1 - 10 of 16 Chapters
[The significant roles played by the notion of effective theories in physical sciences and the renormalization groups are indicated, by referring to Galileo. Then the purpose and structure of the monograph is described with comments on their physical and mathematical significance.]
[Using simple differential equations, we introduce the notion of secular terms, and then demonstrate that secular terms are to appear in general in the naïve perturbation series of solutions of ordinary differential equations. This chapter also constitutes an elementary introduction to some...
[In this chapter, we present some conventional methods to give a partially resummed formula of the perturbative solutions that are valid in a global domain by circumventing the appearance of secular terms. It will be found that all the methods consist of rearranging the equation by introducing...
[After an account is given of the classical theory of envelopes of curves, the so-called renoramalisation group (RG) method is introduced and formulated geometrically on the basis of the theory of envelopes of curves: The central ingredient of the method is identified with a construction of the...
[We formulate the RG method as a powerful reduction theory of dynamical systems in a way that the Kuramoto’s reduction scheme and the center-manifold reduction theory that consist of the construction of the attractive/invariant manifold and the reduced equations on it naturally emerge.]
[The renormalization-group method (RG) method is applied to extract the slow dynamics around a bifurcation point of the Lorenz model and that around the Hopf-bifurcation point in Brusselator with and without a diffusion term. Then a couple of examples are analyzed in the RG method, the...
[The RG method is applied to a derivation of the Fokker-Planck equations and its adiabatic reduction for the system with fast and slow variables as well as the stochastic variable.]
[On the basis of the identification of the fluid dynamics with the slow dynamics of the kinetic equation in the asymptotic regime after a long time, we apply the RG method to derive the fluid dynamics with dissipative effects for the non-relativistic system, i.e., the Navier-Stokes equation and...
[We present a general framework in the RG method to reduce microscopic dynamics to mesoscopic dynamics, which occupies an intermediate level between the descriptions by the microscopic dynamics and macroscopic dynamics. This framework in the RG method is called the doublet scheme. To demonstrate...
[We present the fundamental problems in the theory of relativistic fluid dynamics, whereby argue the need of a derivation of relativistic dissipative fluid dynamic equation from the underlying microscopic theory such as the relativistic Boltzmann equation (RBE). Then after some of basic...
Read and print from thousands of top scholarly journals.
Continue with Facebook
Log in with Microsoft
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Sign Up Log In
To subscribe to email alerts, please log in first, or sign up for a DeepDyve account if you don’t already have one.
To get new article updates from a journal on your personalized homepage, please log in first, or sign up for a DeepDyve account if you don’t already have one.