Moving Boundary PDE Analysis

by William Schiesser

Author	: William Schiesser
Publisher	: CRC Press
Total Pages	: 186
Release	: 2019-05-29
Genre	: Mathematics
ISBN	: 100000788X

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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.

Moving Boundary Pde Analysis

by WILLIAM. SCHIESSER

Author	: WILLIAM. SCHIESSER
Publisher	:
Total Pages	: 0
Release	: 2023-09-25
Genre	:
ISBN	: 9781032654003

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The book is directed to the numerical integration (solution) of systems of partial differential equations (PDEs) for which the boundary conditions move in space. In applications, the physical boundaries move as the solution evolves in time. The book provides examples of the applications in tumor growth and atherosclerosis

Moving Boundary PDE Analysis

by W. E. Schiesser

Author	: W. E. Schiesser
Publisher	: CRC Press
Total Pages	: 182
Release	: 2019
Genre	: Mathematics
ISBN	: 9780429275128

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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.

Finite Difference Methods for Ordinary and Partial Differential Equations

by Randall J. LeVeque

Author	: Randall J. LeVeque
Publisher	: SIAM
Total Pages	: 356
Release	: 2007-01-01
Genre	: Mathematics
ISBN	: 9780898717839

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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.

IUTAM Symposium on Recent Advances in Moving Boundary Problems in Mechanics

by Stefanie Gutschmidt

Author	: Stefanie Gutschmidt
Publisher	: Springer
Total Pages	: 292
Release	: 2019-03-28
Genre	: Technology & Engineering
ISBN	: 3030137201

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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.

Spatiotemporal Modeling of Cancer Immunotherapy

by William E. Schiesser

Author	: William E. Schiesser
Publisher	: Springer
Total Pages	: 117
Release	: 2019-05-30
Genre	: Medical
ISBN	: 3030190803

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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

Materials Phase Change PDE Control & Estimation

by Shumon Koga

Author	: Shumon Koga
Publisher	: Springer Nature
Total Pages	: 352
Release	: 2020-11-01
Genre	: Science
ISBN	: 3030584909

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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.

System Modeling and Optimization

by Adam Korytowski

Author	: Adam Korytowski
Publisher	: Springer Science & Business Media
Total Pages	: 515
Release	: 2009-10-15
Genre	: Technology & Engineering
ISBN	: 3642048013

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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).

Recent Advances in Nonlinear Partial Differential Equations and Applications

by Luis López Bonilla

Author	: Luis López Bonilla
Publisher	: American Mathematical Soc.
Total Pages	: 250
Release	: 2007
Genre	: Mathematics
ISBN	: 0821842110

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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.