相关论文: The gradient flow in a twisted box

We consider a class of optimization problems on the space of probability measures motivated by the mean-field approach to studying neural networks. Such problems can be solved by constructing continuous-time gradient flows that converge to…

Gradient flow has been proposed in the lattice community as a tool to reduce the sensitivity of operator correlation functions to noisy UV fluctuations. We test perturbatively under what conditions doing so may contaminate the results. To…

We propose a definition of the running coupling constant in a SU(2) lattice gauge theory with twisted boundary conditions. It is based on the correlation of Polyakov loops extended in a twisted direction at a distance which is a fixed…

We consider a general formulation of gradient flow evolution for problems whose natural framework is the one of metric spaces. The applications we deal with are concerned with the evolution of {\it capacitary measures} with respect to the…

We propose a supersymmetric gradient flow in ${\cal N}=1$ SQCD in four dimensions. The flow equation is derived in the superfield formalism and is also given for component fields of the Wess-Zumino gauge in a gauge covariant manner. We find…

The effective average action of Yang-Mills theory is analyzed in the framework of exact renormalization group flow equations. Employing the background-field method and using a cutoff that is adjusted to the spectral flow, the running of the…

For a fissured medium with uncertainty in the knowledge of fractures' geometry, a conservative tangential flow field is constructed, which is consistent with the physics of stationary fluid flow in porous media and an interpolated geometry…

Based on the energy gradient method, criteria for turbulent transition are proposed for pressure driven flow and shear driven flow, respectively. For pressure driven flow, the necessary and sufficient condition for turbulent transition is…

The 2d O(3) model is widely used as a toy model for ferromagnetism and for Quantum Chromodynamics. With the latter it shares --- among other basic aspects --- the property that the continuum functional integral splits into topological…

We have performed a systematic, large-scale simulation study of granular media in two- and three-dimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, i.e., chute flows. We find that over a…

Understanding turbulence is the key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multi-scale nature, describing the coupling between different-sized eddies in…

We investigate the shock-induced flow through random particle arrays using particle-resolved Large Eddy Simulations for different incident shock wave Mach numbers, particle volume fractions and particle sizes. We analyze trends in mean flow…

We study topology optimization governed by the incompressible Navier-Stokes flows using a phase field model. Novel stabilized semi-implicit schemes for the gradient flows of Allen-Cahn and Cahn-Hilliard types are proposed for solving the…

A continuous sequence of infinitesimal unitary transformations, combined with an operator product expansion for vertex operators, is used to diagonalize the quantum sine-Gordon model for 2 pi < beta^2 < infinity. The leading order of this…

We have used particle tracking methods to study the dynamics of individual balls comprising a granular flow in a small-angle two-dimensional funnel. We statistically analyze many ball trajectories to examine the mechanisms of shock…

We study numerically the stability of granular flow on a rough slope in collisional flow regime in the two-dimension. We examine the density dependence of the flowing behavior in low density region, and demonstrate that the particle…

Fixed-point (FP) lattice actions are classically perfect, i.e., they have continuum classical properties unaffected by discretization effects and are expected to have suppressed lattice artifacts at weak coupling. Therefore they provide a…

Recent applications of machine-learned normalizing flows to sampling in lattice field theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. However, these demonstrations have been at the…

We consider n-dimensional deterministic flows obtained by perturbing a gradient flow. We assume that the gradient flow admits a stable curve of stationary points, and thus if the perturbation is not too large the perturbed flow also admits…

The effects of three-dimensional perturbations in two-dimensional turbulence are investigated, through a conformal field theory approach. We compute scaling exponents for the energy spectra of enstrophy and energy cascades, in a strong…