Related papers: The gradient flow in simple field theories
Taming the generation outcome of state of the art Diffusion and Flow-Matching (FM) models without having to re-train a task-specific model unlocks a powerful tool for solving inverse problems, conditional generation, and controlled…
We present preliminary result for the step-scaling study of the coupling constant with the Yang-Mills gradient flow, in the twelve-favour SU(3) gauge theory. In this work, the lattice simulation is performed using unimproved staggered…
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…
In this work we review the coarse-to-fine spatial feature pyramid concept, which is used in state-of-the-art optical flow estimation networks to make exploration of the pixel flow search space computationally tractable and efficient. Within…
We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of the interface. We show that the intrinsic variables…
Grid-interfacing inverters serve as the interface between renewable energy resources and the electric power grid, offering fast, programmable control capabilities. However, their operation is constrained by hardware limitations, such as…
Outflow boundaries play an important role in multiphase fluid dynamics simulations that involve transition between liquid and vapor phases. These flows are dominated by low Weber numbers and a sharp jump in pressure, velocity, and…
We give a determination of the phenomenological value of the Wilson (or gradient) flow scales t0 and w0 for 2+1 flavours of dynamical quarks. The simulations are performed keeping the average quark mass constant, which allows the approach…
In this paper, the compact gas-kinetic scheme for compressible flow is extended to hybrid unstructured mesh. Based on both cell-averaged flow variables and their gradients updated from time accurate gas evolution model at cell interfaces, a…
The models that are based of fractional derivatives should be highlighted among promising new models to describe turbulent fluid flows. In the present work, a steady-state flow in a duct is considered under the condition that the turbulent…
We present a data-driven feedforward control to attenuate large transient lift experienced by an airfoil disturbed by an extreme level of discrete vortex gust. The current analysis uses a nonlinear machine-learning technique to compress the…
We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flow…
These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the…
The objective of this paper is to unravel any relations that may exist between turbulent shear flows and statistical mechanics, through a detailed numerical investigation in the simplest case where both can be well defined. The shear flow…
The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomised alternating sine flow…
While convective flows are implicated in many granular segregation processes, the associated particle-scale rearrangements are not well understood. A three-dimensional bidisperse mixture segregates under steady shear, but the cyclically…
We study the sensitivity of the gradient flow coupling to sectors of different topological charge and its implications in practical situations. Furthermore, we investigate an alternative definition of the running coupling that is expected…
We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent…
We construct the next-to-leading order chiral lagrangian for scalar and pseudo-scalar densities defined using the gradient flow. We calculate the chiral condensate and the pion decay constant to this order from operators at positive flow…
We introduce a symmetric, gradient exclusion process within the class of non-cooperative kinetically constrained lattice gases, modelling a non-linear diffusivity in which the exchange of occupation values between two neighbouring sites…