Related papers: Renormalization Group Method Applied to Kinetic Eq…
We derive generic relativistic hydrodynamical equations with dissipative effects from the underlying Boltzmann equation in a mechanical and systematic way on the basis of so called the renormalization-group (RG) method. A macroscopic frame…
We first give a comprehensive review of the renormalization group method for global and asymptotic analysis, putting an emphasis on the relevance to the classical theory of envelopes and on the importance of the existence of invariant…
The renormalization group (RG) method as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RG equation which is analogous to the Wilsonian…
We review our work on the application of the renormalization-group method to obtain first- and second-order relativistic hydrodynamics of the relativistic Boltzmann equation (RBE) as a dynamical system, with some corrections and new…
The renormalization group (RG) method is extended for global asymptotic analysis of discrete systems. We show that the RG equation in the discretized form leads to difference equations corresponding to the Stuart-Landau or Ginzburg-Landau…
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…
We develop a renormalization group (RG) procedure that includes important system-specific features. The key ingredient is to systematize the coarse graining procedure that generates the RG flow. The coarse graining technology comes from…
We present a numerical implementation of the renormalization group (RG) for partial differential equations, constructing similarity solutions and travelling waves. We show that for a large class of well-localized initial conditions,…
We show that renormalization group(RG) theory can be used to give an analytic description of the evolution of a perturbed KdV equation. The equations describing the deformation of its shape as the effect of perturbation are RG equations.…
In the present paper the Renormalization Group (RG) method is adopted as a tool for a constructive analysis of the properties of the Frobenius-Perron Operator. The renormalization group reduction of a generic symplectic map in the case,…
The field theoretic renormalization group is applied to a simple model of random walk on a rough fluctuating surface. We consider the Fokker--Planck equation for a particle in a uniform gravitational field. The surface is modelled by the…
We review the application of field-theoretic renormalization group (RG) methods to the study of fluctuations in reaction-diffusion problems. We first investigate the physical origin of universality in these systems, before comparing RG…
We review the renormalization group method applied to non-equilibrium dynamics by tracing the way how the hydrodynamic equations can be derived as reduced dynamics of the Boltzmann equation as a typical example.
The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG).Linear response is invoked to set up the…
It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations are analyzed. The amplitude equations…
The renormalization group (RG) method is one of the singular perturbation methods which is used in search for asymptotic behavior of solutions of differential equations. In this article, time-independent vector fields and time (almost)…
A non-perturbative and continuous definition of RG transformations as stochastic processes is proposed, inspired by the observation that the functional RG equations for effective Boltzmann factors may be interpreted as Fokker-Planck…
We develop a general framework in the renormalization-group (RG) method for extracting a mesoscopic dynamics from an evolution equation by incorporating some excited (fast) modes as additional components to the invariant manifold spanned by…
We study a generic problem of dissipative quantum mechanics, a small local quantum system with discrete states coupled in an arbitrary way (i.e. not necessarily linear) to several infinitely large particle or heat reservoirs. For both…
The renormalization group (RG) properties of quantum gravity are explored, using the vielbein and the spin connection as the fundamental field variables. The scale dependent effective action is required to be invariant both under space time…