The Classical Stefan Problem

Author : S.C. Gupta
Publisher : Elsevier
Page : 404 pages
File Size : 41,7 Mb
Release : 2003-10-22
Category : Science
ISBN : 9780080529165

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The Classical Stefan Problem by S.C. Gupta Pdf

This volume emphasises studies related to classical Stefan problems. The term "Stefan problem" is generally used for heat transfer problems with phase-changes such as from the liquid to the solid. Stefan problems have some characteristics that are typical of them, but certain problems arising in fields such as mathematical physics and engineering also exhibit characteristics similar to them. The term ``classical" distinguishes the formulation of these problems from their weak formulation, in which the solution need not possess classical derivatives. Under suitable assumptions, a weak solution could be as good as a classical solution. In hyperbolic Stefan problems, the characteristic features of Stefan problems are present but unlike in Stefan problems, discontinuous solutions are allowed because of the hyperbolic nature of the heat equation. The numerical solutions of inverse Stefan problems, and the analysis of direct Stefan problems are so integrated that it is difficult to discuss one without referring to the other. So no strict line of demarcation can be identified between a classical Stefan problem and other similar problems. On the other hand, including every related problem in the domain of classical Stefan problem would require several volumes for their description. A suitable compromise has to be made. The basic concepts, modelling, and analysis of the classical Stefan problems have been extensively investigated and there seems to be a need to report the results at one place. This book attempts to answer that need.

Author : S.C. Gupta
Publisher : Elsevier
Page : 752 pages
File Size : 47,6 Mb
Release : 2017-07-27
Category : Science
ISBN : 9780444635822

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The Classical Stefan Problem by S.C. Gupta Pdf

The Classical Stefan Problem: Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods, New Edition, provides the fundamental theory, concepts, modeling, and analysis of the physical, mathematical, thermodynamical, and metallurgical properties of classical Stefan and Stefan-like problems as applied to heat transfer problems with phase-changes, such as from liquid to solid. This self-contained work reports and derives the results from tensor analysis, differential geometry, non-equilibrium thermodynamics, physics, and functional analysis, and is thoroughly enriched with many appropriate references for in-depth background reading on theorems. Each chapter in this fully revised and updated edition begins with basic concepts and objectives, also including direction on how the subject matter was developed. It contains more than 400 pages of new material on quasi-analytical solutions and methods of classical Stefan and Stefan-like problems.The book aims to bridge the gap between the theoretical and solution aspects of the afore-mentioned problems. Provides both the phenomenology and mathematics of Stefan problems Bridges physics and mathematics in a concrete and readable manner Presents well-organized chapters that start with proper definitions followed by explanations and references for further reading Includes both numerical and quasi-analytical solutions and methods of classical Stefan and Stefan-like problems

Author : A.M. Meirmanov
Publisher : Walter de Gruyter
Page : 257 pages
File Size : 53,9 Mb
Release : 2011-05-03
Category : Mathematics
ISBN : 9783110846720

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The Stefan Problem by A.M. Meirmanov Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Author : L. I. Rubinšteĭn
Publisher : American Mathematical Soc.
Page : 419 pages
File Size : 47,8 Mb
Release : 2000-01-25
Category : Electronic
ISBN : 9781470428501

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The Stefan Problem by L. I. Rubinšteĭn Pdf

Translations of Mathematical Monographs

Author : John Rozier Cannon
Publisher : Cambridge University Press
Page : 522 pages
File Size : 55,8 Mb
Release : 1984-12-28
Category : Mathematics
ISBN : 0521302439

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The One-Dimensional Heat Equation by John Rozier Cannon Pdf

This is a version of Gevrey's classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems and parameter determination problems. The material is presented as a monograph and/or information source book. After the first six chapters of standard classical material, each chapter is written as a self-contained unit except for an occasional reference to elementary definitions, theorems and lemmas in previous chapters.

Author : V. Alexiades
Publisher : CRC Press
Page : 342 pages
File Size : 54,5 Mb
Release : 1992-11-01
Category : Science
ISBN : 1560321253

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Mathematical Modeling Of Melting And Freezing Processes by V. Alexiades Pdf

Presents mathematical models of melting and solidification processes that are the key to the effective performance of latent heat thermal energy storage systems, utilized in a wide range of heat transfer and industrial applications.

Author : A. O. Bolivar
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 52,8 Mb
Release : 2013-04-09
Category : Science
ISBN : 9783662096499

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Quantum-Classical Correspondence by A. O. Bolivar Pdf

At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics. It elucidates the problem of quantum-classical correspondence by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations. The logical consistency of the scheme is then verified by taking the classical limit of the equations of motion and corresponding physical quantities. Perhaps equally important, conceptual problems concerning the relationship between classical and quantum physics are identified and discussed. Graduate students and physical scientists will find this an accessible entrée to an intriguing and thorny issue at the core of modern physics.

Author : James M. Hill
Publisher : Longman Scientific and Technical
Page : 232 pages
File Size : 50,7 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:39015019663775

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One-dimensional Stefan Problems by James M. Hill Pdf

Author : J.-F. Rodrigues
Publisher : Elsevier
Page : 351 pages
File Size : 43,8 Mb
Release : 1987-03-01
Category : Science
ISBN : 008087245X

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Obstacle Problems in Mathematical Physics by J.-F. Rodrigues Pdf

The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics. The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.

Author : Shumon Koga,Miroslav Krstic
Publisher : Springer Nature
Page : 352 pages
File Size : 55,5 Mb
Release : 2020-11-01
Category : Science
ISBN : 9783030584900

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Materials Phase Change PDE Control & Estimation by Shumon Koga,Miroslav Krstic Pdf

This monograph introduces breakthrough control algorithms for partial differential equation models with moving boundaries, the study of which is known as the Stefan problem. The algorithms can be used to improve the performance of various processes with phase changes, such as additive manufacturing. Using the authors' innovative design solutions, readers will also be equipped to apply estimation algorithms for real-world phase change dynamics, from polar ice to lithium-ion batteries. A historical treatment of the Stefan problem opens the book, situating readers in the larger context of the area. Following this, the chapters are organized into two parts. The first presents the design method and analysis of the boundary control and estimation algorithms. Part two then explores a number of applications, such as 3D printing via screw extrusion and laser sintering, and also discusses the experimental verifications conducted. A number of open problems and provided as well, offering readers multiple paths to explore in future research. Materials Phase Change PDE Control & Estimation is ideal for researchers and graduate students working on control and dynamical systems, and particularly those studying partial differential equations and moving boundaries. It will also appeal to industrial engineers and graduate students in engineering who are interested in this area.

Author : Stefan Bergman,Menahem Schiffer
Publisher : Courier Corporation
Page : 450 pages
File Size : 45,5 Mb
Release : 2013-01-23
Category : Mathematics
ISBN : 9780486154657

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Kernel Functions and Elliptic Differential Equations in Mathematical Physics by Stefan Bergman,Menahem Schiffer Pdf

Covers the theory of boundary value problems in partial differential equations and discusses a portion of the theory from a unifying point of view while providing an introduction to each branch of its applications. 1953 edition.

Author : Patricia Dominguez-Marin
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 44,7 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781441985118

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The Discrete Ordered Median Problem: Models and Solution Methods by Patricia Dominguez-Marin Pdf

This is the first book about the discrete ordered median problem (DOMP), which unifies many classical and new facility location problems. Several exact and heuristic approaches are developed in this book in order to solve the DOMP. Audience: The book is suitable for researchers in location theory, and graduate students in combinatorial optimization.

Author : Mike Cullen,Melina A Freitag,Stefan Kindermann,Robert Scheichl
Publisher : Walter de Gruyter
Page : 216 pages
File Size : 43,7 Mb
Release : 2013-08-29
Category : Mathematics
ISBN : 9783110282269

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Large Scale Inverse Problems by Mike Cullen,Melina A Freitag,Stefan Kindermann,Robert Scheichl Pdf

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. Thiscollection of surveyarticlesfocusses onthe large inverse problems commonly arising in simulation and forecasting in the earth sciences. For example, operational weather forecasting models have between 107 and 108 degrees of freedom. Even so, these degrees of freedom represent grossly space-time averaged properties of the atmosphere. Accurate forecasts require accurate initial conditions. With recent developments in satellite data, there are between 106 and 107 observations each day. However, while these also represent space-time averaged properties, the averaging implicit in the measurements is quite different from that used in the models. In atmosphere and ocean applications, there is a physically-based model available which can be used to regularise the problem. We assume that there is a set of observations with known error characteristics available over a period of time. The basic deterministic technique is to fit a model trajectory to the observations over a period of time to within the observation error. Since the model is not perfect the model trajectory has to be corrected, which defines the data assimilation problem. The stochastic view can be expressed by using an ensemble of model trajectories, and calculating corrections to both the mean value and the spread which allow the observations to be fitted by each ensemble member. In other areas of earth science, only the structure of the model formulation itself is known and the aim is to use the past observation history to determine the unknown model parameters. The book records the achievements of Workshop2 "Large-Scale Inverse Problems and Applications in the Earth Sciences". Itinvolves experts in the theory of inverse problems together with experts working on both theoretical and practical aspects of the techniques by which large inverse problems arise in the earth sciences.

Author : Benoît Perthame
Publisher : Springer
Page : 199 pages
File Size : 41,7 Mb
Release : 2015-09-09
Category : Mathematics
ISBN : 9783319195001

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Parabolic Equations in Biology by Benoît Perthame Pdf

This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

Author : Jordan Hristov,Rachid Bennacer
Publisher : Nova Science Publishers
Page : 0 pages
File Size : 52,6 Mb
Release : 2019
Category : Heat
ISBN : 1536146730

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Heat Conduction by Jordan Hristov,Rachid Bennacer Pdf

Heat conduction plays an important role in energy transfer at the macro, micro and nano scales. This book collates research results developed by scientists from different countries but with common research interest in the modelling of heat conduction problems. The results reported encompass heat conduction problems related to the Stefan problem, phase change materials related to energy consumption in buildings, the porous media problem with Bingham plastic fluids, thermosolutal convection, rewetting problems and fractional models with singular and non-singular kernels. The variety of analytical and numerical techniques used includes the classical heat-balance integral method in its refined version, double-integration technique and variational formulation applied to the integer-order and fractional models with memories.This book cannot present the entire rich area of problems related to heat conduction, but allows readers to see some new trends and approaches in the modelling technologies. In this context, the fractional models with singular and non-singular kernels and the development of the integration techniques related to the integral-balance approach form fresh fluxes of ideas to this classical engineering area of research.The book is oriented to researchers, masters and PhD students involved in heat conduction problems with a variety of applications and could serve as a rich reference source and a collection of texts provoking new ideas.