary

structures, kinetic-scale Alfv

en waves, and double

layers that mediate particle heating and anisotropic

pressure distributions. By coupling spacecraft

data with numerical models and theory, scientists

can infer the role of nonlinear wave interactions

in driving magnetospheric substorms, ring current

enhancement, and radiation belt dynamics, enriching

our understanding of space weather and its terrestrial

implications.

1.4.3 Advancing Plasma-Based Technologies

like Particle Accelerators and Pulsed

Power Systems

In laser-plasma and beam-plasma systems,

nonlinear wave dynamics underpin critical mechanisms

of ﬁeld generation, energy transfer, and structure

formation. Researchers explore wakeﬁeld excitation,

parametric instabilities, and wave-breaking phenomena

to optimise the generation of ultra-relativistic particle

beams. In pulsed power devices, nonlinear wave

steepening, magnetic insulation, and sheath formation

1.5 Conclusion

are analysed to improve energy delivery and focus[9].

Such studies inform the design of compact, high-

brilliance accelerators for medical, industrial, and high-

energy physics applications, as well as pulsed fusion

drivers.

1.4.4 Modelling Astrophysical Phenomena

such as Shock Fronts in Supernova

Remnants or Jets from Active Galactic

Nuclei (AGN)

Astrophysical plasmas evolve in regimes where

nonlinear MHD eﬀects dominate, often involving

relativistic speeds, strong ﬁeld gradients, and multi-

scale coupling. Researchers study the nonlinear

evolution of current-driven and shear instabilities in

AGN jets to explain ﬁlamentation, variability, and

energy dissipation. Likewise, in supernova remnants,

nonlinear shock acceleration mechanisms—such as

diﬀusive shock acceleration (DSA) with feedback

from cosmic ray pressure—are modeled to understand

synchrotron emission and elemental composition.

These eﬀorts bridge the gap between microphysical

wave-particle interactions and large-scale observables

in high-energy astrophysics[10].

1.5 Conclusion

In summary, the study of nonlinear plasma

waves unveils a deep and multifaceted understanding

of plasma behaviour beyond linear approximations.

Phenomena such as shock waves, solitons, and

double layers illustrate how nonlinearity gives rise

to coherent structures capable of mediating energy

transport, particle acceleration, and self-organisation

across vastly diﬀerent plasma environments. These

structures are observed in natural systems—from

Earth’s magnetosphere to astrophysical jets—as well as

in laboratory settings critical to fusion energy and

space propulsion technologies. As our diagnostic

capabilities advance and computational methods grow

more sophisticated, we stand at the threshold of not

only decoding but also manipulating these nonlinear

processes for practical beneﬁt.

Looking ahead, future research will likely focus

on integrating multi-scale modelling techniques—from

ﬂuid to kinetic regimes—to resolve the full hierarchy

of nonlinear interactions. The development of

high-resolution, real-time diagnostics may enable

direct observation of wave-particle coupling and

dynamic transitions in shock and soliton behaviour.

Additionally, tailoring plasma parameters to engineer

nonlinear structures may pave the way for novel

applications in propulsion, radiation sources, and

materials processing. Understanding how nonlinear

waves inﬂuence turbulence and anomalous transport

in magnetised plasmas remains a critical challenge

for advancing magnetic and inertial fusion schemes.

Moreover, with increasing access to space-borne

instruments and laboratory analogues, comparative

studies of nonlinear structures across planetary, solar,

and astrophysical contexts will deepen our grasp of

universality and variance in plasma dynamics. In

essence, nonlinear waves are not just signatures of

complexity—they are active agents shaping the physical

universe, and our ability to harness them may hold the

key to future breakthroughs in energy, exploration, and

understanding.

References

[1] Francis, F, Chen., (2015). Introduction

to Plasma Physics and Controlled Fusion (3rd ed.).

Springer Cham. https://doi.org/10.1007/978-3-319-

22309-4

[2] Lewi, Tonks.,The Birth of “Plasma”. Am.

J. Phys. 1 September 1967; 35 (9): 857–858.

https://doi.org/10.1119/1.1974266

[3] Saha, A., & Banerjee, S. (2021). Dynamical

Systems and Nonlinear Waves in Plasmas (1st ed.).

CRC Press. https://doi.org/10.1201/9781003042549

[4] Petviashvili, VLADIMIR .I., & Pohkotelov,

OLEG .A. (1992). Solitary Waves in Plasmas

and in the Atmosphere (1st ed.). Routledge.

https://doi.org/10.4324/9781315075556

[5] D. A. Tidman., (1967). “Turbulent Shock

Waves in Plasmas”. Phys. Fluids.10 (3): 547–564.

https://doi.org/10.1063/1.1762148

1.5 Conclusion

[6] P. Leung, A. Y. Wong, B. H. Quon., (1980).

Formation of double layers”. Phys. Fluid. 23 (5):

992–1004. https://doi.org/10.1063/1.863073

[7] Montgomery, M. D., J. R. Asbridge, and S.

J. Bame (1970). “Vela 4 plasma observations near

the Earth’s bow shock”. J. Geophys. Res., 75(7),

1217–1231, doi:10.1029/JA075i007p01217.

[8] Stacey, W.M., (2007). A Survey of

Thermal Instabilities in Tokamak Plasmas: Theory,

Comparison with Experiment, and Predictions for

Future Devices. Fusion Science and Technology, 52(1),

29-67. https://doi.org/10.13182/FST07-A1485

[9] Joshi, C. (2006). “PLASMA

ACCELERATORS”. Scientiﬁc American, 294(2),

40–47. http://www.jstor.org/stable/26061335

[10] Vink, J. (2004). “Shocks and particle

acceleration in supernova remnants: observational

features”. Advances in Space Research, 33(4), 356-365.

https://doi.org/10.1016/j.asr.2003.05.012

About the Author

Abishek P S is a Research Scholar in

the Department of Physics, Bharata Mata College

(Autonomous) Thrikkakara, kochi. He pursues

research in the ﬁeld of Theoretical Plasma physics.

His works mainly focus on the Nonlinear Wave

Phenomenons in Space and Astrophysical Plasmas.

Black Hole Stories-19

The Detection of Gravitational Waves

by Ajit Kembhavi

airis4D, Vol.3, No.7, 2025

www.airis4d.com

In this story we will see how the passage of

a gravitational wave through a region of space can

eﬀect particles which are present there. We will

then consider how the passage of gravitational waves

can be experimentally detected, using an arrangement

very similar to a Michelson interferometer. That will

provide the background for a description of the LIGO

gravitational wave detector in our next story.

2.1

Eﬀects Produced by Gravitational

Waves

The eﬀects produced by an electromagnetic wave

are easy to understand and discern. An electromagnetic

wave passing in some direction exerts a force on

any charged particles in its path, like electrons, and

accelerates them. The accelerated particles in turn

emit radiation, which results in some of the energy in

the electromagnetic wave being scattered in various

directions, which can be detected. If the wave

encounters an antenna, it sets up a current in it, which

again can be easily detected. Modern life is closely

tied to the generation and detection of electromagnetic

waves.

The eﬀects of gravitational waves are more subtle

and weak, and therefore far more diﬃcult to detect.

We have seen in earlier stories that gravitational waves

are ripples in four dimensional space-time. When a

gravitational wave passes some region of space, the

geometry there gets aﬀected. As a result, there is change

Figure 1: The eﬀect of a gravitational wave on a set of

free point masses arranged in a circle. The gravitational

wave travels into the plane of the paper, in a direction

perpendicular to the plane. The upper and lower parts

of the ﬁgure correspond to two polarisation states, as

explained in the text.

in all measured distances around the location. To see

the eﬀect of such a change, consider tiny particles which

are arranged in a circle in space, as shown in Figure 1.

Now suppose a gravitational wave passes in a

direction perpendicular to the circle into the plane of

the paper. The change in the geometry produced by the

wave is such that when there is contraction along the

x-direction as shown in the ﬁgure, there is expansion

along the y-direction which is perpendicular to it. As

time passes, and the gravitational wave propagates

forward, the directions of contraction and expansion

are exchanged. For particles which are not along the x-

or y-directions, whether expansion or contraction takes

place depends on the direction in which it is located.

The net eﬀect is that the circle of particles changes

shape periodically: it alternately becomes an ellipse

ﬁrst stretched along the x-direction and then stretched

along the y-direction, as shown in the upper part of the

2.2 Bar Detectors

ﬁgure.

The periodic change of shape can occur in a

somewhat diﬀerent way, with the maximum stretching

taking place in a direction which is inclined to the x- and

y- directions, as shown in the lower part of the ﬁgure.

This occurs because of the diﬀerence in a property of

the gravitational waves known as polarisation. If a

gravitational wave approaches the circle in a direction

which is not perpendicular to or there is more than one

gravitational wave passing through at the same time,

then the eﬀects will be similar to those described, with

the details depending on the situation.

2.2 Bar Detectors

The particles we considered above are free

particles, in the sense that they are not under the

inﬂuence of any force and are aﬀected only by the

gravitational wave passing through. The distance

between the particles changes as the space expands

and contracts due to the passage of the gravitational

wave. But what about a bar of steel, say, which is in the

path of the gravitational wave? Would the rod expand

and contract too, if the eﬀect of the gravitational wave

is universal?

The situation with the steel bar is quite diﬀerent

from that of the particles considered above. The bar is

made of particles, in the form of atoms and molecules,

which are in incessant motion, and in interaction with

each other through electrical forces. It is these forces

which hold the particles together so that the bar acquires

a form which is rigid on the large scale. When the bar

changes its length due to the expansion and contraction

of space due to passage of a gravitational wave, there

is a change in the forces between the particles, and

restoring forces are set up. These cause the bar to return

to its original size. The result of the two opposing

eﬀects is that the bar begins to vibrate; these vibrations

continue even after the wave has passed by, until they

are gradually damped out. This is like the ringing of

a bell when it is struck, which persists for some time

after the blow, and gradually reduces in intensity. The

vibrations of the bar are of very low amplitude, i.e.,

they are very feeble, so it is extremely diﬃcult to detect

them. For a bar of cylindrical shape of a given size and

material, there is a particular frequency, known as the

resonance frequency which has the greatest amplitude.

This frequency depends on the length of the bar, its

matter density and on how elastic the material of the

bar is.

In the 1960s, Professor Joseph Weber of the

University of Maryland decided to measure the bar

vibrations triggered by gravitational waves to detect

their passage. For this purpose he constructed a number

of accurately machined bars of aluminium, one of which

was 2 meters long and 1 meter in diameter, with other

bars having similar dimensions. The idea was that when

a gravitational wave of a speciﬁc frequency passed by the

bar, the bar would begin to vibrate, or ring, as described

in the previous section. While vibrations with various

frequencies would be present, the most dominant would

be the resonant or ringing frequency. For the cylinder

used by Weber, this resonant frequency was close to

1660 Hertz, i.e., 1660 vibrations per second. This

frequency was chosen as Weber expected it would be

the dominant frequency emitted by various gravitational

wave sources. Through a series experiments with bar

detectors that he constructed, Weber believed that he

had detected gravitational waves.

Weber’s results could not be reproduced by other

similar experiments, and his analysis of the data

was believed to be incorrect. The community of

scientists therefore did not accept that Weber had

detected gravitational waves. But Weber’s work and his

enthusiasm inspired many other groups to develop other

versions of bar detectors, with improved ability to detect

the waves. These attempts were not successful either

in spite of the great improvement in the technology.

One had to wait until 2015 when the Advanced

LIGO experiment was ﬁnally successful in detecting

gravitational waves from a coalescing binary black hole

system. We now describe a schematic gravitational

wave detector to clarify basic concepts.

2.3 Interferometric Detectors for Gravitational Waves

2.3 Interferometric Detectors for

Gravitational Waves

We have seen above that when a gravitational

wave passes through a circle of free particles, the circle

periodically changes shape to an ellipse which is ﬁrst

stretched in one direction and then in the perpendicular

direction. We will use the arrangement of a Michelson

interferometer, which is a familiar object in physics

laboratories, to see how the change in shape could be

used to detect the passage of a gravitational wave.

Imagine that mirrors

and

are attached to

two particles on a circle as shown on the left in Fig. 2.

and that a third mirror M is placed at the centre of the

circle. The distances

between

and M, and the

distance

between

and M are equal. The two paths

of the beam between M and

and M and

, can be

viewed as two arms of a Michaelson interferometer.

A beam of laser light emitted from the source at

the left of the diagram travels to the mirror M, which

is known as a beam splitter. This mirror allows half

the light of the beam to pass through it, towards mirror

, while the other half of the light is reﬂected towards

mirror

. The light striking the mirrors

and

is reﬂected back towards the beam splitter, and the

combined beam then reaches a light detector at the

bottom of the ﬁgure. The distance travelled by the two

beams is exactly the same and so is the time taken for

the beams to arrive at the detector. Since the light waves

in the beam arise from the same source and travel the

same distance until they reach the detector, they are in

phase and combine constructively, producing a bright

spot at the detector. If, on the other hand, the distance

travelled diﬀers by half the wavelength of the light wave,

then the two waves combine destructively, producing a

dark spot. This can be achieved by moving one of the

mirrors slightly, so that the distances

and

are diﬀer

just enough to produce the half wavelength diﬀerence

in the distance travelled by the beams. Depending on

the exact conﬁguration of the mirrors the combined

beam can produce concentric light and dark circles, or

a pattern of light and dark straight lines at the detector.

The process of combining two wave trains of light to act

Figure 2: An interferometer conﬁguration with the two

mirrors

and

being equidistant from the central

mirror M is shown at the top left of the ﬁgure. The

ensuing constructive interference is shown at bottom

left. When a gravitational wave passes through the

conﬁguration, mirror

moves away from M while

moves towards M as shown at top right. If the

diﬀerence in path length is exactly equal to half a

wavelength, then there is destructive interference, as

shown at the bottom right.

constructively or destructively is known as interference

and the pattern produced is known as an interference

pattern. Constructive and destructive interference is

shown in the lower half of Figure 2.

Now suppose a gravitational wave passes through

the circle of particles, so that it is stretched to form

an ellipse as shown on the right of the ﬁgure. The

mirror

is now farther from M than it was in the

absence of the wave, while

has moved closer to M.

The distances travelled by the two beams are therefore

diﬀerent and there is a change in the interference pattern.

As the mirrors move back and forth the interference

pattern changes periodically, which can be detected if

the change is large enough. The changing interference

pattern therefore becomes a signature of the passage

of a gravitational wave. The idea is schematically

represented in Figure 2.

In the next story we will see how the simple

Michaelson interferometer described above is converted

to a giant LIGO gravitational wave detector.

2.3 Interferometric Detectors for Gravitational Waves

About the Author

Professor Ajit Kembhavi is an emeritus

Professor at Inter University Centre for Astronomy

and Astrophysics and is also the Principal Investigator

of the Pune Knowledge Cluster. He was the former

director of Inter University Centre for Astronomy and

Astrophysics (IUCAA), Pune, and the International

Astronomical Union vice president. In collaboration

with IUCAA, he pioneered astronomy outreach

activities from the late 80s to promote astronomy

research in Indian universities.

X-ray Astronomy: Through Missions

by Aromal P

airis4D, Vol.3, No.7, 2025

www.airis4d.com

3.1 Satellites in 2010s

So far we have covered the X-ray astronomical

satellites launched till 2010. Even though ﬁrst half of

the last decade only had one X-ray speciﬁc mission,

but the second half seen an increase in the number of

missions which had greater scientiﬁc capabilities. In

this article we will discuss 3 of the satellites launched

in the last decade and the rest will be discussed in the

upcoming article.

3.2 NuSTAR

The Nuclear Spectroscopic Telescope Array

(NuSTAR) is the ﬁrst focusing high-energy X-ray

telescope in orbit launched in June 2012. NuSTAR

is classiﬁed as NASA’s 11th Small Explorer (SMEX)

mission and is designated as Explorer 93. It was

launched into an orbit of 600-650 km radius with an

inclination of

○

using Pegasus rocket. The rocket was

air-launched from an ”TriStar” aircraft ﬂying 40,000

feet above the surface.

The stowed conﬁguration of NuSTAR measured

1.2 × 2.2

m. Once orbited, a

10 m

mast was deployed

to focus the high energy X-ray photons which separated

the optic module from the spacecraft. The optic module

consists of two co-aligned hard X-ray grazing-incidence

telescopes pointed at celestial targets. The three-axis

stabilized spacecraft contains the focal plane module,

necessary electronics and solar panel. Telescopes

contain 133 multilayer-coated grazing incidence shells

approximated with Wolter-1 geometry. Each telescope

has its own focal plane which consists of a solid state

Op#cs&

modules&

Deployed&mast&

Focal&plane&bench&

Instrument&star&tracker&

Mast&canister&

Metrology&

detector&(1&of&2)&

Metrology&

lasers&

Focal&plane&

detector&

module&(1&of&2)&

Figure 1: Diagram of the observatory in the stowed

(bottom) and deployed (top) conﬁgurations. Credits:[

]

CdZnTe pixel detector. Detector is not integrated

in CCD style readout hence providing pile-up free

observations for bright sources. It has a timing

resolution of

2 µs

and provides a ﬁeld of view of

′

10 keV

and

′

68 keV

. Detectors also provide

a spectral resolution of

400 eV

10 keV

and

900 eV

at 68 keV [1].

NuSTAR was developed to do scientiﬁc

observations for 2 years and it is still functional. The

mission has successfully identiﬁed numerous heavily

buried supermassive black holes that were previously

undetectable with the help of its high energy X-ray

capabilities. It had also identiﬁed new accreting

millisecond X-ray pulsars and the characterization of

previously unknown neutron star systems [

]. NuSTAR

achieved a major breakthrough by producing the ﬁrst

map of radioactive material in a supernova remnant,

speciﬁcally titanium-44 in Cassiopeia A [

]. NuSTAR’s

ability to detect high-energy X-rays from supernovae

3.3 AstroSat

Figure 2: Diagram of the AstroSat satellite and

scientiﬁc instruments. Credits: AstroSat Archive

shortly after their explosions oﬀers unique insights

into the shock propagation and energy deposition

mechanisms [1].

3.3 AstroSat

AstroSat is India’s ﬁrst multi-wavelength

observatory in space. AstroSat was successfully

launched on September 28, 2015, by the Indian Space

Research Organization (ISRO) using a Polar Satellite

Launch Vehicle (PSLV) from the Sriharikota Range

on the eastern coast of India. Satellite was placed in

a circular low earth orbit of radius

650 km

with an

inclination of 6

○

Astrosat carried 5 primary science instrument

which observed the sky at diﬀerent wavelengths

including UV and X-rays. All the instruments are

co-aligned to give the simultaneous multi-wavelength

observation of the corresponding source.

Large Area X-ray Proportional Counter (LAXPC)

is the primary instrument in AstroSat. It

consists of three identical(LAXPC10, LAXPC20,

LAXPC30) xenon gas ﬁlled proportional counters

with an eﬀective area of

6000 cm

. LAXPC

works in the energy range of

3 − 80 keV

with a

great timing resolution of

10 µs

. It does not have

imaging capabilities and has a moderate spectral

capability [4].

Soft X-ray Telescope (SXT) is a wolter-1 grazing

incident telescope that works in the energy range

0.3–8.0 keV

. It is capable of providing

imaging, spatially resolved spectroscopy and

variability observations of cosmic sources. SXT

has a focal length of

2 m

and geometric area of

250 cm

.The detector used is the CCD-22 MOS

device. It had a timing resolution of 0.28 second

in Fast Window mode and spectral resolution of

approximately 150 eV at 6 keV [5].

The Cadmium Zinc Telluride Imager (CZTI) is

a high-energy, wide-ﬁeld imaging instrument

that operates in the energy range of 20-200 keV.

The instrument is composed of four identical

independent quadrants. Each quadrant features a

Coded Aperture Mask (CAM) positioned at the

top, with sixteen CZT detector modules located

48 cm

below the CAM. The coded aperture mask

provides an angular resolution of

17arcminutes

over a ﬁeld of view measuring 4.6 degrees by 4.6

degrees. Additionally, the instrument has a time

resolution of 20 µs [6].

The Ultra Violet Imaging Telescope (UVIT) is

designed to capture images simultaneously in

near-ultraviolet and far-ultraviolet wavelengths.

The instrument consists of two co-aligned

telescopes, each featuring f/12 Ritchey–Chretien

optics with an aperture of 375 mm, along with

ﬁlters and detectors. One telescope observes in

the far-ultraviolet (FUV) range, spanning from

1,300 to 1,800 angstroms, while the other covers

the near-ultraviolet (NUV) range of 2,000 to

3,000 angstroms, as well as the visible (VIS)

range of 3,200 to 5,500 angstroms. For each of

the three channels, a ﬁlter wheel is employed to

select either a ﬁlter or a grating in the FUV and

NUV ranges [7].

Scanning Sky Monitor (SSM) is an X-ray sky

monitor in the soft X-ray band designed with a

large ﬁeld of view to detect and locate transient X-

ray sources. SSM comprises of position sensitive

proportional counters with 1D coded mask for

imaging. There are three detector units having

a FOV of the order of

○

100

○

mounted on a

platform capable of rotation which helps covering

about 50% of the sky in one full rotation [8].

Although initially planned for 5 years, AstroSat is still

3.4 HITOMI

operational. AstroSat’s CZTI has made groundbreaking

contributions to gamma-ray burst science, detecting

over 650 GRBs during its operational period and these

Analysis revealed that some GRBs have Poynting ﬂux-

dominated jets while others show baryonic-dominated

jets with mild magnetization [

] and CZTI has searched

for electromagnetic counterparts of gravitational wave

events, placing important constraints on theoretical

models [

]. The LAXPC has revolutionized studies of

X-ray binary systems and neutron star physics through its

exceptional timing capabilities. It includes the discovery

of new dip phenomena in X-ray binaries, revealing

insights into accretion ﬂow geometry[

], detection of

Type-I thermonuclear X-ray bursts from neutron stars,

providing constraints on neutron star structure[

], and

ﬁrst detection of evolving low-frequency quasi-periodic

oscillations in hard X-rays up to 100 keV in black hole

systems[

]. UVIT has made signiﬁcant contributions

in understanding stellar evolution, and ﬁrst detected

the extremely low mass white dwarfs as companions to

blue straggler stars in globular clusters [14]

3.4 HITOMI

Hitomi, also known as ASTRO-H, was a joint

Japanese–international X-ray observatory launched

to perform high-resolution, broad-band spectroscopy

of astrophysical sources. Hitomi was launched

on February 2016 aboard an H-IIA rocket from

Tanegashima Space Center. The satellite entered a

circular low-Earth orbit at an altitude of approximately

575 km, with an orbital period of

minutes and

an inclination of

31.01

○

. Hitomi was conceived to

extend the capabilities of previous Japanese X-ray

satellites by covering the energy range from soft X-rays

to soft gamma rays

(0.3–600 keV )

with unprecedented

resolution and sensitivity.

Hitomi carried four co-aligned telescopes and four

primary instruments

Soft X-Ray Spectrometer (SXS) is an imaging

spectrometer that uses charge-coupled devices

(CCDs). The SXI sensor has four CCDs with an

imaging area size of

31 mm × 31 mm

arranged

in a

2 × 2

array. SXI detects x-rays between

0.4 − 12 keV

and covers a

′

× 38

′

ﬁeld of view.

The energy resolution measured is 161 to

170 eV

in full width at half maximum for

5.9 keV

X-rays

[15].

Soft X-ray imaging system consisting of the

Soft X-ray Telescope and the Soft X-ray Image.

Combining the SXT-I and the SXI, is an imaging

system with a focal length of

5.6m

and a ﬁeld of

view of

′

× 8

′

. This was the largest FoV among

focal plane X-ray detectors that cover up to 10

keV. The basic design of the SXT-I is the same as

that of Suzaku XRT which having Wolter-I-type

optic. SXI used CCDs as the imager.[16].

The Hard X-ray Imager (HXI) onboard Hitomi

(ASTRO-H) is an imaging spectrometer covering

hard X-ray energies of 5 to 80 keV. Combined

with the Hard X-ray Telescope, it enables imaging

spectroscopy with an angular resolution of

′

half-power diameter, in a ﬁeld of view of

′

× 9

′

The main imager is composed of four layers of

Si detectors and one layer of CdTe detector [

The Soft Gamma-ray Detector(SGD) was an

instrument that observed the highest energy band

(60 to 600 keV). The SGD design was based on

the success of the Hard X-ray Detector(HXD)

onboard Suzaku. The SGD design includes two

identical units with each holding three Compton

cameras with a geometrical area of

25 cm

. The

Compton camera is employed as a direction-

sensitive gamma-ray detector [18].

After the successful launch of the satellite, its control

was lost when the scientiﬁc operations began. By

April 2016, JAXA announced that they had lost the

control over the satellite and hence the mission was

decommissioned.

References

[1]

Harrison, F. A. et al. The Astrophysical Journal

770, 103. issn: 0004637X, 1538-4357 (May 2013)

[2]

Sanna, A. et al. Astronomy & Astrophysics 617,

L8. issn: 0004-6361, 1432-0746 (Sept. 2018)

REFERENCES

[3]

Grefenstette,B. W. et al. en. Nature 506, 339–342.

issn: 0028-0836, 1476-4687 (Feb.2014).

[4]

Yadav, J. S. et al. Current Science 113, 591. issn:

0011-3891(Aug. 2017).

[5]

Singh, K. P. et al. en. Journal of Astrophysics and

Astronomy 38, 29. issn: 0250-6335, 0973-7758

(June 2017).

[6]

Bhalerao, V. et al. Journal of Astrophysics and

Astronomy

[7]

Tandon, S. N. et al. The Astronomical Journal 154,

128. issn: 0004-6256, 1538-3881 (Sept. 2017).

[8]

Ramadevi, M. C. et al. en. Experimental Astronomy

44, 11–23. issn: 0922-6435, 1572-9508 (Oct.

2017).

[9]

Gupta, R. et al. The Astrophysical Journal 972, 166.

issn: 0004-637X, 1538-4357 (Sept. 2024).

[10]

Waratkar,G., Bhalerao, V. & Bhattacharya, D. The

Astrophysical Journal 976, 123. issn: 0004-637X,

1538-4357 (Nov. 2024).

[11]

Leahy, D. A. & Chen, Y. en.Journal of

Astrophysics and Astronomy 42, 44. issn: 0250-

6335, 0973-7758 (Oct. 2021).

[12]

Bhulla, Y., Roy, J. & Jaaﬀrey, S. Research in

Astronomy and Astrophysics 20, 098. issn: 1674-

4527 (June 2020).

[13]

Nandi, A. et al. en. Monthly Notices of the Royal

Astronomical Society 531, 1149–1157. issn: 0035-

8711, 1365-2966 (May 2024).

[14]

Dattatrey, A. K. et al. The Astrophysical Journal

943, 130. issn: 0004-637X, 1538-4357 (Feb. 2023).

[15]

Tanaka, T. et al. Journal of Astronomical

Telescopes, Instruments, and Systems 4, 1. issn:

2329-4124 (Feb. 2018).

[16]

Nakajima, H. et al. en. Publications of the

Astronomical Society of Japan 70, 21. issn: 0004-

6264, 2053-051X (Mar. 2018).

[17]

Journal of Astronomical Telescopes, Instru- ments,

and Systems 4, 1. issn: 2329-4124 (Mar. 2018).

[18]

Tajima, H., Watanabe, S., Fukazawa, Y. &

Blandford, R. Journal of Astronomical Telescopes,

Instruments, and Systems 4, 1. issn: 2329-4124

(Apr. 2018).

About the Author

Aromal P is a research scholar in

Department of Astronomy, Astrophysics and Space

Engineering (DAASE) in Indian Institute of

Technology Indore. His research mainly focuses on

studies of Thermonuclear X-ray Bursts on Neutron star

surface and its interaction with the Accretion disk and

Corona.

The Bright Centers of Galaxies: A Peek into

Active Galactic Nuclei

by Savithri H. Ezhikode

airis4D, Vol.3, No.7, 2025

www.airis4d.com

4.1 Introduction

At the centres of many galaxies reside

supermassive black holes (SMBHs) with masses

ranging from millions to billions of solar masses. While

most of these black holes remain quiescent, a fraction

exhibit intense activity when accreting substantial

quantities of matter. Such systems are classiﬁed as

active galaxies and their bright core regions are known

as active galactic nuclei (AGN), which represent some

of the most luminous persistent sources in the universe.

Fig. 1 presents a comparative view of the structural

and luminosity diﬀerences between normal galaxy and

active galaxy.

Early indications of AGN activity date back to the

early 20th century. Fath (1909) ﬁrst reported strong

optical emission lines in the spiral nebula NGC 1068,

later supported by Slipher (1917), who noted unusually

broad (width of several hundred km/s) emission lines.

Curtis (1918) subsequently detected an optical jet in

M87, and Hubble (1926) documented similar nuclear

spectral features in several galaxies, including NGC

1068, NGC 4051, and NGC 4151 [

]. A

systematic study of such galaxies was conducted by

Seyfert in 1943 [

], who identiﬁed a class of galaxies

with high surface brightness nuclei and strong high-

excitation emission lines. These galaxies—now known

as Seyfert galaxies—formed one of the ﬁrst well-deﬁned

subclasses of AGN. The advent of radio astronomy in

the mid-20th century further advanced AGN research,

which led to the discovery of Quasars (quasi-stellar radio

sources). Pioneering studies by Reber [

], Bolton and

Stanley [

], Smith [

], Brown [

], Baade and Minkowski

[

], and Schmidt [

], among others, identiﬁed such

compact radio sources with extreme luminosities.

4.2 Observational Signatures

AGN exhibit a diverse range of observational

characteristics that set them apart from normal galactic

nuclei. These include extremely high luminosities,

typically ranging from

erg s

−1

, originating

from compact central regions. AGN display broadband

continuum emission covering the entire electromagnetic

spectrum—from radio waves to

γ−

rays—indicating a

variety of emission mechanisms and spatial regions.

They also show rapid and signiﬁcant variability in

multiple wavebands on timescales ranging from hours

to years, pointing to the small size and dynamic

nature of the emitting zones. Prominent broad and

narrow emission lines are observed in their optical and

ultraviolet spectra, produced by high-velocity gas and

slower-moving material, respectively. Furthermore,

many AGN, especially the radio-loud class, exhibit

relativistic jets—collimated plasma outﬂows moving at

speeds close to that of light—predominantly detected

in radio frequencies [15, 16].

4.3 The AGN Central Engine

The compact size of the AGN emission region

(

≪ 1

parsec) implies that traditional stellar mechanisms

4.4 Components of AGN

Figure 1: Normal galaxy and active galaxy.

(Image Credit: ahead.astro.noa.gr/?p=2444)

Figure 2: A schematic representation of the

components of AGN.

(Image courtesy: [Beckmann & Shrader(2012)])

such as nuclear fusion or supernovae are insuﬃcient

to explain AGN luminosities. Instead, the energy

is believed to arise from the release of gravitational

potential energy as matter accretes onto a SMBH [

The infalling matter forms a geometrically thin, optically

thick accretion disk around the SMBH. The AGN

lumnosity powered by accretion is given by

L = η

where

is the mass accretion rate,

is the radiative

eﬃciency (typically ∼0.1), and c is the speed of light.

4.4 Components of AGN

In the framework of the standard model of AGN,

the central engine comprises a supermassive black hole

surrounded by an optically thick and geometrically

thin accretion disk, composed of high-density gas (

∼

−3

) with substantial column density. It sustains

temperatures between

–

K and resides at radial

distances of

∼ 10

–

100 R

(equivalent to

∼ 10

−3

parsecs)

from the central black hole. The magneto-rotational

instabilities within the accretion disk give rise to a

magnetically active corona above the innermost disk

regions (

∼ 10

−5

pc). This corona, composed of optically

thin, high-temperature plasma (

∼ 10

K). However,

the exact geometry of the corona remains uncertain,

with models proposing slab, sphere-disc, or patchy

conﬁgurations [17].

A salient feature of many AGN is the presence

of relativistic jets. These jets, launched via

magnetohydrodynamic mechanisms in the innermost

zones of the accretion disk, are narrow and highly

collimated plasma outﬂows. They can span

distances up to several hundred kiloparsecs or even

megaparsecs, depending on the system [

Observationally, the strength and velocity of these

jets vary signiﬁcantly—from weak radio outﬂows to

highly relativistic jets extending up to hundreds of

kiloparsecs to even megaparsec scales. Emission-line

regions constitute another integral component of the

AGN structure. These include the Broad Line Region

4.5 Conclusion

(BLR) and Narrow Line Region (NLR), composed of

clouds photoionized by the intense radiation from the

AGN central engine [

]. The BLR, situated

∼ 0.01

–

pc from the central black hole, consists of

high-density gas (

∼ 10

−3

) with column densities

up to

−2

. The NLR, in contrast, lies farther from

the central region (

∼ 100

–

1000

pc) and is composed of

low-density clouds (

∼ 10

−3

) with smaller column

densities (

∼ 10

–

−2

). Enclosing the BLR is

a dusty, molecular toroidal structure that signiﬁcantly

inﬂuences the observed properties of AGN depending

on the orientation with respect to our line of sight. This

torus is geometrically and optically thick, composed of

gas and dust with densities ranging from

–

−3

and column densities exceeding

−2

[

]. The

spatial extent of the torus can range from a few parsecs

up to several hundred parsec.

A schematic of the AGN structure is shown in

Fig. 2. The various physical components of AGN emit

radiation across diﬀerent regions of the electromagnetic

spectrum, from radio waves to γ−rays.

4.5 Conclusion

AGN are among the most powerful and complex

astrophysical systems in the universe, fueled by

accretion onto supermassive black holes residing at the

centers of galaxies. Through decades of observational

and theoretical work, a coherent picture has emerged in

which diverse components—including accretion disks,

relativistic jets, emission-line regions, and obscuring

dusty tori—contribute to the rich phenomenology of

AGN. Emissions across the electromagnetic spectrum,

coupled with temporal variability and morphological

structures, provide vital diagnostics for probing the

physical conditions and dynamic processes near these

cosmic powerhouses. A detailed examination of AGN

multi-wavelength emissions, along with an exploration

of the many outstanding questions in the ﬁeld, will be

featured in forthcoming issues.

References

[1]

Fath, E. A. (1909). Lick Observatory Bulletin, 5,

71.

[2]

Slipher, V. M. (1917). Lowell Observatory

Bulletin, 3, 59.

[3]

Curtis, H. D. (1918). Publications of the

Astronomical Society of the Paciﬁc, 30, 19.

[4]

Hubble, E. (1926). Astrophysical Journal, 64, 321.

[5]

Seyfert, C. K. (1943). Astrophysical Journal, 97,

28.

[6]

Reber, G. (1940). Astrophysical Journal, 91, 621.

[7]

Bolton, J. G., & Stanley, G. J. (1948). Nature, 161,

312.

[8] Smith, F. G. (1952). Nature, 170, 108.

[9]

Hanbury Brown, R., et al. (1952). Monthly Notices

of the Royal Astronomical Society, 112, 445.

[10]

Baade, W., & Minkowski, R. (1954). Astrophysical

Journal, 119, 206.

[11] Schmidt, M. (1963). Nature, 197, 1040.

[12] Lynden-Bell, D. (1969). Nature, 223, 690.

[13]

Bondi, H. (1952). Monthly Notices of the Royal

Astronomical Society, 112, 195.

[14]

Eddington, A. S. (1926). The Internal Constitution

of the Stars, Cambridge University Press.

[15]

Peterson, B. M., An Introduction to Active Galactic

Nuclei, Cambridge University Press, 1997.

[16]

Krolik, J. H., Active Galactic Nuclei: From the

Central Black Hole to the Galactic Environment,

Princeton University Press, 1999.

[17]

Reynolds, C. S., & Nowak, M. A. (1999).

Fluorescent iron lines as a probe of astrophysical

black hole systems. Physics Reports, 377(6), 389–

466. https://doi.org/10.1016/S0370-1573(99)000

51-8

REFERENCES

[18]

Osterbrock, D. E., & Mathews, W.

G. (1986). Emission-line regions of

active galactic nuclei. Annual Review of

Astronomy and Astrophysics, 24, 171–212.

https://doi.org/10.1146/annurev.aa.24.090186.001131

[19]

Netzer, H., & Wills, B. J. (1983). Broad

emission lines in QSOs and active galactic

nuclei. The Astrophysical Journal, 275, 445–456.

https://doi.org/10.1086/161544

[20]

Collin-Souﬀrin, S. (1988). The broad emission-

line region in active galactic nuclei: interpretation

and evolution. Publications of the Astronomical

Society of the Paciﬁc, 100(633), 1041–1058.

https://doi.org/10.1086/132284

[21]

Ferland, G. J., & Netzer, H. (1983).

Radiation transfer in emission-line clouds.

The Astrophysical Journal, 264, 105–115.

https://doi.org/10.1086/160575

[Beckmann & Shrader(2012)]

Beckmann, V. &

Shrader, C. R. 2012,

[22]

Blandford, R. D. & Payne, D. G. 1982, Monthly

Notices of the Royal Astronomical Society, 199,

883. doi:10.1093/mnras/199.4.883

[23]

Begelman, M. C., Blandford, R. D., & Rees, M. J.

1984, Reviews of Modern Physics, 56, 2, 255.

doi:10.1103/RevModPhys.56.255

[24]

Koide, S., Shibata, K., & Kudoh, T. 1999,

The Astrophysical Journal, 522, 2, 727.

doi:10.1086/307667

[25]

Netzer, H. 2015, Annual Review of Astronomy

and Astrophysics, 53, 365. doi:10.1146/annurev-

astro-082214-122302

About the Author

Dr. Savithri H. Ezhikode is an

Assistant Professor at St. Francis de Sales

College (Autonomous), Electronics City, Bengaluru.

Her research focuses on observational astrophysics,

particularly X-ray astronomy, multi-wavelength

investigations of active galactic nuclei (AGN), and

stellar astrophysics.

T Coronae Borealis: A Recurrent Nova on the

Verge of Eruption

by Sindhu G

airis4D, Vol.3, No.7, 2025

www.airis4d.com

5.1 Introduction: The Sleeping Star

in Corona Borealis

In the serene northern constellation of Corona

Borealis lies a star with an explosive past — and

an imminent future. Known as T Coronae Borealis

or T CrB, this object has captured the attention of

astronomers for over a century. It belongs to a rare

class of stars called recurrent novae, which experience

multiple nova explosions over time. Unlike one-time

novae or distant supernovae, recurrent novae give us a

chance to watch the same star go through outbursts in

real time — across generations.

As of June 2025, all eyes are on T CrB. This

system previously erupted in 1866 and 1946, each time

brightening suddenly and dramatically enough to be

seen with the naked eye. Based on the roughly 80-

year interval between those events, scientists believe

that the next eruption is due any day now, most likely

within 2025. Recent observational evidence supports

this, as the star has been undergoing unusual changes

since 2023, suggesting that it is entering the ﬁnal stages

before its next eruption.

5.2 Past Eruptions and Their

Signiﬁcance

The recorded history of T CrB begins with its ﬁrst

known eruption in 1866. That year, observers were

stunned to see a new bright star in the sky, visible without

Figure 1: This Hubble Space Telescope image shows

the classic nova GK Persei. Astronomers are eager to

capture comparable views when T Coronae Borealis

explodes.

(Image Credit: NASA/CXC/RIKEN/D.Takei et al/STScI/NRAO/VLA.)

a telescope. It was one of the earliest well-documented

nova events. T CrB’s sudden transformation from a faint

star to a second-magnitude object intrigued astronomers

and marked the beginning of its reputation as a celestial

time bomb.

Then, in 1946, precisely 80 years later, it erupted

again — reaﬃrming its classiﬁcation as a recurrent nova.

The similarity in brightness and behavior between the

two eruptions established a pattern. Now, after another

79 years of quiet, astronomers have reason to believe

that the star will soon repeat its ﬁery display.

These eruptions aren’t just visually spectacular —

they provide critical data for understanding how mass is

transferred and ignited in binary systems. The regularity

of T CrB’s outbursts gives scientists a rare opportunity

5.3 The Science Behind a Nova Eruption

to predict and observe the entire cycle of a nova before,

during, and after eruption.

5.3 The Science Behind a Nova

Eruption

5.3.1 Binary Systems and Mass Transfer

T CrB is a symbiotic binary system, composed of

two stars in a close gravitational relationship. One is a

white dwarf — the dense, compact remnant of a dead

star. The other is a red giant, a swollen, cool star in

the later stages of its life. The red giant sheds material

through a stellar wind, and this material is pulled toward

the white dwarf by gravity, forming an accretion disk

around it.

Over time, hydrogen from the red giant builds up

on the white dwarf’s surface. This process can continue

for decades until the layer of hydrogen becomes dense

and hot enough to ignite in a thermonuclear explosion

— a nova. The outer layers are blown oﬀ into space,

but the white dwarf itself survives and the cycle begins

again.

5.3.2 Triggering a Nova: The Thermonuclear

Runaway

The explosion of a nova is caused not by

the destruction of a star, but by a surface-level

thermonuclear reaction. As hydrogen accumulates, the

pressure and temperature increase until the conditions

become extreme enough to fuse hydrogen explosively.

This releases a massive amount of energy in a short

time, dramatically brightening the star.

This is known as a thermonuclear runaway, and it

leads to the ejection of material at speeds of thousands

of kilometers per second. The system can remain bright

for days or even weeks, after which it slowly fades back

to its quiescent state.

5.3.3 What Makes T CrB Unique Among

Novae

While novae themselves are not uncommon,

recurrent novae like T CrB are extremely rare. Most

novae are single events in observable timescales, with

recurrence times of tens of thousands of years. T CrB,

however, erupts roughly every 80 years, making it an

ideal system to study the full nova cycle.

Its brightness during eruption, long-term

monitoring data, and clear pattern of activity make T

CrB one of the most scientiﬁcally valuable nova systems

known. Studying it helps scientists better understand

how binary systems evolve, how mass is transferred and

retained by white dwarfs, and whether such systems

might eventually become Type Ia supernovae, which

play a key role in measuring the universe’s expansion.

5.4 Current Observations and Signs

of Imminent Eruption

5.4.1 The 2023–2025 Brightening Phase

Beginning in early 2023, astronomers began to

notice that T CrB was behaving unusually. It entered a

brightening phase, with its optical brightness increasing

by several tenths of a magnitude. This behavior had not

been observed since the lead-up to the 1946 eruption.

The similarity has sparked intense interest.

Brightening before a nova is thought to be caused

by changes in the accretion disk or increased mass ﬂow

from the red giant. Whatever the cause, the pre-eruption

glow is seen as one of the most reliable signs that a

nova is imminent.

5.4.2

Multi-Wavelength Indicators of Activity

Observations across multiple wavelengths —

including ultraviolet (UV), optical, and X-rays — show

changes consistent with a system preparing to erupt.

Instruments aboard NASA’s Swift satellite and other

space-based observatories have detected increases in

high-energy radiation, signaling rising activity in the

region around the white dwarf.

Spectroscopic data show variations in the red

giant’s stellar wind and in the dynamics of the accretion

disk. All of these changes suggest that the system is

entering the ﬁnal stages before detonation.

5.5 The Anticipated Nova Event and Its Scientiﬁc Impact

5.4.3 Prediction Challenges and Timing

Uncertainty

Despite the wealth of observations, astronomers

still cannot pinpoint the exact day or month of the

eruption. Predicting the precise timing of a nova

is notoriously diﬃcult due to complex and poorly

understood processes governing mass ﬂow and ignition

conditions.

What makes T CrB valuable is that it gives

scientists a rare chance to test and improve eruption

prediction models in real time. With dozens of

observatories and amateur astronomers monitoring the

star, any sign of the ﬁnal trigger will be quickly noticed

and studied.

5.5 The Anticipated Nova Event and

Its Scientiﬁc Impact

5.5.1 What to Expect When T CrB Erupts

When the eruption ﬁnally happens, T CrB is

expected to brighten rapidly over a period of hours

to days, reaching a magnitude of 2 or brighter. This

will make it clearly visible to the naked eye, even in

semi-urban skies. The eruption could last for a week or

more, with the star slowly fading over the next several

months.

During the peak, it will rival the North Star

(Polaris) in brightness and may become the brightest

nova seen in the Northern Hemisphere in over a century.

It will be a rare opportunity for both scientists and

casual skywatchers to witness a dramatic stellar event.

5.5.2 Opportunities for Astronomers and the

Public

Professional observatories are preparing for 24/7

monitoring during the eruption. But the event won’t

be limited to scientists. Amateur astronomers can

make valuable contributions by recording the brightness,

taking images, and sharing real-time observations.

Educational institutions and outreach

organizations are also preparing resources to

help the public understand and enjoy this rare

phenomenon. T CrB could inspire a new generation of

astronomers, just as it has captivated observers in 1866

and 1946.

5.5.3 Scientiﬁc Implications of the Eruption

Beyond the beauty of the event, T CrB’s nova

will yield valuable scientiﬁc insights. By studying the

eruption, astronomers can:

Measure how much mass the white dwarf gains

or loses

Assess whether the system is evolving toward a

Type Ia supernova

Test models of binary evolution and disk

instability

Improve predictions for other potential nova

systems

The explosion of T CrB is not just a light show —

it’s a key to understanding the life cycles of stars and

the future of similar systems.

5.6 Conclusion: Awaiting a Celestial

Spectacle

As of mid-2025, the world waits. T Coronae

Borealis has been building toward this moment for

decades, and all the signs suggest that its eruption is

near. Whether it happens tonight, next week, or a few

months from now, the nova will be one of the most

signiﬁcant astronomical events of the decade.

In a time when much of space remains distant and

intangible, T CrB oﬀers something rare: a cosmic event

that we can watch unfold with our own eyes, from our

own backyards. Keep looking up — the sky may light

up at any moment.

References:

When will the next T CrB eruption occur ?

T Coronae Borealis Isn’t the Only Star Ready to

Blow — Meet U Gem

Hold onto your hats! Is the ’Blaze Star’ T Corona

Borealis about to go boom?

5.6 Conclusion: Awaiting a Celestial Spectacle

Recurrent nova T CrB has just started its Pre-

eruption Dip in March/April 2023, so the eruption

should occur around 2024.4 +- 0.3

Wait Continues for Eruption of T Coronae

Borealis

A ‘Once-in-a-Lifetime’ Nova Explosion Is

Running Late

T Coronae Borealis: an image, waiting for its

eruption

A Star on the Edge: T Coronae Borealis Poised

for a Spectacular Cosmic Eruption

T Coronae Borealis

Review of the Recurrent Nova T CrB

About the Author

Sindhu G is a research scholar in Physics

doing research in Astronomy & Astrophysics. Her

research mainly focuses on classiﬁcation of variable

stars using diﬀerent machine learning algorithms. She

is also doing the period prediction of diﬀerent types

of variable stars, especially eclipsing binaries and on

the study of optical counterparts of X-ray binaries.

Part III

Biosciences

Decoding DNA’s Secrets: How Sequence

Shapes Life

by Geetha Paul

airis4D, Vol.3, No.7, 2025

www.airis4d.com

1.1 Introduction

DNA, or deoxyribonucleic acid, stands as the

essential molecular foundation upon which all known

life is built. This remarkable molecule is responsible

for storing, transmitting, and expressing the genetic

instructions that guide the development, functioning,

and evolution of every organism from the simplest

bacteria to the most complex multicellular beings. The

architecture of DNA is elegantly simple yet profoundly

complex: it consists of two long strands twisted into

a double helix, each composed of repeating units

called nucleotides. Each nucleotide, in turn, is made

up of a sugar group, a phosphate group, and one

of four nitrogenous bases, adenine (A), thymine (T),

cytosine (C), and guanine (G). The unique sequence

of these chemical bases along the DNA strand forms a

sophisticated biological language, much like letters in

an alphabet spell out words and sentences. This genetic

language contains all the instructions necessary to build

and maintain an organism, dictating everything from the

color of an individual’s eyes to the speciﬁc enzymes that

drive cellular metabolism. The arrangement of these

bases not only determines the structure and function of

proteins but also regulates when and where genes are

turned on or oﬀ, allowing for the intricate orchestration

of life processes.

This article delves deeply into the mechanisms

by which the precise arrangement of DNA’s bases

encodes biological messages. It examines how these

messages are transcribed and translated into proteins

and regulatory signals that govern cellular activity.

Furthermore, it explores how even minor alterations in

the DNA sequence, such as single base changes can

have diﬀerent consequences for an organism’s health,

survival, and evolution. These principles are brought

to life through real-world examples that illustrate

the profound impact of DNA’s sequence on biology,

medicine, and biotechnology. By understanding how

DNA encodes and transmits genetic information, we

gain insight into the very essence of life itself.

1.2 The Structure of DNA: The

Blueprint of Life

DNA is a double-stranded, helical molecule

that serves as the fundamental repository of genetic

information in all living organisms. Each strand of

DNA is composed of repeating structural units known

as nucleotides. A nucleotide consists of three key

components: a sugar group (deoxyribose), a phosphate

group, and one of four nitrogenous bases, adenine (A),

thymine (T), cytosine (C), or guanine (G). The two

DNA strands are oriented in opposite directions and

are held together by hydrogen bonds that form between

complementary bases: adenine pairs exclusively with

thymine, and cytosine with guanine. This precise

base pairing is essential for maintaining the stability

and integrity of the iconic double helix, a structure

that enables DNA to store vast amounts of genetic

information in a compact and eﬃcient manner.

1.3 Genes: The Units of Heredity

Figure 1: DNA is a double helix formed by base pairs

attached to a sugar-phosphate backbone.

Image courtesy:U.S. National Library of Medicine

The speciﬁc sequence of these four bases along the

DNA strand is what encodes the genetic instructions for

life. Much like the arrangement of letters in an alphabet

spells out words and sentences, the linear order of DNA

bases forms the language of heredity. This language

is organized into functional segments, including genes

and regulatory elements, which together instruct the

cell on how to develop, function, and respond to its

environment. The sequence of bases is not random;

instead, it is highly conserved and precisely arranged to

ensure the accurate transmission of genetic information

from one generation to the next.

1.3 Genes: The Units of Heredity

A gene is a discrete segment of DNA that contains

the complete set of instructions required to produce

a speciﬁc protein or functional RNA molecule. Each

gene is deﬁned by a unique sequence of bases, which

determines the exact order in which amino acids

are assembled during protein synthesis. This amino

acid sequence, in turn, dictates the three-dimensional

structure and biological function of the resulting protein.

Genes are the fundamental units of heredity, and their

precise sequence is crucial for the proper development,

maintenance, and regulation of all cellular processes.

Through the expression of genes, cells are able to

synthesise the proteins and RNAs necessary for growth,

metabolism, repair, and reproduction, ensuring the

continuity and complexity of life.

1.4 The Genetic Code: Triplets and

Codons

The genetic code is read in groups of three bases,

known as codons. Each codon speciﬁes a particular

amino acid or serves as a start or stop signal during

protein synthesis. This triplet code is nearly universal

across all living organisms, reﬂecting its essential role

in biology.

Example: ATG (in DNA) or AUG (in RNA) codes

for methionine, often signaling the start of a protein.

TGG codes for tryptophan. TAA is a stop codon,

signaling the end of protein synthesis.

1.5

From DNA Sequence to Biological

Message

1.5.1 DNA Replication and Repair

Nucleotides are the fundamental units that make

up DNA, and they play a vital role in both the synthesis

and protection of genetic material. During DNA

replication, each nucleotide acts as a precursor for the

construction of a new DNA strand, ensuring that each

daughter cell receives an accurate copy of the genetic

information. This process is essential for cell division

and the inheritance of traits. Additionally, nucleotide

excision repair mechanisms utilize nucleotides to

correct DNA damage caused by environmental factors

such as ultraviolet radiation and chemical mutagens.

By replacing damaged or incorrect bases with new

nucleotides, cells maintain genomic integrity and

prevent mutations that could lead to disease.

1.5.2 Transcription: Copying the Genetic

Code

Before genetic information can be used to build

proteins, it must ﬁrst be transcribed from DNA into

messenger RNA (mRNA), a process facilitated by

1.5 From DNA Sequence to Biological Message

nucleotides. Transcription begins when the DNA

sequence of a gene is read and copied into a

complementary mRNA strand. This mRNA molecule

carries the genetic message out of the nucleus and

into the cytoplasm, where it serves as the template for

protein synthesis.

Example: If the DNA sequence is 3’-TAC GGA

TTT-5’, the corresponding mRNA copy will be 5’-AUG

CCU AAA-3’.

1.5.3 Translation: Building Proteins

The next stage in gene expression is translation,

where the mRNA sequence is decoded to assemble

a speciﬁc protein. At the ribosome, the mRNA is

read in three-base units called codons. Each codon

corresponds to a particular amino acid, which is

delivered to the ribosome by transfer RNA (tRNA).

The tRNA molecules recognize codons on the mRNA

via their complementary anticodons, ensuring the

precise incorporation of amino acids into the growing

polypeptide chain. As the process continues, amino

acids are linked together in the order speciﬁed by

the mRNA sequence, ultimately forming a functional

protein.

Example: The mRNA sequence AUG CCU AAA

codes for the amino acids methionine, proline, and

lysine, respectively. The resulting polypeptide chain

will fold into a speciﬁc three-dimensional structure,

determining its biological function.

1.5.4 Cell Signaling and Gene Expression

Beyond their roles in DNA replication and

protein synthesis, nucleotides are also essential for

cell signaling and the regulation of gene expression.

Nucleotides such as ATP, cAMP, and GTP act as

secondary messengers in signal transduction pathways,

enabling cells to respond to external stimuli and

coordinate complex activities. For example, nucleotides

mediate processes like neurotransmission, hormone

signaling, and immune responses by activating speciﬁc

receptors such as G-protein-coupled receptors.

Additionally, nucleotides help regulate gene

expression by inﬂuencing the structure of chromatin

Figure 2: The sequence of bases in DNA encodes

biological messages by serving as a molecular language

that instructs cells how to build proteins and regulate life

processes. This genetic language is written with four

chemical letters —the nucleotide bases adenine (A),

thymine (T), cytosine (C), and guanine (G)—arranged

in a speciﬁc order along the DNA strand. The precise

sequence of these bases contains all the information

needed to direct the structure and function of every

living organism. Image courtesy: https://www.sciencedirect.com/topics/agricultural-a

nd-biological- sciences/dna

1.6 Protein Folding and Function

and modulating the activity of transcription factors.

These mechanisms allow cells to dynamically control

when and how genes are turned on or oﬀ, supporting

adaptation and development.

1.6 Protein Folding and Function

The sequence of amino acids determines how the

protein folds into its three-dimensional shape. This

shape is crucial for the protein’s function, whether it

acts as an enzyme, a structural component, or a signaling

molecule.

1.6.1 Regulatory Sequences: Controlling

Gene Expression

Not all DNA encodes proteins. Many sequences

serve as regulatory elements that control when, where,

and how much a gene is expressed. These include:

Promoters: Regions where RNA polymerase binds

to initiate transcription. Enhancers and Silencers:

Sequences that increase or decrease gene expression.

Insulators: Elements that block the inﬂuence of

enhancers or silencers.

These regulatory regions ensure that genes are

turned on or oﬀ at the right time and in the right cells,

allowing for complex development and adaptation.

1.7 Real-World Examples of DNA

Messages

1.7.1 Sickle Cell Anemia

A single base change in the hemoglobin gene (from

A to T) alters one codon, resulting in the substitution

of valine for glutamic acid in the protein. This small

change causes red blood cells to become sickle-shaped,

leading to sickle cell anemia.

A single gene mutation (GAG

→

GTG and

CTC

→

CAC) results in a defective haemoglobin that

when exposed to de-oxygenation (depicted in the right

half of the diagram) polymerizes (upper right of the

diagram), resulting in the formation of sickle cells.

Vaso-occlusion can then occur. The disorder is also

Figure 3: Schematic representation of the

pathophysiology (in part) of sickle cell anemia. Image

courtesy: https://pmc.ncbi.nlm.nih.gov/articles/PMC7510211/

characterized by abnormal adhesive properties of sickle

cells; peripheral blood mononuclear cells (depicted in

light blue; shown as the large cells under the sickle cells)

and platelets (depicted in dark blue; shown as the dark

circular shapes on the mononuclear cells) adhere to the

sickled erythrocytes. This aggregate is labelled 1. The

mononuclear cells have receptors (e.g., CD44 (labeled 3

and depicted in dark green on the cell surface)) that bind

to ligands, such as P-selectin (labeled 2 and shown on

the endothelial surface), that are unregulated. The sickle

erythrocytes can also adhere directly to the endothelium.

Abnormal movement or rolling and slowing of cells

in the blood also can occur. These changes result in

endothelial damage. The sickled red cells also become

dehydrated as a result of abnormalities in the Gardos

channel. Hemolysis contributes to oxidative stress and

dysregulation of arginine metabolism, both of which

lead to a decrease in nitric oxide (NO) that, in turn,

contributes to the vasculopathy that characterizes SCD.

1.7.2 Lactose Intolerance

The gene for lactase, the enzyme that digests

lactose, is regulated by a DNA sequence upstream of the

gene. In most mammals, this regulatory sequence turns

oﬀ lactase production after weaning. In some humans, a

mutation keeps the gene active into adulthood, allowing

continued lactose digestion.

1.8 The Universality and Flexibility of the Genetic Code

1.7.3 Eye Colour

Variations in the DNA sequence near the OCA2

gene aﬀect how much pigment is produced in the iris,

resulting in diﬀerent eye colors. These diﬀerences are

due to changes in regulatory DNA, not the coding region

itself.

1.8

The Universality and Flexibility of

the Genetic Code

The genetic code is nearly universal, with only

minor exceptions in some organisms and organelles.

This universality allows scientists to transfer genes

between species, a foundation of genetic engineering

and biotechnology.

Example: The gene for human insulin can be

inserted into bacteria, which then produce insulin for

medical use.

1.9 Conclusion

The sequence of bases in DNA is the fundamental

language of life. Through the genetic code, this

sequence encodes the instructions for building proteins,

regulating genes, and orchestrating the complex

processes that deﬁne living organisms. Even small

changes in the DNA sequence can have profound eﬀects,

leading to diversity, adaptation, and sometimes disease.

As our understanding of the genome deepens, the secrets

of how DNA encodes biological messages continue to

unlock new possibilities in medicine, agriculture, and

biotechnology. Ultimately, DNA is not just a blueprint

for life, it is the story of life itself, written in a language

that scientists are still learning to read and interpret.

References

https://www.nature.com/scitable/topicpage/nucl

eic-acids-to-amino-acids-dna-speciﬁes-935/

https://www.sciencedirect.com/topics/agricultura

l-and-biological-sciences/dnaI

https://pmc.ncbi.nlm.nih.gov/articles/PMC75102

11/

J.D. Watson, F.H.C. Crick. “A Structure for

Deoxyribose Nucleic Acid.” Nature 171 no. 4356

(1953):737–738.

M.H.F. Wilkins et al. “Molecular Structure of

Deoxypentose Nucleic Acids.” Nature 171 no. 4356

(1953):738–740.

About the Author

Geetha Paul is one of the directors of

airis4D. She leads the Biosciences Division. Her

research interests extends from Cell & Molecular

Biology to Environmental Sciences, Odonatology, and

Aquatic Biology.

Part IV

Computer Programming

Understanding Performance Metrics in

Parallel Computing

by Ajay Vibhute

airis4D, Vol.3, No.7, 2025

www.airis4d.com

1.1 Introduction

In parallel computing, designing algorithms that

utilize multiple cores or processors is only part of the

challenge. Equally important is the ability to evaluate

the performance of these algorithms. Performance

metrics oﬀer insight into how eﬃciently an algorithm

uses computing resources and where improvements can

be made. They help developers identify bottlenecks,

quantify the eﬀects of design choices, and guide

optimization eﬀorts.

Without proper analysis, a parallel algorithm may

scale poorly, waste computational resources, or even

underperform compared to its sequential counterpart.

Performance evaluation is therefore essential—not only

for benchmarking but also for validating the practical

beneﬁts of parallelization. This article explores key

metrics such as speedup, eﬃciency, scalability, and the

theoretical limits deﬁned by Amdahl’s Laws, providing

a foundation for understanding and improving parallel

performance.

1.2 Speedup

One of the most fundamental performance metrics

in parallel computing is speedup, which measures how

much faster a parallel algorithm executes compared

to its sequential counterpart. Speedup provides a

simple yet powerful way to assess the eﬀectiveness

of parallelization. It quantiﬁes the beneﬁt gained by

executing a program on multiple processors rather than

just one.

Speedup is deﬁned as the ratio of the time taken

to execute a task on a single processor to the time taken

on multiple processors:

S(P ) =

(1.1)

Where:

is the execution time on a single processor,

is the execution time on P processors,

S(P )

is the speedup achieved with

processors.

The ideal or linear speedup occurs when

S(P ) =

, meaning that doubling the number of processors

halves the execution time. However, this is rarely

achieved in practice due to factors such as:

Communication and synchronization overhead

between processors.

Sequential portions of the code that cannot be

parallelized.

Load imbalance, where some processors are idle

while others are overloaded.

Example

Consider a task that takes 100 seconds to complete

on a single processor. When executed on four

processors, it takes 30 seconds:

S(4) =

100

≈ 3.33

This result indicates a substantial improvement,

but not ideal speedup (which would be S(4) = 4).

1.3 Eﬃciency

In some cases, speedup can exceed the number of

processors (

S(P ) > P

), which is known as superlinear

speedup. Although rare, this can occur due to factors

such as:

Improved cache utilization when the problem is

divided among processors.

Reduction in paging or memory swapping on

multicore systems.

As the number of processors increases, the

incremental gain in speedup usually decreases. This

phenomenon, known as diminishing returns, is due

to the growing inﬂuence of overhead and the limited

parallelizable portion of the task. This is also formally

modeled by Amdahl’s Law, discussed in a later section.

1.3 Eﬃciency

In parallel computing, eﬃciency is a fundamental

metric used to evaluate how eﬀectively computational

resources are utilized when executing a parallel

algorithm. While speedup tells us how much faster a

program runs when using multiple processors, eﬃciency

tells us how well those processors are being used.

Eﬃciency is deﬁned as the ratio of the speedup

(

) achieved to the number of processing units (

)

employed:

E =

P ⋅ T

(1.2)

where:

E is the eﬃciency,

S =

is the speedup,

is the execution time of the algorithm on a

single processor,

is the execution time on P processors.

An eﬃciency value of 1 (or 100%) indicates

perfect parallel eﬃciency, meaning all processors

are fully utilized with no overhead or wasted work.

However, in practical scenarios, eﬃciency typically

decreases as more processors are added due to several

limiting factors, such as communication overhead,

synchronization delays, load imbalance, sequential

bottlenecks.

Example

Suppose a program takes

= 100

seconds to

run on a single processor. When parallelized across

P = 4

processors, the execution time reduces to

= 25

seconds. Then the speedup is:

S =

100

= 4 (1.3)

and the eﬃciency is:

E =

= 1 or 100% (1.4)

This indicates ideal eﬃciency, which is rare in

practice. Now, consider a case where the same task

takes T

= 30 seconds on four processors:

S =

100

≈ 3.33, E =

3.33

≈ 0.833 or 83.3%

(1.5)

This drop in eﬃciency reﬂects that while speedup

is still substantial, not all processors are fully

contributing due to overhead or imbalance.

Eﬃciency provides a normalized view of speedup,

allowing fair comparison across diﬀerent system sizes

and conﬁgurations. A low eﬃciency may suggest:

Over-parallelization, where the overhead of

managing many threads outweighs the beneﬁts.

Poor algorithmic scaling due to inherent serial

sections or frequent communication.

Hardware or runtime limitations such as shared

memory contention or OS scheduling delays.

In performance analysis and optimization,

eﬃciency is crucial for understanding diminishing

returns. For instance, if doubling the number of

processors only increases speedup marginally, eﬃciency

will decline, signaling that simply adding more compute

resources may not be beneﬁcial without architectural

or algorithmic changes. An eﬃciency above 70–

80% is generally considered good, especially on

large-scale systems. Eﬃciency below 50% warrants

investigation and likely optimization. In summary,

eﬃciency complements speedup by capturing the cost-

eﬀectiveness of parallelization. It highlights how well

a parallel program scales relative to the resources

it consumes, making it an indispensable metric in

1.4 Scalability

performance tuning and system design.

This naturally leads to the concept of scalability,

which explores how performance evolves as we scale

the number of processors or the problem size.

1.4 Scalability

Scalability is a fundamental concept in parallel

computing that describes how eﬀectively a system

or algorithm can improve performance as additional

computational resources—such as processors or

cores—are introduced. While eﬃciency focuses on

how well the current resources are utilized, scalability

captures how performance trends evolve as additional

resources are added to the system. It provides insight

into the long-term viability of a parallel solution,

especially as hardware capabilities grow or problem

sizes increase.

A well-designed parallel algorithm is not just

fast—it should also scale. Scalability allows developers

and system architects to answer critical questions

such as - Will performance continue to improve if

I double the number of processors? Can the algorithm

handle signiﬁcantly larger problems without additional

runtime? At what point do overheads outweigh the

beneﬁts of parallelism?

Without scalability, a parallel application may

perform well on a few cores but fail to take advantage of

modern high-core-count CPUs or distributed computing

clusters. In domains like scientiﬁc simulation, machine

learning, and data analytics, poor scalability limits both

performance and usefulness.

1.4.1 Types of Scalability

Scalability is typically categorized into two major

types: strong scalability and weak scalability, each

addressing diﬀerent scaling scenarios.

Strong scalability refers to how the execution time

of a ﬁxed-size problem decreases as more processors are

used. Ideally, the runtime should reduce proportionally

to the number of processors:

(1.6)

where

is the runtime on one processor,

the runtime on

processors, and

is the number of

processors. In practice, strong scaling is mainly limited

by sequential sections of code, communication and

synchronization overheads.

Weak scalability evaluates how execution time

behaves as both the problem size and the number of

processors increase proportionally. The goal is to

maintain constant execution time as the workload per

processor remains ﬁxed:

) ≈ T

) where N

= P ⋅ N

(1.7)

Weak scalability is especially relevant for large-

scale simulations and data-parallel applications, where

the data volume grows with system size.

It’s important to distinguish between high

performance and good scalability. A non-scalable

algorithm may run fast on a small system but fail on

larger conﬁgurations. Conversely, an algorithm that

scales well but has high overhead may be ineﬃcient

at small scales. Thus, scalability analysis must be

interpreted in conjunction with other performance

metrics like execution time, throughput, and resource

utilization. By focusing on scalability early in the

design phase, developers can create software that is

robust, future-proof, and capable of fully leveraging

modern parallel architectures.

1.5 Amdahl’s Law

Amdahl’s Law is a foundational principle in

parallel computing that quantiﬁes the theoretical

maximum speedup achievable for a program as a

function of the fraction that can be parallelized.

Proposed by Gene Amdahl in 1967, the law emphasizes

a key limitation in parallel performance: even if most of

a program can be parallelized, the remaining sequential

portion sets a hard ceiling on performance gains.

Let:

be the fraction of the program that is inherently

sequential and cannot be parallelized,

1 − f

be the fraction of the program that is

parallelizable,

1.6 Conclusion

P be the number of processors,

S(P )

be the speedup achieved with

processors.

Then, Amdahl’s Law deﬁnes the speedup as:

S(P ) =

f +

1−f

(1.8)

This equation reveals that as

P → ∞

, the

maximum achievable speedup approaches:

max

(1.9)

This implies that the speedup is fundamentally

limited by the serial portion

, regardless of how many

processors are used.

Example

If 10% of a program is serial (

f = 0.1

), the

maximum speedup is:

max

0.1

= 10

Even with an inﬁnite number of processors, the

program cannot run more than 10 times faster.

If only 5% is serial (f = 0.05), then:

max

0.05

= 20

For a highly parallelizable program with

f = 0.01

the theoretical limit is:

max

= 100

This illustrates how even small sequential

components in an algorithm can signiﬁcantly constrain

overall speedup, particularly as the number of

processors increases.

While Amdahl’s Law provides valuable insight, it

assumes a ﬁxed workload as the number of processors

increases—an assumption that often fails to reﬂect real-

world scenarios, where workloads tend to grow with

available resources. Moreover, the model does not

account for practical overheads such as synchronization,

communication delays, or memory contention, which

typically increase with processor count (P ).

Despite these simpliﬁcations, Amdahl’s Law

remains a useful guiding principle in software

design and performance optimization. It encourages

developers to reduce serial components early in the

development process, helps set realistic expectations for

scalability, and supports decision-making on whether

parallelization eﬀorts are justiﬁed. Additionally, it

assists performance engineers in identifying when

adding more cores yields diminishing returns during

benchmarking and tuning on multicore systems.

1.6 Conclusion

Eﬀective performance analysis is essential in

parallel computing. Metrics such as speedup, eﬃciency,

scalability, and Amdahl’s Law provide critical insight

into how well parallel algorithms utilize resources and

where bottlenecks occur. While speedup shows absolute

performance gain, eﬃciency reveals how economically

resources are used, and scalability highlights whether

performance can grow with increased computing power.

Amdahl’s Law serves as a cautionary model,

demonstrating how even small sequential components

can limit overall speedup. However, real-world systems

often exhibit scaling behaviors better described by

models that consider growing problem sizes and

hardware complexities.

Ultimately, optimizing parallel programs is an

iterative and context-dependent process. Developers

must balance workload distribution, minimize

communication and synchronization overhead, and

continuously proﬁle and reﬁne their code. Integrating

performance thinking early in the design process—not

just as a post-implementation step—leads to solutions

that are robust, scalable, and well-suited to modern

multicore and distributed architectures.

About the Author

Dr. Ajay Vibhute is currently working

at the National Radio Astronomy Observatory in

the USA. His research interests mainly involve

astronomical imaging techniques, transient detection,

machine learning, and computing using heterogeneous,

accelerated computer architectures.

About airis4D

Artiﬁcial Intelligence Research and Intelligent Systems (airis4D) is an AI and Bio-sciences Research Centre.

The Centre aims to create new knowledge in the ﬁeld of Space Science, Astronomy, Robotics, Agri Science,

Industry, and Biodiversity to bring Progress and Plenitude to the People and the Planet.

Vision

Humanity is in the 4th Industrial Revolution era, which operates on a cyber-physical production system. Cutting-

edge research and development in science and technology to create new knowledge and skills become the key to

the new world economy. Most of the resources for this goal can be harnessed by integrating biological systems

with intelligent computing systems oﬀered by AI. The future survival of humans, animals, and the ecosystem

depends on how eﬃciently the realities and resources are responsibly used for abundance and wellness. Artiﬁcial

intelligence Research and Intelligent Systems pursue this vision and look for the best actions that ensure an

abundant environment and ecosystem for the planet and the people.

Mission Statement

The 4D in airis4D represents the mission to Dream, Design, Develop, and Deploy Knowledge with the ﬁre of

commitment and dedication towards humanity and the ecosystem.

Dream

To promote the unlimited human potential to dream the impossible.

Design

To nurture the human capacity to articulate a dream and logically realise it.

Develop

To assist the talents to materialise a design into a product, a service, a knowledge that beneﬁts the community

and the planet.

Deploy

To realise and educate humanity that a knowledge that is not deployed makes no diﬀerence by its absence.

Campus

Situated in a lush green village campus in Thelliyoor, Kerala, India, airis4D was established under the auspicious

of SEED Foundation (Susthiratha, Environment, Education Development Foundation) a not-for-proﬁt company

for promoting Education, Research. Engineering, Biology, Development, etc.

The whole campus is powered by Solar power and has a rain harvesting facility to provide suﬃcient water supply

for up to three months of drought. The computing facility in the campus is accessible from anywhere through a

dedicated optical ﬁbre internet connectivity 24×7.

There is a freshwater stream that originates from the nearby hills and ﬂows through the middle of the campus.

The campus is a noted habitat for the biodiversity of tropical Fauna and Flora. airis4D carry out periodic and

systematic water quality and species diversity surveys in the region to ensure its richness. It is our pride that the

site has consistently been environment-friendly and rich in biodiversity. airis4D is also growing fruit plants that

can feed birds and provide water bodies to survive the drought.