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Encyclopedia of Applied and Computational Mathematics / edited by Björn Engquist.
Springer Nature - Springer Mathematics and Statistics eBooks 2015 English International Available online
View online- Format:
- Book
- Series:
- Springer reference.
- Springer reference
- Language:
- English
- Subjects (All):
- Mathematics--Data processing.
- Mathematics.
- Computer science--Mathematics.
- Computer science.
- Mathematical physics.
- Engineering mathematics.
- Engineering--Data processing.
- Engineering.
- Computational Mathematics and Numerical Analysis.
- Applications of Mathematics.
- Mathematics of Computing.
- Theory of Computation.
- Theoretical, Mathematical and Computational Physics.
- Mathematical and Computational Engineering Applications.
- Local Subjects:
- Computational Mathematics and Numerical Analysis.
- Applications of Mathematics.
- Mathematics of Computing.
- Theory of Computation.
- Theoretical, Mathematical and Computational Physics.
- Mathematical and Computational Engineering Applications.
- Physical Description:
- 1 online resource (361 illus., 208 illus. in color. eReference.)
- Edition:
- 1st ed. 2015.
- Place of Publication:
- Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015.
- Language Note:
- English
- Summary:
- EACM is a comprehensive reference work covering the vast field of applied and computational mathematics. Applied mathematics itself accounts for at least 60 per cent of mathematics, and the emphasis on computation reflects the current and constantly growing importance of computational methods in all areas of applications. EACM emphasizes the strong links of applied mathematics with major areas of science, such as physics, chemistry, biology, and computer science, as well as specific fields like atmospheric ocean science. In addition, the mathematical input to modern engineering and technology form another core component of EACM.
- Contents:
- 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
- Definition
- Overview
- Error on the Model
- Error on the Discretization
- Error on the Algorithm
- Conclusion
- Absorbing Boundaries and Layers
- Summary
- Absorbing Boundaries
- Absorbing Layers
- Other Issues and Applications
- Actin Cytoskeleton, Multi-scale Modeling
- Introduction
- Single Filament Dynamics
- Bulk Filaments in Solution
- Models of Force Generation and Membrane Protrusion
- Integration of Signaling, Network Dynamics, and Force Generation
- Adaptive Mesh Refinement
- Short Definition
- Basic Principles of Adaptive Refinement
- Some Refinement Strategies
- Cross-References
- ADI Methods
- Mathematics Subject Classification
- Accuracy and Stability
- Closely Related Issues
- Adjoint Methods as Applied to Inverse Problems
- Wave Equation Imaging
- Optical and Impedance Tomography
- Advancing Front Methods
- Basic Algorithm
- Advancing Layers Method
- Agent-Based Models in Infectious Disease and Immunology
- Acronyms
- 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
- Algorithms for Low Frequency Climate Response
- Definition Terms/Glossary
- 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
- Analysis and Computation of Hyperbolic PDEs with Random Data
- 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
- Angiogenesis, Computational Modeling Perspective
- Abstract
- 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
- Angiogenesis, Mathematical Modeling Perspective
- Angiogenesis Modeling
- Movement of ECs
- Blood Flow and Vascular Remodeling
- Application to Vascular Tumor Growth
- Future Directions for Angiogenesis Modeling
- Applications to Real Size Biological Systems
- 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
- Applied Control Theory for Biological Processes
- 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
- Approximation of Manifold-Valued Functions
- Historical Remark
- Adaptation Methods
- Atomistic to Continuum Coupling
- 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
- B
- Backward Differentiation Formulae
- Review of Stiffness
- Stability Concepts for Multistep Methods
- Modified Extended Backward Differentiation Formulae
- Application to DAEs
- Codes
- Bayesian Statistics: Computation.
- Mathematics Subject Classification
- 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
- 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
- Bézier Curves and Surfaces
- Curves
- Tensor-Product Surfaces
- Triangular Surfaces
- Bidomain Model: Analytical Properties
- Bidomain Model: Applications
- Extracellularly Applied Electric Fields and Tissue Polarization
- Pacing
- Shock-Induced Arrhythmogenesis and Defibrillation
- Bath Loading Effects and the Forward Problem of Electrocardiography
- Bidomain Model: Computation
- Computational Methods
- Discretization in Space and Time
- Spatial Discretization
- Time Discretization
- Solving Linear Systems
- Adaptive Methods
- Parallel Solvers
- Key Research Findings
- Bifurcations: Computation
- Computation of Branches
- Bifurcation Test Functions
- Computation of Bifurcation Points
- Branch Switching
- Biofilm Structure and Function, Modeling
- Biofilms
- Mass Balances
- Material Transport
- Active and Reactive Layers
- Bootstrapping
- References and Recommended Reading
- 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
- Boundary Control Method
- Inverse Problem
- BCm Devices
- Solving Inverse Problem
- Boundary Element Methods
- Boundary Integral Equation for Potential Problems
- The Boundary Element Method
- Boundary Element Formulations for General Problems
- Boundary Value Methods: GAMD, TOM
- Discrete Problem and Block BVMs
- The Codes GAM and GAMD
- The Code TOM
- Boussinesq Equations
- B-Series
- 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
- Burgers Equation
- Origin and Motivating Application
- Behavior of Solutions
- Inviscid Case
- Viscous Case
- Vanishing Viscosity Limit
- C
- Calcium Dynamics
- Ubiquitous Calcium
- Calcium Transport
- Mathematical Description
- Calculation of Ensemble Averages
- Mathematical Subject Classification
- Description.
- Computation of Macroscopic Properties.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Includes bibliographical references.
- ISBN:
- 3-540-70529-5
- OCLC:
- 932170536
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