Mathematical modeling through topological surgery and applications. (2018)

• Record Type: Book
• Further Information: Note: Stathis Antoniou.
• Authors: Antoniou, Stathis
• Contents: Intro; Supervisor's Foreword; Abstract; Acknowledgements; Contents; 1 Introduction; References; 2 Useful Mathematical Notions; 2.1 Topological Spaces; 2.2 Non-technical Definition of a Manifold; 2.3 Properties of Manifolds; 2.4 Examples of Manifolds; 2.4.1 1-Manifolds; 2.4.2 2-Manifolds; 2.4.3 3-Manifolds; 2.4.4 n-Balls and n-Spheres; 2.4.5 The Compactification of mathbbRn; 2.4.6 Product Spaces; 2.5 Defining Manifolds; 2.5.1 Hausdorff Space; 2.5.2 Bases of Topological Spaces; 2.5.3 The Rigorous Definition of a Manifold; 2.6 Homeomorphisms; 2.7 Embeddings; 2.8 The Idea of Topological Surgery 6.1 Solid 1-Dimensional Topological Surgery6.2 Solid 2-Dimensional Topological Surgery; 6.3 Modeling Phenomena Exhibiting Solid 2-Dimensional 0-Surgery; 6.4 Modeling Phenomena Exhibiting Solid 2-Dimensional 1-Surgery; References; 7 A Dynamical System Modeling Solid 2-Dimensional 0-Surgery; 7.1 The Dynamical System and Its Steady State Points; 7.2 Local Behavior and Numerical Simulations; 7.3 Connecting the Dynamical System with Solid 2-Dimensional 0-Surgery; References; 8 The Ambient Space S3; 8.1 Descriptions of S3; 8.1.1 Via mathbbR3; 8.1.2 Via Two 3-Balls; 8.1.3 Via Two Solid Tori 8.2 Connecting the Descriptions of S38.2.1 Via Corking; 8.2.2 Via Surgery; 8.3 Dynamical Systems Exhibiting the Topology of S3; 8.3.1 The 3-Dimensional Lotka-Volterra System; 8.3.2 The Pair of Linear Harmonic Oscillators; References; 9 Embedded Surgery; 9.1 Embedded 1-Dimensional Surgery; 9.2 Embedded 2-Dimensional Surgery; 9.3 Modeling Phenomena Exhibiting Embedded Solid 2-Dimensional Surgery; 9.3.1 A Topological Model for the Density Distribution in Black Hole Formation; 9.3.2 A Topological Model for the Formation of Tornadoes; 9.3.3 Embedded Solid 2-Dimensional 1-Surgery on M=D3
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 514/.34; Physics; Topological manifolds; Homeomorphisms; MATHEMATICS / Topology; Mathematics -- Topology; Science -- Cosmology; Science -- Mathematical Physics; Mathematics -- Mathematical Analysis; Topology; Relativity physics; Statistical physics; Nonlinear science; Mathematical physics; Topology; Statistical physics; Differentiable dynamical systems; Mathematical physics; Electronic books
• Languages: English
• ISBNs: 9783319970677; 3319970674
• Related ISBNs: 9783319970660; 3319970666
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed August 28, 2018).
• 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.