Mathematical Biofluiddynamics


Book Description

Addresses external biofluiddynamics concerning animal locomotion and internal biofluiddynamics concerning heat and mass transport.




Mathematical Biofluiddynamics


Book Description

Addresses external biofluiddynamics concerning animal locomotion and internal biofluiddynamics concerning heat and mass transport.




Mathematical Aspects of Geometric Modeling


Book Description

Examines concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies them.




Lectures on Geometric Methods in Mathematical Physics


Book Description

A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.




The Mathematics of Mechanobiology


Book Description

This book presents the state of the art in mathematical research on modelling the mechanics of biological systems – a science at the intersection between biology, mechanics and mathematics known as mechanobiology. The book gathers comprehensive surveys of the most significant areas of mechanobiology: cell motility and locomotion by shape control (Antonio DeSimone); models of cell motion and tissue growth (Benoît Perthame); numerical simulation of cardiac electromechanics (Alfio Quarteroni); and power-stroke-driven muscle contraction (Lev Truskinovsky). Each section is self-contained in terms of the biomechanical background, and the content is accessible to all readers with a basic understanding of differential equations and numerical analysis. The book disentangles the phenomenological complexity of the biomechanical problems, while at the same time addressing the mathematical complexity with invaluable clarity. The book is intended for a wide audience, in particular graduate students and applied mathematicians interested in entering this fascinating field.




Mathematical Theories of Populations


Book Description

Mathematical theories of populations have appeared both implicitly and explicitly in many important studies of populations, human populations as well as populations of animals, cells and viruses. They provide a systematic way for studying a population's underlying structure. A basic model in population age structure is studied and then applied, extended and modified, to several population phenomena such as stable age distributions, self-limiting effects, and two-sex populations. Population genetics are studied with special attention to derivation and analysis of a model for a one-locus, two-allele trait in a large randomly mating population. The dynamics of contagious phenomena in a population are studied in the context of epidemic diseases.




Perspectives in Ecological Theory


Book Description

This volume presents an overview of current accomplishments and future directions in ecological theory. The twenty-three chapters cover a broad range of important topics, from the physiology and behavior of individuals or groups of organisms, through population dynamics and community structure, to the ecology of ecosystems and the geochemical cycles of the entire biosphere. The authors focus on ways in which theory, whether expressed mathematically or verbally, can contribute to defining and solving fundamental problems in ecology. A second aim is to highlight areas where dialogue between theorists and empiricists is likely to be especially rewarding. The authors are R. M. Anderson, C. W. Clark, M. L. Cody, J. E. Cohen, P. R. Ehrlich, M. W. Feldman, M. E. Gilpin, L. J. Gross, M. P. Hassell, H. S. Horn, P. Kareiva, M.A.R. Koehl, S. A. Levin, R. M. May, L. D. Mueller, R. V. O'Neill, S. W. Pacala, S. L. Pimm, T. M. Powell, H. R. Pulliam, J. Roughgarden, W. H. Schlesinger, H. H. Shugart, S. M. Stanley, J. H. Steele, D. Tilman, J. Travis, and D. L. Urban. Originally published in 1989. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.




Mathematical Analysis of Viscoelastic Flows


Book Description

This monograph is based on a series of lectures presented at the 1999 NSF-CBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics.




Advances in Applied Mechanics


Book Description

Mechanics is defined as a branch of physics that focuses on motion and the reaction of physical systems to internal and external forces. This highly acclaimed series provides survey articles on the present state and future direction of research in important branches of applied solid and fluid mechanics.




Finite Element Exterior Calculus


Book Description

Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world?wave propagation, thermodynamics, fluid flow, solid deformation, electricity and magnetism, quantum mechanics, general relativity, and many more?are described by differential equations. We depend on numerical methods for the ability to simulate, explore, predict, and control systems involving these processes. The finite element exterior calculus, or FEEC, is a powerful new theoretical approach to the design and understanding of numerical methods to solve partial differential equations (PDEs). The methods derived with FEEC preserve crucial geometric and topological structures underlying the equations and are among the most successful examples of structure-preserving methods in numerical PDEs. This volume aims to help numerical analysts master the fundamentals of FEEC, including the geometrical and functional analysis preliminaries, quickly and in one place. It is also accessible to mathematicians and students of mathematics from areas other than numerical analysis who are interested in understanding how techniques from geometry and topology play a role in numerical PDEs.