A Fast Marching Level Set Method For The Stefan Problem
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A Fast Marching Level Set Method For The Stefan Problem
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Author : Gabriel T. Wood
language : en
Publisher:
Release Date : 2015
A Fast Marching Level Set Method For The Stefan Problem written by Gabriel T. Wood and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Algorithms categories.
The Stefan problem describes the change in temperature distribution with respect to time in a medium undergoing phase change. In this thesis we provide a unique combination of established numerical techniques to solve the single phase Stefan problem in two dimensions. For this purpose it is necessary to solve the heat equation and to track the location of the free boundary as it moves. We define the finite difference method for approximating the solution to partial differential equations which forms the basis for our computations and a collection algorithms using finite difference approximations that we use to find the solution. To track the free boundary we use a level set method, combined with a fast marching method to determine the velocity with which the boundary will move according to the Stefan condition. The heat equation is solved with a second order accurate implicit approach.
Level Set Methods And Fast Marching Methods
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Author : J. A. Sethian
language : en
Publisher: Cambridge University Press
Release Date : 1999-06-13
Level Set Methods And Fast Marching Methods written by J. A. Sethian and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-13 with Computers categories.
This new edition of Professor Sethian's successful text provides an introduction to level set methods and fast marching methods, which are powerful numerical techniques for analyzing and computing interface motion in a host of settings. They rely on a fundamental shift in how one views moving boundaries; rethinking the natural geometric Lagrangian perspective and exchanging it for an Eulerian, initial value partial differential equation perspective. For this edition, the collection of applications provided in the text has been expanded, including examples from physics, chemistry, fluid mechanics, combustion, image processing, material science, fabrication of microelectronic components, computer vision, computer-aided design, and optimal control theory. This book will be a useful resource for mathematicians, applied scientists, practising engineers, computer graphic artists, and anyone interested in the evolution of boundaries and interfaces.
Pde And Level Sets
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Author : Swamy Laxminarayan
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Pde And Level Sets written by Swamy Laxminarayan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Technology & Engineering categories.
PDE & Level Sets: Algorithmic Approaches to Static & Motion Imagery is specially dedicated to the segmentation of complex shapes from the field of imaging sciences using level sets and PDEs. It covers the fundamentals of level sets, different kinds of concepts of both geodesic curvature flows and planar flows, as well as the power of incorporation of regional-statistics in level set framework. In covering this material, this book presents segmentation of object-in-motion imagery based on level sets in eigen analysis framework, while also presenting classical problems of boundary completion in cognitive images, like the pop-up of subjective contours in the famous triangle of Kanizsa using surface evolution framework, or the mean curvature evolution of a graph with respect to the Riemannian metric induced by the image. All results are presented for modal completion of cognitive objects with missing boundaries.
Fast Marching Methods And Level Set Methods
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Author : Jeff Dicker
language : en
Publisher:
Release Date : 2006
Fast Marching Methods And Level Set Methods written by Jeff Dicker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Interfaces (Physical sciences) categories.
Encyclopedia Of Two Phase Heat Transfer And Flow Iii Macro And Micro Flow Boiling And Numerical Modeling Fundamentals A 4 Volume Set
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Author : Thome John R
language : en
Publisher: World Scientific
Release Date : 2018-03-13
Encyclopedia Of Two Phase Heat Transfer And Flow Iii Macro And Micro Flow Boiling And Numerical Modeling Fundamentals A 4 Volume Set written by Thome John R and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-13 with Technology & Engineering categories.
Set III of this encyclopedia is a new addition to the previous Sets I and II. It contains 26 invited chapters from international specialists on the topics of numerical modeling of two-phase flows and evaporation, fundamentals of evaporation and condensation in microchannels and macrochannels, development and testing of micro two-phase cooling systems for electronics, and various special topics (surface wetting effects, microfin tubes, two-phase flow vibration across tube bundles). The chapters are written both by renowned university researchers and by well-known engineers from leading corporate research laboratories. Numerous 'must read' chapters cover the fundamentals of research and engineering practice on boiling, condensation and two-phase flows, two-phase heat transfer equipment, electronics cooling systems, case studies and so forth. Set III constitutes a 'must have' reference together with Sets I and II for thermal engineering researchers and practitioners.
Recent Advances In Scientific Computing And Partial Differential Equations
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Author : S.-Y. Cheng
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Recent Advances In Scientific Computing And Partial Differential Equations written by S.-Y. Cheng 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 2003 with Mathematics categories.
The volume is from the proceedings of the international conference held in celebration of Stanley Osher's sixtieth birthday. It presents recent developments and exciting new directions in scientific computing and partial differential equations for time dependent problems and its interplay with other fields, such as image processing, computer vision and graphics. Over the past decade, there have been very rapid developments in the field. This volume emphasizes the strong interaction of advanced mathematics with real-world applications and algorithms. The book is suitable for graduate students and research mathematicians interested in scientific computing and partial differential equations.
Crc Handbook Of Thermal Engineering
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Author : Raj P. Chhabra
language : en
Publisher: CRC Press
Release Date : 2017-11-08
Crc Handbook Of Thermal Engineering written by Raj P. Chhabra and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-08 with Science categories.
The CRC Handbook of Thermal Engineering, Second Edition, is a fully updated version of this respected reference work, with chapters written by leading experts. Its first part covers basic concepts, equations and principles of thermodynamics, heat transfer, and fluid dynamics. Following that is detailed coverage of major application areas, such as bioengineering, energy-efficient building systems, traditional and renewable energy sources, food processing, and aerospace heat transfer topics. The latest numerical and computational tools, microscale and nanoscale engineering, and new complex-structured materials are also presented. Designed for easy reference, this new edition is a must-have volume for engineers and researchers around the globe.
The Immersed Interface Method
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Author : Zhilin Li
language : en
Publisher: SIAM
Release Date : 2006-07-01
The Immersed Interface Method written by Zhilin Li and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-01 with Mathematics categories.
"This book will be a useful resource for mathematicians, numerical analysts, engineers, graduate students, and anyone who uses numerical methods to solve computational problems, particularly problems with fixed and moving interfaces, free boundary problems, and problems on regular domains."--BOOK JACKET.
Free Boundary Problems
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Author : Ioannis Athanasopoulos
language : en
Publisher: Routledge
Release Date : 2019-11-11
Free Boundary Problems written by Ioannis Athanasopoulos and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.
Free boundary problems arise in an enormous number of situations in nature and technology. They hold a strategic position in pure and applied sciences and thus have been the focus of considerable research over the last three decades. Free Boundary Problems: Theory and Applications presents the work and results of experts at the forefront of current research in mathematics, material sciences, chemical engineering, biology, and physics. It contains the plenary lectures and contributed papers of the 1997 International Interdisciplinary Congress proceedings held in Crete. The main topics addressed include free boundary problems in fluid and solid mechanics, combustion, the theory of filtration, and glaciology. Contributors also discuss material science modeling, recent mathematical developments, and numerical analysis advances within their presentations of more specific topics, such as singularities of interfaces, cusp cavitation and fracture, capillary fluid dynamics of film coating, dynamics of surface growth, phase transition kinetics, and phase field models. With the implications of free boundary problems so far reaching, it becomes important for researchers from all of these fields to stay abreast of new developments. Free Boundary Problems: Theory and Applications provides the opportunity to do just that, presenting recent advances from more than 50 researchers at the frontiers of science, mathematics, and technology.
Modeling Tumor Vasculature
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Author : Trachette L. Jackson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-23
Modeling Tumor Vasculature written by Trachette L. Jackson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-23 with Medical categories.
To profoundly understand biology and harness its intricacies for human benefit and the mitigation of human harm requires cross-disciplinary approaches that incorporate sophisticated computational and mathematical modeling techniques. These integrative strategies are essential to achieve rapid and significant progress in issues, in health and disease, which span molecular, cellular and tissue levels. The use of mathematical models to describe various aspects of tumor growth has a very long history, dating back over six decades. Recently, however, experimental and computational advances have improved our in the understanding of how processes act at multiple scales to mediate the development of tumor vasculature and drive the advancement of cancer. This book will showcase the development and utilization of new computational and mathematical approaches to address multiscale challenges associated with tumor vascular development. In Part I: Cell Signaling and Molecular Aspects of Tumor Blood Vessel Formation, it will be come clear that mathematical modeling can help to biochemically and biomechanically phenotype one of the most important cell types involved in cancer progression: vascular endothelial cells. When subverted by the tumor modulated environment, vascular endothelial cells form a new vascular supply capable of nourishing and translocating cancer cells to other tissues. The models in Part I illustrate the importance of quantitative approaches for gaining a deeper understanding of how normal and abnormal aspects of signal integration culminate in the cell proliferation, migration, and survival decisions that result in pathological tumor angiogenesis. The focus of Part II is the angiogenesis cascade and all of its complexities. Successful angiogenesis is mediated by the intricate interplay between biochemical and biomechanical mechanisms, including cell-cell and cell-matrix interactions, cell surface receptor binding, and intracellular signal transduction. A major challenge facing the cancer research community is to integrate known information in a way that improves our understanding of the principal underpinnings driving tumor angiogenesis and that will advance efforts aimed at the development of new therapies for treating cancer. The chapters in Part II will highlight several mathematical and computational approaches for that can potentially address this challenge. While the first two thirds of the book’s chapters demonstrate how important insights can be gained by studying cell signaling and vascular morphology and function, the series of chapters in Part III: Whole Organ Modeling of Tumor Growth and Vasculature, will integrate vasculature development with tumor growth dynamics. These two processes strongly depend on one another in ways that can only be theoretically investigated by biophysical approaches that cut across several levels of biological organization and describe both the tumor and the developing vasculature as they co-evolve. The purpose of this edited volume is not to provide a comprehensive review of all modeling efforts that address tumor vascular modeling; instead, a variety of interesting and innovative mathematical modeling approaches for understanding the development and effects of tumor vasculature are highlighted in order to illustrate some of the emerging trends in the field.