Search

This book publishes select papers presented at the 4th International Conference on Frontiers in Industrial and Applied Mathematics (FIAM-2021), held at the Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India, from 21–22 December 2021. Most of the papers deal with mathematical theory embedded with its applications to engineering and sciences. This book illustrates numerical simulation of scientific problems and the state-of-the-art research in industrial and applied mathematics, including various computational and modeling techniques with case studies and concrete examples. Graduate students and researchers, who are interested in real applications of mathematics in the areas of computational and theoretical fluid dynamics, solid mechanics, optimization and operations research, numerical analysis, bio-mathematics, fuzzy, control and systems theory, dynamical systems and nonlinear analysis, algebra and approximation theory, will find the book useful.

This book, following the three published volumes of the book, provides the main purpose to collect research papers and review papers to provide an overview of the main issues, results, and open questions in the cutting-edge research on the fields of modeling, optimization, and dynamics and their applications to biology, economy, energy, industry, physics, psychology and finance. Assuming the scientific relevance of the presenting innovative applications as well as merging issues in these areas, the purpose of this book is to collect papers of the world experts in mathematics, economics, and other applied sciences that is seminal to the future research developments. The majority of the papers presented in this book is authored by the participants in The Joint Meeting 6th International Conference on Dynamics, Games, and Science – DGSVI – JOLATE and in the 21st ICABR Conference. The scientific scope of the conferences is focused on the fields ofmodeling, optimization, and dynamics and their applications to biology, economy, energy, industry, physics, psychology, and finance. Assuming the scientific relevance of the presenting innovative applications as well as merging issues in these areas, the purpose of the conference is to bring together some of the world experts in mathematics, economics, and other applied sciences that reinforce ongoing projects and establish future works and collaborations.

The papers presented in this open access book address diverse challenges in decarbonizing energy systems, ranging from operational to investment planning problems, from market economics to technical and environmental considerations, from distribution grids to transmission grids, and from theoretical considerations to data provision concerns and applied case studies. While most papers have a clear methodological focus, they address policy-relevant questions at the same time. The target audience therefore includes academics and experts in industry as well as policy makers, who are interested in state-of-the-art quantitative modelling of policy relevant problems in energy systems. The 2nd International Symposium on Energy System Optimization (ISESO 2018) was held at the Karlsruhe Institute of Technology (KIT) under the symposium theme “Bridging the Gap Between Mathematical Modelling and Policy Support” on October 10th and 11th 2018. ISESO 2018 was organized by the KIT,the Heidelberg Institute for Theoretical Studies (HITS), the Heidelberg University, the German Aerospace Center and the University of Stuttgart.

Proceedings volume contains carefully selected papers presented during the 17th IFIP Conference on System Modelling and Optimization. Optimization theory and practice, optimal control, system modelling, stochastic optimization, and technical and non-technical applications of the existing theory are among areas mostly addressed in the included papers. Main directions are treated in addition to several survey papers based on invited presentations of leading specialists in the respective fields. Publication provides state-of-the-art in the area of system theory and optimization and points out several new areas (e.g fuzzy set, neural nets), where classical optimization topics intersects with computer science methodology.

This volume contains the courses given at the Sixth Summer School on Complex Systems held at Facultad de Ciencias Fisicas y Maternaticas, Universidad de Chile at Santiago, Chile, from 14th to 18th December 1998. This school was addressed to graduate students and researchers working on areas related with recent trends in Complex Systems, including dynamical systems, cellular automata, complexity and cutoff in Markov chains. Each contribution is devoted to one of these subjects. In some cases they are structured as surveys, presenting at the same time an original point of view and showing mostly new results. The paper of Pierre Arnoux investigates the relation between low complex systems and chaotic systems, showing that they can be put into relation by some re­ normalization operations. The case of quasi-crystals is fully studied, in particular the Sturmian quasi-crystals. The paper of Franco Bagnoli and Raul Rechtman establishes relations be­ tween Lyapunov exponents and synchronization processes in cellular automata. The principal goal is to associate tools, usually used in physical problems, to an important problem in cellularautomata and computer science, the synchronization problem. The paper of Jacques Demongeot and colleagues gives a presentation of at­ tractors of dynamical systems appearing in biological situations. For instance, the relation between positive or negative loops and regulation systems.

The Fourth ECMI Conference on Industrial Mathematics took place at Strobl in Aus­ tria, May 29-June 2, 1989. The conference was devoted to the exchange of ideas, models and methods from various fields of industrial applications of mathematics. About 140 people from 21 countries attended the meeting. The aim was to bring together peo­ ple from industry and from university. In this respect the organizers were only partly successful!. The participance of about 20 people from industry shows that there is still much work to be done to increase the acceptance from this side. 72 speakers presented their results as invited or contributed lectures, or in the frame of 2 minisymposia. One minisymposium was organized by Heinz W. Engl and focused on steel processing, the other one, organized by Hansjorg Wacker, dealt with chemical engineering. These proceedings consist of 56 papers. The articles within each of the sections: Invited Lectures, Minisymposium Steel Processing, Minisymposium Chemical Engi­ neering, and Contributed Lectures are in alphabetical order of the first author. Exept for the contributions to the minisymposia, which clearly concentrate on the corre­ sponding topics, it is hard to find a reasonable classification of the papers. This, we believe, is typical for industrial mathematics and underlines the vast variety of fields where mathematics could be used to support problem solving. We would like to acknowlegde the valuable work of the referees of the articles who certainly helped to improve the quality of this volume.

This proceedings volume gathers selected, peer-reviewed papers presented at the Dynamical Systems Theory and Applications International Conference - DSTA 2021, held virtually on December 6-9, 2021, organized by the Department of Automation, Biomechanics, and Mechatronics at Lodz University of Technology, Poland. This volume focuses on numerical and analytical approaches, while Volume I concentrates on studies on applications.Being a truly international conference, this 16th iteration of DSTA received submissions from authors representing 52 countries. The program covered both theoretical and experimental approaches to widely understood dynamical systems, including topics devoted to bifurcations and chaos, control in dynamical systems, asymptotic methods in nonlinear dynamics, stability of dynamical systems, lumped mass and continuous systems vibrations, original numerical methods of vibration analysis, non-smooth systems, dynamics in life sciences and bioengineering, as well as engineering systems and differential equations.DSTA conferences aim to provide a common platform for exchanging new ideas and results of recent research in scientific and technological advances in modern dynamical systems. Works contained in this volume can appeal to researchers in the field, whether in mathematics or applied sciences, and practitioners in myriad industries.

This proceedings volume gathers selected, peer-reviewed papers presented at the Dynamical Systems Theory and Applications International Conference - DSTA 2021, held virtually on December 6-9, 2021, organized by the Department of Automation, Biomechanics, and Mechatronics at Lodz University of Technology, Poland. This volume concentrates on studies on applications, while Volume II focuses on numerical and analytical approaches.Being a truly international conference, this 16th iteration of DSTA received submissions from authors representing 52 countries. The program covered both theoretical and experimental approaches to widely understood dynamical systems, including topics devoted to bifurcations and chaos, control in dynamical systems, asymptotic methods in nonlinear dynamics, stability of dynamical systems, lumped mass and continuous systems vibrations, original numerical methods of vibration analysis, nonsmooth systems, dynamics in life sciences and bioengineering, as well as engineering systems and differential equations.DSTA conferences aim to provide a common platform for exchanging new ideas and results of recent research in scientific and technological advances in modern dynamical systems. Works contained in this volume can appeal to researchers in the field, whether in mathematics or applied sciences, and practitioners in myriad industries.

This book discusses a variety of topics related to industrial and applied mathematics, focusing on wavelet theory, sampling theorems, inverse problems and their applications, partial differential equations as a model of real-world problems, computational linguistics, mathematical models and methods for meteorology, earth systems, environmental and medical science, and the oil industry. It features papers presented at the International Conference in Conjunction with 14th Biennial Conference of ISIAM, held at Guru Nanak Dev University, Amritsar, India, on 2–4 February 2018. The conference has emerged as an influential forum, bringing together prominent academic scientists, experts from industry, and researchers. The topics discussed include Schrodinger operators, quantum kinetic equations and their application, extensions of fractional integral transforms, electrical impedance tomography, diffuse optical tomography, Galerkin method by using wavelets, a Cauchy problem associated with Korteweg–de Vries equation, and entropy solution for scalar conservation laws. This book motivates and inspires young researchers in the fields of industrial and applied mathematics.

This volume provides a unique collection of mathematical tools and industrial case studies in digital manufacturing. It addresses various topics, ranging from models of single production technologies, production lines, logistics and workflows to models and optimization strategies for energy consumption in production. The digital factory represents a network of digital models and simulation and 3D visualization methods for the holistic planning, realization, control and ongoing improvement of all factory processes related to a specific product. In the past ten years, all industrialized countries have launched initiatives to realize this vision, sometimes also referred to as Industry 4.0 (in Europe) or Smart Manufacturing (in the United States). Its main goals are • reconfigurable, adaptive and evolving factories capable of small-scale production • high-performance production, combining flexibility, productivity, precision and zero defects •energy and resource efficiency in manufacturing None of these goals can be achieved without a thorough modeling of all aspects of manufacturing together with a multi-scale simulation and optimization of process chains; in other words, without mathematics. To foster collaboration between mathematics and industry in this area the European Consortium for Mathematics in Industry (ECMI) founded a special interest group on Math for the Digital Factory (M4DiFa). This book compiles a selection of review papers from the M4DiFa kick-off meeting held at the Weierstrass Institute for Applied Analysis and Stochastics in Berlin, Germany, in May 2014. The workshop aimed at bringing together mathematicians working on modeling, simulation and optimization with researchers and practitioners from the manufacturing industry to develop a holistic mathematical view on digital manufacturing. This book is of interest to practitioners from industry who want to learn about important mathematical concepts, as well as to scientists who want to find out about an exciting new area of application that is of vital importance for today's highly industrialized and high-wage countries.

Operations Research in Space and Air is a selection of papers reflecting the experience and expertise of international OR consulting companies and academic groups. The global market and competition play a crucial part in the decision making processes within the Space and Air industries and this book gives practical examples of how advanced applications can be used by Space and Air industry management. The material within the book provides both the basic background for the novice modeler and a useful reference for experienced modelers. Students, researchers and OR practitioners will appreciate the details of the modeling techniques, the processes that have been implemented and the computational results that demonstrate the benefits in applying OR in the Space and Airline industries. Advances in PC and Workstations technology, in optimiza­ tion engines and in modeling techniques now enable solving problems, never before attained by Operations Research. In recent years the Ital­ ian OR Society (AfRO, www. airo. org) has organized annual forums for researchers and practitioners to meet together to present and dis­ cuss the various scientific and technical OR achievements. The OR in Space 8 Air session of AfR02001 and AfR02002 Conferences, together with optimization tools'applications, presented recent results achieved by Alenia Spazio S. p. A. (Turin), Alitalia, Milan Polytechnic and Turin Polytechinc. With additional contributions from academia and indus­ try they have enabled us to capture, in print, today's'state-of-the-art'optimization and data mining solutions.

The electric power industry is currently undergoing an unprecedented reform. The deregulation of electricity supply industry has introduced new opportunity for competition to reduce the cost and cut the price. It is a tremendous challenge for utilities to maintain an economical and reliable supply of electricity in such an environment. Faced by an increasingly complicated existence, power utilities need efficient tools and aids to ensure that electrical energy of the desired quality can be provided at the lowest cost. The overall objective, both for short-term and long-term operations, is then to find the best compromise between the requirements of security and economy. That is, effective tools are urgently required to solve highly constrained optimisation problems. In recent years, several major modem optimisation techniques have been applied to power systems. A large number of papers and reports have been published. In this respect, it is timely to edit a book on this topic with an aim to report the state of the art development internationally in this area.

This volume developed from a Workshop on Natural Locomotion in Fluids and on Surfaces: Swimming, Flying, and Sliding which was held at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota, from June 1-5, 2010. The subject matter ranged widely from observational data to theoretical mechanics, and reflected the broad scope of the workshop. In both the prepared presentations and in the informal discussions, the workshop engaged exchanges across disciplines and invited a lively interaction between modelers and observers. The articles in this volume were invited and fully refereed. They provide a representative if necessarily incomplete account of the field of natural locomotion during a period of rapid growth and expansion. The papers presented at the workshop, and the contributions to the present volume, can be roughly divided into those pertaining to swimming on the scale of marine organisms, swimming of microorganisms at low Reynolds numbers, animal flight, and sliding and other related examples of locomotion.

Real-life problems are often quite complicated in form and nature and, for centuries, many different mathematical concepts, ideas and tools have been developed to formulate these problems theoretically and then to solve them either exactly or approximately.This book aims to gather a collection of papers dealing with several different problems arising from many disciplines and some modern mathematical approaches to handle them. In this respect, the book offers a wide overview on many of the current trends in Mathematics as valuable formal techniques in capturing and exploiting the complexity involved in real-world situations. Several researchers, colleagues, friends and students of Professor María Luisa Menéndez have contributed to this volume to pay tribute to her and to recognize the diverse contributions she had made to the fields of Mathematics and Statistics and to the profession in general. She had a sweet and strong personality, and instilled great values and work ethics in her students through her dedication to teaching and research. Even though the academic community lost her prematurely, she would continue to provide inspiration to many students and researchers worldwide through her published work.

Human-Like Biomechanics is a comprehensive introduction into modern geometrical methods to be used as a unified research approach in two apparently separate and rapidly growing fields: mathematical biomechanics and humanoid robotics. The book contains six Chapters and an Appendix. The first Chapter is an Introduction, giving a brief review of mathematical techniques to be used in the text. The second Chapter develops geometrical basis of human-like biomechanics, while the third Chapter develops its mechanical basis, mainly from generalized Lagrangian and Hamiltonian perspective. The fourth Chapter develops topology of human-like biomechanics, while the fifth Chapter reviews related nonlinear control techniques. The sixth Chapter develops covariant biophysics of electro-muscular stimulation. The Appendix consists of two parts: classical muscular mechanics and modern path integral methods, which are both used frequently in the main text. The whole book is based on the authors'own research papers in human-like biomechanics.

Petri nets model concurrent and distributed systems where active components communicate through the production and absorption of various kinds of resources. Although the dynamic properties of such systems may be very complex, they may sometimes be connected to the static structure of a Petri net. Many properties are decidable, but their complexity may be huge. It is often opportune to restrict oneself to classes of systems, to partial algorithms, and to similar but simpler properties. Instead of analysing a given system, it is also possible to search for a system satisfying some desired properties by construction. This comprehensive textbook/reference presents and discusses these issues in-depth in the context of one of the most fundamental Petri net models, called place/transition nets. The presentation is fortified by means of many examples and worked exercises. Among topics addressed: • In which order may actions may be generated and scheduled? • What states and configurations may be reached in a concurrent system? • Which interesting classes of systems can be analysed relatively efficiently? • Is it possible to synthesise a system of some class from its behaviour? • How can systems be represented algebraically, compositionally, and concisely? This unique text, based on introductory as well as on advanced courses on distributed systems, will serve as an invaluable guide for students and (future) researchers interested in theoretical—as well as in practical—aspects of Petri nets and related system models. Eike Best has been a full professor (now retired) affiliated to Carl von Ossietzky Universität Oldenburg, Germany. Raymond Devillers has been a full professor (now retired) affiliated to Université Libre de Bruxelles, Belgium. The authors have a long record as collaborators in the fields of Petri nets and the semantics of concurrency.

This book gathers selected research articles presented in the “6th International Conference on Mathematical Modelling, Applied Analysis and Computation (ICMMAAC)”, held at JECRC University, Jaipur, during August 3–5, 2023. This book is focused on articles dealing with necessary theory and techniques in a balanced manner, and contributes towards solving mathematical problems arising in physics, engineering, chemistry, biological systems, medicine, networking system, control systems, environmental sciences, social issues of current interest and more. Annually held since 2018, the ICMMAAC conference aimed, in particular, to foster cooperation among practitioners and theoreticians in these fields. This proceedings is an invaluable resource for researchers, academicians and professionals associated or interested in current advances in different aspects of mathematical modelling, computational algorithms and analysis necessary for handling real-world problems.

The 20th International Conference on Systems Engineering Research (CSER 2023) pushes the boundaries of systems engineering research and responds to new challenges for systems engineering. CSER 2023 invited researchers and practitioners to submit their work in alignment with the thematic focus on a smart and sustainable world. CSER was founded in 2003 by Stevens Institute of Technology and the University of Southern California, and in 2023 the conference returned to the Stevens campus in Hoboken, New Jersey.

This book highlights several methods and quantitative implementations of both probabilistic and fuzzy-based approaches to uncertainty quantification and uncertainty propagation through environmental subsurface pollution models with uncertain input parameters. The book focuses on methods as well as applications in hydrogeology, soil hydrology, groundwater contamination, and related areas (e.g., corrosion of nuclear waste canisters). The methods are illustrated for a broad spectrum of models, from non-differential I/O models to complex PDE solvers, including a novel 3D quasi-analytical model of contaminant transport, and a site-specific computer model of dissolved contaminant migration from a DNAPL (Dense Non Aqueous Phase Liquid) pollution source.

This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. The volume begins with an overview of analytical problems related to crowd modeling. Attention is then given to the importance of considering the social and psychological factors that influence crowd behavior – such as emotions, communication, and decision-making processes – in order to create reliable models. Finally, specific features of crowd behavior are explored, including single-file traffic, passenger movement, modeling multiple groups in crowds, and the interplay between crowd dynamics and the spread of disease.Crowd Dynamics, Volume 4 is ideal for mathematicians, engineers, physicists, and other researchers working in the rapidly growing field of modeling and simulation of human crowds.

The book presents recent applications and developments in the field of control of industrial systems, covering a wide range of modeling and feedback control using various robust approaches such as fuzzy systems, sliding mode control, and H-infinity. This book provides insights into theory, applications, and perspectives relevant to the field of robotic systems, exoskeletons, power systems, photovoltaic systems, etc., as well as general methodologies and paradigms around them. Each chapter provides an enriched understanding of a research topic along with a balanced treatment of the relevant theories, methods, or applications. It reports on the latest advances in the field. This book is a good reference for graduate students, researchers, educators, engineers, and scientists and contains a total of 15 chapters divided into five parts as follows. The first part of this book focuses on the application of fuzzy control to robotic systems and consists of threechapters. The second part of this book proposes the control of lower and upper limb exoskeletons and includes two chapters. The third part is dedicated to the control of power systems and comprises three chapters. The fourth part deals with various approaches to the modeling and control of industrial processes and comprises four chapters. The fifth and final part describes observers and fault-tolerant control systems and comprises five chapters.

This book uses new ideas and language for understanding how self-organization and complexity trend toward increased efficiency. Different measures for efficiency from multiple disciplines are used to probe the ones that provide the most insight. One major goal is to seek a common framework to trace the increase of efficiency as a measure of the level of organization and evolutionary stage of a complex system. The chapters come from a satellite meeting hosted at the Conference on Complex Systems, in Cancun, 2017. The contributions will be peer-reviewed and contributors from outside the conference will be invited to submit chapters to ensure full coverage of the topics. This text will appeal to students and researchers working on complex systems and efficiency.

This book contains several contemporary topics in the areas of mathematical modelling and computation for complex systems. The readers find several new mathematical methods, mathematical models and computational techniques having significant relevance in studying various complex systems. The chapters aim to enrich the understanding of topics presented by carefully discussing the associated problems and issues, possible solutions and their applications or relevance in other scientific areas of study and research. The book is a valuable resource for graduate students, researchers and educators in understanding and studying various new aspects associated with complex systems. Key Feature • The chapters include theory and application in a mix and balanced way. • Readers find reasonable details of developments concerning a topic included in this book. • The text is emphasized to present in self-contained manner with inclusion ofnew research problems and questions.

This book includes contributions about mathematics, physics, philosophy of science, economics and finance and resulted from the Summer School “Complexity and Emergence: Ideas, Methods, with a Special Attention to Economics and Finance” held in Lake Como School of Advanced Studies, on 22–27 July 2018.The aim of the book is to provide useful instruments from the theory of complex systems, both on the theoretical level and the methodological ones, profiting from knowledge and insights from leading experts of different communities. It moves from the volume editors'conviction that to achieve progress in understanding socio-economical as well as ecological problems of our complex word such preparation is needed, together with a critical reconsideration of our basic scientific and economical approach.The potential readers are primarily master and doctorate students of mathematics, information sciences, theoretical physics and economics, as well as research workers in those areas, who want to enlarge their spectrum of knowledge towards the area of complexity and emergence. Since ideas and methods of the theory of complex systems also apply to other areas (from engineering and architecture to biology and medicine, e.g.), students and research workers from those areas will also profit from this book.

This volume is part of collection of contributions devoted to analytical and experimental techniques of dynamical systems, presented at the 15th International Conference “Dynamical Systems: Theory and Applications”, held in Łódź, Poland on December 2-5, 2019. The wide selection of material has been divided into three volumes, each focusing on a different field of applications of dynamical systems.The broadly outlined focus of both the conference and these books includes bifurcations and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, optimization problems in applied sciences, stability of dynamical systems, experimental and industrial studies, vibrations of lumped and continuous systems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.

This edited volume collects six surveys that present state-of-the-art results on modeling, qualitative analysis, and simulation of active matter, focusing on specific applications in the natural sciences. Following the previously published Active Particles volumes, these chapters are written by leading experts in the field and reflect the diversity of subject matter in theory and applications within an interdisciplinary framework. Topics covered include:Variability and heterogeneity in natural swarmsMultiscale aspects of the dynamics of human crowdsMathematical modeling of cell collective motion triggered by self-generated gradientsClustering dynamics on graphsRandom Batch Methods for classical and quantum interacting particle systemsThe consensus-based global optimization algorithm and its recent variantsMathematicians and other members of the scientific community interested in active matter and its many applications will find this volume to be a timely, authoritative, and valuable resource.

This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. In light of the recent COVID-19 pandemic, special consideration is given to applications of crowd dynamics to the prevention of the spreading of contagious diseases. Some of the specific topics covered in this volume include: - Impact of physical distancing on the evacuation of crowds- Generalized solutions of opinion dynamics models- Crowd dynamics coupled with models for infectious disease spreading- Optimized strategies for leaders in controlling the dynamics of a crowdCrowd Dynamics, Volume 3 is ideal for mathematicians, engineers, physicists, and other researchers working in the rapidly growing field of modeling and simulation of human crowds.

This book creates the emergence of disruptive technologies that have led to a significant change in the role of mathematics and statistics for problem solving, with the use of sophisticated software and hardware in solving complex systems and process. In the era of digital technology, mathematics and statistics need to be highly relevant to be able to cater for the needs of IR4.0 such as big data analytics, simulation, autonomous system, and cloud computing. Motivated by this development, a total of 26 chapters are contributed by respectable experts for this book. The main scope of the book is to conduct a new system of modeling and simulations on solving differential equations, nonlinear equations, energy, epidemiology, and risk assessment. This book is of interest for postgraduate students, researchers as well as other scientists who are working in numerical modeling and simulations based on efficient mathematical and statistical techniques.

This text addresses systems with persistent memory that are common mathematical models used in the study of viscoelasticity and thermodynamics with memory. In particular, this class of systems is used to model non-Fickian diffusion in the presence of complex molecular structures. Hence, it has wide applications in biology.The book focuses on the properties and controllability of the archetypal heat and wave equations with memory and introduces the dynamic approach to identification problems and the basic techniques used in the study of stability.The book presents several approaches currently used to study systems with persistent memory: Volterra equation in Hilbert spaces, Laplace transform techniques and semigroup methods. The text is intended for a diverse audience in applied mathematics and engineering and it can be used in PhD courses. Readers are recommended to have a background in the elements of functional analysis. Topics of functional analysis which younger readers may need to familiarize with are presented in the book.

More than 300 years ago, Isaac Newton created a mathematical model of the solar system that predicted the existence of a yet unknown planet: Neptune. Today, driven by the digital revolution, modern scientists are creating complex models of society itself to shed light on topics as far-ranging as epidemic outbreaks and economic growth. But how do these scientists gather and interpret their data? How accurate are their models? Can we trust the numbers? With a rare background in physics, economics and sociology, the author is able to present an insider's view of the strengths, weaknesses and dangers of transforming our lives into numbers. After reading this book, you'll understand how different numerical models work and how they are used in practice. The author begins by exploring several simple, easy-to-understand models that form the basis for more complex simulations. What follows is an exploration of the myriad ways that models have come to describe and define our world, from epidemiology and climate change to urban planning and the world chess championship. Highly engaging and nontechnical, this book will appeal to any readers interested in understanding the links between data and society and how our lives are being increasingly captured in numbers.

This book features recent research in mathematical modeling of indirectly and directly transmitted infectious diseases in humans, animals, and plants. It compiles nine not previously published studies that illustrate the dynamic spread of infectious diseases, offering a broad range of models to enrich understanding. It demonstrates the capability of mathematical modeling to capture disease spread and interaction dynamics as well as the complicating factors of various evolutionary processes. In addition, it presents applications to real-world disease control by commenting on key parameters and dominant pathways related to transmission. While aimed at early-graduate level students, the book can also provide insights to established researchers in that it presents a survey of current topics and methodologies in a constantly evolving field.

This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. After providing a critical analysis of the current state of the field and an overview of the current research perspectives, chapters focus on three main research areas: pedestrian interactions, crowd control, and multiscale modeling. Specific topics covered in this volume include: crowd dynamics through conservation lawsrecent developments in controlled crowd dynamicsmixed traffic modelinginsights and applications from crowd psychology Crowd Dynamics, Volume 2 is ideal for mathematicians, engineers, physicists, and other researchers working in therapidly growing field of modeling and simulation of human crowds.

This volume contains the proceedings of the IUTAM Symposium on Model Order Reduction of Coupled System, held in Stuttgart, Germany, May 22–25, 2018. For the understanding and development of complex technical systems, such as the human body or mechatronic systems, an integrated, multiphysics and multidisciplinary view is essential. Many problems can be solved within one physical domain. For the simulation and optimization of the combined system, the different domains are connected with each other. Very often, the combination is only possible by using reduced order models such that the large-scale dynamical system is approximated with a system of much smaller dimension where the most dominant features of the large-scale system are retained as much as possible. The field of model order reduction (MOR) is interdisciplinary. Researchers from Engineering, Mathematics and Computer Science identify, explore and compare the potentials, challenges and limitations of recentand new advances.

Robust Integration of Model-Based Fault Estimation and Fault-Tolerant Control is a systematic examination of methods used to overcome the inevitable system uncertainties arising when a fault estimation (FE) function and a fault-tolerant controller interact as they are employed together to compensate for system faults and maintain robustly acceptable system performance. It covers the important subject of robust integration of FE and FTC with the aim of guaranteeing closed-loop stability. The reader's understanding of the theory is supported by the extensive use of tutorial examples, including some MATLAB®-based material available from the Springer website and by industrial-applications-based material. The text is structured into three parts:Part I examines the basic concepts of FE and FTC, providing extensive insight into the importance of and challenges involved in their integration;Part II describes five effective strategiesfor the integration of FE and FTC: sequential, iterative, simultaneous, adaptive-decoupling, and robust decoupling; andPart III begins to extend the proposed strategies to nonlinear and large-scale systems and covers their application in the fields of renewable energy, robotics and networked systems. The strategies presented are applicable to a broad range of control problems, because in the absence of faults the FE-based FTC naturally reverts to conventional observer-based control. The book is a useful resource for researchers and engineers working in the area of fault-tolerant control systems, and supplementary material for a graduate- or postgraduate-level course on fault diagnosis and FTC.Advances in Industrial Control reports and encourages the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

This volume looks at the study of dynamical systems with discontinuities. Discontinuities arise when systems are subject to switches, decisions, or other abrupt changes in their underlying properties that require a ‘non-smooth'definition. A review of current ideas and introduction to key methods is given, with a view to opening discussion of a major open problem in our fundamental understanding of what nonsmooth models are. What does a nonsmooth model represent: an approximation, a toy model, a sophisticated qualitative capturing of empirical law, or a mere abstraction? Tackling this question means confronting rarely discussed indeterminacies and ambiguities in how we define, simulate, and solve nonsmooth models. The author illustrates these with simple examples based on genetic regulation and investment games, and proposes precise mathematical tools to tackle them.The volume is aimed at students and researchers who have some experience of dynamical systems, whether as a modelling tool or studying theoretically. Pointing to a range of theoretical and applied literature, the author introduces the key ideas needed to tackle nonsmooth models, but also shows the gaps in understanding that all researchers should be bearing in mind.Mike Jeffrey is a researcher and lecturer at the University of Bristol with a background in mathematical physics, specializing in dynamics, singularities, and asymptotics.

This edited volume provides an essential resource for urban morphology, the study of urban forms and structures, offering a much-needed mathematical perspective. Experts on a variety of mathematical modeling techniques provide new insights into specific aspects of the field, such as street networks, sustainability, and urban growth. The chapters collected here make a clear case for the importance of tools and methods to understand, model, and simulate the formation and evolution of cities.The chapters cover a wide variety of topics in urban morphology, and are conveniently organized by their mathematical principles. The first part covers fractals and focuses on how self-similar structures sort themselves out through competition. This is followed by a section on cellular automata, and includes chapters exploring how they generate fractal forms. Networks are the focus of the third part, which includes street networks and other forms as well. Chapters that examine complexity and its relation to urban structures are in part four.The fifth part introduces a variety of other quantitative models that can be used to study urban morphology. In the book's final section, a series of multidisciplinary commentaries offers readers new ways of looking at the relationship between mathematics and urban forms.Being the first book on this topic, Mathematics of Urban Morphology will be an invaluable resource for applied mathematicians and anyone studying urban morphology. Additionally, anyone who is interested in cities from the angle of economics, sociology, architecture, or geography will also find it useful.'This book provides a useful perspective on the state of the art with respect to urban morphology in general and mathematics as tools and frames to disentangle the ideas that pervade arguments about form and function in particular. There is much to absorb in the pages that follow and thereare many pointers to ways in which these ideas can be linked to related theories of cities, urban design and urban policy analysis as well as new movements such as the role of computation in cities and the idea of the smart city. Much food for thought. Read on, digest, enjoy.'From the foreword by Michael Batty

This book offers a comprehensive presentation of optimization and polyoptimization methods. The examples included are taken from various domains: mechanics, electrical engineering, economy, informatics, and automatic control, making the book especially attractive. With the motto “from general abstraction to practical examples,” it presents the theory and applications of optimization step by step, from the function of one variable and functions of many variables with constraints, to infinite dimensional problems (calculus of variations), a continuation of which are optimization methods of dynamical systems, that is, dynamic programming and the maximum principle, and finishing with polyoptimization methods. It includes numerous practical examples, e.g., optimization of hierarchical systems, optimization of time-delay systems, rocket stabilization modeled by balancing a stick on a finger, a simplified version of the journey to the moon, optimization of hybrid systems and of the electrical long transmission line, analytical determination of extremal errors in dynamical systems of the rth order, multicriteria optimization with safety margins (the skeleton method), and ending with a dynamic model of bicycle. The book is aimed at readers who wish to study modern optimization methods, from problem formulation and proofs to practical applications illustrated by inspiring concrete examples.

The book comprehensively covers the various aspects of risk modeling and analysis in technological contexts. It pursues a systems approach to modeling risk and reliability concerns in engineering, and covers the key concepts of risk analysis and mathematical tools used to assess and account for risk in engineering problems. The relevance of incorporating risk-based structures in design and operations is also stressed, with special emphasis on the human factor and behavioral risks. The book uses the nuclear plant, an extremely complex and high-precision engineering environment, as an example to develop the concepts discussed. The core mechanical, electronic and physical aspects of such a complex system offer an excellent platform for analyzing and creating risk-based models. The book also provides real-time case studies in a separate section to demonstrate the use of this approach. There are many limitations when it comes to applications of risk-based approaches to engineeringproblems. The book is structured and written in a way that addresses these key gap areas to help optimize the overall methodology. This book serves as a textbook for graduate and advanced undergraduate courses on risk and reliability in engineering. It can also be used outside the classroom for professional development courses aimed at practicing engineers or as an introduction to risk-based engineering for professionals, researchers, and students interested in the field.

This book introduces characteristic features of the protein structure prediction (PSP) problem. It focuses on systematic selection and improvement of the most appropriate metaheuristic algorithm to solve the problem based on a fitness landscape analysis, rather than on the nature of the problem, which was the focus of methodologies in the past. Protein structure prediction is concerned with the question of how to determine the three-dimensional structure of a protein from its primary sequence. Recently a number of successful metaheuristic algorithms have been developed to determine the native structure, which plays an important role in medicine, drug design, and disease prediction. This interdisciplinary book consolidates the concepts most relevant to protein structure prediction (PSP) through global non-convex optimization. It is intended for graduate students from fields such as computer science, engineering, bioinformatics and as a reference for researchers and practitioners.

The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are: • Weighted residual methods and Galerkin approximations,• A model problem for one-dimensional linear elastostatics,• Weak formulations in one dimension,• Minimum principles in one dimension,• Error estimation in one dimension,• Construction of Finite Element basis functions in one dimension,• Gaussian Quadrature,• Iterative solvers and element by element data structures,• A model problem for three-dimensional linear elastostatics,• Weak formulations in three dimensions,• Basic rules for element construction in three-dimensions,• Assembly of the system and solution schemes,• An introduction to time-dependent problems and• An introduction to rapid computation based on domain decomposition and basic parallel processing. The approach is to introduce the basic concepts first in one-dimension, then move on to three-dimensions. A relatively informal style is adopted. This primer is intended to be a “starting point”, which can be later augmented by the large array of rigorous, detailed, books in the area of Finite Element analysis. In addition to overall improvements to the first edition, this second edition also adds several carefully selected in-class exam problems from exams given over the last 15 years at UC Berkeley, as well as a large number of take-home computer projects. These problems and projects are designed to be aligned to the theory provided in the main text of this primer.

This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples.Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences.The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach. Drawing upon the author's extensive teaching and research experience and consulting work, the book offers a valuable guide for researchers, graduate students and professionals alike.

Focusing on applications to science and engineering, this book presents the results of the ITN-FP7 SADCO network's innovative research in optimization and control in the following interconnected topics: optimality conditions in optimal control, dynamic programming approaches to optimal feedback synthesis and reachability analysis, and computational developments in model predictive control. The novelty of the book resides in the fact that it has been developed by early career researchers, providing a good balance between clarity and scientific rigor. Each chapter features an introduction addressed to PhD students and some original contributions aimed at specialist researchers. Requiring only a graduate mathematical background, the book is self-contained. It will be of particular interest to graduate and advanced undergraduate students, industrial practitioners and to senior scientists wishing to update their knowledge.

This book addresses recent technological progress that has led to an increased complexity in many natural and artificial systems. The resulting complexity research due to the emergence of new properties and spatio-temporal interactions among a large number of system elements - and between the system and its environment - is the primary focus of this text.This volume is divided into three parts: Part one focuses on societal and ecological systems, Part two deals with approaches for understanding, modeling, predicting and mastering socio-technical systems, and Part three includes real-life examples. Each chapter has its own special features; it is a self-contained contribution of distinguished experts working on different fields of science and technology relevant to the study of complex systems. Advances in Complex Systems of Contemporary Reality: Societal, Environmental and Engineered Systems will provide postgraduate students, researchers and managers with qualitative and quantitative methods for handling the many features of complex contemporary reality.

This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by:Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book;Presenting different mathematical approaches to formulate exact and solvable models;Identifying the concrete links between approximate models and their rigorous mathematical representation;Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity;Providing a reference source for advanced undergraduate students, as well as doctoral students, postdoctoral researchers and academic experts who are engaged in modeling stochastic processes on networks;Providing software that can solve differential equation models or directly simulate epidemics on networks.Replete with numerous diagrams, examples, instructive exercises, and online access to simulation algorithms and readily usable code, this book will appeal to a wide spectrum of readers from different backgrounds and academic levels. Appropriate for students with or without a strong background in mathematics, this textbook can form the basis of an advanced undergraduate or graduate course in both mathematics and other departments alike.

This book reports on an outstanding research devoted to modeling and control of dynamic systems using fractional-order calculus. It describes the development of model-based control design methods for systems described by fractional dynamic models. More than 300 years had passed since Newton and Leibniz developed a set of mathematical tools we now know as calculus. Ever since then the idea of non-integer derivatives and integrals, universally referred to as fractional calculus, has been of interest to many researchers. However, due to various issues, the usage of fractional-order models in real-life applications was limited. Advances in modern computer science made it possible to apply efficient numerical methods to the computation of fractional derivatives and integrals. This book describes novel methods developed by the author for fractional modeling and control, together with their successful application in real-world process control scenarios.

This monograph aims to lay the groundwork for the design of a unified mathematical approach to the modeling and analysis of large, complex systems composed of interacting living things. Drawing on twenty years of research in various scientific fields, it explores how mathematical kinetic theory and evolutionary game theory can be used to understand the complex interplay between mathematical sciences and the dynamics of living systems. The authors hope this will contribute to the development of new tools and strategies, if not a new mathematical theory.The first chapter discusses the main features of living systems and outlines a strategy for their modeling. The following chapters then explore some of the methods needed to potentially achieve this in practice. Chapter Two provides a brief introduction to the mathematical kinetic theory of classical particles, with special emphasis on the Boltzmann equation; the Enskog equation,mean field models, and Monte Carlo methods are also briefly covered. Chapter Three uses concepts from evolutionary game theory to derive mathematical structures that are able to capture the complexity features of interactions within living systems. The book then shifts to exploring the relevant applications of these methods that can potentially be used to derive specific, usable models. The modeling of social systems in various contexts is the subject of Chapter Five, and an overview of modeling crowd dynamics is given in Chapter Six, demonstrating how this approach can be used to model the dynamics of multicellular systems. The final chapter considers some additional applications before presenting an overview of open problems. The authors then offer their own speculations on the conceptual paths that may lead to a mathematical theory of living systems hoping to motivate future research activity in the field.A truly unique contribution to the existing literature, A Quest Toward a Mathematical Theory of Living Systems is an important book that will no doubt have a significant influence on the future directions of the field. It will be of interest to mathematical biologists, systems biologists, biophysicists, and other researchers working on understanding the complexities of living systems.

Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô's formula, the optional stopping theorem and Girsanov's theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter.Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides astrong theoretical background to the reader interested in such developments.Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.

This book focuses on the analysis of cancer dynamics and the mathematically based synthesis of anticancer therapy. It summarizes the current state-of-the-art in this field and clarifies common misconceptions about mathematical modeling in cancer. Additionally, it encourages closer cooperation between engineers, physicians and mathematicians by showing the clear benefits of this without stating unrealistic goals. Development of therapy protocols is realized from an engineering point of view, such as the search for a solution to a specific control-optimization problem. Since in the case of cancer patients, consecutive measurements providing information about the current state of the disease are not available, the control laws are derived for an open loop structure. Different forms of therapy are incorporated into the models, from chemotherapy and antiangiogenic therapy to immunotherapy and gene therapy, but the class of models introduced is broad enough to incorporate other forms of therapy as well. The book begins with an analysis of cell cycle control, moving on to control effects on cell population and structured models and finally the signaling pathways involved in carcinogenesis and their influence on therapy outcome. It also discusses the incorporation of intracellular processes using signaling pathway models, since the successful treatment of cancer based on analysis of intracellular processes, might soon be a reality. It brings together various aspects of modeling anticancer therapies, which until now have been distributed over a wide range of literature. Written for researchers and graduate students interested in the use of mathematical and engineering tools in biomedicine with special emphasis on applications in cancer diagnosis and treatment, this self-contained book can be easily understood with only a minimal basic knowledge of control and system engineering methods as well as the biology of cancer. Its interdisciplinary character and the authors'extensive experience in cooperating with clinicians and biologists make it interesting reading for researchers from control and system engineering looking for applications of their knowledge. Systems and molecular biologists as well as clinicians will also find new inspiration for their research.

This book highlights recent compelling research results and trends in various aspects of contemporary mathematics, emphasizing applicabilitions to real-world situations. The chapters present exciting new findings and developments in situations where mathematical rigor is combined with common sense. A multi-disciplinary approach, both within each chapter and in the volume as a whole, leads to practical insights that may result in a more synthetic understanding of specific global issues as well as their possible solutions. The volume will be of interest not only to experts in mathematics, but also to graduate students, scientists, and practitioners from other fields including physics, biology, geology, management, and medicine.