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We study a stochastically perturbed mean curvature flow for graphs in $\mathbb{R}^3$ over the two-dimensional unit-cube subject to periodic boundary conditions. In particular, we establish the existence of a weak martingale solution. The…
Mixed boundary conditions are introduced to finite element exterior calculus. We construct smoothed projections from Sobolev de Rham complexes onto finite element de Rham complexes which commute with the exterior derivative, preserve…
We consider solutions of the Navier-Stokes equations in $3d$ with vortex filament initial data of arbitrary circulation, that is, initial vorticity given by a divergence-free vector-valued measure of arbitrary mass supported on a smooth…
A method to treat frictional contact problems along embedded surfaces in the finite element framework is developed. Arbitrarily shaped embedded surfaces, cutting through finite element meshes, are handled by the X-FEM. The frictional…
Previous calculation of spin torques for small-amplitude magnetization dynamics around a uniformly magnetized state [J. Phys. Soc. Jpn. {\bf 75} (2006) 113706] is extended here to the case of finite-amplitude dynamics. This is achieved by…
In this article we present a novel staggered semi-implicit hybrid finite-volume/finite-element (FV/FE) method for the resolution of weakly compressible flows in two and three space dimensions. The pressure-based methodology introduced in…
We utilize a combination of vector magnetic field and scanning tunneling microscopy to elucidate the 3D field-based electronic phase diagram of a correlated iron-based superconductor, LiFeAs. We observe, under a zero-field-cooled method, an…
Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible flow around a circular cylinder is presented in this work. The ROM…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
State-of-the-art atmospheric turbulence image restoration methods utilize standard image processing tools such as optical flow, lucky region and blind deconvolution to restore the images. While promising results have been reported over the…
A prevalent problem in general state-space models is the approximation of the smoothing distribution of a state, or a sequence of states, conditional on the observations from the past, the present, and the future. The aim of this paper is…
Analytical and numerical vortex solutions for the extended Skyrme-Faddeev model in a (3+1) dimensional Minkowski space-time are investigated. The extension is obtained by adding to the Lagrangian a quartic term, which is the square of the…
The smoothed particle hydrodynamics (SPH) method has been widely used to simulate incompressible and slightly compressible fluid flows. Adaptive refinement strategies to dynamically increase the resolution of the particles to capture sharp…
The observation of vortices in superconductors was a major breakthrough in developing the conceptual background for superconducting applications. Each vortex carries a flux quantum, and the magnetic field radially decreases from the center.…
We propose an innovative quantum emulator based on Moire superlattices showing that, by employing periodical modulation on each lattice site, one can create tunable, artificial gauge fields with imprinting Peierls phases on the hopping…
In this paper we address smoothing-that is, optimisation-based-estimation techniques for localisation problems in the case where motion sensors are very accurate. Our mathematical analysis focuses on the difficult limit case where motion…
Recent lattice measurements of the topological susceptibility of SU(2) gauge theory using improved cooling and inverse-blocking are in disagreement. We use the overlap method, which probes the fermionic sector of the theory directly, to…
Results from a calculation of the low-lying glueball spectrum of pure-gauge SU(3) are used as a test of the effectiveness of improved discretisation schemes in reducing finite spacing errors. Glueball masses are extracted from simulations…
Recently, a new gauging procedure called Sculpting mechanism was proposed to obtain the M-theory origin of type II gauged Supergravity theories in 9D. We study this procedurein detail and give a better understanding of the different…
Modelling the vortex structures and then translating them into the corresponding velocity fields are two essential aspects for the vortex-based modelling works in wall-bounded turbulence. This work develops a datadriven method, which allows…