Entropy theory in hydraulic engineering : an introduction / / Vijay P. Singh

• Record Nr.: UNINA9910464293103321
• Autore: Singh V. P (Vijay P.)
• Pubbl/distr/stampa: Reston, Virginia : , : American Society of Civil Engineers, , 2014; ©2014
• ISBN: 1-68015-798-1; 0-7844-7825-2
• Descrizione fisica: 1 online resource (xv, 785 p.) : ill
• Disciplina: 627/.042
• Soggetti: Hydrodynamics; Hydraulics - Mathematics; Entropy; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
• Nota di contenuto: ""Contents""; ""Preface""; ""Chapter 1 Entropy Theory""; ""1.1 Overview of This Volume""; ""1.2 Entropy Concept""; ""1.3 Entropy Theory""; ""1.4 Types of Entropy""; ""1.5 Application of Entropy Theory to Hydraulic Engineering Problems""; ""1.6 Hypothesis on the Cumulative Distribution Function""; ""1.7 Methodology for Application of Entropy Theory""; ""Appendix 1.1""; ""Questions""; ""References""; ""Additional Reading""; ""Part 1: Velocity Distributions""; ""Chapter 2 One-Dimensional Velocity Distributions""; ""2.1 Preliminaries""; ""2.2 Derivation of One-Dimensional Velocity Distributions""; ""2.3 One-Dimensional Velocity Distribution with No Physical Constraint""""2.4 One-Dimensional Velocity Distribution with One Physical Constraint""; ""2.5 Testing of One-Physical-Constraint Velocity Distribution""; ""2.6 One-Dimensional Velocity Distribution with Two Physical Constraints""; ""2.7 One-Dimensional Velocity Distribution with Three Physical Constraints""; ""Appendix 2.1: Method of Lagrange Multipliers""; ""Questions""; ""References""; ""Additional Reading""; ""Chapter 3 Two-Dimensional Velocity Distributions""; ""3.1 Derivation ; of Velocity Distributions""; ""3.2 Construction of Isovels and Relation between (x, y) Coordinates and (r, s) Coordinates""""3.3 Estimation of Parameters of Velocity Distribution""; ""3.4 Maximum and Mean Velocities""; ""3.5 Comparison of Mean Velocity Estimates""; ""3.6 Alternative Method for Estimation of the Cross-Sectional Area Mean Velocity for New River Sites""; ""3.7 Derivation of 2-D Velocity Distribution Using a Mathematically Sound Coordinate System""; ""3.8 Trapezoidal Domain""; ""Appendix 3.1""; ""Appendix 3.2""; ""Questions""; ""References""; ""Additional Reading""; ""Chapter 4 Power Law and Logarithmic Velocity Distributions""""4.1 Preliminaries""; ""4.2 One-Dimensional Power Law Velocity Distribution""; ""4.3 One-Dimensional Prandtlâ€?von Karman Universal Velocity Distribution""; ""4.4 Two-Dimensional Power Law Velocity Distribution""; ""4.5 Two-Dimensional Prandtlâ€?von Karman Velocity Distribution""; ""4.6 Two-Dimensional Representation of Velocity Using a General Framework""; ""Questions""; ""References""; ""Additional Reading""; ""Chapter 5 Applications of Velocity Distributions""; ""5.1 Sampling Velocity Measurements""; ""5.2 Use of k[sub(1)]â€?Entropy Relation for Characterizing Open-Channel Flows""""5.3 Energy and Momentum Coefficients""; ""5.4 Shear Stress Distribution""; ""5.5 Relation between Maximum Velocity, Darcyâ€?s Friction Factor, and Entropy Number""; ""5.6 Discharge Measurements""; ""5.7 Determination of Discharge at Remote Locations""; ""5.8 Determination of Flow Depth Distribution""; ""5.9 Determination of Entropy Parameter from Hydraulic and Geometric Characteristics""; ""Questions""; ""References""; ""Additional Reading""; ""Chapter 6 Velocity Distribution in Pipe Flow""; ""6.1 Derivation of Velocity Distribution""

Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems / / Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini

• Record Nr.: UNINA9910481052303321
• Autore: Gangbo Wilfrid
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2010; ©2010
• ISBN: 1-4704-0610-1
• Descrizione fisica: 1 online resource (77 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 211, Number 993
• Disciplina: 515/.39
• Soggetti: Differential forms; Hamiltonian systems; Infinite-dimensional manifolds; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 211, Number 993 (third of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""Chapter 2. The topology on M and a differential calculus of curves""; ""2.1. The space of distributions""; ""2.2. The topology on M""; ""2.3. Tangent spaces and the divergence operator""; ""2.4. Analytic justification for the tangent spaces""; ""Chapter 3. The calculus of curves, revisited""; ""3.1. Embedding the geometry of RD into M""; ""3.2. The intrinsic geometry of M""; ""3.3. Embedding the geometry of M into (Cc)*""; ""3.4. Further comments""; ""Chapter 4. Tangent and cotangent bundles""; ""4.1. Push-forward operations on M and TM""""4.2. Differential forms on M""; ""4.3. Discussion""; ""Chapter 5. Calculus of pseudo differential 1-forms""; ""5.1. Green's formula for smooth surfaces and 1-forms""; ""5.2. Regularity and differentiability of pseudo 1-forms""; ""5.3. Regular forms and absolutely continuous curves""; ""5.4. Green's formula for annuli""; ""5.5. Example: 1-forms on the space of discrete measures""; ""5.6. Discussion""; ""Chapter 6. A symplectic foliation of M""; ""6.1. The group of Hamiltonian diffeomorphisms""; ""6.2. A symplectic foliation of M""; ""6.3. Algebraic properties of the symplectic distribution""""Chapter 7. The symplectic foliation as a Poisson structure""; ""7.1. Review of ; Poisson geometry""; ""7.2. The symplectic foliation of M, revisited""; ""Appendix A. Review of relevant notions of Differential Geometry""; ""A.1. Calculus of vector fields and differential forms""; ""A.2. Lie groups and group actions""; ""A.3. Cohomology and invariant cohomology""; ""A.4. The group of diffeomorphisms""; ""Bibliography""