High Dimensional Nonlinear Diffusion Stochastic Processes
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High Dimensional Nonlinear Diffusion Stochastic Processes
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Author : Yevgeny Mamontov
language : en
Publisher: World Scientific
Release Date : 2001-01-19
High Dimensional Nonlinear Diffusion Stochastic Processes written by Yevgeny Mamontov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-19 with Mathematics categories.
This book is the first one devoted to high-dimensional (or large-scale) diffusion stochastic processes (DSPs) with nonlinear coefficients. These processes are closely associated with nonlinear Ito's stochastic ordinary differential equations (ISODEs) and with the space-discretized versions of nonlinear Ito's stochastic partial integro-differential equations. The latter models include Ito's stochastic partial differential equations (ISPDEs).The book presents the new analytical treatment which can serve as the basis of a combined, analytical-numerical approach to greater computational efficiency in engineering problems. A few examples discussed in the book include: the high-dimensional DSPs described with the ISODE systems for semiconductor circuits; the nonrandom model for stochastic resonance (and other noise-induced phenomena) in high-dimensional DSPs; the modification of the well-known stochastic-adaptive-interpolation method by means of bases of function spaces; ISPDEs as the tool to consistently model non-Markov phenomena; the ISPDE system for semiconductor devices; the corresponding classification of charge transport in macroscale, mesoscale and microscale semiconductor regions based on the wave-diffusion equation; the fully time-domain nonlinear-friction aware analytical model for the velocity covariance of particle of uniform fluid, simple or dispersed; the specific time-domain analytics for the long, non-exponential “tails” of the velocity in case of the hard-sphere fluid.These examples demonstrate not only the capabilities of the developed techniques but also emphasize the usefulness of the complex-system-related approaches to solve some problems which have not been solved with the traditional, statistical-physics methods yet. From this veiwpoint, the book can be regarded as a kind of complement to such books as “Introduction to the Physics of Complex Systems. The Mesoscopic Approach to Fluctuations, Nonlinearity and Self-Organization” by Serra, Andretta, Compiani and Zanarini, “Stochastic Dynamical Systems. Concepts, Numerical Methods, Data Analysis” and “Statistical Physics: An Advanced Approach with Applications” by Honerkamp which deal with physics of complex systems, some of the corresponding analysis methods and an innovative, stochastics-based vision of theoretical physics.To facilitate the reading by nonmathematicians, the introductory chapter outlines the basic notions and results of theory of Markov and diffusion stochastic processes without involving the measure-theoretical approach. This presentation is based on probability densities commonly used in engineering and applied sciences.
High Dimensional Nonlinear Diffusion Stochastic Processes
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Author : Yevgeny Mamontov
language : en
Publisher: World Scientific
Release Date : 2001
High Dimensional Nonlinear Diffusion Stochastic Processes written by Yevgeny Mamontov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Annotation This book is one of the first few devoted to high-dimensional diffusion stochastic processes with nonlinear coefficients. These processes are closely associated with large systems of Ito's stochastic differential equations and with discretized-in-the-parameter versions of Ito's stochastic differential equations that are nonlocally dependent on the parameter. The latter models include Ito's stochastic integro-differential, partial differential and partial integro-differential equations.The book presents the new analytical treatment which can serve as the basis of a combined, analytical -- numerical approach to greater computational efficiency. Some examples of the modelling of noise in semiconductor devices are provided
Stochastic Processes Physics And Geometry New Interplays I
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Author : Sergio Albeverio
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Stochastic Processes Physics And Geometry New Interplays I written by Sergio Albeverio and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This volume and "IStochastic Processes, Physics and Geometry: New Interplays II" present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers. Members of the Canadian Mathematical Society may order at the AMS member price.
Computational Methods For Pde In Mechanics
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Author : Berardino D'Acunto
language : en
Publisher: World Scientific Publishing Company
Release Date : 2004-10-12
Computational Methods For Pde In Mechanics written by Berardino D'Acunto and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-12 with categories.
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.
Clusters And Nano Assemblies Physical And Biological Systems
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Author : Purusottam Jena
language : en
Publisher: World Scientific
Release Date : 2005-05-09
Clusters And Nano Assemblies Physical And Biological Systems written by Purusottam Jena and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-09 with Technology & Engineering categories.
While the field of clusters and nano-structures in the physical sciences has been actively pursued only over the past two decades, nature has known the benefits of the nanoscale for a very long time. The focus of the International Symposium on Clusters and Nano-Assemblies: Physical and Biological Systems was to explore ways in which an understanding of the unique properties of nano-scale biological systems such as proteins, enzyme reactions, RNA, and DNA can help us design novel materials composed of inorganic nano-scale systems, and how techniques developed in the physical sciences can lead to a fundamental understanding of biological systems. Bringing together the expert contributions from the conference, this book deals with the fundamental science and technology of atomic clusters, nano-structures and their assemblies in physical and biological systems. It explores in fascinating detail the manner in which finite size, low dimensionality, and reduced symmetry affect the properties of nano-assemblies.
Generalized Kinetic Models In Applied Sciences
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Author : Luisa Arlotti
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-08-12
Generalized Kinetic Models In Applied Sciences written by Luisa Arlotti and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-12 with Science categories.
This book deals with analytic problems related to some developments and generalizations of the Boltzmann equation toward the modeling and qualitative analysis of large systems that are of interest in applied sciences. These generalizations are documented in the various surveys edited by Bellomo and Pulvirenti with reference to models of granular media, traffic flow, mathematical biology, communication networks, and coagulation models. The above literature motivates applied mathematicians to study the Cauchy problem and to develop an asymptotic analysis for models regarded as developments of the Boltzmann equation. This book aims to initiate the research plan by the analyzing afore mentioned analysis problems. The first generalization dealt with refers to the averaged Boltzmann equation, which is obtained by suitable averaging of the distribution function of the field particles into the action domain of the test particle. This model is further developed to describe equations with dissipative collisions and a class of models that are of interest in mathematical biology. In this latter case the state of the particles is defined not only by a mechanical variable but also by a biological microscopic state. The book is essentially devoted to analytic aspects and deals with the analysis of the Cauchy problem and with the development of an asymptotic theory to obtain the macroscopic description from the mesoscopic one.
Mathematical Methods For The Natural And Engineering Sciences
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Author : Ronald E. Mickens
language : en
Publisher: World Scientific
Release Date : 2004
Mathematical Methods For The Natural And Engineering Sciences written by Ronald E. Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Technology & Engineering categories.
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.
Mathematical Models And Methods For Smart Material
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Author : Mauro Fabrizio
language : en
Publisher: World Scientific
Release Date : 2002
Mathematical Models And Methods For Smart Material written by Mauro Fabrizio and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book contains the papers presented at the conference on OC Mathematical Models and Methods for Smart MaterialsOCO, held in Italy in 2001. The papers are divided into four parts: OCOMethods in Materials ScienceOCO deals mainly with mathematical techniques for the investigation of physical systems, such as liquid crystals, materials with internal variables, amorphous materials, and thermoelastic materials. Also, techniques are exhibited for the analysis of stability and controllability of classical models of continuum mechanics and of dynamical systems.OCOModelling of Smart MaterialsOCO is devoted to models of superfluids, superconductors, materials with memory, nonlinear elastic solids, and damaged materials. In the elaboration of the models, thermodynamic aspects play a central role in the characterization of the constitutive properties.OCOWell-Posedness in Materials with MemoryOCO deals with existence, uniqueness and stability for the solution of problems, most often expressed by integrodifferential equations, which involve materials with fading memory. Also, attention is given to exponential decay in viscoelasticity, inverse problems in heat conduction with memory, and automatic control for parabolic equations.OCOAnalytic Problems in Phase TransitionsOCO discusses nonlinear partial differential equations associated with phase transitions, and hysteresis, possibly involving fading memory effects. Particular applications are developed for the phase-field model with memory, the Stefan problem with a Cattaneo-type equation, the hysteresis in thermo-visco-plasticity, and the solid-solid phase transition."
Numerical Methods For Viscosity Solutions And Applications
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Author : Maurizio Falcone
language : en
Publisher: World Scientific
Release Date : 2001
Numerical Methods For Viscosity Solutions And Applications written by Maurizio Falcone and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Geometrical optics and viscosity solutions / A.-P. Blanc, G. T. Kossioris and G. N. Makrakis -- Computation of vorticity evolution for a cylindrical Type-II superconductor subject to parallel and transverse applied magnetic fields / A. Briggs ... [et al.] -- A characterization of the value function for a class of degenerate control problems / F. Camilli -- Some microstructures in three dimensions / M. Chipot and V. Lecuyer -- Convergence of numerical schemes for the approximation of level set solutions to mean curvature flow / K. Deckelnick and G. Dziuk -- Optimal discretization steps in semi-lagrangian approximation of first-order PDEs / M. Falcone, R. Ferretti and T. Manfroni -- Convergence past singularities to the forced mean curvature flow for a modified reaction-diffusion approach / F. Fierro -- The viscosity-duality solutions approach to geometric pptics for the Helmholtz equation / L. Gosse and F. James -- Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations / L. Grune -- Solution and application of anisotropic curvature driven evolution of curves (and surfaces) / K. Mikula -- An adaptive scheme on unstructured grids for the shape-from-shading problem / M. Sagona and A. Seghini -- On a posteriori error estimation for constant obstacle problems / A. Veeser.
Stability And Time Optimal Control Of Hereditary Systems
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Author : E N Chukwu
language : en
Publisher: World Scientific Publishing Company
Release Date : 2001-12-28
Stability And Time Optimal Control Of Hereditary Systems written by E N Chukwu and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-28 with Mathematics categories.
Stability and Time-Optimal Control of Hereditary Systems is the mathematical foundation and theory required for studying in depth the stability and optimal control of systems whose history is taken into account. In this edition, the economic application is enlarged, and explored in some depth. The application holds out the hope that full employment and high income growth will be compatible with low prices and low inflation, provided that the control matrix has full rank, i.e., the existing controls are fully effectively used. The book concludes with a new appendix containing complete programs, data, graphs and quantitative results for the US economy.