Background -- The Equations of Motion for Extensible Strings -- Elementary Problems for Elastic Strings -- Planar Steady-State Problems for Elastic Rods -- to Bifurcation Theory and its Applications to Elasticity -- Global Bifurcation Problems for Strings and Rods -- Variational Methods -- Theory of Rods Deforming in Space -- Spatial Problems for Rods -- Axisymmetric Equilibria of Shells -- Ten…
Multiscale Discontinuous Galerkin Methods for Elliptic Problems with Multiple Scales -- Discrete Network Approximation for Highly-Packed Composites with Irregular Geometry in Three Dimensions -- Adaptive Monte Carlo Algorithms for Stopped Diffusion -- The Heterogeneous Multi-Scale Method for Homogenization Problems -- A Coarsening Multigrid Method for Flow in Heterogeneous Porous Media -- On th…
Why probability and statistics? -- Outcomes, events, and probability -- Conditional probability and independence -- Discrete random variables -- Continuous random variables -- Simulation -- Expectation and variance -- Computations with random variables -- Joint distributions and independence -- Covariance and correlation -- More computations with more random variables -- The Poisson process -- …
Constraint Retraction for Dynamic Constraint Satisfaction Problems over Disjoint Real Intervals -- Computational Methods for Large Distributed Parameter Estimation Problems in 3D -- Robust Parameter Estimation for Identifying Satellite Injection Orbits -- On the Numerical Simulation of the Free Fall Problem -- Searching the Web: a Semantics-Based Approach -- Adaptive Computation with Perfectly …
Basic Material -- Approximation of Integrals -- Boundary Layer Behaviour -- Two-Point Boundary Value Problems -- Nonlinear Boundary Value Problems -- Elliptic Boundary Value Problems -- Boundary Layers in Time -- Evolution Equations with Boundary Layers -- The Continuation Method -- Averaging and Timescales -- Advanced Averaging -- Averaging for Evolution Equations -- Wave Equations on Unbounde…
4d Formalism -- On Establishing Balance and Conservation Laws in Elastodynamics -- From Mathematical Physics to Engineering Science -- Evolving Interfaces -- The Unifying Nature of the Configurational Force Balance -- Generalized Stefan Models -- Explicit Kinetic Relation from “First Principles” -- Growth & Biomechanics -- Surface and Bulk Growth Unified -- Mechanical and Thermodynamical Mo…
The Dilute Bose Gas in 3D -- The Dilute Bose Gas in 2D -- Generalized Poincaré Inequalities -- Bose-Einstein Condensation and Superfluidity for Homogeneous Gases -- Gross-Pitaevskii Equation for Trapped Bosons -- Bose-Einstein Condensation and Superfluidity for Dilute Trapped Gases -- One-Dimensional Behavior of Dilute Bose Gases in Traps -- Two-Dimensional Behavior in Disc-Shaped Traps -- The…
Part I: The Neural Foundations -- From Classical Connectionist Models to Probabilistic / Generalised Regression Neural Networks (PNNs / GRNNs) -- The Kernel Memory Concept – A Paradigm Shift from Conventional Connectionism -- The Self-Organising Kernel Memory (SOKM) -- Part II: Artificial Mind Systems -- The Artificial Mind System (AMS), Modules, and their Interactions -- Sensation and Percep…
Assessment of characteristic shear strength parameters of soil and its implication in geotechnical design -- Ambiguity of safety definition in geotechnical models -- The fuzziness and sensitivity of failure probabilities -- The mathematics of uncertainty: models, methods and interpretations -- Multi-parameter models: rules and computational methods for combining uncertainties -- Sensitivity ana…
Physics of Unsteady Flows -- The Differential Equations of Fluid Flow -- Panel Methods -- Applications of Panel Method -- Boundary-Layer Methods -- Applications of Boundary-Layer Methods: Flows Without Separation -- Applications of Boundary-Layer Methods: Flows with Separation -- Navier-Stokes Methods -- Applications of Navier-Stokes Methods -- Companion Computer Programs.This book provides an …