相关论文: Multi-vortices are Wall Vortices: A Numerical Proo…
We prove a vertex domination conjecture of Erd\H os, Faudree, Gould, Gy\'arf\'as, Rousseau, and Schelp, that for every n-vertex complete graph with edges coloured using three colours there exists a set of at most three vertices which have…
An earlier four-loop calculation of the fluctuation pressure of a fluid membrane between two infinite walls is extended to five loops. Variational perturbation theory is used to extract the hard-wall limit from perturbative results obtained…
In an inviscid and incompressible fluid in dimension 3, we prove the existence of several helical filaments, or vortex helices, collapsing into each others.
The splitting of a high-order optical vortex into a constellation of unit vortices, upon total reflection, is described and analyzed. The vortex constellation generalizes, in a local sense, the familiar longitudinal Goos-H\"anchen and…
Scattering methods make it possible to compute the effects of renormalized quantum fluctuations on classical field configurations. As a classic example of a topologically nontrivial classical solution, the Abrikosov-Nielsen-Olesen vortex in…
Suppose that a polygon $P$ is given as an array containing the vertices in counterclockwise order. We analyze how many vertices (including the index of each of these vertices) we need to know before we can bound $P$, i.e., report a bounded…
The influence of an axial through-flow on the spatiotemporal growth behavior of different vortex structures in the Taylor-Couette system with radius ratio eta=0.5 is determined. The Navier Stokes equations (NSE) linearized around the basic…
Wall turbulence consists of various sizes of vortical structures that induce flow circulation around a wide range of closed Eulerian loops. Here we investigate the multiscale properties of circulation around such loops in statistically…
Robbins conjectured, and Zeilberger recently proved, that there are 1!4!7!...(3n-2)!/n!/(n+1)!/.../(2n-1)! alternating sign matrices of order n. We give a new proof of this result using an analysis of the six-vertex state model (also called…
We prove existence and multiplicity of periodic motions for the forced 2-body problem under conditions of topological character. In the different cases, the lower bounds obtained for the number of solutions are related to the winding number…
We have extended our previous work [1] on rotating holographic superfluids to include Lifshitz scaling. Presence of this scaling breaks relativistic invariance of the boundary superfluid system and indicates the existence of a Lifshitz…
The unknotting number of knots is a difficult quantity to compute, and even its behavior under basic satelliting operations is not understood. We establish a lower bound on the unknotting number of cable knots and iterated cable knots…
In this paper, the flow around each ring-like vortex is investigated by high order DNS including first sweep, first ejection, second sweep, second ejection, positive spike, momentum deficit, vortex shape, vortex location, strength of…
We propose a new method for the evaluation of intersection numbers for twisted meromorphic $n$-forms, through Stokes' theorem in $n$ dimensions. It is based on the solution of an $n$-th order partial differential equation and on the…
Recent numerical explorations of extremely intense circulation fluctuations at high Reynolds number flows have brought to light novel aspects of turbulent intermittency. Vortex gas modeling ideas, introduced alongside such developments,…
This article presents a formulation that extends the variational multiscale modelling for compressible large-eddy simulation to a vast family of compact nodal numerical methods represented by the high-order flux reconstruction scheme. The…
In an earlier paper \cite{yu2021Finiteness}, we showed that there are finitely many stationary configurations (consisting of equilibria, rigidly translating configurations, relative equilibria and collapse configurations) in the planar…
The excitations of the vortex in Abelian Higgs model with small ratio of vector and Higgs particle masses are considered. Three main modes encountered in numerical computations are described in detail. They are also compared to analytic…
The twist and writhe numbers and magnetic energy of an orthogonally perturbed vortex filaments are obtained from the computation of the magnetic helicity of geodesic and abnormal magnetohydrodynamical (MHD) vortex filament solutions. Twist…
Context. A universally accepted definition of what a vortex is has not yet been reached. Therefore, we lack an unambiguous and rigorous method for the identification of vortices in fluid flows. Such a method would be necessary to conduct…