{ "item_title" : "Geometrical Formulation of Renormalization-Group Method as an Asymptotic Analysis", "item_author" : [" Teiji Kunihiro", "Yuta Kikuchi", "Kyosuke Tsumura "], "item_description" : "PART I Introduction to Renormalization Group (RG) Method1 Introduction: Notion of Effective Theories in Physical Sciences 2 Divergence and Secular Term in the Perturbation Series of Ordinary Differential Equations 3 Traditional Resummation Methods 3.1 Reductive Perturbation Theory 3.2 Lindstedt's Method 3.3 Krylov-Bogoliubov-Mitropolsky's Method for Nonlinear Oscillators 4 Elementary Introduction of the RG method in Terms of the Notion of Envelopes 4.1 Notion of Envelopes of Family of Curves Adapted for a Geometrical Formulation of the RG Method 4.2 Elementary Examples: Damped Oscillator and Boundary-Layer Problem 5 General Formulation and Foundation of the RG Method: Ei-Fujii-KunihiroFormulation and Relation to Kuramoto's reduction scheme 6 Relation to the RG Theory in Quantum Field Theory 7 Resummation of the Perturbation Series in Quantum Methods PART II Extraction of Slow Dynamics Described by Differential and Difference Equations 8 Illustrative Examples 8.1 Rayleigh/Van der Pol equation and jumping phenomena 8.2 Lotka-Volterra Equation 8.3 Lorents Model9 Slow Dynamics Around Critical Point in Bifurcation Phenomena 10 Dynamical Reduction of A Generic Non-linear Evolution Equation with Semi-simple Linear Operator 11 A Generic Case when the Linear Operator Has a Jordan-cell Structure 12 Dynamical Reduction of Difference Equations (Maps) 13 Slow Dynamics in Some Partial Differential Equations 13.1 Dissipative One-Dimensional Hyperbolic Equation 13.2 Swift-Hohenberg Equation 13.3 Damped Kuramoto-Shivashinsky Equation 13.4 Diffusion in Porus Medium --- Barrenblatt Equation 14 Appendix: Some Mathematical FormulaePART III Application to Extracting Slow Dynamics of Non-equilibrium Phenomena 15 Dynamical Reduction of Kinetic Equations 15.1 Derivation of Boltzmann Equation from Liouville Equation15.2 Derivation of the Fokker-Planck (FP) Equation from Langevin Equation 15.3 Adiabatic Elimination of Fast Variables in FP Equation: Derivation of Generalized Kramers Equations 16 Relativistic First-Order Fluid Dynamic Equation 17 Doublet Scheme and its Applications 17.1 ", "item_img_path" : "https://covers3.booksamillion.com/covers/bam/9/81/168/188/9811681880_b.jpg", "price_data" : { "retail_price" : "169.99", "online_price" : "169.99", "our_price" : "169.99", "club_price" : "169.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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