Discrete and continuous models in the theory of networks. (2020)

• Record Type: Book
• Further Information: Note: Fatihcan M. Atay, Pavel B. Kurasov, Delio Mugnolo, editors.
• Other Names: Atay, Fatihcan M; Kurasov, P; Mugnolo, Delio
• Contents: Intro -- Preface -- Contents -- Stability Matters for Reaction-Diffusion-Equations on Metric Graphs Under the Anti-Kirchhoff Vertex Condition -- 1 Metric Graphs -- 2 Stationary Solutions -- 3 Stability -- 4 Nonlinearities Vanishing at 0 -- 5 Constant Nonlinearities -- 6 Odd Nonlinearities -- 7 Loops -- References -- Many-Particle Quantum Graphs: A Review -- 1 Introduction -- 2 Preliminaries -- 2.1 One-Particle Quantum Graphs -- 2.2 Many-Particle Kinematics -- 3 Singular Pair Interactions -- 3.1 Vertex-Induced Singular Interactions -- 3.2 Contact Interactions 3.3 A Lieb-Liniger Model on Graphs -- 4 Bose-Einstein Condensation -- 4.1 Free Bosons -- 4.2 Interacting Bosons -- 5 Exactly Solvable Many-Particle Quantum Graphs -- 6 Many-Particle Models on a Quantum Wire -- 6.1 The Model Without Hard-Wall Binding Potential -- 6.2 The Model with a Hard-Wall Binding Potential -- 6.3 Random Singular Pair Interactions -- 6.4 The Condensation of Electron Pairs in a Quantum Wire -- 6.5 The Impact of Surface Defects on a Condensate of Electrons -- References -- Deterministic and Stochastic Mean-Field SIRS Models on Heterogeneous Networks -- 1 Introduction 2 The Deterministic Model -- 3 The Critical Threshold -- 3.1 Computing the Meta-Stable State -- 3.2 The Heterogeneous Case -- 4 Simulations for the Deterministic Heterogeneous Case -- 5 Stochastic SIRS Model -- 6 Conclusion -- References -- Kreĭn Formula and Convergence of Hamiltonians with Scaled Potentials in Dimension One -- 1 Introduction -- 2 Main Result -- 3 Kreĭn resolvent Formula -- 3.1 Operators in the Outer Space -- 3.2 Operators in the Inner Space -- 3.3 Operator in the Full Space -- 4 Limit of R(z) -- 4.1 Limiting Hamiltonian: Generic Case -- 4.2 Limiting Hamiltonian: Non-generic Case 4 The Asymptotic Expansion of the Regularized Trace of the Heat Kernel -- Appendix 1: Notations -- Appendix 2: Integral Identities for the K0-Macdonald Function -- 2.1 A Converse Watson Lemma -- References -- Modeling Dynamic Coupling in Social Interactions -- 1 Introduction -- 2 Coupling and Information Exchange -- 3 Dynamic Exchanges and Coupling in Sensorimotor Synchronisation -- 4 Quantifying Interactive Coupling -- 5 Applying Dynamic Timecourse Models to Sensorimotor Synchronisation Data -- 5.1 Nature of the Partner -- 5.2 Nature of the Information Being Exchanged
• Publisher Details: Cham : Birkhäuser
• Publication Date: 2020
• Copyright Date: 2020
• Extent: 1 online resource (357 pages)
• Subjects: 511/.5; Graph theory; Mathematical analysis; Ergodic theory; Calculus & mathematical analysis; Nonlinear science; Dynamics & vibration; Functional analysis & transforms; Mathematics -- Mathematical Analysis; Technology & Engineering -- Mechanical; Mathematics -- Functional Analysis; Ergodic theory; Graph theory; Mathematical analysis; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030440978
• Related ISBNs: 9783030440961
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.