Moving Boundary Pde Analysis

Author : William Schiesser
Publisher : CRC Press
Page : 182 pages
File Size : 51,8 Mb
Release : 2019-05-29
Category : Mathematics
ISBN : 9781000001044

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Moving Boundary PDE Analysis by William Schiesser Pdf

Mathematical models stated as systems of partial differential equations (PDEs) are broadly used in biology, chemistry, physics and medicine (physiology). These models describe the spatial and temporial variations of the problem system dependent variables, such as temperature, chemical and biochemical concentrations and cell densities, as a function of space and time (spatiotemporal distributions). For a complete PDE model, initial conditions (ICs) specifying how the problem system starts and boundary conditions (BCs) specifying how the system is defined at its spatial boundaries, must also be included for a well-posed PDE model. In this book, PDE models are considered for which the physical boundaries move with time. For example, as a tumor grows, its boundary moves outward. In atherosclerosis, the plaque formation on the arterial wall moves inward, thereby restricting blood flow with serious consequences such as stroke and myocardial infarction (heart attack). These two examples are considered as applications of the reported moving boundary PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of documented routines coded in R, a quality, open-source scientific programming system. The routines are provided as a download so that the reader/analyst/researcher can use MFPDE models without having to first study numerical methods and computer programming.

Author : William Schiesser
Publisher : CRC Press
Page : 195 pages
File Size : 51,7 Mb
Release : 2019-05-29
Category : Mathematics
ISBN : 9781000007886

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Moving Boundary PDE Analysis by William Schiesser Pdf

Mathematical models stated as systems of partial differential equations (PDEs) are broadly used in biology, chemistry, physics and medicine (physiology). These models describe the spatial and temporial variations of the problem system dependent variables, such as temperature, chemical and biochemical concentrations and cell densities, as a function of space and time (spatiotemporal distributions). For a complete PDE model, initial conditions (ICs) specifying how the problem system starts and boundary conditions (BCs) specifying how the system is defined at its spatial boundaries, must also be included for a well-posed PDE model. In this book, PDE models are considered for which the physical boundaries move with time. For example, as a tumor grows, its boundary moves outward. In atherosclerosis, the plaque formation on the arterial wall moves inward, thereby restricting blood flow with serious consequences such as stroke and myocardial infarction (heart attack). These two examples are considered as applications of the reported moving boundary PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of documented routines coded in R, a quality, open-source scientific programming system. The routines are provided as a download so that the reader/analyst/researcher can use MFPDE models without having to first study numerical methods and computer programming.

Author : William Schiesser
Publisher : CRC Press
Page : 128 pages
File Size : 45,7 Mb
Release : 2019
Category : Electronic
ISBN : 0367224836

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Moving Boundary Pde Analysis by William Schiesser Pdf

Mathematical models stated as systems of partial differential equations (PDEs) are broadly used in biology, chemistry, physics and medicine (physiology). These models describe the spatial and temporial variations of the problem system dependent variables, such as temperature, chemical and biochemical concentrations and cell densities, as a function of space and time (spatiotemporal distributions). For a complete PDE model, initial conditions (ICs) specifying how the problem system starts and boundary conditions (BCs) specifying how the system is defined at its spatial boundaries, must also be included for a well-posed PDE model. In this book, PDE models are considered for which the physical boundaries move with time. For example, as a tumor grows, its boundary moves outward. In atherosclerosis, the plaque formation on the arterial wall moves inward, thereby restricting blood flow with serious consequences such as stroke and myocardial infarction (heart attack). These two examples are considered as applications of the reported moving boundary PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of documented routines coded in R, a quality, open-source scientific programming system. The routines are provided as a download so that the teacher/analyst/researcher can use MFPDE models without having to rst study numerical methods and computer programming P>These two examples are considered as applications of the reported moving boundary PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of documented routines coded in R, a quality, open-source scientific programming system. The routines are provided as a download so that the teacher/analyst/researcher can use MFPDE models without having to rst study numerical methods and computer programming

Author : Stefanie Gutschmidt,James N. Hewett,Mathieu Sellier
Publisher : Springer
Page : 296 pages
File Size : 41,8 Mb
Release : 2019-03-28
Category : Technology & Engineering
ISBN : 9783030137205

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IUTAM Symposium on Recent Advances in Moving Boundary Problems in Mechanics by Stefanie Gutschmidt,James N. Hewett,Mathieu Sellier Pdf

Many problems in mechanics involve deformable domains with moving boundaries, including fluid-structure interaction, multiphase flows, flows over soft tissues and textiles, or flows involving accretion/erosion to name but a few. The presence of a moving boundary presents considerable challenges when it comes to modelling and understanding the underlying system dynamics. This proceedings volume collects contributions made at the IUTAM Symposium on Recent Advances in Moving Boundary Problems in Mechanics held in Christchurch, New Zealand in February 2018.

Author : William E. Schiesser
Publisher : Springer
Page : 117 pages
File Size : 41,9 Mb
Release : 2019-05-30
Category : Medical
ISBN : 9783030190804

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Spatiotemporal Modeling of Cancer Immunotherapy by William E. Schiesser Pdf

The focus of this book is a detailed discussion of a dual cancer vaccine (CV)-immune checkpoint inhibitor (ICI) mathematical model formulated as a system of partial differential equations (PDEs) defining the spatiotemporal distribution of cells and biochemicals during tumor growth. A computer implementation of the model is discussed in detail for the quantitative evaluation of CV-ICI therapy. The coding (programming) consists of a series of routines in R, a quality, open-source scientific computing system that is readily available from the internet. The routines are based on the method of lines (MOL), a general PDE algorithm that can be executed on modest computers within the basic R system. The reader can download and use the routines to confirm the model solutions reported in the book, then experiment with the model by varying the parameters and modifying/extending the equations, and even studying alternative models with the PDE methodology demonstrated by the CV-ICI model. Spatiotemporal Modeling of Cancer Immunotherapy: Partial Differential Equation Analysis in R facilitates the use of the model, and more generally, computer- based analysis of cancer immunotherapy mathematical models, as a step toward the development and quantitative evaluation of the immunotherapy approach to the treatment of cancer. To download the R routines, please visit: http://www.lehigh.edu/~wes1/ci_download

Author : Adam Korytowski,Maciej Szymkat,Kazimierz Malanowski,Wojciech Mitkowski
Publisher : Springer
Page : 507 pages
File Size : 41,9 Mb
Release : 2009-10-27
Category : Technology & Engineering
ISBN : 9783642048029

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System Modeling and Optimization by Adam Korytowski,Maciej Szymkat,Kazimierz Malanowski,Wojciech Mitkowski Pdf

rd This book constitutes a collection of extended versions of papers presented at the 23 IFIP TC7 Conference on System Modeling and Optimization, which was held in C- cow, Poland, on July 23–27, 2007. It contains 7 plenary and 22 contributed articles, the latter selected via a peer reviewing process. Most of the papers are concerned with optimization and optimal control. Some of them deal with practical issues, e. g. , p- formance-based design for seismic risk reduction, or evolutionary optimization in structural engineering. Many contributions concern optimization of infini- dimensional systems, ranging from a general overview of the variational analysis, through optimization and sensitivity analysis of PDE systems, to optimal control of neutral systems. A significant group of papers is devoted to shape analysis and opti- zation. Sufficient optimality conditions for ODE problems, and stochastic control methods applied to mathematical finance, are also investigated. The remaining papers are on mathematical programming, modeling, and information technology. The conference was the 23rd event in the series of such meetings biennially org- ized under the auspices of the Seventh Technical Committee “Systems Modeling and Optimization” of the International Federation for Information Processing (IFIP TC7).

Author : A. Bossavit,M. Fremond
Publisher : Unknown
Page : 328 pages
File Size : 42,9 Mb
Release : 1985
Category : Boundary value problems
ISBN : 0273086774

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Free Boundary Problems by A. Bossavit,M. Fremond Pdf

Author : Shumon Koga,Miroslav Krstic
Publisher : Springer Nature
Page : 352 pages
File Size : 45,6 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 : Luis López Bonilla
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 45,6 Mb
Release : 2007
Category : Differential equations, Nonlinear
ISBN : 9780821842119

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Recent Advances in Nonlinear Partial Differential Equations and Applications by Luis López Bonilla Pdf

The articles of this book are written by leading experts in partial differential equations and their applications, who present overviews here of recent advances in this broad area of mathematics. The formation of shocks in fluids, modern numerical computation of turbulence, the breaking of the Einstein equations in a vacuum, the dynamics of defects in crystals, effects due to entropy in hyperbolic conservation laws, the Navier-Stokes and other limits of the Boltzmann equation, occupancy times for Brownian motion in a two dimensional wedge, and new methods of analyzing and solving integrable systems are some of this volume's subjects. The reader will find an exposition of important advances without a lot of technicalities and with an emphasis on the basic ideas of this field.

Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 46,5 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567

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Partial Differential Equations by Walter A. Strauss Pdf

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Author : X. W. Gao,A. H-D. Cheng,C. A. Brebbia
Publisher : WIT Press
Page : 569 pages
File Size : 55,6 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781845648411

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Boundary Elements and Other Mesh Reduction Methods XXXVI by X. W. Gao,A. H-D. Cheng,C. A. Brebbia Pdf

The Conference on Boundary Elements and Mesh Reduction Methods (BEM/MRM) is recognised as the international forum for the latest advances in these techniques and their applications in science and engineering. Launched in 1978 the Conference continues to attract original contributions and has become the forum for their rapid dissemination throughout the international scientific community. Practically all new boundary element ideas have first appeared in the proceedings of these meetings.

Author : J. P. Zolésio
Publisher : Springer
Page : 410 pages
File Size : 44,9 Mb
Release : 1988
Category : Mathematics
ISBN : UCAL:B4405510

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Boundary Control and Boundary Variations by J. P. Zolésio Pdf

This volume comprises the proceedings of the Working Conference "Boundary variations and boundary control" held in Nice (France), June 10-13, 1986. The aim of this Conference was to stimulate exchange of ideas between the group working on shape optimization (including free boundary problems) and the group working on boundary control of hyperbolic systems (including stabilization). An important remark is that if one considers a dynamical system governed by linear elasticity the choice of Lagrangian coordinates leads to discuss boundary conditions, or boundary control (for example to stabilize), while the choice of Eulerian coordinates lead to a moving boundary and moving domain . This remark challenges us to consider the domain (or its boundary) as a control.

Author : Graham Griffiths,William E. Schiesser
Publisher : Academic Press
Page : 461 pages
File Size : 51,5 Mb
Release : 2010-12-09
Category : Mathematics
ISBN : 0123846536

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Traveling Wave Analysis of Partial Differential Equations by Graham Griffiths,William E. Schiesser Pdf

Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods. This book surveys some of these new developments in analytical and numerical methods, and relates the two through a series of PDE examples. The PDEs that have been selected are largely "named'' since they carry the names of their original contributors. These names usually signify that the PDEs are widely recognized and used in many application areas. The authors’ intention is to provide a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs. The Matlab and Maple software will be available for download from this website shortly. www.pdecomp.net Includes a spectrum of applications in science, engineering, applied mathematics Presents a combination of numerical and analytical methods Provides transportable computer codes in Matlab and Maple

Author : Randall J. LeVeque
Publisher : SIAM
Page : 356 pages
File Size : 46,5 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 0898717833

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Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque Pdf

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Author : John Cagnol,Jean-Paul Zolesio
Publisher : CRC Press
Page : 306 pages
File Size : 55,8 Mb
Release : 2005-03-04
Category : Mathematics
ISBN : 1420027425

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Control and Boundary Analysis by John Cagnol,Jean-Paul Zolesio Pdf

This volume comprises selected papers from the 21st Conference on System Modeling and Optimization in Sophia Antipolis, France. It covers over three decades of studies involving partial differential systems and equations. Topics include: the modeling of continuous mechanics involving fixed boundary, control theory, shape optimization and moving boundaries, and topological shape optimization. This edition discusses all developments that lead to current moving boundary analysis and the stochastic approach.