Coverart for item
The Resource Recent progress and modern challenges in applied mathematics, modeling and computational science, Roderick Melnik, Roman Makarov, Jacques Belair, editors, (electronic resource)

Recent progress and modern challenges in applied mathematics, modeling and computational science, Roderick Melnik, Roman Makarov, Jacques Belair, editors, (electronic resource)

Label
Recent progress and modern challenges in applied mathematics, modeling and computational science
Title
Recent progress and modern challenges in applied mathematics, modeling and computational science
Statement of responsibility
Roderick Melnik, Roman Makarov, Jacques Belair, editors
Contributor
Subject
Language
eng
Member of
Cataloging source
YDX
Dewey number
510
Index
index present
LC call number
QA39.3
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Melnik, Roderick
  • Makarov, Roman
  • Belair, Jacques
Series statement
Fields Institute communications,
Series volume
v. 79
http://library.link/vocab/subjectName
  • Mathematics
  • Mathematical models
  • Computer science
Label
Recent progress and modern challenges in applied mathematics, modeling and computational science, Roderick Melnik, Roman Makarov, Jacques Belair, editors, (electronic resource)
Instantiates
Publication
Note
Includes index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Contents; Part I Modern Challenges and Interdisciplinary Interactions via Mathematical, Statistical, and Computational Models; Modern Challenges and Interdisciplinary Interactionsvia Mathematical, Statistical, and Computational Models; 1 The Role of Mathematical and Statistical Models; 2 Application Areas and State-of-the-Art Developments; 2.1 Large Deviation Theory and Random Perturbations of Dynamical Systems with Applications; 2.2 Nonlinear waves, Hyperbolic Problems, and their Applications; 2.3 Group-Theoretical Approaches to Conservation Lawsand Their Applications
  • 2.4 Materials Science, Engineering, and New Technologies2.5 Finance and Systemic Risk; 2.6 Life and Environmental Sciences; 2.7 Number Theory and Algebraic Geometry in Cryptography and Other Applications; 2.8 Sustainability and Cooperation; 3 Conclusions; References; Part II Large Deviation Theory and Random Perturbations of Dynamical Systems with Applications; Long Term Effects of Small Random Perturbations on Dynamical Systems: Theoretical and Computational Tools; 1 Introduction; 2 Freidlin-Wentzell Large Deviation Theory (LDT); 2.1 Some Key Concepts in LDT; 2.2 Geometric Action Functional
  • 3 Numerical Minimization of the Geometric Action3.1 Geometric Minimum Action Method; 3.2 A Simplified gMAM; 3.3 Connection to gMAM; 3.4 Simplifications for SDEs with Additive Noise; 3.5 Simplifications for General SDEs (Multiplicative Noise); 3.6 Comments on Improving the Numerical Efficiency; 3.7 SPDEs with Additive Noise; 4 Illustrative Applications; 4.1 Maier-Stein Model; 4.2 Allen-Cahn/Cahn-Hilliard System; 4.2.1 Reduced Allen-Cahn/Cahn-Hilliard Model; 4.2.2 Full Allen-Cahn/Cahn-Hilliard Model; 4.3 Burgers-Huxley Model; 4.4 Noise-Induced Transitions Between Climate Regimes
  • 4.4.1 Metastable Climate Regimes in Egger's Model4.4.2 Metastable Climate Regimes in the Charney-DeVore Model; 4.5 Generalized Voter/Ising Model; 4.6 Bi-Stable Reaction-Diffusion Model; 4.7 Slow-Fast Systems; 5 Concluding Remarks; References; Part III Nonlinear Waves, Hyperbolic Problems, and their Applications; Long Time Dynamics and Coherent States in NonlinearWave Equations; 1 Introduction; 2 General Hamiltonian Formulation; 3 Coherent States; 3.1 Variational Methods: Existence and Stability of Ground States; 3.2 Bifurcation Methods; 3.3 Orbital Stability
  • 4 Asymptotic Stability of Coherent States5 Conclusions; References; About Non Linear Stabilization for Scalar Hyperbolic Problems; 1 Introduction; 2 Formulation of Residual Distribution Schemes; 2.1 Definition, Connection to Finite Element Methods; 2.2 Structure Conditions; 2.2.1 Conservation; 2.2.2 Accuracy; 3 Construction of Monotonicity Preserving Arbitrary Accurate Schemes; 3.1 A Preliminary Remark; 3.2 Explicit Construction; 3.3 Filtering; 3.3.1 Streamline Filtering; 3.3.2 Jump Filtering; 4 Numerical Examples; 5 Conclusions; References
Dimensions
unknown
Extent
1 online resource.
Form of item
online
Isbn
9781493969692
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System control number
on1003313796
Label
Recent progress and modern challenges in applied mathematics, modeling and computational science, Roderick Melnik, Roman Makarov, Jacques Belair, editors, (electronic resource)
Publication
Note
Includes index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Contents; Part I Modern Challenges and Interdisciplinary Interactions via Mathematical, Statistical, and Computational Models; Modern Challenges and Interdisciplinary Interactionsvia Mathematical, Statistical, and Computational Models; 1 The Role of Mathematical and Statistical Models; 2 Application Areas and State-of-the-Art Developments; 2.1 Large Deviation Theory and Random Perturbations of Dynamical Systems with Applications; 2.2 Nonlinear waves, Hyperbolic Problems, and their Applications; 2.3 Group-Theoretical Approaches to Conservation Lawsand Their Applications
  • 2.4 Materials Science, Engineering, and New Technologies2.5 Finance and Systemic Risk; 2.6 Life and Environmental Sciences; 2.7 Number Theory and Algebraic Geometry in Cryptography and Other Applications; 2.8 Sustainability and Cooperation; 3 Conclusions; References; Part II Large Deviation Theory and Random Perturbations of Dynamical Systems with Applications; Long Term Effects of Small Random Perturbations on Dynamical Systems: Theoretical and Computational Tools; 1 Introduction; 2 Freidlin-Wentzell Large Deviation Theory (LDT); 2.1 Some Key Concepts in LDT; 2.2 Geometric Action Functional
  • 3 Numerical Minimization of the Geometric Action3.1 Geometric Minimum Action Method; 3.2 A Simplified gMAM; 3.3 Connection to gMAM; 3.4 Simplifications for SDEs with Additive Noise; 3.5 Simplifications for General SDEs (Multiplicative Noise); 3.6 Comments on Improving the Numerical Efficiency; 3.7 SPDEs with Additive Noise; 4 Illustrative Applications; 4.1 Maier-Stein Model; 4.2 Allen-Cahn/Cahn-Hilliard System; 4.2.1 Reduced Allen-Cahn/Cahn-Hilliard Model; 4.2.2 Full Allen-Cahn/Cahn-Hilliard Model; 4.3 Burgers-Huxley Model; 4.4 Noise-Induced Transitions Between Climate Regimes
  • 4.4.1 Metastable Climate Regimes in Egger's Model4.4.2 Metastable Climate Regimes in the Charney-DeVore Model; 4.5 Generalized Voter/Ising Model; 4.6 Bi-Stable Reaction-Diffusion Model; 4.7 Slow-Fast Systems; 5 Concluding Remarks; References; Part III Nonlinear Waves, Hyperbolic Problems, and their Applications; Long Time Dynamics and Coherent States in NonlinearWave Equations; 1 Introduction; 2 General Hamiltonian Formulation; 3 Coherent States; 3.1 Variational Methods: Existence and Stability of Ground States; 3.2 Bifurcation Methods; 3.3 Orbital Stability
  • 4 Asymptotic Stability of Coherent States5 Conclusions; References; About Non Linear Stabilization for Scalar Hyperbolic Problems; 1 Introduction; 2 Formulation of Residual Distribution Schemes; 2.1 Definition, Connection to Finite Element Methods; 2.2 Structure Conditions; 2.2.1 Conservation; 2.2.2 Accuracy; 3 Construction of Monotonicity Preserving Arbitrary Accurate Schemes; 3.1 A Preliminary Remark; 3.2 Explicit Construction; 3.3 Filtering; 3.3.1 Streamline Filtering; 3.3.2 Jump Filtering; 4 Numerical Examples; 5 Conclusions; References
Dimensions
unknown
Extent
1 online resource.
Form of item
online
Isbn
9781493969692
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System control number
on1003313796

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