Mathematical Modelling of Natural Systems

Comprehensive and thorough, this monograph emphasizes the main role differential geometry and convex analysis play in the understanding of physical, chemical, and mechanical notions. Central focus is

Prior to the so-called "energy crisis" of 1973, energy played a relatively minor role in our daily lives.and received limited attention from economists, planners and politicians. As a means of product

This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging diffe

Systems and their mathematical description play an important role in all branches of science. This book offers an introduction to mathematical modeling techniques. It is intended for undergrad student

Mathematical modelling has become an indispensable tool for engineers, scientists, planners, decision makers and many other professionals for making predictions of future scenarios as well as real imp

Action selection is the task of doing the right thing at the right time. It requires the assessment of available alternatives, executing those most appropriate, and resolving conflicts among competing goals and possibilities. Using advanced computational modelling, this book explores cutting-edge research into action selection in nature from a wide range of disciplines, from neuroscience to behavioural ecology, and even political science. It delivers new insights into both detailed and systems-level attributes of natural intelligence and demonstrates advances in methodological practice. Contributions from leading researchers cover issues including whether biological action selection is optimal, neural substrates for action selection in the vertebrate brain, perceptual selection in decision making, and interactions between group and individual action selection. This first integrated review of action selection in nature contains a balance of review and original research material, consoli

Mathematical Models of Biological Systems provides a practical introduction to basic mathematical modelling methodology and analysis. It covers a variety of biological applications and uses these topi

Mathematical Models of Biological Systems provides a practical introduction to basic mathematical modelling methodology and analysis. It covers a variety of biological applications and uses these topi

This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. It is devoted to the analysis of dynamical systems and c

This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. It is devoted to the analysis of dynamical systems and c

Mathematical modelling of communicable diseases has in the past decades been the subject of intense research activity, on the part of both epidemiologists and biomathematicians; nonlinear forces of in

Mathematical and numerical modelling of the human cardiovascular system has attracted remarkable research interest due to its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. This book addresses the two principal components of the cardiovascular system: arterial circulation and heart function. It systematically describes all aspects of the problem, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, reviewing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiovascular system and the need for computational methods that are stable, reliable and efficient. The final part is devoted to control and inverse problems, including parameter estimation, uncertainty quantification and the developmen

This book demonstrates the power of mathematical thinking in understanding the biological complexity that exists within the brain. It looks at the latest research on modelling of biochemical pathways

Systems and their mathematical description play an important role in all branches of science. This book offers an introduction to mathematical modeling techniques. It is intended for undergrad student

Mathematical Modelling in One Dimension demonstrates the universality of mathematical techniques through a wide variety of applications. Learn how the same mathematical idea governs loan repayments, drug accumulation in tissues or growth of a population, or how the same argument can be used to find the trajectory of a dog pursuing a hare, the trajectory of a self-guided missile or the shape of a satellite dish. The author places equal importance on difference and differential equations, showing how they complement and intertwine in describing natural phenomena.

This book examines key issues in designing semantics-oriented natural language processing systems. A broad conceptual framework for describing structured meanings of NL-texts is obtained by defining

Understanding and predicting the behaviour of natural and human environmental systems is crucial for the effective management of the Earth’s limited resources. Recently, great advances have been

Probabilistic modelling is the most cost-effective means of performance and reliability evaluation of complex dynamic systems. This self-contained text will be welcomed by students and teachers for its no-nonsense treatment of the basic results and examples of their application. The only mathematical background that is assumed is basic calculus. The necessary fundamentals of probability theory are included, as well as an introduction to renewal, Poisson and Markov processes. Models arising in the fields of manufacturing, computing and communications, involving single or multiple service stations and one or more customer classes, are examined in some detail. Both exact and approximate solution methods are discussed, including recent techniques such as spectral expansion. Special attention is devoted to models of systems subject to breakdowns and repairs. Throughout the book, strong emphasis is placed on explaining the ideas behind the results and helping the reader to use them, making t

Probabilistic modelling is the most cost-effective means of performance and reliability evaluation of complex dynamic systems. This self-contained text will be welcomed by students and teachers for its no-nonsense treatment of the basic results and examples of their application. The only mathematical background that is assumed is basic calculus. The necessary fundamentals of probability theory are included, as well as an introduction to renewal, Poisson and Markov processes. Models arising in the fields of manufacturing, computing and communications, involving single or multiple service stations and one or more customer classes, are examined in some detail. Both exact and approximate solution methods are discussed, including recent techniques such as spectral expansion. Special attention is devoted to models of systems subject to breakdowns and repairs. Throughout the book, strong emphasis is placed on explaining the ideas behind the results and helping the reader to use them, making t

Geomathematics provides a comprehensive summary of the mathematical principles behind key topics in geophysics and geodesy, covering the foundations of gravimetry, geomagnetics and seismology. Theorems and their proofs explain why physical realities in geoscience are the logical mathematical consequences of basic laws. The book also derives and analyzes the theory and numerical aspects of established systems of basis functions; and presents an algorithm for combining different types of trial functions. Topics cover inverse problems and their regularization, the Laplace/Poisson equation, boundary-value problems, foundations of potential theory, the Poisson integral formula, spherical harmonics, Legendre polynomials and functions, radial basis functions, the Biot-Savart law, decomposition theorems (orthogonal, Helmholtz, and Mie), basics of continuum mechanics, conservation laws, modelling of seismic waves, the Cauchy-Navier equation, seismic rays, and travel-time tomography. Each chapte

Living systems are dynamic and extremely complex and their behaviour is often hard to predict by studying their individual parts. Systems biology promises to reveal and analyse these highly connected, regulated and adaptable systems, using mathematical modelling and computational analysis. This new systems approach is already having a broad impact on biological research and has potentially far-reaching implications for our understanding of life. Written in an informal and non-technical style, this book provides an accessible introduction to systems biology. Self-contained vignettes each convey a key theme and are intended to enlighten, provoke and interest readers of different academic disciplines, but also to offer new insight to those working in the field. Using a minimum amount of jargon and no mathematics, Voit manages to convey complex ideas and give the reader a genuine sense of the excitement that systems biology brings with it, as well as the current challenges and opportunitie

Living systems are dynamic and extremely complex and their behaviour is often hard to predict by studying their individual parts. Systems biology promises to reveal and analyse these highly connected, regulated and adaptable systems, using mathematical modelling and computational analysis. This new systems approach is already having a broad impact on biological research and has potentially far-reaching implications for our understanding of life. Written in an informal and non-technical style, this book provides an accessible introduction to systems biology. Self-contained vignettes each convey a key theme and are intended to enlighten, provoke and interest readers of different academic disciplines, but also to offer new insight to those working in the field. Using a minimum amount of jargon and no mathematics, Voit manages to convey complex ideas and give the reader a genuine sense of the excitement that systems biology brings with it, as well as the current challenges and opportunitie

This book provides a self-contained presentation of the physical and mathematical laws governing complex systems. Complex systems arising in natural, engineering, environmental, life and social scienc

Mesoscale weather systems are responsible for numerous natural disasters, such as damaging winds, blizzards and flash flooding. A fundamental understanding of the underlying dynamics involved in these weather systems is essential in forecasting their occurrence. This 2007 book provides a systematic approach to this subject. The opening chapters introduce the basic equations governing mesoscale weather systems and their approximations. The subsequent chapters cover four major areas of mesoscale dynamics: wave dynamics, moist convection, front dynamics and mesoscale modelling. This is an ideal book on the subject for researchers in meteorology and atmospheric science. With over 100 problems, and password-protected solutions available to instructors at www.cambridge.org/9780521808750, this book could also serve as a textbook for graduate students. Modelling projects, providing hands-on practice for building simple models of stratified fluid flow from a one-dimensional advection equation,

Mathematical modelling of physiological systems promises to advance our understanding of complex biological phenomena and pathophysiology of diseases. In this book, the authors adopt a mathematical approach to characterize and explain the functioning of the gastrointestinal system. Using the mathematical foundations of thin shell theory, the authors patiently and comprehensively guide the reader through the fundamental theoretical concepts, via step-by-step derivations and mathematical exercises, from basic theory to complex physiological models. Applications to nonlinear problems related to the biomechanics of abdominal viscera and the theoretical limitations are discussed. Special attention is given to questions of complex geometry of organs, effects of boundary conditions on pellet propulsion, as well as to clinical conditions, e.g. functional dyspepsia, intestinal dysrhythmias and the effect of drugs to treat motility disorders. With end of chapter problems, this book is ideal for

An interval is a natural way of specifying a number that is specified only within certain tolerances. Interval analysis consists of the tools and methods needed to solve linear and nonlinear systems of equations in the presence of data uncertainties. Applications include the sensitivity analysis of solutions of equations depending on parameters, the solution of global nonlinear problems, and the verification of results obtained by finite-precision arithmetic. In this book emphasis is laid on those aspects of the theory which are useful in actual computations. On the other hand, the theory is developed with full mathematical rigour. In order to keep the book self-contained, various results from linear algebra (Perron-Frobenius theory, M- and H- matrices) and analysis (existence of solutions to nonlinear systems) are proved, often from a novel and more general viewpoint. An extensive bibliography is included.

This book, based on a successful undergraduate course designed by the author, describes mathematical modelling and its application to the solution of problems in industry and commerce. In the early chapters of the book the author first sets out a clear introduction to the principles of mathematical modelling, including sections on the various methodologies of mathematical modelling and their relationship to systems methodologies. He then offers some insights into practical aspects of mathematical modelling and proceeds to describe the development and operation of the undergraduate course upon which the book is based. In the later chapters seven case studies, based on real problems contributed by mathematicians working in industry, are introduced. Each chapter describes a problem, the solution originally adopted and variations on that solution introduced by students over a number of years use of the case studies.

This text provides a thorough treatment of the fundamental principles of fluid mechanics and convection heat transfer and shows how to apply the principles to a wide variety of fluid flow problems. The book is intended for use by final year undergraduate and beginning graduate students in engineering. The focus is on incompressible viscous flows with special applications to non-Newtonian fluid flows, turbulent flows, and free-forced convection flows. A special feature of the text is its coverage of generalised mass, momentum, and heat transfer equations, cartesian tensor manipulations, scale analyses, mathematical modelling techniques and practical solution methods. The final chapter is unique in its case-study approach, applying general modelling principles to analyse non-isothermal flow systems found in a wide range of engineering disciplines. Numerous end-of-chapter sample problem solutions, homework assignments, and mathematical aids are provided to enhance the reader's understandi

Famous mathematical constants include the ratio of circular circumference to diameter, pi=3.14 …, and the natural logarithmic base, e=2.178 … Students and professionals usually can name at most a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. Topics covered include the statistics of continued fractions, chaos in nonlinear systems, prime numbers, sum-free sets, isoperimetric problems, approximation theory, self-avoiding walks and the Ising model (from statistical physics), binary and digital search trees (from theoretical computer science), the Prouhet-Thue-Morse sequence, complex analysis, geometric probability and the traveling salesman problem. This book will be helpful both to readers seeking information about a specific constant, and to readers