Related papers: Flows of co-closed $G_{2}$-structures
In this work we construct the $\Co^{\r}$-completion and $\Co^{\l}$-completion of a dynamical system. If $X$ is a flow, we construct canonical maps $X\to \Co^{\r}(X)$ and $X\to \Co^{\l}(X)$ and when these maps are homeomorphism we have the…
Generative modeling seeks to uncover the underlying factors that give rise to observed data that can often be modeled as the natural symmetries that manifest themselves through invariances and equivariances to certain transformation laws.…
We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility $\chi_{\rm t}$ is measured directly, and by the slab method, which is based on the topological content of…
A review is given of recent theoretical work on the superfluid dynamics of trapped Bose gases at finite temperatures, where there is a significant fraction of non-condensate atoms. One can now reach large enough densities and collision…
An open question is whether the liquid and glassy phases of water are thermodynamically distinct or continuous. Here we address this question using molecular dynamics simulations in comparison with neutron scattering experiments to study…
We study the generalized K\"ahler-Ricci flow on complex surfaces with nondegenerate Poisson structure, proving long time existence and convergence of the flow to a weak hyperK\"ahler structure.
The aim of this paper is to report on recent development on the conformal fractional Laplacian, both from the analytic and geometric points of view, but especially towards the PDE community.
We introduce a parabolic flow of almost Kahler structures, providing an approach to constructing canonical geometric structures on symplectic manifolds. We exhibit this flow as one of a family of parabolic flows of almost Hermitian…
Experimental and numerical study of the steady-state cyclonic vortex from isolated heat source in a rotating fluid layer is described. The structure of laboratory cyclonic vortex is similar to the typical structure of tropical cyclones from…
We present a numerical study of finite-temperature superfluid turbulence using the vortex filament model for superfluid helium. We examine the phenomenon of vorticity locking between the normal and superfluid components across a wide range…
This paper initiates a classification programme of flows of $\mathrm{SU}(2)$-structures on $4$-manifolds which have short-time existence and uniqueness. Our approach adapts a representation-theoretic method originally due to Bryant in the…
The stochastics two-layer quasi-geostrophic flow model is an intermediate system between the single-layer two dimensional barotropic flow model and the continuously stratified three dimensional baroclinic flow model. This model is widely…
We consider flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are treated with Neumann type flow conditions, and a…
We describe a class of completely integrable $G$-invariant magnetic geodesic flows on (co)adjoint orbits of a compact connected Lie group $G$ with magnetic field given by the Kirillov-Konstant 2-form.
In this note, we provide some general discussion on the two main versions in the study of Kahler-Ricci flows over closed manifolds, aiming at smooth convergence to the corresponding Kahler-Einstein metrics with assumptions on the volume…
Low-temperature grid generated turbulence is investigated by using numerical simulations of the Gross-Pitaevskii equation. The statistics of regularized velocity increments are studied. Increments of the incompressible velocity are found to…
On the space of positive 3-forms on a seven-manifold, we study a natural functional whose critical points induce metrics with holonomy contained in $G_2$. We prove short-time existence and uniqueness for its negative gradient flow.…
We study evolution of (strong K\"ahler with torsion) SKT structures via the pluriclosed flow on complex nilmanifolds, i.e. on compact quotients of simply connected nilpotent Lie groups by discrete subgroups endowed with an invariant complex…
In this note, a modified K\"ahler-Ricci flow is introduced and studied. The main point is to show the flexibility of K\"ahler-Ricci flow and summarize some useful techniques.
Streets and Tian introduced a parabolic flow of pluriclosed metrics. We classify the long time behavior of homogeneous solutions of this flow on closed complex surfaces including minimal Hopf, Inoue, Kodaira, and non-Kahler, properly…