相关论文: Solving non-perturbative flow equations

In this work we develop implicit Active Flux schemes for the scalar advection equation. At every cell interface we approximate the solution by a polynomial in time. This allows to evolve the point values using characteristics and to update…

We investigate a one dimensional flow described with the non-compressible coupled Euler and non-compressible Navier-Stokes equations in Cartesian coordinate systems. We couple the two fluids through the continuity equation where different…

Starting from the hypothesis of scaling solutions, the general exact form of the scalar field potential is found. In the case of two fluids, it turns out to be a negative power of hyperbolic sine. In the case of three fluids the analytic…

The flow equations of the renormalisation group permit to analyse the perturbative $n$-point functions of renormalisable quantum field theories. Rigorous bounds implying renormalisablility allow to control large momentum behaviour, infrared…

Transport of scalar fields in compressible flow is investigated. The effective equations governing the transport at scales large compared to those of the advecting flow are derived by using multi-scale techniques. Ballistic transport…

The functional flow equations for the Legendre effective action, with respect to changes in a smooth cutoff, are approximated by a derivative expansion; no other approximation is made. This results in a set of coupled non-linear…

We derive a system of coupled flow equations for the proper-vertices of the background effective average action and we give an explicit representation of these by means of diagrammatic and momentum space techniques. This explicit…

We apply pseudo-spectral methods to integrate functional flow equations with high accuracy, extending earlier work on functional fixed point equations \cite{Borchardt:2015rxa}. The advantages of our method are illustrated with the help of…

We construct a non-perturbative method to investigate the phase structure of the scalar theory at finite temperature. The derivative of the effective potential with respect to the mass square is expressed in terms of the full propagator.…

This paper focuses on the optimal control of weak (i.e. in general non smooth) solutions to the continuity equation with non local flow. Our driving examples are a supply chain model and an equation for the description of pedestrian flows.…

The critical effective potential is the nonperturbative part of the effective action at a phase transition. It equals the scale invariant effective average potential and can be calculated from the renormalization group flow of the effective…

Forced advection of passive tracer, $\theta $, in nonlinear relaxational medium by large scale (Batchelor problem) incompressible velocity field at scales less than the correlation length of the flow and larger than the diffusion scale is…

We study the gradient flow equation for the O(N) nonlinear sigma model in two dimensions at large N. We parameterize solution of the field at flow time t in powers of bare fields by introducing the coefficient function X_n for the n-th…

Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…

The scaling form of the critical equation of state is computed for $O(N)$-symmetric models. We employ a method based on an exact flow equation for a coarse grained free energy. A suitable truncation is solved numerically.

We show that a reformulation of the governing equations for incompressible multi-phase flow in the volume of fluid setting leads to a well defined energy rate. Weak nonlinear inflow-outflow and solid wall boundary conditions complement the…

We discuss the exact renormalization group or flow equation for the effective action and its decomposition into one particle irreducible N point functions. With the help of a truncated flow equation for the four point function we study the…

The aim of this paper is to derive the averaged governing equations for non-degenerated oscillatory flows, in which the magnitudes of mean velocity and oscillating velocity are similar. We derive the averaged equations for a scalar passive…

A nonperturbative method is proposed for the approximative solution of the exact evolution equation which describes the scale dependence of the effective average action. It consists of a combination of exact evolution equations for…

In this paper we derive a hierarchy of integral equations from the 4PI effective action which have the form of Bethe-Salpeter equations. We show that the vertex functions defined by these equations can be used to truncate the exact…