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Author : Fengxin Chen
Publisher :
ISBN 13 :
Total Pages : 123 pages
Book Rating : 4.:/5 (781 download)
Download or read book On Nonlocal Phase Field Models written by Fengxin Chen and published by . This book was released on 1999 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Hintermüller
Publisher : Springer Nature
ISBN 13 : 3030331164
Total Pages : 396 pages
Book Rating : 4.0/5 (33 download)
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.
Author : Pavel Krejčí
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (764 download)
Download or read book Nonlocal Phase Field Models for Non-isothermal Phase Transitions and Hysteresis written by Pavel Krejčí and published by . This book was released on 2003 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Timon Rabczuk
Publisher : MDPI
ISBN 13 : 3039216864
Total Pages : 406 pages
Book Rating : 4.0/5 (392 download)
Download or read book Computational Methods for Fracture written by Timon Rabczuk and published by MDPI. This book was released on 2019-10-28 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a collection of 17 scientific papers about the computational modeling of fracture. Some of the manuscripts propose new computational methods and/or how to improve existing cutting edge methods for fracture. These contributions can be classified into two categories: 1. Methods which treat the crack as strong discontinuity such as peridynamics, scaled boundary elements or specific versions of the smoothed finite element methods applied to fracture and 2. Continuous approaches to fracture based on, for instance, phase field models or continuum damage mechanics. On the other hand, the book also offers a wide range of applications where state-of-the-art techniques are employed to solve challenging engineering problems such as fractures in rock, glass, concrete. Also, larger systems such as fracture in subway stations due to fire, arch dams, or concrete decks are studied.
Author : Pavel Krejčí
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (18 download)
Download or read book A Nonlocal Phase Field Model with Nonconstant Specific Heat written by Pavel Krejčí and published by . This book was released on 2006 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pavel Krejčí
Publisher :
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4.:/5 (18 download)
Download or read book Nonlocal Temperature Dependent Phase Field Models for Non-isothermal Phase Transitions written by Pavel Krejčí and published by . This book was released on 2005 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jürgen Sprekels
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (59 download)
Download or read book Global Existence and Asymptotic Behaviour for a Nonlocal Phase Field Model for Non-isothermal Phase Transitions written by Jürgen Sprekels and published by . This book was released on 2001 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Chi-Kan Chen
Publisher :
ISBN 13 :
Total Pages : 204 pages
Book Rating : 4.:/5 (397 download)
Download or read book Nonlocal Thermoelastic Phase Field Models written by Chi-Kan Chen and published by . This book was released on 1998 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nikolas Provatas
Publisher : John Wiley & Sons
ISBN 13 : 3527632379
Total Pages : 323 pages
Book Rating : 4.5/5 (276 download)
Download or read book Phase-Field Methods in Materials Science and Engineering written by Nikolas Provatas and published by John Wiley & Sons. This book was released on 2011-07-26 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive and self-contained, one-stop source discusses phase-field methodology in a fundamental way, explaining advanced numerical techniques for solving phase-field and related continuum-field models. It also presents numerical techniques used to simulate various phenomena in a detailed, step-by-step way, such that readers can carry out their own code developments. Features many examples of how the methods explained can be used in materials science and engineering applications.
Author : Zhangxin Chen
Publisher : SIAM
ISBN 13 : 0898716063
Total Pages : 551 pages
Book Rating : 4.8/5 (987 download)
Download or read book Computational Methods for Multiphase Flows in Porous Media written by Zhangxin Chen and published by SIAM. This book was released on 2006-04-01 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a fundamental and practical introduction to the use of computational methods. A thorough discussion of practical aspects of the subject is presented in a consistent manner, and the level of treatment is rigorous without being unnecessarily abstract. Each chapter ends with bibliographic information and exercises.
Author : Zhang, Tao
Publisher : KIT Scientific Publishing
ISBN 13 : 3731510022
Total Pages : 224 pages
Book Rating : 4.7/5 (315 download)
Download or read book Phase-field Modeling of Phase Changes and Mechanical Stresses in Electrode Particles of Secondary Batteries written by Zhang, Tao and published by KIT Scientific Publishing. This book was released on 2021-09-27 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most storage materials exhibit phase changes, which cause stresses and, thus, lead to damage of the electrode particles. In this work, a phase-field model for the cathode material NaxFePO4 of Na-ion batteries is studied to understand phase changes and stress evolution. Furthermore, we study the particle size and SOC dependent miscibility gap of the nanoscale insertion materials. Finally, we introduce the nonlocal species concentration theory, and show how the nonlocality influences the results.
Author : Tina R. Hartley
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (246 download)
Download or read book An Analysis of Phase Separation Processes for Stochastic and Nonlocal Extensions of the Classical Phase-field Model written by Tina R. Hartley and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase separation in composite materials, or materials that are made up of two or more different components, is a process in which the material separates over time into regions of predominantly one component or the other. Because these composite materials are often developed to be used under certain conditions, significant changes of this nature in their material composition can dramatically affect their performance, thus it is important to understand the dynamic behavior of these changes. One mathematical model of phase separation is the classical phase field model, which is a system of nonlinear evolution equations that describes nonisothermal phase separation. Instead of a composite material, the phase field model describes pure materials which can assume two different phases; for example, a solid and a liquid phase. In this dissertation, I analyze the behavior of solutions of the phase field model, along with two extensions to the classical model. One extension is the addition of stochastic terms to the model, thus incorporating random behavior into the equations to address fluctuations in temperature, structural imperfections of the material, or other unknown effects. The other extension is the addition of a nonlocal operator to account for long range interactions. The behavior of all three variations of the phase field model is studied through numerical simulations, and the results compared to describe the differences between the models. In addition, I present a proof showing that the numerical method converges to the true solution of the phase field model.
Author : Blaise Bourdin
Publisher : Springer Science & Business Media
ISBN 13 : 1402063954
Total Pages : 173 pages
Book Rating : 4.4/5 (2 download)
Download or read book The Variational Approach to Fracture written by Blaise Bourdin and published by Springer Science & Business Media. This book was released on 2008-04-19 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting original results from both theoretical and numerical viewpoints, this text offers a detailed discussion of the variational approach to brittle fracture. This approach views crack growth as the result of a competition between bulk and surface energy, treating crack evolution from its initiation all the way to the failure of a sample. The authors model crack initiation, crack path, and crack extension for arbitrary geometries and loads.
Author : Qiang Du
Publisher : SIAM
ISBN 13 : 161197562X
Total Pages : 168 pages
Book Rating : 4.6/5 (119 download)
Download or read book Nonlocal Modeling, Analysis, and Computation written by Qiang Du and published by SIAM. This book was released on 2019-03-20 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.
Author : Pierluigi Colli
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (962 download)
Download or read book Distributed Optimal Control of a Nonstandard Nonlocal Phase Field System with Double Obstacle Potential written by Pierluigi Colli and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with a distributed optimal control problem for a nonlocal phase field model of Cahn-Hilliard type, which is a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion. The local model has been investigated in a series of papers by P. Podio-Guidugli and the present authors the nonlocal model studied here consists of a highly nonlinear parabolic equation coupled to an ordinary differential inclusion of subdifferential type. The inclusion originates from a free energy containing the indicator function of the interval in which the order parameter of the phase segregation attains its values. It also contains a nonlocal term modeling long-range interactions. Due to the strong nonlinear couplings between the state variables (which even involve products with time derivatives), the analysis of the state system is difficult. In addition, the presence of the differential inclusion is the reason that standard arguments of optimal control theory cannot be applied to guarantee the existence of Lagrange multipliers. In this paper, we employ recent results proved for smooth logarithmic potentials and perform a so-called 'deep quench' approximation to establish existence and first-order necessary optimality conditions for the nonsmooth case of the double obstacle potential.
Author : Pierluigi Colli
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (962 download)
Download or read book Distributed Optimal Control of a Nonstandard Nonlocal Phase Field System written by Pierluigi Colli and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate a distributed optimal control problem for a nonlocal phase field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. Podio-Guidugli and the present authors. The model consists of a highly nonlinear parabolic equation coupled to an ordinary differential equation. The latter equation contains both nonlocal and singular terms that render the analysis difficult. Standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.
Author : Timon Rabczuk
Publisher : Springer Nature
ISBN 13 : 3031209060
Total Pages : 327 pages
Book Rating : 4.0/5 (312 download)
Download or read book Computational Methods Based on Peridynamics and Nonlocal Operators written by Timon Rabczuk and published by Springer Nature. This book was released on 2023-02-15 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of computational methods based on peridynamics and nonlocal operators and their application to challenging numerical problems which are difficult to deal with traditional methods such as the finite element method, material failure being “only” one of them. The authors have also developed a higher-order nonlocal operator approaches capable of solving higher-order partial differential equations on arbitrary domains in higher-dimensional space with ease. This book is of interest to those in academia and industry.
