LEADER 05027nam 22006615 450 001 9910743362603321 005 20251202165719.0 010 $a981-16-8189-9 010 $a981-16-8188-0 010 $a981-16-8189-9 024 7 $a10.1007/978-981-16-8189-9 035 $a(MiAaPQ)EBC6944952 035 $a(Au-PeEL)EBL6944952 035 $a(CKB)21459957600041 035 $a(PPN)262167654 035 $a(BIP)83742514 035 $a(BIP)81972302 035 $a(DE-He213)978-981-16-8189-9 035 $a(EXLCZ)9921459957600041 100 $a20220401d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometrical Formulation of Renormalization-Group Method as an Asymptotic Analysis $eWith Applications to Derivation of Causal Fluid Dynamics /$fby Teiji Kunihiro, Yuta Kikuchi, Kyosuke Tsumura 205 $a1st ed. 2022. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2022. 215 $a1 online resource (493 pages) 225 1 $aFundamental Theories of Physics,$x2365-6425 ;$v206 311 08$aPrint version: Kunihiro, Teiji Geometrical Formulation of Renormalization-Group Method As an Asymptotic Analysis Singapore : Springer Singapore Pte. Limited,c2022 9789811681882 320 $aIncludes bibliographical references and index. 327 $aNotion of Effective Theories in Physical Sciences -- Divergence and Secular Term in the Perturbation Series of Ordinary Differential Equations -- Traditional Resummation Methods -- Elementary Introduction of the RG method in Terms of the Notion of Envelopes -- Ei-Fujii-Kunihiro Formulation and Relation to Kuramoto?s reduction scheme -- Relation to the RG Theory in Quantum Field Theory -- Resummation of the Perturbation Series in Quantum Methods -- Illustrative Examples -- Slow Dynamics Around Critical Point in Bifurcation Phenomena -- Dynamical Reduction of A Generic Non-linear Evolution Equation with Semi-simple Linear Operator -- A Generic Case when the Linear Operator Has a Jordan-cell Structure -- Dynamical Reduction of Difference Equations -- Slow Dynamics in Some Partial Differential Equations -- Some Mathematical Formulae -- Dynamical Reduction of Kinetic Equations -- Relativistic First-Order Fluid Dynamic Equation -- Doublet Scheme and its Applications -- Relativistic Causal Fluid dynamic Equation -- Numerical Analysis of Transport Coefficients and Relaxation Times -- Reactive Multi-component Systems -- Non-relativistic Case and Application to Cold Atoms -- Summary and Future Prospects. 330 $aThis book presents a comprehensive account of the renormalization-group (RG) method and its extension, the doublet scheme, in a geometrical point of view. It extract long timescale macroscopic/mesoscopic dynamics from microscopic equations in an intuitively understandable way rather than in a mathematically rigorous manner and introduces readers to a mathematically elementary, but useful and widely applicable technique for analyzing asymptotic solutions in mathematical models of nature. The book begins with the basic notion of the RG theory, including its connection with the separation of scales. Then it formulates the RG method as a construction method of envelopes of the naive perturbative solutions containing secular terms, and then demonstrates the formulation in various types of evolution equations. Lastly, it describes successful physical examples, such as stochastic and transport phenomena including second-order relativistic as well as nonrelativistic fluid dynamics with causality and transport phenomena in cold atoms, with extensive numerical expositions of transport coefficients and relaxation times. Requiring only an undergraduate-level understanding of physics and mathematics, the book clearly describes the notions and mathematical techniques with a wealth of examples. It is a unique and can be enlightening resource for readers who feel mystified by renormalization theory in quantum field theory. 410 0$aFundamental Theories of Physics,$x2365-6425 ;$v206 606 $aMathematical physics 606 $aNonlinear optics 606 $aMathematical Methods in Physics 606 $aTheoretical, Mathematical and Computational Physics 606 $aMathematical Physics 606 $aNonlinear Optics 615 0$aMathematical physics. 615 0$aNonlinear optics. 615 14$aMathematical Methods in Physics. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aMathematical Physics. 615 24$aNonlinear Optics. 676 $a530.133 700 $aKunihiro$b Teiji$01426686 702 $aKikuchi$b Yuta 702 $aTsumura$b Kyosuke 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910743362603321 996 $aGeometrical formulation of renormalization-group method as an asymptotic analysis$93558780 997 $aUNINA