6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

/pdf/quantum-mechanical-continuum-solvation-models-3edv963g14.pdf

Quantum mechanical continuum solvation models.

A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

http://ieeexplore.ieee.org/iel5/5/31047/01444179.pdf

Fundamentals of acoustics

Introduction: Realistic Image Synthesis, Goals and Limitations A Short Historical Perspective of Image Synthesis Radiosity and Finite Element Methods The Radiosity Algorithm and This Book Rendering Concepts: Motivation Basic Optics Radiometry and Photometry The Light Field Reflection Functions The Rendering Equation Discretizing the Radiosity Equation: the Radiosity Function Making Image Synthesis Tractable The Radiosity Approach Approximating the Radiosity Across a Surface Error Metrics Constant Element Radiosities Higher Order Basic Functions Parametric Mapping to a Master Element Summary The Form Factor, The Form Factor Integral: the Coefficients of K The Differential Form Factor Three Formulations of the Form Factor Computing the Form Factor Closed Form Solutions for the Form Factor: Formulae for Simple Shapes Differential Area to Convex Polygon General Polygon to Polygon Numerical Solutions for the Form Factor: Numerical Integration in General Evaluating the Inner Integral Full Area to Area Quadrature Contour Integral Formulation A Simple Test Environment Non-Constant Basis Functions Acceleration Techniques Radiosity Matrix Solutions: Qualities of the Matrix Linear System Solution Methods Relaxation Methods Dynamic Environments Parallel Implementations Domain Subdivision: Error Metrics Mesh Characteristics and Accuracy Automatic Meshing Algorithms Hierarchical and Importance Based Algorithms: Observations About K Two Level Hierarchy Multi-Level Hierarchy Importance Meshing Hierarchical Basis Functions Summary of Hierarchical Radiosity Methods Meshing: Basic Subdivision Techniques Mesh Template Methods Decomposition Methods Mesh Smoothing Discontinuity Meshing Topological Data Structures and Operators Alternatives to Meshing Rendering: Reconstructing the Radiosity Functions Interpolation Methods for Rendering Two-Pass Methods Incorporating Surface Detail Mapping Radiosities to Pixel Colours Colour Summary Extensions: Non-Diffuse Light Sources Directional Reflection Participating Media Conclusion and Future Directions

Radiosity and Realistic Image Synthesis

SUMMARY The present paper is concerned with the effective numerical implementation of the two-dimensional dual boundary element method, for linear elastic crack problems. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region formulation. Both crack surfaces are discretized with discontinuous quadratic boundary elements; this strategy not only automatically satisfies the necessary conditions for the existence of the finite-part integrals, which occur naturally, but also circumvents the problem of collocation at crack tips, crack kinks and crack-edge corners. Examples of geometries with edge, and embedded crack are analysed with the present method. Highly accurate results are obtained, when the stress intensity factor is evaluated with the J-integral technique. The accuracy and efficiency of the implementation described herein make this formulation ideal for the study of crack growth problems under mixed-mode conditions.

https://msvlab.hre.ntou.edu.tw/cite/DualBEM_Crack_Aliabadi_IJNME_1992.pdf

The dual boundary element method: Effective implementation for crack problems

Boundary concepts are introduced and immediately applied in simple - but useful - computer codes. These codes facilitate the comprehension of boundary elements. This text also discusses basic concepts, potential problems, elastostatics and other topics of interest to engineers.

Boundary Elements: An Introductory Course

Part 1 Basic equations and fundamentals of wave propagation: basic equations of linear elastodynamics formulation of the elastodynamic problem in terms of dilatation and rotation. Part 2 Harmonic problems - integral formulation and boundary elements for two dimensions: plane harmonic waves in elastic solids reflection and refraction of plane harmonic elastic waves. Part 3 Harmonic problems - boundary elements for three dimensions: scalar wave propagation computer code for three-dimensional scalar wave propagation using constant elements [CONDTHSH]. Part 4 Time domain formulation: fundamental solution and boundary integral formulation for transient scalar wave propagation two-dimensional formulation. Part 5 Dual reciprocity approach for transient elastodynamics: boundary integral formulation transformation of the domain integral. Part 6 Dynamic fracture mechanics: some basic fracture mechanics ideas dynamic stress intensity factors. Part 7 Dynamic soil-structure interaction: dynamic stiffness of foundations three-dimensional foundations. Part 8 Dynamic analysis of dam-soil-reservoir systems: some characteristics of the B.E. model gravity dams. Part 9 Dynamic analysis of poroelastic media: basic equations for dynamic poroelasticity boundary integral formulation. (Part Contents).

José Domínguez

Papers

Boundary Elements: An Introductory Course

Boundary elements in dynamics

Fully three-dimensional analysis of high-speed train–track–soil-structure dynamic interaction

Experimental and numerical analyses of vibrations induced by high-speed trains on the Córdoba–Málaga line

Boundary element methods for potential problems