Integral Methods in Science and Engineering: Computational and Analytic Aspects

ISBN-13: 9780817682378 / Angielski / Twarda / 2011 / 448 str.

Christian Constanda; Paul J. Harris

Opis

An enormous array of problems encountered by scientists and engineers are based on the design of mathematical models using many different types of ordinary differential, partial differential, integral, and integro-differential equations. Accordingly, the solutions of these equations are of great interest to practitioners and to science in general. Presenting a wealth of cutting-edge research by a diverse group of experts in the field, Integral Methods in Science and Engineering: Computational and Analytic Aspects gives a vivid picture of both the development of theoretical integral techniques and their use in specific science and engineering problems.This book will be valuable for researchers in applied mathematics, physics, and mechanical and electrical engineering. It will likewise be a useful study guide for graduate students in these disciplines, and for various other professionals who use integration as an essential technique in their work.

Spis treści

Preface.- Collocation Method for Cauchy Integral Equations in L^2.- On a New Definition of the Reynolds Number from the Interplay of Macroscopic and Microscopic Phenomenology.- A Self-Consistent Monte Carlo Validation Procedure for Hadron Cancer Therapy Simulation.- A General Analytical Solution of the Advection–Diffusion Equation for Fickian Closure.- A Novel Method for Simulating Spectral Nuclear Reactor Criticality by Spatially Dependent Volume Size Control.- Adaptive Particle Filter for Stable Distribution.- On the Analytical Solution of the Multi-Group Neutron Kinetic Diffusion Equations in One-Dimensional Cartesian Geometry by the Integral Transformation Technique.- Estimating the Validity of Statistical Energy Analysis Using Dynamic Energy Analysis.- Efficient Iterative Methods for Fast Solution of Integral Operators.- Analysis of Some Localized Boundary–Domain Integral Equations for Transmission Problems with Variable Coefficients.- Analysis of Segregated Boundary–Domain Integral Equations for Variable-Coefficient BVPs in Exterior Domains.- Thermoelastic Plates with Arc-Shaped Cracks.- Almost Periodicity in Semilinear Systems.- Bubble Behavior Near a Two-Fluid Interface.- Spectral Stiff Problems in Domains with Strongly Oscillating Boundary.- Spectra and Pseudospectra of the Convection–Diffusion Operator.- A Necessary and Sufficient Condition for the Existence of Absolute Minimizers for Energy Functionals with Scale Invariance.- Nonlinear Abel-Type Integral Equation Modeling in Creep Crack Propagation.- Some Thoughts on Methods for Evaluating a Class of Highly Oscillatory Integrals.- Numerical Experiments for Mammary Adenocarcinoma Cell Progression.- Limiting Cases of Subdiffusion.- A New Hybrid Method to Predict the Distribution of Vibro-Acoustic Energy in Complex Built-up Structures.- 2-D and 3-D Elastodynamic Contact Problems for Interface Cracks Under Harmonic Loading.- Asymptotic Behavior of Elliptic Quadric Algebraic Equations with Variable Coefficients and Aerodynamical Applications.- Artificial Neural Networks for Estimating Atmospheric Pollutant Sources.- A Theoretical Study of the Stratified Atmospheric Boundary Layer Through Perturbation Techniques.- Integro-Differential Equations for Stress Analysis at the Bridged Zone of an Interface Crack.- Design and Performance of Gas–Liquid Cylindrical Cyclone/Slug Damper System.- On the Quasimodes for compact Operators and Associated Evolution Problems.- Error Estimation by Means of Richardson Extrapolation with the Boundary Element Method in a Dirichlet Problem for the Laplace Equation.- Convergence of a Discretization Scheme Based on the Characteristics Method for a Fluid-Rigid System.- An Efficient Algorithm to Solve the GITT-Transformed 2-D Neutron Diffusion Equation.- Nonlinear Localized Dissipative Structures for Solving Wave Equations over Long Distances.- Semianalytical Approach to the Computation of the Laplace Transform of Source Functions.- Asymptotic Analysis of Singularities for Pseudodifferential Equations in Canonical Non-Smooth Domains.- Optimizing Water Quality in a River Section.- Boundary Integral Equations for Arbitrary Geometry Shells.

On the Determination of the Albedo Boundary Conditions by Solving the One-Speed Neutron Transport Equation in Slab-Geometry with the LTSN Method. Numerical Solution of the Electric Field Integral Equation on Polyhedral Surfaces.- A High Frequency Problem of Scattering by Convex Polygons with Impedance Boundary Conditions.- Localized Segregated Boundary–Domain Integral Equation Formulation for Transmission Problems.- Distributional Solutions for Boundary Integral Methods in the Theory of Bending of Thermoelastic Plates. New Spaces: A Semi-linear Case.- Generalized Particle Filter: PDF with Undefined Statistical Moments.- Droplet Heating and Evaporation in the Presence of a Moving Boundary: Numerical Analysis Based on Analytical Solutions.- Solution of a Nonlinear Abel-type Integral Equation Modeling Crack Propagation Under Creep and Fatigue.- Some Thoughts on Methods for Evaluating a Class of Highly Oscillatory Integrals.- Domain Decomposition with Lagrange Multipliers for Hypersingular Integral Equations.- Numerical Integration Methods for Functions with Singularities by Partition Integration.- Multiple Trace Boundary Integral Formulation for Helmholtz Transmission Problems.- Limiting Cases of Subdiffusion.-New Trends in Inverse Scattering Theory.- Transient Mechanistic Model for Slug Damper/ (GLCC)Compact Separator System.- Exact 3-D Galerkin Integrals for Planar Cracks.- Interface Cracks Under Harmonic Loading: Effect of Crack Face Contact Interaction.- Localized Segregated Boundary–Domain Integral Equation Formulation for Mixed Type Boundary Value Problems.- On the Robustness of the GITT Solution for the 2-D Neutron Diffusion Equation in Cartesian Geometry.- Conditioning Numerical Models with Application to Petroleum Reservoir Chracterization.- Computation of the Spectrum for Some Elliptic Operators on Periodic Waveguides with Variable Density.- Numerical Simulation of Short Waves over Long Distances as Nonlinear Solitary Waves.- Pseudodifferential Equations in Domains with Boundary Singularities.- Optimizing Water Quality in a River Section.- Semi-analytical Approach to the Computation of the Laplace Transform of 3-D Source Functions.- Boundary Integral Equations for Shells of Arbitrary Geometry.- Solutions to Model Equations for Cancer Growth.

Blurb

The systematic study of the physical world is largely based on the design of mathematical models using many different types of ordinary differential, partial differential, integral, and integro-differential equations. The solutions of these equations are therefore of great interest to practitioners and to science in general. With a wealth of cutting-edge research in the field, Integral Methods in Science and Engineering: Computational and Analytic Aspects provides a vivid picture of both the development of theoretical integral techniques and their use in specific science and engineering problems.

The volume is an outgrowth of talks presented by world-renowned researchers at the Eleventh International Conference on Integral Methods in Science and Engineering held in Brighton, UK, July 12–14, 2010. The array of topics they address is immense, ranging from theoretical advances in boundary integral methods to applications of analytic and numerical quadrature techniques as diverse as integral equations, finite and boundary elements, conservation laws, hybrid approaches, and more.

With ample coverage of theory and applications, this book will be a valuable resource for researchers in applied mathematics, physics, and mechanical and electrical engineering, for graduate students in these disciplines, and for various other professionals who use integration as an essential technique in their work.