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Written by a specialist in geophysical fluid dynamics and an applied mathematician, this book provides an accessible introduction to new methods for analysing Lagrangian motion in geophysical flows, and surveys research in geophysical fluid dynamics that makes use of them.

Stochastic elasticity is a fast developing field that combines nonlinear elasticity and stochastic theories in order to significantly improve model predictions by accounting for uncertainties in the mechanical responses of materials. However, in contrast to the tremendous development of computational methods for large-scale problems, which have been proposed and implemented extensively in recent years, at the fundamental level, there is very little understanding of the uncertainties in the behaviour of elastic materials under large strains.Based on the idea that every large-scale problem starts as a small-scale data problem, this book combines fundamental aspects of finite (large-strain) elasticity and probability theories, which are prerequisites for the quantification of uncertainties in the elastic responses of soft materials. The problems treated in this book are drawn from the analytical continuum mechanics literature and incorporate random variables as basic concepts along with mechanical stresses and strains. Such problems are interesting in their own right but they are also meant to inspire further thinking about how stochastic extensions can be formulated before they can be applied to more complex physical systems.

This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. In the second edition the material has been significantly expanded, particularly within the context of nonequilibrium and self-organizing systems. Given the amount of additional material, the book has been divided into two volumes, with volume I mainly covering molecular processes and volume II focusing on cellular processes. A wide range of biological topics are covered in the new edition, including stochastic ion channels and excitable systems, molecular motors, stochastic gene networks, genetic switches and oscillators, epigenetics, normal and anomalous diffusion in complex cellular environments, stochastically-gated diffusion, active intracellular transport, signal transduction, cell sensing, bacterial chemotaxis, intracellular pattern formation, cell polarization, cell mechanics, biological polymers and membranes, nuclear structure and dynamics, biological condensates, molecular aggregation and nucleation, cellular length control, cell mitosis, cell motility, cell adhesion, cytoneme-based morphogenesis, bacterial growth, and quorum sensing. The book also provides a pedagogical introduction to the theory of stochastic and nonequilibrium processes - Fokker Planck equations, stochastic differential equations, stochastic calculus, master equations and jump Markov processes, birth-death processes, Poisson processes, first passage time problems, stochastic hybrid systems, queuing and renewal theory, narrow capture and escape, extreme statistics, search processes and stochastic resetting, exclusion processes, WKB methods, large deviation theory, path integrals, martingales and branching processes, numerical methods, linear response theory, phase separation, fluctuation-dissipation theorems, age-structured models, and statistical field theory. This text is primarily aimed at graduate students and researchers working in mathematical biology, statistical and biological physicists, and applied mathematicians interested in stochastic modeling. Applied probabilists should also find it of interest. It provides significant background material in applied mathematics and statistical physics, and introduces concepts in stochastic and nonequilibrium processes via motivating biological applications. The book is highly illustrated and contains a large number of examples and exercises that further develop the models and ideas in the body of the text. It is based on a course that the author has taught at the University of Utah for many years.

This monograph explores the application of the potential method to three-dimensional problems of the mathematical theories of elasticity and thermoelasticity for multi-porosity materials.

This text addresses systems with persistent memory that are common mathematical models used in the study of viscoelasticity and thermodynamics with memory.

This book is the first thorough introduction to and comprehensive treatment of the theory and applications of integrodifference equations in spatial ecology. The book contains step-by-step model construction, explicitly solvable models, abstract theory and numerical recipes for integrodifference equations.

This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations, and in particular with the theory of mechanical systems subject to motion constraints.

This book builds inviscid flow analysis from an undergraduate-level treatment of potential flow to the level required for research.

Emphasizing kinematics and mechanics of growth, this book presents the state of knowledge in morpho-elasticity, providing a rigorous foundation and offering a set of mathematical tools for the analysis of specific problems arising in biology.

This book investigates the mathematical analysis of biological invasions. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes.

This monograph describes and discusses the properties of heterogeneous materials, including conductivity, elastic moduli, and dielectrical constant. This multidisciplinary book will appeal to applied physicists, materials scientists, chemical and mechanical engineers, chemists, and applied mathematicians.

In its revised and expanded second edition, this book examines the theoretical aspects of small strain theory of elastoplasticity with hardening assumptions, offering a comprehensive and unified treatment of mathematical theory and numerical analysis.

Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.

A description of the theoretical foundations of inelasticity, its numerical formulation and implementation, constituting a representative sample of advanced methodology used in inelastic calculations. It is of interest to researchers and graduate students in various branches of engineering.

This accessible text presents a unified approach of treating the microstructure and effective properties of heterogeneous media. Part II treats a wide variety of effective properties of heterogeneous materials and how they are linked to the microstructure, accomplished by using rigorous methods.

This richly illustrated third edition provides a thorough training in practical mathematical biology and shows how exciting mathematical challenges can arise from a genuinely interdisciplinary involvement with the biosciences.

Providing an in-depth look at the practical use of math modeling, it features exercises throughout that are drawn from a variety of bioscientific disciplines - population biology, developmental biology, physiology, epidemiology, and evolution, among others.

This book provides an introduction into physiology using the tools and perspectives of mathematical modeling and analysis. It contains a variety of physiological problems and the current and new mathematical techniques used in this area.

This book introduces the geometry of 3-D vision, that is, the reconstruction of 3-D models of objects from a collection of 2-D images. It details the classic theory of two view geometry and shows that a more proper tool for studying the geometry of multiple views is the so-called rank consideration of the multiple view matrix.

Here is a comprehensive review of the fundamental conditions for optimality for finite-dimensional, deterministic, optimal control problems. Includes worked examples ranging from minimum surfaces of revolution to cancer treatment for novel therapy approaches.

The state of the art in Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics Modeling is presented in this new second edition book. This second edition has new information on reaction limited models of dissolution, non binary biopharmaceutic classification system, time varying models, and interface models.

This book is an overview of mathematical physiology. It contains a variety of physiological problems and the current and new mathematical techniques used in this area. Numerous exercises and models are included.

This book offers a comprehensive reference to the mathematical modeling of environmental and geophysical problems. It provides an abundance of mathematical models, both simple and complex, and elaborates them with approximation techniques.

An Accelerated Course with Applications in Computational Sciences and Engineering

This book offers a new method for studying hybrid models: Generalized Principal Component Analysis. Coverage includes statistical, geometric and algebraic concepts associated with estimation and segmentation of hybrid models, especially hybrid linear models.