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Fatigue and Corrosion in Metals
by Pietro Paolo MilellaThis textbook, suitable for students, researchers and engineers, gathers the experience of more than 20 years of teaching fracture mechanics, fatigue and corrosion to professional engineers and running experimental tests and verifications to solve practical problems in engineering applications. As such, it is a comprehensive blend of fundamental knowledge and technical tools to address the issues of fatigue and corrosion. The book initiates with a systematic description of fatigue from a phenomenological point of view, since the early signs of submicroscopic damage in few surface grains and continues describing, step by step, how these precursors develop to become mechanically small cracks and, eventually, macrocracks whose growth is governed by fracture mechanics. But fracture mechanics is also introduced to analyze stress corrosion and corrosion assisted fatigue in a rather advanced fashion. The author dedicates a particular attention to corrosion starting with an electrochemical treatment that mechanical engineers with a rather limited knowledge of electrochemistry will well digest without any pain. The electrochemical introduction is considered an essential requirement to the full understanding of corrosion that is essentially an electrochemical process. All stress corrosion aspects are treated, from the generalized film rupture-anodic dissolution process that is the base of any corrosion mechanism to the aggression occurring in either mechanically or thermally sensitized alloys up to the universe of hydrogen embrittlement, which is described in all its possible modes of appearance. Multiaxial fatigue and out-of-phase loading conditions are treated in a rather comprehensive manner together with damage progression and accumulation that are not linear processes. Load spectra are analyzed also in the frequency domain using the Fourier transform in a rather elegant fashion full of applications that are generally not considered at all in fatigue textbooks, yet they deserve a special place and attention. The issue of fatigue cannot be treated without a probabilistic approach unless the designer accepts the shame of one-out-of-two pieces failure. The reader is fully introduced to the most promising and advanced analytical tools that do not require a normal or lognormal distribution of the experimental data, which is the most common case in fatigue. But the probabilistic approach is also used to introduce the fundamental issue of process volume that is the base of any engineering application of fatigue, from the probability of failure to the notch effect, from the metallurgical variability and size effect to the load type effect. Fractography plays a fundamental role in the post mortem analysis of fatigue and corrosion failures since it can unveil the mystery encrypted in any failure.
Fatigue and Fracture Reliability Engineering
by J. J. Xiong R. A. ShenoiFatigue and Fracture Reliability Engineering is an attempt to present an integrated and unified approach to reliability determination of fatigue and fracture behaviour, incorporating probability, statistics and other related areas. A series of original and practical approaches, are suggested in Fatigue and Fracture Reliability Engineering, including new techniques in determining fatigue and fracture performances. It also carries out an investigation into static and fatigue properties, and into the failure mechanisms of unnotched and notched CFR composite laminates with different lay-ups to optimize the stacking sequence effect. Further benefits include: a novel convergence-divergence counting procedure to extract all load cycles from a load history of divergence-convergence waves;practical scatter factor formulae to determine the safe fatigue crack initiation and propagation lives from the results of a single full-scale test of a complete structure; anda nonlinear differential kinetic model for describing the dynamical behaviour of an atom at a fatigue crack tip.Fatigue and Fracture Reliability Engineering is intended for practising engineers in marine, civil construction, aerospace, offshore, automotive and chemical industries. It is also useful reading for researchers on doctoral programmes, and is appropriate for advanced undergraduate and postgraduate programmes in any mechanically-oriented engineering discipline.
Fault Diagnosis Inverse Problems: Solution with Metaheuristics (Studies in Computational Intelligence #763)
by Orestes Llanes Santiago Lídice Camps Echevarría Haroldo Fraga Campos Velho Antônio José Silva NetoThis book presents a methodology based on inverse problems for use in solutions for fault diagnosis in control systems, combining tools from mathematics, physics, computational and mathematical modeling, optimization and computational intelligence. This methodology, known as fault diagnosis – inverse problem methodology or FD-IPM, unifies the results of several years of work of the authors in the fields of fault detection and isolation (FDI), inverse problems and optimization. The book clearly and systematically presents the main ideas, concepts and results obtained in recent years. By formulating fault diagnosis as an inverse problem, and by solving it using metaheuristics, the authors offer researchers and students a fresh, interdisciplinary perspective for problem solving in these fields. Graduate courses in engineering, applied mathematics and computing also benefit from this work.
Fault-tolerant Control and Diagnosis for Integer and Fractional-order Systems: Fundamentals of Fractional Calculus and Differential Algebra with Real-Time Applications (Studies in Systems, Decision and Control #328)
by Rafael Martínez-Guerra Fidel Meléndez-Vázquez Iván Trejo-ZúñigaThis book is about algebraic and differential methods, as well as fractional calculus, applied to diagnose and reject faults in nonlinear systems, which are of integer or fractional order. This represents an extension of a very important and widely studied problem in control theory, namely fault diagnosis and rejection (using differential algebraic approaches), to systems presenting fractional dynamics, i.e. systems whose dynamics are represented by derivatives and integrals of non-integer order. The authors offer a thorough overview devoted to fault diagnosis and fault-tolerant control applied to fractional-order and integer-order dynamical systems, and they introduce new methodologies for control and observation described by fractional and integer models, together with successful simulations and real-time applications. The basic concepts and tools of mathematics required to understand the methodologies proposed are all clearly introduced and explained. Consequently, the book is useful as supplementary reading in courses of applied mathematics and nonlinear control theory. This book is meant for engineers, mathematicians, physicists and, in general, to researchers and postgraduate students in diverse areas who have a minimum knowledge of calculus. It also contains advanced topics for researchers and professionals interested in the area of states and faults estimation.
Fear of a Black Universe: An Outsider's Guide to the Future of Physics
by Stephon AlexanderIn this important guide to science and society, a cosmologist argues that physics must embrace the excluded, listen to the unheard, and be unafraid of being wrong. Years ago, cosmologist Stephon Alexander received life-changing advice: to discover real physics, he needed to stop memorizing and start taking risks. In Fear of a Black Universe, Alexander shows that great physics requires us to think outside the mainstream -- to improvise and rely on intuition. His approach leads him to three principles that shape all theories of the universe: the principle of invariance, the quantum principle, and the principle of emergence. Alexander uses them to explore some of physics' greatest mysteries, from what happened before the big bang to how the universe makes consciousness possible. Drawing on his experience as a Black physicist, he makes a powerful case for diversifying our scientific communities. Compelling and empowering, Fear of a Black Universe offers remarkable insight into the art of physics.
Feast For 10
by Cathryn FalwellA counting book that features an African-American family shopping for food, preparing dinner, and sitting down to eat. Lively read-aloud text paired with bright collage illustrations.
Feature Engineering and Selection: A Practical Approach for Predictive Models (Chapman & Hall/CRC Data Science Series)
by Max Kuhn Kjell JohnsonThe process of developing predictive models includes many stages. Most resources focus on the modeling algorithms but neglect other critical aspects of the modeling process. This book describes techniques for finding the best representations of predictors for modeling and for nding the best subset of predictors for improving model performance. A variety of example data sets are used to illustrate the techniques along with R programs for reproducing the results.
Feature Engineering for Machine Learning and Data Analytics (Chapman & Hall/CRC Data Mining and Knowledge Discovery Series)
by Huan Liu Guozhu DongFeature engineering plays a vital role in big data analytics. Machine learning and data mining algorithms cannot work without data. Little can be achieved if there are few features to represent the underlying data objects, and the quality of results of those algorithms largely depends on the quality of the available features. Feature Engineering for Machine Learning and Data Analytics provides a comprehensive introduction to feature engineering, including feature generation, feature extraction, feature transformation, feature selection, and feature analysis and evaluation. The book presents key concepts, methods, examples, and applications, as well as chapters on feature engineering for major data types such as texts, images, sequences, time series, graphs, streaming data, software engineering data, Twitter data, and social media data. It also contains generic feature generation approaches, as well as methods for generating tried-and-tested, hand-crafted, domain-specific features. The first chapter defines the concepts of features and feature engineering, offers an overview of the book, and provides pointers to topics not covered in this book. The next six chapters are devoted to feature engineering, including feature generation for specific data types. The subsequent four chapters cover generic approaches for feature engineering, namely feature selection, feature transformation based feature engineering, deep learning based feature engineering, and pattern based feature generation and engineering. The last three chapters discuss feature engineering for social bot detection, software management, and Twitter-based applications respectively. This book can be used as a reference for data analysts, big data scientists, data preprocessing workers, project managers, project developers, prediction modelers, professors, researchers, graduate students, and upper level undergraduate students. It can also be used as the primary text for courses on feature engineering, or as a supplement for courses on machine learning, data mining, and big data analytics.
Federated Learning: A Primer for Mathematicians (ICIAM2023 Springer Series #4)
by Mei KobayashiThis book serves as a primer on a secure computing framework known as federated learning. Federated learning is the study of methods to enable multiple parties to collaboratively train machine learning/AI models, while each party retains its own, raw data on-premise, never sharing it with others. This book is designed to be accessible to anyone with a background in undergraduate applied mathematics. It covers the basics of topics from computer science that are needed to understand examples of simple federated computing frameworks. It is my hope that by learning basic concepts and technical jargon from computer science, readers will be able to start collaborative work with researchers interested in secure computing. Chap. 1 provides the background and motivation for data security and federated learning and the simplest type of neural network. Chap. 2 introduces the idea of multiparty computation (MPC) and why enhancements are needed to provide security and privacy. Chap. 3 discusses edge computing, a distributed computing model in which data processing takes place on local devices, closer to where it is being generated. Advances in hardware and economies of scale have made it possible for edge computing devices to be embedded in everyday consumer products to process large volumes of data quickly and produce results in near real-time. Chap. 4 covers the basics of federated learning. Federated learning is a framework that enables multiple parties to collaboratively train AI models, while each party retains control of its own raw data, never sharing it with others. Chap. 5 discusses two attacks that target weaknesses of federated learning systems: (1) data leakage, i.e., inferring raw data used to train an AI model by unauthorized parties, and (2) data poisoning, i.e., a cyberattack that compromises data used to train an AI model to manipulate its output.
Feedback Arc Set: A History of the Problem and Algorithms (SpringerBriefs in Computer Science)
by Robert KudelićThe main aim of the book is to give a review of all relevant information regarding a well-known and important problem of Feedback Arc Set (FAS). This review naturally also includes a history of the problem, as well as specific algorithms. To this point such a work does not exist: There are sources where one can find incomplete and perhaps untrustworthy information. With this book, information about FAS can be found easily in one place: formulation, description, theoretical background, applications, algorithms etc. Such a compendium will be of help to people involved in research, but also to people that want to quickly acquaint themselves with the problem and need reliable information. Thus research, professional work and learning can proceed in a more streamlined and faster way.
Feedback Control in Systems Biology
by Carlo Cosentino Declan BatesLike engineering systems, biological systems must also operate effectively in the presence of internal and external uncertainty-such as genetic mutations or temperature changes, for example. It is not surprising, then, that evolution has resulted in the widespread use of feedback, and research in systems biology over the past decade has shown that
Feedback Systems: An Introduction for Scientists and Engineers
by Richard M. Murray Karl Johan Aström<p>This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. <p>Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available. Feedback Systems is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences. <p> <li>Covers the mathematics needed to model, analyze, and design feedback systems <li>Serves as an introductory textbook for students and a self-contained resource for researchers <li>Includes exercises at the end of every chapter <li>Features an electronic solutions manual <li>Offers techniques applicable across a range of disciplines</li>
Feedback in digitalen Lernumgebungen: Eine Interventionsstudie zu dem Lernpfad „Quadratische Funktionen erkunden“ (Studien zur theoretischen und empirischen Forschung in der Mathematikdidaktik)
by Elena de VriesOpen Educational Resources werden heute von der breiten Masse wahrgenommen und als gewinnbringende Unterrichtsmaterialien ausgewiesen, sofern sie unter pädagogischen bzw. fachdidaktischen Gesichtspunkten entwickelt und eingesetzt werden. Im Rahmen dieser Analyse wird eine digitale Lernumgebung – ein Lernpfad – zum Einstieg in das Themenfeld quadratische Funktionen konzipiert. Es werden zwei Versionen der Lernumgebung umgesetzt, die sich einzig durch das implementierte Feedback unterschieden. Auf dieser Grundlage wird der Frage nachgegangen, ob ein Lernpfad zu quadratischen Funktionen mit elaboriertem Feedback einen positiveren Einfluss auf die Mathematikleistung von Schülerinnen und Schülern hat als der gleiche Lernpfad mit KCR Feedback.
Feedback: How to Destroy or Save the World
by Péter ÉrdiThe book offers an exciting, non-technical intellectual journey around applying feedback control to emerging and managing local and global crises, thus keeping the world on a sustainable trajectory. There is a narrow border between destruction and prosperity: to ensure reasonable growth but avoid existential risk, we must find the fine-tuned balance between positive and negative feedback. This book addresses readers belonging to various generations, such as: young people growing up in a world where everything seems to be falling apart; people in their 30s and 40s who are thinking about how to live a fulfilling life; readers in their 50s and 60s thinking back on life; and Baby Boomers reflecting on their past successes and failures. Albert-László Barabási, Robert Gray Dodge Professor of Network Science, Northeastern University: “In a world where interconnectedness has fostered global prosperity, it has also introduced vulnerabilities that can escalate local failures into worldwide crises. “Feedback” by Peter Erdi explores this double-edged sword, offering a solution through the power of feedback mechanisms. These tools are designed to mitigate the negative impacts of connectedness, steering the complexity of modern life towards outcomes that enhance human welfare.” Patrick Grim, Philosopher in Residence Visiting Scholar Center for Complex Systems University of Michigan: “Érdi demonstrates that many of the critical problems we face—from climate crises to economic instability to the threat of terrorism—operate as runaway feedback loops. The first challenge is to understand them. The second is to introduce control mechanisms on the model of biological homeostasis—a different form of feedback—that will guide us toward a more sustainable social future. Érdi applies the analytic tools of complex systems to some of the most complex issues we face.” Ichiro Tsuda, Specially Appointed Professor at Sapporo City University, Sapporo, Japan, leaving Chubu University Academy of Emerging Sciences (Director and Professor), Chubu University, Japan: “This book is dangerous, because of making your own consideration on feedback impossible to stop by a continual feedback process of yourself. Nevertheless, you must be given a method of finding very narrow boundaries between prosperity and destruction, therefore this book is extremely valuable. We all must read.”
Feferman on Foundations: Logic, Mathematics, Philosophy (Outstanding Contributions To Logic Ser. #13)
by Gerhard Jäger Wilfried SiegThis volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community.With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Gödel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory.In his philosophical research, Feferman explored questions such as “What is logic?” and proposed particular positions regarding the foundations of mathematics including, for example, his “conceptual structuralism.” The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman’s work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman’s distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.
Feflow
by Hans-Jörg G. DierschFEFLOW is an acronym of Finite Element subsurface FLOW simulation system and solves the governing flow, mass and heat transport equations in porous and fractured media by a multidimensional finite element method for complex geometric and parametric situations including variable fluid density, variable saturation, free surface(s), multispecies reaction kinetics, non-isothermal flow and multidiffusive effects. FEFLOW comprises theoretical work, modeling experiences and simulation practice from a period of about 40 years. In this light, the main objective of the present book is to share this achieved level of modeling with all required details of the physical and numerical background with the reader. The book is intended to put advanced theoretical and numerical methods into the hands of modeling practitioners and scientists. It starts with a more general theory for all relevant flow and transport phenomena on the basis of the continuum approach, systematically develops the basic framework for important classes of problems (e. g. , multiphase/multispecies non-isothermal flow and transport phenomena, discrete features, aquifer-averaged equations, geothermal processes), introduces finite-element techniques for solving the basic balance equations, in detail discusses advanced numerical algorithms for the resulting nonlinear and linear problems and completes with a number of benchmarks, applications and exercises to illustrate the different types of problems and ways to tackle them successfully (e. g. , flow and seepage problems, unsaturated-saturated flow, advective-diffusion transport, saltwater intrusion, geothermal and thermohaline flow).
Fehlerkultur in Organisationen: Eine organisationsethnografische Studie in der stationären Altenpflege (Organisation und Pädagogik #33)
by Kerstin BestvaterIm Zentrum dieser Studie steht die Frage nach der Verflechtung der Fehlerkultur mit den Entscheidungs- und Handlungspraktiken in einer Alten- und Pflegeeinrichtung. Dafür wurde mit der pädagogischen Organisationsethnografie ein explorativer Zugang zum Forschungsgegenstand gewählt, der einen tiefen Einblick in die soziale Welt der Altenpflege gewährt. Kernstück ist eine konzeptualisierende Darstellung feldtypischer Praktiken und eine gegenstandsbezogene Theorieentwicklung, die im Sinne der Grounded Theory umgesetzt wurde. Das genuine Dilemma der Altenpflege zwischen Wirtschaftlichkeit und Pflegeethos führt zu Praxismustern, die als Problemlösungsstrategien auch die Fehlerkultur prägen.
Feistel Ciphers
by Valerie Nachef Jacques Patarin Emmanuel VolteThis book provides a survey on different kinds of Feistel ciphers, with their definitions and mathematical/computational properties. Feistel ciphers are widely used in cryptography in order to obtain pseudorandom permutations and secret-key block ciphers. In Part 1, we describe Feistel ciphers and their variants. We also give a brief story of these ciphers and basic security results. In Part 2, we describe generic attacks on Feistel ciphers. In Part 3, we give results on DES and specific Feistel ciphers. Part 4 is devoted to improved security results. We also give results on indifferentiability and indistinguishability.
Female Employment and Gender Gaps in China (Hitotsubashi University IER Economic Research Series #48)
by Xinxin MaThis open access book investigates female employment and the gender gap in the labor market and households during China’s economic transition period. It provides the reader with academic evidence for understanding the mechanism of female labor force participation, the determinants of the gender gap in the labor market, and the impact of policy transformation on women’s wages and employment in China from an economics perspective. The main content of this book includes three parts―women’s family responsibilities and women’s labor supply (child care, parent care, and women’s employment), the gender gap in the labor market and society (gender gaps in wages, Communist Party membership, and participation in social activity), and the impacts of policy transformation on women’s wages and employment (the social security system and the educational expansion policy on women’s wages and employment) in China. This book provides academic evidence about these issues based on economics theories and econometric analysis methods using many kinds of long-term Chinese national survey data. This book is highly recommended to readers who are interested in up-to-date and in-depth empirical studies of the gender gap and women’s employment in China during the economic transition period. This book is of interest to various groups such as readers who are interested in the Chinese economy, policymakers, and scholars with econometric analysis backgrounds.
Female Innovators Who Changed Our World: How Women Shaped STEM (Trailblazing Women Ser.)
by Emma GreenWe are not all born with equal opportunities. Yet there have been countless of women who have overcome a range of barriers such as prejudice, illness, and personal tragedy to advance our understanding of science, technology, engineering, and mathematics (STEM). They used their knowledge to change the world, and their stories are fascinating. This book offers a concise introduction of the lives of 46 women, taking you into the cultural and social context of the world they lived in. Through their intelligence, courage, and resilience, they used STEM to defy expectations and inspire generations to follow in their footsteps. Some of them invented items we use day-to-day and discovered causes and treatments for epidemics that ostracised whole sections of society, whilst others campaigned for the reproductive rights of women and harnessed mathematics to send people into space and break ciphers. These women are proof that females can and did have a hugely significant role in shaping the world we live in today.
Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem
by Simon Singhxn + yn = zn, where n represents 3, 4, 5, ...no solution"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years. In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it. Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.
Fermi-Aufgaben im inklusiven Mathematikunterricht der Grundschule: Eine qualitative Studie zu Lösungsstrategien und kooperativem Lernen „Aus der Sache heraus“ (Bielefelder Schriften zur Didaktik der Mathematik #16)
by Nina FlottmannIn ihrem Buch beschäftigt sich Nina Flottmann mit Lösungsstrategien, die Kinder beim Modellieren ausgewählter Fermi-Aufgaben wählen und anwenden, als auch mit den kooperativen Mustern, die beim Lernen am gemeinsamen Gegenstand abbildbar sind. Im Zentrum stehen dabei die konzeptionellen Eckpfeiler des bildungspolitisch begründeten Anspruchs des Von- und Miteinanderlernens, als auch der inklusive Mathematikunterricht und seine wissenschaftliche Rahmung, die Wahl von geeigneten Aufgaben für den Mathematikunterricht und das Postulat des Lernens am gemeinsamen Gegenstand. Die Arbeit ist an der Schnittstelle von Mathematikdidaktik und Erziehungswissenschaft zu verorten und nimmt die zunehmende Heterogenität der Schüler*innen zum Ausgangspunkt.
Fermions and Anomalies in Quantum Field Theories (Theoretical and Mathematical Physics)
by Loriano BonoraThis book presents a modern view of anomalies in quantum field theories. It is divided into six parts. The first part is preparatory covering an introduction to fermions, a description of the classical symmetries, and a short introduction to conformal symmetry. The second part of the book is devoted to the relation between anomalies and cohomology. The third part deals with perturbative methods to compute gauge, diffeomorphism and trace anomalies. In the fourth part the same anomalies are calculated with non-perturbative heat-kernel-like methods. Part five is devoted to the family's index theorem and its application to chiral anomalies, and to the differential characters and their applications to global anomalies. Part six is devoted to special topics including a complete calculation of trace and diffeomorphism anomalies of a Dirac fermion in a MAT background in two dimensions, Wess-Zumino terms in field theories, sigma models, their local and global anomalies and their cancelation, and finally the analysis of the worldsheet, sigma model, and target space anomalies of string and superstring theories. The book is targeted to researchers and graduate students.
Ferronematics and Living Liquid Crystals (SpringerBriefs in Physics)
by Sanjay Puri Aditya Vats Varsha BanerjeeThis book delves into the intricate world of soft matter physics, specifically focusing on two contemporary complex systems: ferronematics and living liquid crystals. These systems amalgamate passive and active inclusion in the nematic liquid crystals. From a pedagogical description to advanced dynamics, this book provides a solid foundation for understanding these complex systems. Practical insights through simulations and analytical expressions bridge the gap between theory and real-world applications, making the knowledge gained highly relevant. This book caters to students, researchers, and scholars in the field of soft matter physics. A strong foundation in statistical physics and mathematical physics is recommended, especially in areas related to liquid crystal physics, statistical mechanics and complex systems. The book provides a plethora of theoretical knowledge, simulations, and analytical expressions, serving as an indispensable resource for those eager to delve into the intriguing domains of soft matter physics.