Computational Methods and Mathematical Modeling in Cyberphysics and Engineering Applications 1

Name: Computational Methods and Mathematical Modeling in Cyberphysics and Engineering Applications 1
Brand: Wiley
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Dmitri Koroliouk Sergiy Lyashko Nikolaos Limnios(Herausgeber*in)

Wiley (Verlag)

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Erschienen am 10. April 2024

448 Seiten

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Inhalt

Cover
Title Page
Copyright Page
Contents
Preface
Chapter 1. The Hydrodynamic-type Equations and the Solitary Solutions
1.1. Introduction
1.2. The Korteweg-de Vries equation and the soliton solutions
1.3. The Korteweg-de Vries equation with a small perturbation
1.4. The linear WKB technique and its generalization
1.5. Acknowledgments
1.6. References
Chapter 2. The Nonlinear WKB Technique and Asymptotic Soliton-like Solutions to the Korteweg-de Vries Equation with Variable Coefficients and Singular Perturbation
2.1. Introduction
2.2. Main notations and definitions
2.3. The structure of the asymptotic one-phase soliton-like solution
2.4. The KdV equation with quadratic singularity
2.5. Equations for the regular part of the asymptotics and their analysis
2.6. Equations for the singular part of the asymptotics and their analysis
2.6.1. The main term of the singular part
2.6.2. The higher terms of the singular part and the orthogonality condition
2.6.3. The orthogonality condition and the discontinuity curve
2.6.4. Prolongation of the singular terms from the discontinuity curve
2.7. Justification of the algorithm
2.8. Discussion and conclusion
2.9. Acknowledgments
2.10. References
Chapter 3. Asymptotic Analysis of the vcKdV Equation with Weak Singularity
3.1. Introduction
3.2. The asymptotic soliton-like solutions
3.3. The examples of the asymptotic soliton-like solutions
3.3.1. The asymptotic step-wise solutions
3.3.2. The asymptotic solutions of soliton type
3.4. Discussion and conclusion
3.5. Acknowledgments
3.6. References
Chapter 4. Modeling of Heterogeneous Fluid Dynamics with Phase Transitions and Porous Media
4.1. Introduction
4.2. The large particle method
4.3. The particle-in-cell method
4.4. Modeling of heterogeneous fluid dynamics
4.5. Modeling of heterogeneous fluid dynamics with phase transitions
4.6. Modeling of viscous fluid dynamics and porous media
4.7. References
Chapter 5. Mathematical Models and Control of Functionally Stable Technological Process
5.1. Introduction
5.2. Analysis of production process planning procedure
5.3. Mathematical model of the production process management system of an industrial enterprise
5.4. Control design
5.5. Algorithm of control of production process
5.6. Conclusion
5.7. Acknowledgments
5.8. References
Chapter 6. Alternative Direction Multiblock Method with Nesterov Acceleration and Its Applications
6.1. Introduction
6.2. Proximal operators
6.3. ADMM (alternating direction method of multipliers)
6.4. Bregman iteration
6.5. Forward-backward envelope (FBE)
6.6. Douglas-Rachford envelope (DRE)
6.7. Proximal algorithms for complex functions
6.8. Fast alternative directions methods
6.9. Numerical experiments
6.9.1. Exchange problem
6.9.2. Basis pursuit problem
6.9.3. Constrained LASSO problem
6.10. Conclusion
6.11. References
Chapter 7. Modified Extragradient Algorithms for Variational Inequalities
7.1. Introduction
7.2. Preliminaries
7.3. Overview of the main algorithms for solving variational inequalities and approximations of fixed points
7.4. Modified extragradient algorithm for variational inequalities
7.5. Modified extragradient algorithm for variational inequalities and operator equations with a priori information
7.6. Strongly convergent modified extragradient algorithm
7.6.1. Algorithm variant for variational inequalities
7.6.2. Variant for problems with a priori information
7.7. References
Chapter 8. On Multivariate Algorithms of Digital Signatures on Secure El Gamal-Type Mode
8.1. On post-quantum, multivariate and non-commutative cryptography
8.2. On stable subgroups of formal Cremona group and privatization of multivariate public keys based on maps of bounded degree
8.3. Multivariate Tahoma protocol for stable Cremona generators and its usage for multivariate encryption algorithms
8.4. On multivariate digital signature algorithms and their privatization scheme
8.5. Examples of stable cubical groups
8.5.1. Simplest graph-based example
8.5.2. Other stable subgroups defined via linguistic graphs
8.5.3. Special homomorphisms of linguistic graphs and corresponding semigroups
8.5.4. Example of stable subsemigroups of arbitrary degree
8.6. Conclusion
8.7. References
Chapter 9. Metasurface Model of Geographic Baric Field Formation
9.1. Introduction
9.2. The parametric scalar field model principle
9.3. Local isobaric scalar field model
9.4. Modeling Chladni figures based on the proposed model
9.5. The frequency of forcing influences and the problem of its detection
9.6. Conclusion
9.7. References
Chapter 10. Simulation of the Electron-Hole Plasma State by Perturbation Theory Methods
10.1. Introduction. Nonlinear boundary value problems of the p-i-n diodes theory
10.2. Construction of an asymptotic solution of a boundary value problem for the system of the charge carrier current continuity equations and the Poisson equation
10.3. Simulation of the charge carriersâ?T stationary distribution in the electron-hole plasma of the p-i-n diode assembly elements
10.4. Modeling the charge carriers stationary distribution in the active region of the integrated surface-oriented p-i-n structures
10.5. Final considerations
10.6. References
Chapter 11. Diffusion Perturbations in Models of the Dynamics of Infectious Diseases Taking into Account the Concentrated Effects
11.1. Introduction
11.2. Model problem of infectious disease dynamics taking into account diffusion perturbation and asymptotics of the solution
11.3. Modeling of diffusion perturbations of infectious disease process taking into account the concentrated effects and immunotherapy
11.4. Modeling the influence of diffusion perturbations on development of infectious diseases under convection
11.5. Numerical experiment results
11.6. Conclusion
11.7. References
Chapter 12. Solitary Waves in "Shallow Water" Environments
12.1. Introduction
12.2. T-forms for the solitary wave approximation
12.3. Existence of the solution of the gas dynamics equations in the form of solitary waves
12.4. Analysis of the localized wave trajectories
12.5. Numerical results
12.6. Conclusion
12.7. References
Chapter 13. Instrument Element and Grid Middleware in Metrology Problems
13.1. Introduction
13.2. Security in the grid
13.3. Grid element for measuring instruments
13.4. Grid and some problems of metrology
13.5. Discussion and conclusion
13.6. References
Chapter 14. Differential Evolution for Best Uniform Spline Approximation
14.1. Introduction
14.2. Problem statement
14.3. Review of methods for spline approximation
14.4. Algorithm
14.5. Experimental results and discussion
14.6. Conclusion
14.7. References
Chapter 15. Finding a Nearest Pair of Points Between Two Smooth Curves in Euclidean Space
15.1. Introduction
15.2. Define the problem and notations
15.3. Lagrange function with energy dissipation
15.4. Lagrange equation
15.5. Hamiltonian equations
15.6. Numerical experiments
15.7. Concluding remarks
15.8. References
Chapter 16. Constrained Markov Decision Process for the Industry
16.1. Introduction
16.2. Introduction to constrained Markov decision processes
16.2.1. Introduction
16.2.2. Model
16.2.3. Economic criteria
16.2.4. Infinite horizon expected discounted reward
16.2.5. Infinite horizon expected average reward
16.3. Markov decision process with a constraint on the asymptotic availability
16.3.1. Introduction
16.3.2. Model
16.3.3. Algorithm
16.3.4. Application
16.4. Markov decision process with a constraint on the asymptotic failure rate
16.4.1. Introduction
16.4.2. Model
16.4.3. Algorithm
16.4.4. Application
16.5. Conclusion
16.6. References
List of Authors
Index
EULA

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