SERIES ON ADVANCES IN MATHEMATICS FOR APPLIED SCIENCES – serie

This book presents applications to several fluid dynamics problems in both the bounded and unbounded domains in the framework of the discrete velocity models of kinetic theory. The proposition of new models for dense gases, gases with multi-components, and gases with chemical reactions are also included. This is an up-to-date book on the applications of the discrete Boltzmann equation.

Part of a series which aims to cover advances in mathematics for the applied sciences, this volume presents essays on diverse mathematical problems relating to the Navier-Stokes equation.

This book deals with aspects of thermodynamic restrictions in modern continuum mechanics and with particular problems of the kinetic theory and statistical mechanics. It stresses the interplay between statistical and phenomenological modelling of physical phenomena including homogenization techniques for media with microstructure. Diverse approaches to either derivation or justification of macroscopic models by microscopic theories are presented. From the kinetic theory, the problem of existence of solutions to the Boltzmann equation and particular solutions to the discrete velocity models are also considered. The book includes papers concerning viscoelasticity treated within the framework of both rational and extended thermodynamics. Phenomenological theories of hyperbolic heat conduction in solids and fluids are also discussed.

One of a series in mathematics for applied sciences, this volume discusses nonlinear kinetic theory and mathematical aspects of hyperbolic systems. Topics covered include generalizations of the Boltzmann equation and developments in mathematical biology, and the formation of Maxwellian tails.

This book presents a unified treatment of the mechanics of mixtures of several constituents within the context of continuum mechanics. After an introduction to the basic theory in the first few chapters, the book deals with a detailed exposition of the mechanics of a mixture of a fluid and an elastic solid, which is either isotropic or anisotropic and is capable of undergoing large deformations. Issues regarding the specification of boundary conditions for mixtures are discussed in detail and several boundary value and initial-boundary value problems are solved. The status of some special theories like those of Darcy and Biot are discussed. Such a study has relevance to several technologically significant problems in geomechanics, biomechanics, diffusion of contaminants and the swelling and absorption of fluids in polymers and polymer composites, to mention a few.

Time is considered as an independent entity which cannot be reduced to the concept of matter, space or field. The point of discussion is the “time flow” conception of N A Kozyrev (1908–1983), an outstanding Russian astronomer and natural scientist. In addition to a review of the experimental studies of “the active properties of time”, by both Kozyrev and modern scientists, the reader will find different interpretations of Kozyrev's views and some developments of his ideas in the fields of geophysics, astrophysics, general relativity and theoretical mechanics.

This book is an exposition of a new approach to the Navier-Stokes equations, using powerful techniques provided by nonstandard analysis, as developed by the authors. The topics studied include the existence and uniqueness of weak solutions, statistical solutions and the solution of general stochastic equations.The authors provide a self-contained introduction to nonstandard analysis, designed with applied mathematicians in mind and concentrated specifically on techniques applicable to the Navier-Stokes equations. The subsequent exposition shows how these new techniques allow a quick and intuitive entrance into the mathematical theory of hydrodynamics, as well as provide a research tool that has proven useful in solving open problems concerning stochastic equations.

This book provides the reader with basic tools to solve problems of electromagnetism in their natural functional frameworks thanks to modern mathematical methods: integral surface methods, and also semigroups, variational methods, etc., well adapted to a numerical approach.As examples of applications of these tools and concepts, we solve several fundamental problems of electromagnetism, stationary or time-dependent: scattering of an incident wave by an obstacle, bounded or not, by gratings; wave propagation in a waveguide, with junctions and cascades. We hope that mathematical notions will allow a better understanding of modelization in electromagnetism and emphasize the essential features related to the geometry and nature of materials.

The book starts with an historical overview of road vehicles. The first part deals with the forces exchanged between the vehicle and the road and the vehicle and the air with the aim of supplying the physical facts and the relevant mathematical models about the forces which dominate the dynamics of the vehicle.The second part deals with the dynamic behaviour of the vehicle in normal driving conditions with some extensions towards conditions encountered in high-speed racing driving.

Part of a series which aims to cover advances in mathematics for the applied sciences, this volume presents essays on diverse mathematical problems relating to the Navier-Stokes equation.

This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions.Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.

This book constitutes a comprehensive survey of the balance equations for mass, momentum and energy for the interfaces in pure fluids and mixtures. Constitutive laws are presented for many situations in engineering science, and examples are provided, including surface viscosity effects, variable surface tension and vapor recoil. In addition, some extensions of existing theory are given: stretch effect in premixed flames, relaxation zones downstream two-phase shock waves, and effective surface tension for steep gradient zones.

The aim of this book is to provide a basic and self-contained introduction to the ideas underpinning fractal analysis. The book illustrates some important applications issued from real data sets, real physical and natural phenomena as well as real applications in different fields, and consequently, presents to the readers the opportunity to implement fractal analysis in their specialties according to the step-by-step guide found in the book.Besides advanced undergraduate students, graduate students and senior researchers, this book may also serve scientists and research workers from industrial settings, where fractals and multifractals are required for modeling real-world phenomena and data, such as finance, medicine, engineering, transport, images, signals, among others.For the theorists, rigorous mathematical developments are established with necessary prerequisites that make the book self-containing. For the practitioner often interested in model building and analysis, we provide the cornerstone ideas.

This volume contains original, refereed contributions by researchers from national metrology institutes, universities and laboratories across the world involved in metrology and testing. The volume has been produced by the International Measurement Confederation Technical Committee 21, Mathematical Tools for Measurements and is the twelfth in the series. The papers cover topics in numerical analysis and computational tools, statistical inference, regression, calibration and metrological traceability, computer science and data provenance, and describe applications in a wide range of application domains. This volume is useful to all researchers, engineers and practitioners who need to characterize the capabilities of measurement systems and evaluate measurement data. It will also be of interest to scientists and engineers concerned with the reliability, trustworthiness and reproducibility of data and data analytics in data-driven systems in engineering, environmental and life sciences.

What do economic chaos and uncertainties mean in rational or irrational economic theories? How do simple deterministic interactions among a few variables lead to unpredictable complex phenomena? Why is complexity of economies causing so many conflicts and confusions worldwide?This book provides a comprehensive introduction to recent developments of complexity theory in economics. It presents different models based on well-accepted economic mechanisms such as the Solow model, Ramsey model, and Lucas model. It is focused on presenting complex behaviors, such as business cycles, aperiodic motion, bifurcations, catastrophes, chaos, and hidden attractors, in basic economic models with nonlinear behavior. It shows how complex nonlinear phenomena are identified from various economic mechanisms and theories. These models demonstrate that the traditional or dominant economic views on evolution of, for instance, capitalism market, free competition, or Keynesian economics, are not generally valid. Markets are unpredictable and nobody knows with certainty the consequences of policies or other external factors in economic systems with simple interactions.

This is the first book on the problems of mathematical modelling that combines a generalised approach to the problem of mathematical modelling processes and phenomena in the real world with developing modelling methods in relation to specific objects and processes. Some of the problems discussed here include the stability and bifurcation of simplified models of supply and demand, and resultants of various approaches, such as standardisation, unification, partial ordering and data packaging.As well as touching upon the general principles of modelling, the book studies the stability of mathematical models using the generalised direct Lyapunov method based on matrix-valued auxiliary functions. It has significant potential for application in the design of new moving objects (nano-robots, manipulators, drones, etc.) and processes related to artificial intelligence (multidimensional interaction of related data arrays) that can be described by differential equations of different types.Written by two respected specialists in the field of the qualitative theory of equations and problems of modelling real-world phenomena, this book is primarily targeted at specialists in the field of engineering sciences, but is also suitable for graduate courses.

This book provides a variety of methods required for the analysis and solution of equations which arise in the modeling of phenomena from the natural and engineering sciences. It can be used productively by both undergraduate and graduate students, as well as others who need to learn and understand these techniques. A detailed discussion is also presented for several topics that are usually not included in standard textbooks at this level: qualitative methods for differential equations, dimensionalization and scaling, elements of asymptotics, difference equations, and various perturbation methods. Each chapter contains a large number of worked examples and provides references to the appropriate literature.

This book provides a good introduction to modern computational methods for Partial Differential Equations in Mechanics. Finite-difference methods for parabolic, hyperbolic as well as elliptic partial differential equations are discussed.A gradual and inductive approach to the numerical concepts has been used, such that the presentation of the theory is easily accessible to upper-level undergraduate and graduate students. Special attention has been given to the applications, with many examples and exercises provided along with solutions. For each type of equation, physical models are carefully derived and presented in full details.Windows programs developed in C++ language have been included in the accompanying CD-ROM. These programs can be easily modified to solve different problems, and the reader is encouraged to take full advantage of the innovative features of this powerful development tool.

Although the application of differential equations to economics is a vast and vibrant area, the subject has not been systematically studied; it is often treated as a subsidiary part of mathematical economics textbooks. This book aims to fill that void by providing a unique blend of the theory of differential equations and their exciting applications to dynamic economics. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been widely applied to economic analysis in recent years. It provides comprehensive coverage of the most important concepts and theorems in the theory of differential equations in a way that can be understood by any reader who has a basic knowledge of calculus and linear algebra. In addition to traditional applications of the theory to economic dynamics, the book includes many recent developments in different fields of economics.

This volume provides students with the necessary tools to better understand the fields of neurobiological modeling, cluster analysis of proteins and genes. The theory is explained starting from the beginning and in the most elementary terms, there are many exercises solved and not useful for the understanding of the theory. The exercises are specially adapted for training and many useful Matlab programs are included, easily understood and generalizable to more complex situations. This self-contained text is particularly suitable for an undergraduate course of biology and biotechnology.New results are also provided for researchers such as the description and applications of the Kohonen neural networks to gene classification and protein classification with back propagation neutral networks.

This volume contains pedagogical and elementary introductions to genetics for mathematicians and physicists as well as to mathematical models and techniques of population dynamics. It also offers a physicist's perspective on modeling biological processes.Each chapter starts with an overview followed by the recent results obtained by authors. Lectures are self-contained and are devoted to various phenomena such as the evolution of the genetic code and genomes, age-structured populations, demography, sympatric speciation, the Penna model, Lotka-Volterra and other predator-prey models, evolutionary models of ecosystems, extinctions of species, and the origin and development of language. Authors analyze their models from the computational and mathematical points of view.

With the advent of a host of new materials ranging from shape memory alloys to biomaterials to multiphase alloys, acquiring the capacity to model inelastic behavior and to choose the right model in a commercial analysis software has become a pressing need for practicing engineers. Even with the traditional materials, there is a continued emphasis on optimizing and extending their full range of capability in the applications. This textbook builds upon the existing knowledge of elasticity and thermodynamics, and allows the reader to gain confidence in extending one's skills in understanding and analyzing problems in inelasticity. By reading this textbook and working through the assigned exercises, the reader will gain a level of comfort and competence in developing and using inelasticity models. Thus, the book serves as a valuable book for practicing engineers and senior-level undergraduate/graduate-level students in the mechanical, civil, aeronautical, metallurgical and other disciplines.The book is written in three parts. Part 1 is primarily focused on lumped parameter models and simple structural elements such as trusses and beams. This is suitable for an advanced undergraduate class with just a strength of materials background. Part II is focused on small deformation multi-dimensional inelasticity and is suitable for a beginning graduate class. Sufficient material is included on how to numerically implement an inelastic model and solve either using a simple stress function type of approach or using commercial software. Case studies are included as examples. There is also an extensive discussion of thermodynamics in the context of small deformations. Part III focuses on more advanced situations such as finite deformation inelasticity, thermodynamical ideas and crystal plasticity. More advanced case studies are included in this part.• This textbook takes a new, task- or scenario-based approach to teaching and learning inelasticity. The book is written in an active learning style that appeals to engineers and students who wish to design or analyze structures and components that are subject to inelasticity.• The book incorporates thermodynamical considerations into the modeling right from an early stage. Extensive discussions are provided throughout the book on the thermodynamical underpinnings of the models.• This textbook is the first to make extensive use of MATLAB to implement many inelasticity models. It includes the use of concepts such as Airy stress functions to solve plane problems for inelastic materials. The MATLAB codes are listed in the appendix for one to modify with their own models and requirements.• Step-by-step procedures for formulations and calculations are provided for the reader to readily adapt to the inelastic problems that he or she attempts to solve.• A large number of problems, exercises and projects for one to teach or learn from are included. These can be assigned as homework, in-class exercises or projects.• The book is written in a modular fashion, which provides adequate flexibility for adaptation in classes that cater to different audiences such as senior-level students, graduate students, research scholars, and practicing engineers.

The main theme of the AMCTM 2008 conference, reinforced by the establishment of IMEKO TC21, was to provide a central opportunity for the metrology and testing community worldwide to engage with applied mathematicians, statisticians and software engineers working in the relevant fields.This review volume consists of reviewed papers prepared on the basis of the oral and poster presentations of the Conference participants. It covers all the general matters of advanced statistical modeling (e.g. uncertainty evaluation, experimental design, optimization, data analysis and applications, multiple measurands, correlation, etc.), metrology software (e.g. engineering aspects, requirements or specification, risk assessment, software development, software examination, software tools for data analysis, visualization, experiment control, best practice, standards, etc.), numerical methods (e.g. numerical data analysis, numerical simulations, inverse problems, uncertainty evaluation of numerical algorithms, applications, etc.), and data fusion techniques and design and analysis of inter-laboratory comparisons.

This second edition provides a broad range of methods and concepts required for the analysis and solution of equations which arise in the modeling of phenomena in the natural, engineering, and applied mathematical sciences. It may be used productively by both undergraduate and graduate students, as well as others who wish to learn, understand, and apply these techniques. Detailed discussions are also given for several topics that are not usually included in standard textbooks at this level of presentation: qualitative methods for differential equations, dimensionalization and scaling, elements of asymptotics, difference equations and several perturbation procedures. Further, this second edition includes several new topics covering functional equations, the Lambert–W function, nonstandard sets of periodic functions, and the method of dominant balance. Each chapter contains a large number of worked examples and provides references to the appropriate books and literature.

This volume contains original, refereed contributions by researchers from institutions and laboratories across the world that are involved in metrology and testing. They were adapted from presentations made at the eleventh edition of the Advanced Mathematical and Computational Tools in Metrology and Testing conference held at the University of Strathclyde, Glasgow, in September 2017, organized by IMEKO Technical Committee 21, the National Physical Laboratory, UK, and the University of Strathclyde. The papers present new modeling approaches, algorithms and computational methods for analyzing data from metrology systems and for evaluation of the measurement uncertainty, and describe their applications in a wide range of measurement areas.This volume is useful to all researchers, engineers and practitioners who need to characterize the capabilities of measurement systems and evaluate measurement data. Through the papers written by experts working in leading institutions, it covers the latest computational approaches and describes applications to current measurement challenges in engineering, environment and life sciences.

This book provides an up-to-date overview of research articles in applied and industrial mathematics in Italy. This is done through the presentation of a number of investigations focusing on subjects as nonlinear optimization, life science, semiconductor industry, cultural heritage, scientific computing and others.This volume is important as it gives a report on modern applied and industrial mathematics, and will be of specific interest to the community of applied mathematicians.This book collects selected papers presented at the 9th Conference of SIMAI. The subjects discussed include image analysis methods, optimization problems, mathematics in the life sciences, differential models in applied mathematics, inverse problems, complex systems, innovative numerical methods and others.

This volume contains original, refereed worldwide contributions. They were prompted by presentations made at the ninth AMCTM Conference held in Göteborg (Sweden) in June 2011 on the theme of advanced mathematical and computational tools in metrology and also, in the title of this book series, in testing.The themes in this volume reflect the importance of the mathematical, statistical and numerical tools and techniques in metrology and testing and, also in keeping the challenge promoted by the Metre Convention, to access a mutual recognition for the measurement standards.Sample Chapter(s)

This second part of Continuum Thermodynamics is designed to match almost one-to-one the chapters of Part I. This is done so that the reader studying thermodynamics will have a deepened understanding of the subjects covered in Part I. The aims of the book are in particular: the illustration of basic features of some simple thermodynamical models such as ideal and viscous fluids, non-Newtonian fluids, nonlinear solids, interactions with electromagnetic fields, and diffusive porous materials. A further aim is the illustration of the above subjects by examples and simple solutions of initial and boundary problems as well as simple exercises to develop skills in the construction of interdisciplinary macroscopic models.

This volume contains original and refereed contributions from the tenth AMCTM Conference (http://www.nviim.ru/AMCTM2014) held in St. Petersburg (Russia) in September 2014 on the theme of advanced mathematical and computational tools in metrology and testing.The themes in this volume reflect the importance of the mathematical, statistical and numerical tools and techniques in metrology and testing and, also keeping the challenge promoted by the Metre Convention, to access a mutual recognition for the measurement standards.