{"product_id":"geometrical-formulation-of-renormalization-group-method-as-an-asymptotic-analysis-with-applications-to-derivation-of-causal-fluid-dynamics-9789811681882","title":"Geometrical Formulation of Renormalization-Group Method as an Asymptotic Analysis: With Applications to Derivation of Causal Fluid Dynamics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book presents a comprehensive account of the  renormalization-group (RG) method and its extension, the doublet scheme, in a geometrical point of view.\u003c\/p\u003e \u003cp\u003e It extract long timescale macroscopic\/mesoscopic dynamics from microscopic equations in an intuitively understandable way rather than in a mathematically rigorous manner and introduces readers to a mathematically elementary, but useful and widely applicable technique for analyzing asymptotic solutions in mathematical models of nature.\u003c\/p\u003e \u003cp\u003e The book begins with the basic notion of the RG theory, including its connection with the separation of scales. Then it formulates the RG method as a construction method of envelopes of the naive perturbative solutions containing secular terms, and then demonstrates the formulation in various types of evolution equations. Lastly, it describes successful physical examples, such as stochastic and transport phenomena including second-order relativistic as well as nonrelativistic fluid dynamics with causality and  transport phenomena in cold atoms, with extensive numerical expositions of transport coefficients and relaxation times.\u003c\/p\u003e \u003cp\u003e Requiring only an undergraduate-level understanding of physics and mathematics, the book clearly describes the notions and mathematical techniques with a wealth of examples. It is a unique and can be enlightening resource for readers who feel mystified by renormalization theory in quantum field theory.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePART I           Introduction to Renormalization Group (RG) Method  \u003c\/p\u003e  \u003cp\u003e1          Introduction: Notion of Effective Theories in Physical Sciences\u003c\/p\u003e  \u003cp\u003e2          Divergence and Secular Term in the Perturbation Series of Ordinary Differential Equations\u003c\/p\u003e  \u003cp\u003e3           Traditional Resummation Methods\u003c\/p\u003e  \u003cp\u003e3.1          Reductive Perturbation Theory\u003c\/p\u003e  \u003cp\u003e3.2          Lindstedt's Method\u003c\/p\u003e  \u003cp\u003e3.3          Krylov-Bogoliubov-Mitropolsky's Method for Nonlinear Oscillators\u003c\/p\u003e  \u003cp\u003e4          Elementary Introduction of the RG method in Terms of the Notion of Envelopes\u003c\/p\u003e  \u003cp\u003e4.1          Notion of Envelopes of Family of Curves Adapted for  a Geometrical Formulation of  the RG Method\u003c\/p\u003e  \u003cp\u003e4.2          Elementary Examples: Damped Oscillator and Boundary-Layer Problem\u003c\/p\u003e  \u003cp\u003e5          General Formulation and Foundation of the RG Method: Ei-Fujii-Kunihiro \u003c\/p\u003e  \u003cp\u003eFormulation and Relation to Kuramoto’s reduction scheme\u003c\/p\u003e  \u003cp\u003e6          Relation to the RG Theory in Quantum Field Theory\u003c\/p\u003e  \u003cp\u003e7          Resummation of the Perturbation Series in Quantum Methods\u003c\/p\u003e  \u003cp\u003ePART II     Extraction of Slow Dynamics Described by Differential and Difference Equations\u003c\/p\u003e  \u003cp\u003e8          Illustrative Examples\u003c\/p\u003e  \u003cp\u003e8.1          Rayleigh\/Van der Pol equation and jumping phenomena\u003c\/p\u003e  \u003cp\u003e8.2          Lotka-Volterra Equation\u003c\/p\u003e  \u003cp\u003e8.3          Lorents Model \u003c\/p\u003e  \u003cp\u003e9          Slow Dynamics Around Critical Point in Bifurcation Phenomena\u003c\/p\u003e  10       Dynamical Reduction of A Generic Non-linear Evolution Equation with Semi-simple Linear Operator\u003cp\u003e11       A Generic Case when the Linear Operator Has a Jordan-cell Structure\u003c\/p\u003e  \u003cp\u003e12       Dynamical Reduction of Difference Equations (Maps)\u003c\/p\u003e  \u003cp\u003e13       Slow Dynamics in Some Partial Differential Equations\u003c\/p\u003e  \u003cp\u003e13.1       Dissipative One-Dimensional Hyperbolic Equation\u003c\/p\u003e  \u003cp\u003e13.2       Swift-Hohenberg Equation\u003c\/p\u003e  \u003cp\u003e13.3       Damped Kuramoto-Shivashinsky Equation\u003c\/p\u003e  \u003cp\u003e13.4       Diffusion in Porus Medium --- Barrenblatt Equation\u003c\/p\u003e  \u003cp\u003e14       Appendix: Some Mathematical Formulae\u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e  \u003cp\u003ePART III       Application to Extracting Slow Dynamics of Non-equilibrium Phenomena\u003c\/p\u003e  \u003cp\u003e15       Dynamical Reduction of Kinetic Equations\u003c\/p\u003e  \u003cp\u003e15.1       Derivation of Boltzmann Equation from Liouville Equation \u003c\/p\u003e  \u003cp\u003e15.2       Derivation of the Fokker-Planck (FP) Equation from Langevin Equation\u003c\/p\u003e  \u003cp\u003e15.3       Adiabatic Elimination of Fast Variables in FP Equation: Derivation of Generalized Kramers Equations\u003c\/p\u003e  \u003cp\u003e16       Relativistic First-Order Fluid Dynamic Equation\u003c\/p\u003e  \u003cp\u003e17       Doublet Scheme and its Applications\u003c\/p\u003e  \u003cp\u003e17.1       General Formulation\u003c\/p\u003e  \u003cp\u003e17.2        Lorentz Model Revisited\u003c\/p\u003e  \u003cp\u003e18       Relativistic Causal Fluid dynamic Equation\u003c\/p\u003e  \u003cp\u003e19       Numerical Analysis of Transport Coefficients and Relaxation Times\u003c\/p\u003e  \u003cp\u003e20       Reactive-Multi-component Systems\u003c\/p\u003e  \u003cp\u003e21       Non-relativistic Case and Application to Cold Atoms\u003c\/p\u003e  \u003cp\u003ePART IV        Summary and Future Prospect\u003c\/p\u003e  \u003cp\u003e22       Summary and Future Prospects\u003c\/p\u003e","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":53518304084311,"sku":"9789811681882","price":113.99,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/geometrical-formulation-of-renormalization-group-method-as-an-asymptotic-analysis-with-applications-to-derivation-of-causal-fluid-dynamics-9789811681882","provider":"Book Curl","version":"1.0","type":"link"}