相关论文: Renormgroup symmetry for solution functionals
The result from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are reviewed. The main achievement is the…
An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries, based on modern group analysis are described.…
Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
The functional renormalization group method is used to take into account the vacuum polarization around localized bound states generated by external potential. The application to Atomic Physics leads to improved Hartree-Fock and Kohn-Sham…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
Evolution of the concept known in the theoretical physics as the Renormalization Group (RG) is presented. The corresponding symmetry, that has been first introduced in QFT in mid-fifties, is a continuous symmetry of a solution with respect…
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…
Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…
This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…
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 relationship between mappings of sets and renormalization group transformations is established, and renormalization group invariants of such mappings are found. These results are valid both for continuous and discrete mappings and for…
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…
We revisit here the problem of generalized cosmology using renormalization group approach. A complete analysis of these cosmologies, where specific models appear as asymptotic fixed-points, is given here along with their linearized…
We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A…
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic…
We extend the concept of the functional renormalization for quantum many-body problems to non-equilibrium situations. Using a suitable generating functional based on the Keldysh approach, we derive a system of coupled differential equations…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…