Computational Methods and Mathematical Modeling in Cyberphysics and Engineering Applications 1

• Record Nr.: UNINA9911019125103321
• Autore: Koroliouk Dmitri
• Pubbl/distr/stampa: Newark : , : John Wiley & Sons, Incorporated, , 2024; ©2024
• ISBN: 9781394284344; 1394284349; 9781394284320; 1394284322
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (444 pages)
• Altri autori (Persone): LyashkoSergiy; LimniosN (Nikolaos)
• Disciplina: 530.0285
• Soggetti: Mathematical models; Engineering mathematics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: 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 carriers’ 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.
• Sommario/riassunto: This book, 'Computational Methods and Mathematical Modeling in Cyberphysics and Engineering Applications,' explores advanced mathematical techniques and computational methods applied in cyberphysical systems and engineering contexts. It delves into the Korteweg–de Vries equation, soliton solutions, and their perturbations, offering a comprehensive study of nonlinear WKB techniques and asymptotic soliton-like solutions. The book also covers the modeling of heterogeneous fluid dynamics, phase transitions, and porous media, alongside mathematical models for technological process control in ; industrial settings. Aimed at researchers and practitioners in mathematics and engineering, it provides insights into the application of complex mathematical frameworks for solving real-world engineering problems.