A Renormalization Group Method for Nonlinear Oscillators

We present a new approach for finding the asymptotic solution of certain weakly nonlinear oscillator equations. In particular, we develop a simplified version of the renormalization group method of Chen, et al. to obtain higher-order approximations on longer time intervals than are typically provided by averaging and two-timing. The technique, which has much greater potential, is illustrated on three challenging examples from the literature for which better than usual asymptotic solutions are obtained.     

Renormalization Group and the Ricci Flow

We discuss from a geometric point of view the connection between the renormalization group flow for non–linear sigma models and the Ricci flow. This offers new perspectives in providing a geometrical landscape for 2D quantum field theories. In particular we argue that the structure of Ricci flow singularities suggests a natural way for extending, beyond the weak coupling regime, the embedding of the Ricci flow into the renormalization group flow.     

A Renormalization Group Method by Harmonic Extensions and the Classical Dipole Gas

In this paper, we develop a new renormalization group method, which is based on conditional expectations and harmonic extensions, to study functional integrals of small perturbations of Gaussian fields. In this new method, one integrates Gaussian fields inside domains at all scales conditioning on the fields outside these domains, and by the variation principle solves local elliptic problems. It does not rely on an a priori decomposition of the Gaussian covariance. We apply this method to the model of classical dipole gas on the lattice, and show that the scaling limit of the generating function with smooth test functions is the generating function of the renormalized Gaussian free field.     

Renormalization Group and Stochastic PDEs

We develop a renormalization group (RG) approach to the study of existence and uniqueness of solutions to stochastic partial differential equations driven by space-time white noise. As an example, we prove well-posedness and independence of regularization for the \({\phi^4}\) model in three dimensions recently studied by Hairer and Catellier and Chouk. Our method is “Wilsonian”: the RG allows to construct effective equations on successive space-time scales. Renormalization is needed to control the parameters in these equations. In particular, no theory of multiplication of distributions enters our approach.     

Holographic Renormalization Group Flows

Theoretical and Mathematical Physics - We briefly review recent applications of holographic renormalization group flow equations in a hot and dense quark-gluon plasma (QGP). We especially focus on...     

Singularly Perturbed Renormalization Group Method and Its Significance in Dynamical Systems Theory

In this paper,we mainly investigate three topics on the renormaliza-tion group(RG)method to singularly perturbed problems:1)We will present an explicit strategy...     

One Property of the Renormalization Group Operator

We use an isotropic ferromagnet as an example to show that the renormalization group operator can be interpreted as an evolution operator for a system of spins evolving with an increase of the reduced temperature, i.e., as the order operator of the system.     

The Homotopy Perturbation Renormalization Group Method to Solve the WKB Problem with Turn Points

In this paper, we give the homotopy perturbation renormalization group method, this is a new method for turning point problem. Using this method, the independent variables are introduced by transformation without introducing new related variables and no matching is needed. The WKB approximation method problem can be solved.     

Holographic Renormalization Group Flow in Anisotropic Matter

Theoretical and Mathematical Physics - We consider holographic renormalization group flow equations in an anisotropic quark—gluon plasma and present anisotropic solutions for some special cases.     

On the Renormalization Group Approach to Perturbation Theory for PDEs

We investigate the rigorous application of the renormalization group method to (singular) perturbation theory for nonlinear partial differential equations. As a paradigm, we consider the concrete example of the nonlinear Schrödinger equation with quadratic nonlinearity in three spatial dimensions. We obtain an approximate solution using the RG method together with an estimate of the difference between the true and approximate solutions. Our analysis applies to cases where (space–time) resonances are present.     

The Renormalization Group According to Balaban III. Convergence

This is an expository account of Balaban’s approach to the renormalization group. The method is illustrated with a treatment of the ultraviolet problem for the scalar \({\phi^4}\) model on a toroidal lattice in dimension d = 3. In this third paper we demonstrate convergence of the expansion and complete the proof of a stability bound.     

Zone Structure of the Renormalization Group Flow in a Fermionic Hierarchical Model

The Gaussian part of the Hamiltonian of the four-component fermion model on a hierarchical lattice is invariant under the block-spin transformation of the renormalization group with a given degree of normalization (the renormalization group parameter). We describe the renormalization group transformation in the space of coefficients defining the Grassmann-valued density of a free measure as a homogeneous quadratic map. We interpret this space as a two-dimensional projective space and visualize it as a disk. If the renormalization group parameter is greater than the lattice dimension, then the unique attractive fixed point of the renormalization group is given by the density of the Grassmann delta function. This fixed point has two different (left and right) invariant neighborhoods. Based on this, we classify the points of the projective plane according to how they tend to the attracting point (on the left or right) under iterations of the map. We discuss the zone structure of the obtained regions and show that the global flow of the renormalization group is described simply in terms of this zone structure.     

复杂系统演化方程的重正化群解研究

很多复杂系统本身具有长大倾向导致微观系统会表现出向宏观发展的趋势.而对于具有多层次多要素的复杂系统来说,重正化群是一种非常好的研究方法,就是对复杂系统演化方程的重正化群解研究.给出了衰减因子、激发因子和综合因子作用下的重正化群变换解,并以中国股票市场为例计算了以演化时间和投资者开户数增长率为自变量的股票市场重正化群函数.     

Turbulent Prandtl Number in Two Spatial Dimensions: Two-Loop Renormalization Group Analysis

Theoretical and Mathematical Physics - Using the field theory renormalization group technique in the framework of the so-called double-expansion scheme, which takes additional divergences that...     

Renormalization and central extensions

The stochastic limit of quantum theory [1] motivated a new approach to the renormalization program. Subsequent investigations brought to light unexpected connections with conformal field theory and some subtle relationships between renormalization and central extensions. In the present paper we review the path that has lead to these connections at the light of some recent results.     

Potential Renormalization Method for a Model of the Hartree–Fock–Slater Type

We propose a new potential renormalization method for a semiclassical model of the Hartree–Fock–Slater type. The method allows easily constructing the wave functions and, in contrast to most of the similar methods, does not require an explicit form of the potential.     

常数变易法详释

介绍非齐次线性微分方程可用常数变易法求解的原理,旨在帮助学生加深对这一方法的理解.     

基于三参数区间数群决策的第三方物流服务商选择方法研究

对第三方物流服务质量评价与选择属于多属性的群决策问题.为解决传统物流服务商的选择和评价中专家主观性问题,提出了基于三参数区间数群决策的第三方物流服务商选择方法.分析了三参数区间数的概念,对三参数区间数运用偏差函数确定决策专家的权重,根据三参数区间数偏好序概率矩阵和权重,求解第三方物流服务商的排序问题.最后通过实例验证了三参数区间数群决策算法的有效性和可行性.