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OverviewFull Product DetailsAuthor: Teiji Kunihiro , Yuta Kikuchi , Kyosuke TsumuraPublisher: Springer Verlag, Singapore Imprint: Springer Verlag, Singapore Edition: 1st ed. 2022 Volume: 206 Weight: 0.765kg ISBN: 9789811681912ISBN 10: 9811681910 Pages: 486 Publication Date: 04 April 2023 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPART I Introduction to Renormalization Group (RG) Method 1 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-Kunihiro Formulation 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 Model 9 Slow Dynamics Around Critical Point in Bifurcation Phenomena 10 Dynamical Reduction of A Generic Non-linear Evolution Equation with Semi-simple Linear Operator11 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 Formulae PART III Application to Extracting Slow Dynamics of Non-equilibrium Phenomena 15 Dynamical Reduction of Kinetic Equations 15.1 Derivation of Boltzmann Equation from Liouville Equation 15.2 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 General Formulation 17.2 Lorentz Model Revisited 18 Relativistic Causal Fluid dynamic Equation 19 Numerical Analysis of Transport Coefficients and Relaxation Times 20 Reactive-Multi-component Systems 21 Non-relativistic Case and Application to Cold Atoms PART IV Summary and Future Prospect 22 Summary and Future ProspectsReviewsAuthor InformationTeiji Kunihiro is Professor Emeritus at Kyoto University in Japan and specializes in research in nuclear and hadron physics theory and mathematical physics. He received his Doctor of Science in Physics from Kyoto University in 1981. After serving as Associate Professor and Professor at Ryukoku University, he was appointed as Professor at the Yukawa Institute for Theoretical Physics, Kyoto University in 2000, and was Vice Director of the institute from 2006 to 2007, before moving to the Department of Physics in 2008. Yuta Kikuchi is a Goldhaber Fellow at Brookhaven National Laboratory in the USA at the completion of the present book, and appointed to a scientist at Cambridge Quantum Computing starting in 2022. He received his Doctor of Science in Physics from Kyoto University in 2018. He was awarded the Research Fellowship for Young Scientists by Japan Society for the Promotion of Science (JSPS) in 2015, and the Goldhaber distinguished fellowship by Brookhaven National Laboratory in 2020. He currently focuses on designing quantum algorithms for near-term quantum computing. Kyosuke Tsumura is Primary Research Scientist at the Analysis Technology Center, Fujifilm Corporation in Japan. He joined the Analysis Technology Center as a Researcher in 2006 and was promoted to current position. He received his Doctor of Science in Physics from Kyoto University in 2013. He is Leader of a project developing a novel computational method for efficient drug design. Tab Content 6Author Website:Countries AvailableAll regions |
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