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Density Functionals For Many-particle Systems: Mathematical Theory And Physical Applications Of Effective Equations
  • Language: en
  • Pages: 397

Density Functionals For Many-particle Systems: Mathematical Theory And Physical Applications Of Effective Equations

Density Functional Theory (DFT) first established it's theoretical footing in the 1960s from the framework of Hohenberg-Kohn theorems. DFT has since seen much development in evaluation techniques as well as application in solving problems in Physics, Mathematics and Chemistry.This review volume, part of the IMS Lecture Notes Series, is a collection of contributions from the September 2019 Workshop on the topic, held in the Institute for Mathematical Sciences, National University of Singapore.With contributions from prominent Mathematicians, Physicists, and Chemists, the volume is a blend of comprehensive review articles on the Mathematical and the Physicochemical aspects of DFT and shorter contributions on particular themes, including numerical implementations.The book will be a useful reference for advanced undergraduate and postgraduate students as well as researchers.

Transport Phenomena and Kinetic Theory
  • Language: en
  • Pages: 274

Transport Phenomena and Kinetic Theory

The study of kinetic equations related to gases, semiconductors, photons, traffic flow, and other systems has developed rapidly in recent years because of its role as a mathematical tool in areas such as engineering, meteorology, biology, chemistry, materials science, nanotechnology, and pharmacy. Written by leading specialists in their respective fields, this book presents an overview of recent developments in the field of mathematical kinetic theory with a focus on modeling complex systems, emphasizing both mathematical properties and their physical meaning. Transport Phenomena and Kinetic Theory is an excellent self-study reference for graduate students, researchers, and practitioners working in pure and applied mathematics, mathematical physics, and engineering. The work may be used in courses or seminars on selected topics in transport phenomena or applications of the Boltzmann equation.

Aspects Of Computation And Automata Theory With Applications
  • Language: en
  • Pages: 492

Aspects Of Computation And Automata Theory With Applications

This volume results from two programs that took place at the Institute for Mathematical Sciences at the National University of Singapore: Aspects of Computation — in Celebration of the Research Work of Professor Rod Downey (21 August to 15 September 2017) and Automata Theory and Applications: Games, Learning and Structures (20-24 September 2021).The first program was dedicated to the research work of Rodney G. Downey, in celebration of his 60th birthday. The second program covered automata theory whereby researchers investigate the other end of computation, namely the computation with finite automata, and the intermediate level of languages in the Chomsky hierarchy (like context-free and context-sensitive languages).This volume contains 17 contributions reflecting the current state-of-art in the fields of the two programs.

Applied Partial Differential Equations:
  • Language: en
  • Pages: 210

Applied Partial Differential Equations:

This book presents topics of science and engineering which occur in nature or are part of daily life. It describes phenomena which are modelled by partial differential equations, relating to physical variables like mass, velocity and energy, etc. to their spatial and temporal variations. The author has chosen topics representing his career-long interests, including the flow of fluids and gases, granular flows, biological processes like pattern formation on animal skins, kinetics of rarified gases and semiconductor devices. Each topic is presented in its scientific or engineering context, followed by an introduction of applicable mathematical models in the form of partial differential equations.

Hyperbolic Problems: Theory, Numerics, Applications
  • Language: en
  • Pages: 481

Hyperbolic Problems: Theory, Numerics, Applications

  • Type: Book
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  • Published: 2013-12-01
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  • Publisher: Birkhäuser

The Eighth International Conference on Hyperbolic Problems - Theory, Nu merics, Applications, was held in Magdeburg, Germany, from February 27 to March 3, 2000. It was attended by over 220 participants from many European countries as well as Brazil, Canada, China, Georgia, India, Israel, Japan, Taiwan, und the USA. There were 12 plenary lectures, 22 further invited talks, and around 150 con tributed talks in parallel sessions as well as posters. The speakers in the parallel sessions were invited to provide a poster in order to enhance the dissemination of information. Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineerin...

Stationary and Time Dependent Gross-Pitaevskii Equations
  • Language: en
  • Pages: 192

Stationary and Time Dependent Gross-Pitaevskii Equations

This volume looks at the Gross-Pitaevskii equation, an example of a defocusing nonlinear Schrodinger equation, which is a model for phenomena such as the Bose-Einstein condensation of ultra cold atomic gases, the superfluidity of Helium II, and the 'dark solitons' of nonlinear optics.

Recent Progress in Computational and Applied PDES
  • Language: en
  • Pages: 433

Recent Progress in Computational and Applied PDES

The book discusses some key scientific and technological developments in computational and applied partial differential equations. It covers many areas of scientific computing, including multigrid methods, image processing, finite element analysis and adaptive computations. It also covers software technology, algorithms and applications. Most papers are of research level, and are contributed by some well-known mathematicians and computer scientists. The book will be useful to engineers, computational scientists and graduate students.

Understanding Degradation Phenomena in Solid-Oxide Fuel-Cell Anodes by Phase-Field Modeling and Analytics
  • Language: en
  • Pages: 298

Understanding Degradation Phenomena in Solid-Oxide Fuel-Cell Anodes by Phase-Field Modeling and Analytics

The current work analyzes degradation effects in solid-oxide fuel cell anodes with the phase-field method. A model extension for interface diffusion is formulated and calibrated. Large-scale 3D-simulations provide interesting insights into phenomena at the microscale which are responsible for the degradation

Environmental Hazards
  • Language: en
  • Pages: 330

Environmental Hazards

One of the priority areas of ICSU (The International Council for Science) is “Natural and Human-Induced Environmental Hazards and Disasters”. The School — held at the Institute for Mathematical Sciences, Singapore from 20 April to 2 May 2009 — on which this volume is based on was sponsored by ICSU and by its members from IUTAM (the International Union of Theoretical and Applied Mechanics) and IUGG (the International Union of Geodesy and Geophysics).This volume provides an indepth graduate-level introduction to the fluid dynamics and geophysics of hazards such as tropical cyclones, flooding, atmospheric pollution and tsunamis. It also includes discussion of the possible effects of climate change on these phenomena. Indeed, the current importance of this area is of great public concern.

Modeling and Computational Methods for Kinetic Equations
  • Language: en
  • Pages: 360

Modeling and Computational Methods for Kinetic Equations

In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused works. Specific applications presented include plasma kinetic models, traffic flow models, granular media models, and coagulation-fragmentation problems. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.