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Moving Boundary Pde Analysis
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Book Synopsis Moving Boundary PDE Analysis by : W. E. Schiesser
Download or read book Moving Boundary PDE Analysis written by W. E. Schiesser and published by CRC Press. This book was released on 2019 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Moving Boundary PDE Analysis by : William Schiesser
Download or read book Moving Boundary PDE Analysis written by William Schiesser and published by CRC Press. This book was released on 2019-05-29 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Moving Boundary PDE Analysis by : William Schiesser
Download or read book Moving Boundary PDE Analysis written by William Schiesser and published by CRC Press. This book was released on 2019-05-29 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Free and Moving Boundaries by : Roland Glowinski
Download or read book Free and Moving Boundaries written by Roland Glowinski and published by CRC Press. This book was released on 2007-06-06 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addressing algebraic problems found in biomathematics and energy, Free and Moving Boundaries: Analysis, Simulation and Control discusses moving boundary and boundary control in systems described by partial differential equations (PDEs). With contributions from international experts, the book emphasizes numerical and theoretical control of mo
Book Synopsis Control of Moving Boundary Parabolic Partial Differential Equations (PDEs) by : Mojtaba Izadi
Download or read book Control of Moving Boundary Parabolic Partial Differential Equations (PDEs) written by Mojtaba Izadi and published by . This book was released on 2014 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models of many transport processes are in the forms given by parabolic partial differential equations (PDEs). There are phenomena which may cause changes in shape and material properties of the process domain resulting in a moving boundary parabolic PDE model of the process. The focus of this thesis is to develop two control methods for parabolic PDE systems with time-dependent spatial domain. The first approach uses the PDE backstepping tool for stabilization of a class of one-dimensional unstable parabolic PDEs. In this method, an integral transformation maps the PDE system to a suitably selected exponentially stable target system. The kernel of transformation is defined by the solution of the kernel PDE that is of higher-order in space. It is shown that the kernel PDE is well-posed and a numerical solution is provided with the error analysis to establish the accuracy. The stabilizing control law is shown in the form of state-feedback with the gain in terms of kernel function. In addition, the backstepping-based observer design for state estimation of parabolic PDEs with time-dependent spatial domain is provided for a collocated boundary measurement and actuation. Specifically, the PDE system that describes the observation error dynamics is also transformed to the exponentially stable target system. The exponential stability of the closed-loop system with observer-based output-feedback controller is established by the use of a Lyapunov function. Finally, numerical solutions to the kernel PDEs and simulations are given to demonstrate successful stabilization of the unstable system. Modal decomposition techniques have been extensively used for the order-reduction of dissipative systems. The second approach is the use of Karhunen-Loeve (KL) decomposition to find the empirical eigenfunctions of the solution of moving boundary PDE systems. A mapping functional is obtained, which relates the evolution of the solution of the parabolic PDE with time-varying domain to a fixed reference configuration, while preserving space invariant properties of the initial solution ensemble. Subsequently, a low dimensional set of empirical eigenfunctions on the fixed domain is found and is mapped on the original time-varying domain resulting in the basis for the construction of the reduced-order model of the parabolic PDE system with time-varying domain. These modes are used as the basis set of functions in the Galerkin's method to find a reduced-order model for the optimal control design and state observation.
Book Synopsis Weak and Variational Methods for Moving Boundary Problems by : Charles M. Elliott
Download or read book Weak and Variational Methods for Moving Boundary Problems written by Charles M. Elliott and published by Pitman Publishing. This book was released on 1982 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Moving Boundaries IV by : R. van Keer
Download or read book Moving Boundaries IV written by R. van Keer and published by Computational Mechanics. This book was released on 1997 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the Fourth International Conference on Computational Modelling of Free and Moving Boundary Problems, held during August 1997. The purpose of this text is to promote the interaction between engineers, applied mathematicians and numerical analysts involved in the creation, development and application of computational methods to free and moving boundary problems.
Book Synopsis Free and Moving Boundary Problems by : John Crank
Download or read book Free and Moving Boundary Problems written by John Crank and published by Oxford University Press, USA. This book was released on 1984 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a wide-ranging, comprehensive account of the mathematical formulation of problems involving free boundaries as they occur in such diverse areas as hydrology, metallurgy, chemical engineering, soil science, molecular biology, materials science, and steel and glass production. Many newmethods of solution are discussed, including modern computer techniques which address multidimensional, multiphase practical problems.
Book Synopsis Control and Boundary Analysis by : John Cagnol
Download or read book Control and Boundary Analysis written by John Cagnol and published by CRC Press. This book was released on 2005-03-04 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Boundary Control and Boundary Variations by : J. P. Zolésio
Download or read book Boundary Control and Boundary Variations written by J. P. Zolésio and published by Springer. This book was released on 1988 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Materials Phase Change PDE Control & Estimation by : Shumon Koga
Download or read book Materials Phase Change PDE Control & Estimation written by Shumon Koga and published by Springer Nature. This book was released on 2020-11-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Numerical Analysis of a Phase Field Model in Moving Boundary Problems by : Jian-Tong Lin
Download or read book The Numerical Analysis of a Phase Field Model in Moving Boundary Problems written by Jian-Tong Lin and published by . This book was released on 1986 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Unified Approach to Boundary Value Problems by : Athanassios S. Fokas
Download or read book A Unified Approach to Boundary Value Problems written by Athanassios S. Fokas and published by SIAM. This book was released on 2008-11-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel approach to analysing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, based on ideas of the inverse scattering transform that the author introduced in 1997. This method is unique in also yielding novel integral representations for linear PDEs. Several new developments are addressed in the book, including a new transform method for linear evolution equations on the half-line and on the finite interval; analytical inversion of certain integrals such as the attenuated Radon transform and the Dirichlet-to-Neumann map for a moving boundary; integral representations for linear boundary value problems; analytical and numerical methods for elliptic PDEs in a convex polygon; and integrable nonlinear PDEs. An epilogue provides a list of problems on which the author's new approach has been used, offers open problems, and gives a glimpse into how the method might be applied to problems in three dimensions.
Book Synopsis IUTAM Symposium on Recent Advances in Moving Boundary Problems in Mechanics by : Stefanie Gutschmidt
Download or read book IUTAM Symposium on Recent Advances in Moving Boundary Problems in Mechanics written by Stefanie Gutschmidt and published by Springer. This book was released on 2019-03-28 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Free Boundary Problems by : A. Bossavit
Download or read book Free Boundary Problems written by A. Bossavit and published by . This book was released on 1985 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spatiotemporal Modeling of Cancer Immunotherapy by : William E. Schiesser
Download or read book Spatiotemporal Modeling of Cancer Immunotherapy written by William E. Schiesser and published by Springer. This book was released on 2019-05-30 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Numerical Analysis for Moving Boundary Problems Using the Boundary Tracking Method by : Masato Kimura
Download or read book Numerical Analysis for Moving Boundary Problems Using the Boundary Tracking Method written by Masato Kimura and published by . This book was released on 1995 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A new numerical scheme of the boundary tracking method for moving boundary problems is proposed. A key point of the scheme is to avoid concentration of tracking points on the moving boundary, and a convergence theorem is proved for the curve shortening problem. Some numerical examples for the curve shortening problem and the Hele-Shaw problem by the proposed scheme are shown."
