Nota di contenuto |
Intro -- Preface -- About the Editor -- Section Editors -- Contributors -- A -- A Posteriori Error Estimates of Quantities of Interest -- Synonyms -- Short Description -- Description -- Model Problem, Quantities of Interest, and Adjoint Problem -- Goal-Oriented Error Estimation -- Adaptive Strategies -- Extension to Nonlinear Problems -- Concluding Remarks -- References -- A Priori and A Posteriori Error Analysis in Chemistry -- Synonyms -- Definition -- Overview -- Error on the Model -- Error on the Discretization -- Error on the Algorithm -- Conclusion -- References -- Absorbing Boundaries and Layers -- Synonyms -- Summary -- Absorbing Boundaries -- Absorbing Layers -- Other Issues and Applications -- References -- Actin Cytoskeleton, Multi-scale Modeling -- Synonyms -- Introduction -- Single Filament Dynamics -- Bulk Filaments in Solution -- Models of Force Generation and Membrane Protrusion -- Integration of Signaling, Network Dynamics, and Force Generation -- Summary -- References -- Adaptive Mesh Refinement -- Synonyms -- Short Definition -- Basic Principles of Adaptive Refinement -- Some Refinement Strategies -- Cross-References -- References -- ADI Methods -- Mathematics Subject Classification -- Synonyms -- Description -- Accuracy and Stability -- Closely Related Issues -- References -- Adjoint Methods as Applied to Inverse Problems -- Synonyms -- Definition -- Overview -- Wave Equation Imaging -- Optical and Impedance Tomography -- References -- Advancing Front Methods -- Mathematics Subject Classification -- Synonyms -- Short Definition -- Description -- Basic Algorithm -- Advancing Layers Method -- References -- Agent-Based Models in Infectious Disease and Immunology -- Synonyms -- Acronyms -- Short Definition -- Description -- ABMs as Natural Descriptions of the Immune Response and Infectious Diseases.
The Main Agents of the Immune Response -- ABM Representation of the Immune Response and Infectious Diseases -- Example: Influenza Infection Within a Host -- Platforms for the Implementation of ABMs of Immunology and Infectious Diseases -- References -- Algorithms for Low Frequency Climate Response -- Definition Terms/Glossary -- Description -- Deterministic Dynamics, Fluctuation-Response relation -- Chaotic Dissipative Dynamics, Short-Time FDR -- Chaotic Dissipative Dynamics, Axiom A Response Formula -- Chaotic Dissipative Dynamics, Shadowing -- Chaotic Dissipative Dynamics, UPO Expansion -- Stochastic Dynamics, Fluctuation-Response Relation -- References -- Analysis and Computation of Hyperbolic PDEs with Random Data -- Introduction -- Problem Statement -- Nonintrusive Numerical Methods -- Stochastic Regularity and Convergence of Stochastic Collocation -- Examples: General Stochastic Regularity Properties -- General Results: Stochastic Regularity -- Convergence Results for Stochastic Collocation -- References -- Angiogenesis, Computational Modeling Perspective -- Abstract -- Introduction -- Angiogenesis Modeling Methodology -- Network-Level Modeling -- Molecular-Level Modeling: Reaction Diffusion Modeling -- Intracellular signaling models -- Cell-Based Modeling -- Agent-based programming -- Cellular automata -- Potts model -- Bioinformatics -- Multiscale Modeling -- Conclusions and Therapeutic Applications -- References -- Angiogenesis, Mathematical Modeling Perspective -- Angiogenesis Modeling -- Movement of ECs -- Blood Flow and Vascular Remodeling -- Application to Vascular Tumor Growth -- Future Directions for Angiogenesis Modeling -- References -- Applications to Real Size Biological Systems -- Mathematics Subject Classification -- Synonyms -- Short Definition -- Description -- MD Simulations of Biological Systems: A Computational Challenge.
Brute-Force Molecular Dynamics to Address Biological Complexity -- Preferential Sampling and the Simulation of Slow Processes -- A Turning Point in Structural Biology -- References -- Applied Control Theory for Biological Processes -- Synonyms -- Short Definition -- Description -- Model Predictive Control -- Adaptive Model Predictive Control -- Sensitivity and Identifiability Analyses -- Brief Literature Survey of Cellular Process Model Predictive Control -- Illustration of Adaptive Nonlinear Model Predictive Control with Selective Parameter Identification -- Concluding Remarks -- References -- Approximation of Manifold-Valued Functions -- Mathematics Subject Classification -- Definition -- Description -- Historical Remark -- Adaptation Methods -- References -- Atomistic to Continuum Coupling -- Mathematics Subject Classification -- Synonyms -- Short Definition -- Description -- Atomistic Models -- Continuum Models -- Accuracy of the Cauchy-Born Approximation -- Crystal Defects and Motivation for A/C Methods -- Energy-Based Methods -- The Energy-Based Quasicontinuum Method -- Accuracy of QCE -- The Blended Quasicontinuum Energy -- Accuracy of the BQCE Method -- Energy-Based Ghost-Force Removal -- Accuracy of Consistent a/c Methods -- Force-Based Methods -- Force-Based a/c Coupling -- Accuracy of the Force-Based a/c Method -- Iterative Solution of Force-Based a/c Coupling -- Extensions -- Overlapping Methods and Weak Coupling -- Multilattices -- Quantum Mechanics -- Finite-Temperature Equilibrium and Dynamics -- References -- B -- Backward Differentiation Formulae -- Synonyms -- Definition -- Review of Stiffness -- Stability Concepts for Multistep Methods -- Backward Differentiation Formulae -- Modified Extended Backward Differentiation Formulae -- Application to DAEs -- Codes -- References -- Bayesian Statistics: Computation.
Mathematics Subject Classification -- Synonyms -- Short Definition -- Description -- Prehistory -- Latent Variable Methods in Likelihood Inference: The EM Algorithm -- Bayesian Computation in the 1980s -- Formulation of the Gibbs Sampler -- Introduction of Latent Variables and Collective Moves -- Conclusion -- References -- Belousov-Zhabotinsky Reaction -- What is the Belousov-Zhabotinsky Reaction? -- How to Experiment with the Light Sensitive BZ Reaction -- Qualitative Modelling -- Two-Variable Oregonator -- Very Fast Prototyping: Cellular Automata -- References -- Bézier Curves and Surfaces -- Definition -- Curves -- Tensor-Product Surfaces -- Triangular Surfaces -- References -- Bidomain Model: Analytical Properties -- References -- Bidomain Model: Applications -- Overview -- Extracellularly Applied Electric Fields and Tissue Polarization -- Pacing -- Shock-Induced Arrhythmogenesis and Defibrillation -- Bath Loading Effects and the Forward Problem of Electrocardiography -- Conclusion -- References -- Bidomain Model: Computation -- Overview -- Computational Methods -- Discretization in Space and Time -- Spatial Discretization -- Time Discretization -- Solving Linear Systems -- Adaptive Methods -- Parallel Solvers -- Key Research Findings -- Cross-References -- References -- Bifurcations: Computation -- Computation of Branches -- Bifurcation Test Functions -- Computation of Bifurcation Points -- Branch Switching -- References -- Biofilm Structure and Function, Modeling -- Mathematics Subject Classification -- Synonyms -- Short Definition -- Description -- Biofilms -- Mass Balances -- Material Transport -- Active and Reactive Layers -- Summary -- References -- Bootstrapping -- Synonyms -- Short Definition -- Description -- References and Recommended Reading -- References -- Born-Oppenheimer Approximation, Adiabatic Limit, and Related Math. Issues.
Introduction -- The Quantum Mechanical Adiabatic Approximation -- The Traditional Quantum Adiabatic Theorem -- Geometric Phases -- Higher Order Approximations -- Further Generalizations with a Gap -- Adiabatic Theorems Without a Gap -- Adiabatic Theorems with Level Crossings -- Adiabatic Theorems with Avoided Crossings -- Time-Dependent Born-Oppenheimer Approximations -- References -- Boundary Control Method -- Introduction -- Inverse Problem -- BCm Devices -- Solving Inverse Problem -- References -- Boundary Element Methods -- Mathematics Subject Classification -- Synonyms -- Short Definition -- Description -- Boundary Integral Equation for Potential Problems -- The Boundary Element Method -- Boundary Element Formulations for General Problems -- References -- Boundary Value Methods: GAMD, TOM -- Synonyms -- Definition -- Overview -- Discrete Problem and Block BVMs -- The Codes GAM and GAMD -- The Code TOM -- References -- Boussinesq Equations -- References -- B-Series -- Synonyms -- Short Definition -- Description -- Introduction -- Order Conditions of Runge-Kutta Methods and B-Series -- Composition of B-Series -- Changes of Variables and Preservation of First Integrals -- Modified Equations for B-Series Methods -- Preservation of Geometric Properties of B-Series Methods -- Cross-References -- References -- Burgers Equation -- Mathematics Subject Classification -- Synonyms -- Short Definition -- Description -- Origin and Motivating Application -- Behavior of Solutions -- Inviscid Case -- Viscous Case -- Vanishing Viscosity Limit -- References -- C -- Calcium Dynamics -- Mathematics Subject Classification -- Short Definition -- Description -- Ubiquitous Calcium -- Calcium Transport -- Mathematical Description -- References -- Calculation of Ensemble Averages -- Mathematical Subject Classification -- Short Definition -- Description.
Computation of Macroscopic Properties.
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