Methods of mathematical modelling and computation for complex systems / / Jagdev Singh [and four others], editors

• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©2022
• Descrizione fisica: 1 online resource (435 pages)
• Disciplina: 003
• Soggetto topico: System analysis - Mathematics
• Persona (resp. second.): SinghJagdev
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Contents -- About the Editors -- On the Diffusion with Decaying Time-Dependent Diffusivity: Formulations and Approximate Solutions Pertinent to Diffusion in Concretes -- 1 Introduction -- 1.1 General Assumptions -- 1.2 Common Approaches in Modelling and Solutions -- 2 Motivation of This Study -- 2.1 Aim and Chapter Organization -- 3 Existing Functional Relationships of D(t): A Brief Overview -- 3.1 Singular (Power-Law) Time Dependence of D(t) -- 3.2 Non-singular Forms of D(t) -- 4 New Forms of D(t) and Method of Approximate Solutions -- 4.1 New Non-singular Forms of D(t) -- 4.2 Integral-Balance Method -- 5 Approximate Solutions of (4) with Different D(t) -- 5.1 Solutions with D1(t) -- 5.2 Solutions with D2(t) -- 5.3 Solutions with D3(t) -- 5.4 Numerical Experiments with the Approximate Solutions -- 5.5 Comparative Study with Non-singular D(t) From Literature Sources -- 5.6 Solution Optimization -- 6 Outcomes of the Approximate Solutions -- 6.1 Causality of Dynamic Models: Basic Principles -- 6.2 Subdiffusion Front Propagation: Two Formal Explanations -- 6.3 Finite Penetration Depth and Finite Speed of the Front -- 7 Final Comments -- References -- Laminar Convection of Power-Law Fluids in Differentially Heated Closed Region: CFD Analysis -- 1 Introduction -- 2 Numerical Method -- 2.1 Governing Equations -- 2.2 Boundary Conditions -- 2.3 Grid Dependency -- 2.4 Benchmark Comparison -- 3 Discussion and Computational Results -- 3.1 The Effects of Rayleigh Number -- 3.2 Bingham Fluids -- 3.3 Pseudo Plastic Fluid -- 3.4 Dilatant Fluids -- 4 Conclusions -- References -- Mathematical Perspective of Hodgkin-Huxley Model and Bifurcation Analysis -- 1 Neurological Backgrounds -- 1.1 How Does Neuron Work? -- 1.2 How Does a Neuron Fire? -- 1.3 How Neurons Communicate? -- 2 Hodgkin and Huxley Model (HH Model) -- 3 Review of HH Model:. ; 4 Modified HH Models -- 5 Comparative Studies of Modified HH Models -- 5.1 Stability Analysis -- 5.2 Comparative Study of Time Series Analysis -- 5.3 Comparative Study of One-Parameter Bifurcation -- 5.4 Comparative Study of Two-Parameter Bifurcation -- 6 Results -- 7 Discussions -- References -- Mathematical Analysis of Two Unequal Collinear Cracks in a Piezo-Electro-Magnetic Media -- 1 Introduction -- 2 Basic Equations for Piezoelectromagnetic Media -- 2.1 Crack Face Boundary Conditions -- 3 Fundamental Formulation and Solution Methodology -- 4 Statement of the Problem -- 5 Solution of the Problem -- 6 Applications -- 6.1 Crack Opening Displacement (COD) -- 6.2 Crack Opening Potential Drop (COPD) -- 6.3 Crack Opening Induction Drop (COID) -- 6.4 Stress Intensity Factor (SIF) -- 6.5 Electric Displacement Intensity Factor (EDIF) -- 6.6 Magnetic Induction Intensity Factor (MIIF) -- 7 Case Study -- 7.1 Effect of Inter-Crack Distance -- 7.2 Effect of Crack Length -- 8 Conclusions -- References -- Advanced Analysis of Local Fractional Calculus Applied to the Rice Theory in Fractal Fracture Mechanics -- 1 Introduction -- 2 The LFD and LFI in the Fractional Real and Complex Sets -- 2.1 The LFD and LFI in the Fractional Real Set -- 2.2 The LFD and LFI in the Fractional Complex Set -- 3 Analysis of the Local Fractional Differential and Integral Equations -- 3.1 The Uniqueness of the Solutions of the Local Fractional Differential Equations -- 3.2 The Uniqueness of the Solutions of the Local Fractional Integral Equations -- 4 Local Fractional Inequalities -- 5 The Series and Transforms Involving the Mittag-Leffler Function Defined on Cantor Sets -- 5.1 The Fourier Type Series Via the Mittag-Leffler Function Defined On Cantor Sets -- 5.2 The Fourier Type Transform Via Mittag-Leffler Function Defined on Cantor Sets. ; 6 Local Fractional Vector Calculus with an Application in Fractal Fracture Mechanics -- 6.1 Local Fractional Vector Calculus -- 6.2 An Application to Rice Theory in Fractal Mechanics -- 7 Conclusion -- References -- General Fractional Calculus with Nonsingular Kernels: New Prospective on Viscoelasticity -- 1 Introduction -- 2 Mathematical Tools -- 2.1 The Special Functions with Power Law -- 2.2 GFC in a Kernel Function -- 2.3 FC Within the Singular Power-Law Kernel -- 2.4 GFC with the Nonsingular Power-Law Kernel -- 2.5 GFC with the Nonsingular Mittag-Leffler Function Kernel -- 2.6 GFC with the Nonsingular Wiman Kernel -- 2.7 GFC with the Nonsingular Prabhakar Kernel -- 3 The Rheological Models with GFCs Involving the Nonsingular Kernels -- 3.1 Complex Phenomena in Viscoelasticity -- 3.2 The Viscoelastic Elements with GFDs -- 3.3 The Maxwell Models with GFDs -- 3.4 The Voigt Models with GFDs -- 4 Conclusion -- References -- Group Dynamical Systems on C*-Algebras Generated by Countable Infinitely Many Semicircular Elements -- 1 Introduction -- 1.1 Background -- 1.2 Motivation -- 1.3 Overview -- 2 Preliminaries -- 2.1 Free Probability -- 2.2 Semicircularity -- 3 Catalan Numbers -- 4 Free Distributions of Multi Semicircular Elements -- 4.1 Free-Distributional Data (13) of ρ -- 4.2 Free-Distributional Data (14) of ρ -- 4.3 The Joint Free Distribution ρx1,...,xN -- 5 A C*-Probability Space ( mathfrakX, ) Generated by | mathbbN| -Many Semicircular Elements -- 5.1 Free-Homomorphisms -- 5.2 A C*-Probability Space ( mathfrakX, midmathfrakX) -- 5.3 Free-Distributional Data on mathfrakX -- 6 Free-Isomorphisms on mathfrakX -- 6.1 Shifts on mathbbZ -- 6.2 Integer Shifts on mathfrakX -- 6.3 Free-Isomorphic Relations on mathfrakX -- 7 A Group Dynamical System ( λ, ΛmathfrakX, α) -- 7.1 A Group C*-Dynamical System Γ=( λ, ΛmathfrakX, α). ; 7.2 The Γ-Dynamical Algebra mathbbXΓ of λ -- 8 Free Probability on mathbbXΓ -- 8.1 Free Probability on ΛmathfrakX = ( ΛmathfrakX, τ) -- 8.2 Free-Distributional Data on mathbbXΓ -- References -- Lie Group Theory for Nonlinear Fractional K(m, n) Type Equation with Variable Coefficients -- 1 Introduction -- 2 Lie Symmetry Analysis Method for FPDEs -- 3 Fractional Lie Symmetries for Time-Fractional K(m, n) -- 4 Fractional Lie Symmetries for Time-Fractional K(2, 3) -- 5 Reduced Equations and Invariant Solution of Eq. (20) -- 6 Conclusion -- References -- Generalized Rayleigh Wave Propagation in Heterogeneous Substratum Over Homogeneous Half-Space Under Gravity -- 1 Introduction -- 2 Formulation of the Problem -- 2.1 Equations of Motion and Solution for Upper Layer -- 2.2 Equations of Motion and Solution for Half Space -- 3 Boundary Conditions -- 3.1 Particular Cases -- 4 Results and Discussions -- 5 Conclusion -- References -- On Defining Trigonometric Box Spline-Like Surface on Type-I Triangulation -- 1 Introduction -- 2 Trigonometric Spline Surface on Arbitrary Topology -- 3 Construction of the New Non-stationary Subdivision Scheme -- 3.1 Construction of the Scheme -- 3.2 Regular Subdivision Rules -- 3.3 Subdivision Surface -- 4 Convergence Analysis -- 5 Application of the Proposed Scheme -- 6 Conclusion -- References -- Mathematical Modelling for Perishable Product Supply Chain Under Inflation and Variable Lead Time -- 1 Introduction -- 2 Literature Review -- 3 Research Gap -- 4 The Model Framework -- 5 Result and Discussion -- 5.1 Future Scope and Limitations of the Research Work -- 6 Conclusion -- References -- Mexican Hat Wavelet Transform and Its Applications -- 1 Introduction -- 2 Necessary Conditions for Mexican Hat Wavelet and MHWST -- 3 Sufficient Conditions for Mexican Hat Wavelet and MHWST -- References. ; Fractal Fractional Derivative Operator Method on MCF-7 Cell Line Dynamics -- 1 Introduction -- 2 Mathematical Analysis of the Models -- 2.1 Preliminaries -- 2.2 Uniqueness and Continuous Dependence of the Solution -- 2.3 Physiological Level for the Dynamics -- 2.4 Asymptotic Stability Conditions for the Dynamics -- 3 Construction of the Fractal Fractional Operator Numerical Method -- 4 Numerical Results and Discussions -- 5 Conclusion -- References -- The Exponentiated Half Logistic-Topp-Leone-G Power Series Class of Distributions: Model, Properties and Applications -- 1 Introduction -- 2 The Model, Sub-Classes and Properties -- 2.1 The Model -- 2.2 Quantile Function -- 2.3 Expansion of Density -- 2.4 Moments and Generating Function -- 2.5 Conditional Moments -- 2.6 Mean Deviation, Lorenz and Bonferroni Curves -- 2.7 Order Statistics and Rényi Entropy -- 2.8 Maximum Likelihood Estimation -- 3 Some Special Classes of the EHL-TL-GPS Class of Distributions -- 3.1 Exponentiated Half Logistic Topp-Leone-Log-Logistic Power Series (EHL-TL-LLoGPS) Class of Distributions -- 3.2 Exponentiated Half Logistic-Topp-Leone-Weibull Power Series (EHL-TL-WPS) Class of Distributions -- 4 Simulation Study -- 5 Applications -- 5.1 Guinea Pigs Survival Times Data -- 5.2 Skin Folds Data -- 6 Concluding Remarks -- References -- Fixed Points of Multivalued (αast-φ)-Contractions and Metric Transforms -- 1 Introduction and Preliminaries -- 2 Extensions by Using Multivalued ( αast-φ) Contractions -- 3 Generalized (αast-φ) Multivalued Contractions -- References -- Approximation of Signals Via Different Summability Means with Effects of Gibbs Phenomenon -- 1 Introduction and Preliminaries -- 2 Definitions and Motivation -- 3 Classical Approximation Theorems -- 4 Statistical Korovkin-Type Approximation Results -- 5 Effects of Gibbs Phenomenon. ; 6 Concluding Remarks and Observations.
• Titolo autorizzato: Methods of mathematical modelling and computation for complex systems
• ISBN: 3-030-77169-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910522933103321
• Lo trovi qui: Univ. Federico II
• Serie: Studies in systems, decision and control ; ; Volume 373.