Page 1
Page 1
Vorticity, Statistical Mechanics, and Monte Carlo Simulation
This book is drawn from across many active fields of mathematics and physics, and has connections to atmospheric dynamics, spherical codes, graph theory, constrained optimization problems, Markov Chains, and Monte Carlo methods. It addresses how to access interesting, original, and publishable research in statistical modeling of large-scale flows and several related fields. The authors f this book explicitly reach around the major branches of mathematics and physics, showing how the use of a few straightforward approaches can create a cornucopia of intriguing questions and the tools to answer them. In reading this book, the reader will learn how to research a topic and how to understand statistical mechanics treatments of fluid dynamics.
VI Hotine-Marussi Symposium on Theoretical and Computational Geodesy ; IAG Symposium Wuhan, China 29 May - 2 June, 2006
Cover almost every topic of geodesy, with particular emphasis on satellite gravity modelling, geodynamics, GPS data processing and applications, statistical estimation and prediction theory, and geodetic inverse problem theory and geodetic boundary value problems.
Variational Problems in Materials Science
This volume contains the proceedings of the international workshop Variational Problems in Materials Science, which was jointly organized by the International School for Advanced Studies (SISSA) of Trieste and by the Dipartimento di Matematica
Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes
The book presents variational methods combined with boundary integral equation techniques in application to a model of dynamic bending of plates with transverse shear deformation. The emphasis is on the rigorous mathematical investigation of the model, which covers a complete study of the well-posedness of a number of initial-boundary value problems, their reduction to time-dependent boundary integral equations by means of suitable potential representations, and the solution of the latter in Sobolev spaces.
Variational Analysis and Applications
This book discusses a new discipline, variational analysis, which contains the calculus of variations, differential calculus, optimization, and variational inequalities. To such classic branches of mathematics, variational analysis provides a uniform theoretical base that represents a powerful tool for the applications.
Trends in Partial Differential Equations of Mathematical Physics
Vsevolod Alekseevich Solonnikov is known as one of the outstanding mathematicians from the St Petersburg Mathematical School. This book contains twenty original contributions on many topics related to V A Solonnikov's work, selected from the invited talks of an international conference held on the occasion of his 70th birthday.
Topological Degree Approach to Bifurcation Problems
Topological bifurcation theory is one of the most essential topics in mathematics. This book contains original bifurcation results for the existence of oscillations and chaotic behaviour of differential equations and discrete dynamical systems under variation of involved parameters. Using topological degree theory and a perturbation approach in dynamical systems, a broad variety of nonlinear problems are studied, including: non-smooth mechanical systems with dry frictions; weakly coupled oscillators; systems with relay hysteresis; differential equations on infinite lattices of Frenkel-Kontorova and discretized Klein-Gordon types; blue sky catastrophes for reversible dynamical systems; buckling of beams; and discontinuous wave equations.
Topics in Analysis and its Applications
Most topics dealt with here deal with complex analysis of both one and several complex variables. Several contributions come from elasticity theory. Areas covered include the theory of p-adic analysis, mappings of bounded mean oscillations, quasiconformal mappings of Klein surfaces, complex dynamics of inverse functions of rational or transcendental entire functions, the nonlinear Riemann-Hilbert problem for analytic functions with nonsmooth target manifolds, the Carleman-Bers-Vekua system, the logarithmic derivative of meromorphic functions, G-lines, computing the number of points in an arbitrary finite semi-algebraic subset, linear differential operators, explicit solution of first and second order systems in bounded domains degenerating at the boundary, the Cauchy-Pompeiu representation in L2 space, strongly singular operators of Calderon-Zygmund type, quadrature solutions to initial and boundary-value problems, the Dirichlet problem, operator theory, tomography, elastic displacements and stresses, quantum chaos, and periodic wavelets.
Theory of Function Spaces III
Deals with the recent theory of function spaces as it stands now. Special attention is paid to some developments in the last 10–15 years which are closely related to the nowadays numerous applications of the theory of function spaces to some neighbouring areas such as numerics, signal processing and fractal analysis.
Theoretical numerical analysis : A functional analysis framework
This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solution, numerical methods for solving integral equations of the second kind, and boundary integral equations for planar regions.
The Maximum Principle
Maximum principles are bedrock results in the theory of second order elliptic equations. This principle, simple enough in essence, lends itself to a quite remarkable number of subtle uses when combined appropriately with other notions. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations.
Symmetry in modeling and analysis of dynamic systems
Real-world systems exhibit complex behavior, therefore novel mathematical approaches or modifications of classical ones have to be employed to precisely predict, monitor, and control complicated chaotic and stochastic processes. One of the most basic concepts that has to be taken into account while conducting research in all natural sciences is symmetry, and it is usually used to refer to an object that is invariant under some transformations including translation, reflection, rotation or scaling.The following Special Issue is dedicated to investigations of the concept of dynamical symmetry in the modelling and analysis of dynamic features occurring in various branches of science like physics, chemistry, biology, and engineering, with special emphasis on research based on the mathematical models of nonlinear partial and ordinary differential equations.
Sturm-Liouville Theory : Past and Present
This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey is made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research.
Stroh Formalism and Rayleigh Waves
The exposition is divided into three chapters. Chapter 1 gives a succinct introduction to the Stroh formalism so that the reader can grasp the essentials as quickly as possible. In Chapter 2 several important topics in static elasticity, which include fundamental solutions, piezoelectricity, and inverse boundary value problems, are studied on the basis of the Stroh formalism. Chapter 3 is devoted to Rayleigh waves, which has long been a topic of the utmost importance in nondestructive evaluation, seismology, and materials science. Here existence, uniqueness, phase velocity, polarization, and perturbation of Rayleigh waves are discussed through the Stroh formalism.
Static and dynamic analysis of engineering structures : Incorporating the boundary element method
Illustrates the modern methods of static and dynamic analysis of structures ; Provides methods for solving boundary value problems of structural mechanics and soil mechanics ; Offers a wide spectrum of applications of modern techniques and methods of calculation of static, dynamic and seismic problems of engineering design; Presents a new foundation model.
Slow Rarefied Flows : Theory and Application to Micro-Electro-Mechanical Systems
Presents the mathematical tools used to deal with problems related to slow rarefied flows, with particular attention to basic concepts and problems which arise in the study of micro- and nanomachines. The mathematical theory of slow flows is presented in a practically complete fashion and provides a rigorous justification for the use of the linearized Boltzmann equation, which avoids costly simulations based on Monte Carlo methods.
Singularly Perturbed Boundary-Value Problems
It is well known that many phenomena in biology, chemistry, engineering, physics can be described by boundary value problem sassociated with various types of partial differential equations or systems. When we associate a mathematical model with a phenomenon, we generally try to capture what is essential, retaining the important quantities and omitting the negligible ones which involve small parameters. The model that would be obtained by maintaining the small parameters is called the perturbed model, whereas the simplifed model (the one that does not include the small parameters) is called unperturbed (or reduced model). Of course, the unperturbed model is to be preferred, because it is simpler.
Singular Sets of Minimizers for the Mumford-Shah Functional
Studies regularity properties of Mumford-Shah minimizers. The Mumford-Shah functional was introduced in the 1980s as a tool for automatic image segmentation, but its study gave rise to many interesting questions of analysis and geometric measure theory. The main object under scrutiny is a free boundary K where the minimizer may have jumps. The book presents an extensive description of the known regularity properties of the singular sets K, and the techniques to get them. Some time is spent on the C^1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques. In particular, global minimizers in the plane are studied in full detail.
Sign-Changing Critical Point Theory
Many nonlinear problems in physics, engineering, biology, and social sciences can be reduced to finding critical points of functionals. While minimax and Morse theories provide answers to many situations and problems on the existence of multiple critical points of a functional, they often cannot provide much-needed additional properties of these critical points. Sign-changing critical point theory has emerged as a new area of rich research on critical points of a differentiable functional with important applications to nonlinear elliptic PDEs.
Shear Localization in Granular Bodies with Micro-Polar Hypoplasticity
This book presents numerical simulations of shear localization in granular materials using a hypoplastic constitutive model enhanced by a characteristic length of the micro-structure in the form of a mean grain diameter. Due to the presence of the characteristic length, the boundary value problems are well-posed, the numerical results are mesh-independent (load-displacement diagrams, spacing and thickness of shear zones), and a deterministic size effect related to the ratio between a mean grain diameter and specimen size is captured.
