Related papers: The gradient flow at higher orders in perturbation…
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…
Considering the action for the theory $\lambda\phi^{4}$ for a massive scalar bosonic field as an entropy functional on the space of coupling constants and on the space of fields, we determine the gradient flows for the scalar field, the…
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We…
Grad-div stabilization, adding a term -gamma grad div u, has proven to be a useful tool in the simulation of incompressible flows. Such a term requires a choice of the coefficient gamma and studies have begun appearing with various…
A nonlinear parabolic equation of sixth order is analyzed. The equation arises as a reduction of a model from quantum statistical mechanics, and also as the gradient flow of a second-order information functional with respect to the…
The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite…
Existing analyses of optimization in deep learning are either continuous, focusing on (variants of) gradient flow, or discrete, directly treating (variants of) gradient descent. Gradient flow is amenable to theoretical analysis, but is…
The energy gradient theory was proposed in our previous studies. The mechanism of flow instability is very different in shear driven flows from pressure driven flows. In present paper, the relationship for the energy variation, work done,…
Motivated by the occurrence in rate functions of time-dependent large-deviation principles, we study a class of non-negative functions $\mathscr L$ that induce a flow, given by $\mathscr L(\rho_t,\dot\rho_t)=0$. We derive necessary and…
The Yang-Mills gradient flow in finite volume is used to define a running coupling scheme. As our main result the discrete beta-function, or step scaling function, is calculated for scale change s=3/2 at several lattice spacings for SU(3)…
In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model…
Studying various functionals and associated gradient ows are known problems in differential geometry. The perpose of this article is to provide a general overview of curvature functionals in Finsler geometry and use their information for…
The predictive power of mean-field theory is emphasized by comparing theory with simulations under controlled conditions. The recently developed test-field method is used to extract turbulent transport coefficients both in kinematic as well…
We introduce a new variational method for finding periodic orbits of flows and spatio-temporally periodic solutions of classical field theories, a generalization of the Newton method to a flow in the space of loops. The feasibility of the…
To go beyond Gaussian approximation to the Hohenberg-Kohn free energy playing the key role in the density functional theory (DFT), the density functional \textit{integral} representation would be relevant, because field theoretical approach…
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of application are studied, in particular,…
We study a gradient flow on Sobolev diffeomorphisms for the problem of image registration. The energy functional quantifies the effect of transforming a template to a target, while also penalizing deformation of the metric tensor. The main…
The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible…
In lattice gauge theories, the gradient flow has been used extensively both, for scale setting and for defining finite volume renormalization schemes for the gauge coupling. Unfortunately, rather large cutoff effects have been observed in…
The dispersion of a passive scalar in a fluid through the combined action of advection and molecular diffusion is often described as a diffusive process, with an effective diffusivity that is enhanced compared to the molecular value.…