Related papers: Renormalizing Partial Differential Equations
We present a renormalization group (RG) approach to explain universal features of extreme statistics, applied here to independent, identically distributed variables. The outlines of the theory have been described in a previous Letter, the…
We present a method of short-distance analysis in quantum field theory that does not require choosing a renormalization prescription a priori. We set out from a local net of algebras with associated pointlike quantum fields. The net has a…
Schr\"odinger equation with potential $-g/r^2$ exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at $r=0$. Instead, we use the renormalization group…
We give a pedagogical introduction into the functional renormalization group treatment of disordered systems. After a review of its phenomenology, we show why in the context of disordered systems a functional renormalization group treatment…
The renormalisation group approach is applied to the study of the short-time critical behaviour of the $d$-dimensional Ginzburg-Landau model with long-range interaction of the form $p^{\sigma} s_{p}s_{-p}$ in momentum space. Firstly the…
The quantum kinetics of photons is studied directly in real time by implementing the dynamical renormalization group. In contrast to conventional approach, the dynamical renormalization group method consistently includes off-shell (energy…
This article provides a brief introduction to the a posteriori error analysis of parabolic partial differential equations, with an emphasis on challenges distinct from those of steady-state problems. Using the heat equation as a model…
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…
We shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non-analytic perturbation (the latter will be assumed to have continuous derivatives up to a sufficiently large order). We shall…
We give a holographic explanation how the renormalization group approach to singular perturbations in non-linear differential equations proposed by Chen, Goldenfeld and Oono is indeed equivalent to a renormalization group method in quantum…
We review recent developments in the use of renormalization group (RG) methods in low-energy nuclear physics. These advances include enhanced RG technology, particularly for three-nucleon forces, which greatly extends the reach and accuracy…
We study linearization models for continuous one-parameter semigroups of parabolic type. In particular, we introduce new limit schemes to obtain solutions of Abel's functional equation and to study asymptotic behavior of such semigroups.…
In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…
We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method…
In this paper, we develop a systematical approach in applying an asymptotic method of moving planes to investigate qualitative properties of positive solutions for fractional parabolic equations. We first obtain a series of needed key…
We construct simple analytical solutions of renormalization group equations for the running coupling and for the Green functions in QCD in the asymptotic regime. These solutions have an explicit form and subsequently sum up the leading,…
Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equation. We apply this principle by finding dilatations and…
A regularization of the Cross-Newell equation is presented. It is based on a secondary re-modulation along characteristics. This new characteristic Cross-Newell equation is not isotropic (has preferred directions), but is universal…
A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method uses a separation ansatz to solve an equivalent first-order…
Two approaches to renormalization-group improvement are examined: the substitution of the solutions of running couplings, masses and fields into perturbatively computed quantities is compared with the systematic sum of all the leading log…