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Solutions Of The Cahn Hilliard Equations
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Book Synopsis Solutions of the CAHN HILLIARD Equations by : Rahul Basu
Download or read book Solutions of the CAHN HILLIARD Equations written by Rahul Basu and published by . This book was released on 2024-02-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Solutions of the Cahn Hilliard Equations" is a groundbreaking exploration of the Cahn Hilliard equations, a set of partial differential equations that describe the evolution of phase boundaries in materials. This comprehensive guide provides a thorough analysis of the equations and their solutions, offering valuable insights for researchers, engineers, and students in the field of materials science and engineering. The book begins with a detailed introduction to the Cahn-Hilliard equations, providing a clear and accessible overview of their mathematical formulation and physical significance. It then delves into the various analytical and numerical methods for solving the equations, offering step-by-step guidance on how to obtain accurate and reliable solutions. Throughout the book, the author presents a wealth of real-world examples and case studies, demonstrating the practical applications of the Cahn-Hilliard equations in materials science and engineering. From phase separation in polymers to microstructure evolution in alloys, readers will gain a deep understanding of how these equations can be used to model and predict the behavior of complex materials systems. With its comprehensive coverage and practical approach, "Solutions of the Cahn Hilliard Equations" is an indispensable resource for anyone seeking to understand and apply these important equations in their research or professional work. Whether you are a seasoned researcher or a student new to the field, this book will empower you to tackle challenging problems and make meaningful contributions to the advancement of materials science and engineering.
Book Synopsis The Cahn–Hilliard Equation: Recent Advances and Applications by : Alain Miranville
Download or read book The Cahn–Hilliard Equation: Recent Advances and Applications written by Alain Miranville and published by SIAM. This book was released on 2019-09-09 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.
Book Synopsis Solving Frontier Problems of Physics: The Decomposition Method by : G. Adomian
Download or read book Solving Frontier Problems of Physics: The Decomposition Method written by G. Adomian and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundary-value problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationally-intensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundary-value problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations.
Book Synopsis Coarsening Dynamics for Solutions of the Cahn-Hilliard Equation in One Dimension by : David J. Eyre
Download or read book Coarsening Dynamics for Solutions of the Cahn-Hilliard Equation in One Dimension written by David J. Eyre and published by . This book was released on 1992 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :University of Minnesota. Institute for Mathematics and Its Applications Publisher : ISBN 13 : Total Pages :31 pages Book Rating :4.:/5 (123 download)
Book Synopsis Global Asymptotic Limit of Solutions of the Cahn-Hilliard Equation by : University of Minnesota. Institute for Mathematics and Its Applications
Download or read book Global Asymptotic Limit of Solutions of the Cahn-Hilliard Equation written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1995 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Differential Equations of Monotone Types in Banach Spaces by : Viorel Barbu
Download or read book Nonlinear Differential Equations of Monotone Types in Banach Spaces written by Viorel Barbu and published by Springer Science & Business Media. This book was released on 2010-01-01 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is concerned with the basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. It focuses on major results in recent decades.
Book Synopsis Stability and Boundary Layer Properties of Solutions of Cahn- Hilliard Equations by : Ha Thi Minh Dang
Download or read book Stability and Boundary Layer Properties of Solutions of Cahn- Hilliard Equations written by Ha Thi Minh Dang and published by . This book was released on 1995 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convergence to Steady States of Solutions of the Cahn-Hilliard Equation with Dynamic Boundary Conditions by : Ralph Chill
Download or read book Convergence to Steady States of Solutions of the Cahn-Hilliard Equation with Dynamic Boundary Conditions written by Ralph Chill and published by . This book was released on 2004 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stationary Solutions of Driven Fourth- and Sixth Order Cahn-Hilliard Type Equations by :
Download or read book Stationary Solutions of Driven Fourth- and Sixth Order Cahn-Hilliard Type Equations written by and published by . This book was released on 2007 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Global Weak Solutions to a Sixth Order Cahn-Hilliard Type Equation by : Maciek D. Korzec
Download or read book Global Weak Solutions to a Sixth Order Cahn-Hilliard Type Equation written by Maciek D. Korzec and published by . This book was released on 2010 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Properties of Mild Solutions of the Stochastic Cahn-Hilliard Equation by : Philipp Wacker
Download or read book Geometric Properties of Mild Solutions of the Stochastic Cahn-Hilliard Equation written by Philipp Wacker and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Maximal Regularity and Asymptotic Behavior of Solutions for the Cahn-Hilliard Equation with Dynamic Boundary Conditions by : Jan Prüss
Download or read book Maximal Regularity and Asymptotic Behavior of Solutions for the Cahn-Hilliard Equation with Dynamic Boundary Conditions written by Jan Prüss and published by . This book was released on 2003 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-local Cahn-Hilliard Equation by : Jianlong Han
Download or read book Non-local Cahn-Hilliard Equation written by Jianlong Han and published by . This book was released on 2005 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Analysis of a Coupled Pair of Cahn-Hilliard Equations with Non-smooth Free Energy by :
Download or read book Numerical Analysis of a Coupled Pair of Cahn-Hilliard Equations with Non-smooth Free Energy written by and published by . This book was released on 2007 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topics in Applied Analysis and Optimisation by : Michael Hintermüller
Download or read book Topics in Applied Analysis and Optimisation written by Michael Hintermüller and published by Springer Nature. This book was released on 2019-11-27 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.
Book Synopsis Discrete Variational Derivative Method by : Daisuke Furihata
Download or read book Discrete Variational Derivative Method written by Daisuke Furihata and published by CRC Press. This book was released on 2010-12-09 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of "structure-preserving num
Book Synopsis Numerical Solutions of Advection-difussion and Convective Cahn-Hilliard Equations by : Hagos Hailu Gidey
Download or read book Numerical Solutions of Advection-difussion and Convective Cahn-Hilliard Equations written by Hagos Hailu Gidey and published by . This book was released on 2016 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this PhD thesis, we construct numerical methods to solve problems described by advectiondiffusion and convective Cahn-Hilliard equations. The advection-diffusion equation models a variety of physical phenomena in fluid dynamics, heat transfer and mass transfer or alternatively describing a stochastically-changing system. The convective Cahn-Hilliard equation is an equation of mathematical physics which describes several physical phenomena such as spinodal decomposition of phase separating systems in the presence of an external field and phase transition in binary liquid mixtures (Golovin et al., 2001; Podolny et al., 2005). In chapter 1, we define some concepts that are required to study some properties of numerical methods. In chapter 2, three numerical methods have been used to solve two problems described by 1D advection-diffusion equation with specified initial and boundary conditions. The methods used are the third order upwind scheme (Dehghan, 2005), fourth order scheme (Dehghan, 2005) and Non-Standard Finite Difference scheme (NSFD) (Mickens, 1994). Two test problems are considered. The first test problem has steep boundary layers near the region x = 1 and this is challenging problem as many schemes are plagued by nonphysical oscillation near steep boundaries. Many methods suffer from computational noise when modelling the second test problem especially when the coefficient of diffusivity is very small for instance 0.01. We compute some errors, namely L2 and L1 errors, dissipation and dispersion errors, total variation and the total mean square error for both problems and compare the computational time when the codes are run on a matlab platform. We then use the optimization technique devised by Appadu (2013) to find the optimal value of the time step at a given value of the spatial step which minimizes the dispersion error and this is validated by some numerical experiments. In chapter 3, a new finite difference scheme is presented to discretize a 3D advectiondiffusion equation following the work of Dehghan (2005, 2007). We then use this scheme and two existing schemes namely Crank-Nicolson and implicit Chapeau function to solve a 3D advection-diffusion equation with given initial and boundary conditions. We compare the performance of the methods by computing L2- error, L1-error, dispersion error, dissipation error, total mean square error and some performance indices such as mass distribution ratio, mass conservation ratio, total mass and R2 which is a measure of total variation in particle distribution. We also compute the rate of convergence to validate the order of accuracy of the numerical methods. We then use optimization techniques to improve the results from the numerical methods. In chapter 4, we present and analyze four linearized one-level and multilevel (Bousquet et al., 2014) finite volume methods for the 2D convective Cahn-Hilliard equation with specified initial condition and periodic boundary conditions. These methods are constructed in such a way that some properties of the continuous model are preserved. The nonlinear terms are approximated by a linear expression based on Mickens' rule (Mickens, 1994) of nonlocal approximations of nonlinear terms. We prove the existence and uniqueness, convergence and stability of the solution for the numerical schemes formulated. Numerical experiments for a test problem have been carried out to test the new numerical methods. We compute L2-error, rate of convergence and computational (CPU) time for some temporal and spatial step sizes at a given time. For the 1D convective Cahn-Hilliard equation, we present numerical simulations and compute convergence rates as the analysis is the same with the analysis of the 2D convective Cahn-Hilliard equation.
