Related papers: A Grad-Shafranov model for compact quasisymmetric …
We analyze and test using Fourier extensions that minimize a Hilbert space norm for the purpose of solving partial differential equations (PDEs) on surfaces. In particular, we prove that the approach is arbitrarily high-order and also show…
Challenging stellar dynamical problems, such as the study of gravothermal oscillations in star clusters, have in the past initiated the very successful building of GRAPE special purpose computers. It is discussed, that present day tasks…
We show the existence of a complete, strictly locally convex hypersurface within $\mathbb{H}^{n+1}$ that adheres to a curvature equation applicable to a broad range of curvature functions. This hypersurface possesses a prescribed asymptotic…
Stellarators are magnetic confinement devices under active development to deliver steady-state carbon-free fusion energy. Their design involves a high-dimensional, constrained optimization problem that requires expensive physics simulations…
The Hahm--Kulsrud (HK) [T. S. Hahm and R. M. Kulsrud, Phys. Fluids {\bf 28}, 2412 (1985)] solutions for a magnetically sheared plasma slab driven by a resonant periodic boundary perturbation illustrate fully shielded (current sheet) and…
We provide an overview of the Gross-Pitaevskii-Poisson equation (GPPE) that is used to model self-gravitating superfluid systems, which include gravitationally collapsed boson and axion stars and dark-matter haloes. We outline how this…
We develop a framework that enables direct and meaningful comparison of two early fault-tolerant methods for the computation of eigenenergies, namely \gls{qksd} and \gls{spe}, within which both methods use expectation values of Chebyshev…
We study the gravitational collapse of a non-interacting mix of perfect fluid and a spatially homogeneous scalar field within a Chiellini-integrable framework. We choose an extended Higgs-type self-interaction potential and reduce the…
In this paper we provide regularity results for active scalars that are weak solutions of almost critical drift-diffusion equations in general surfaces. This includes models of anisotropic non-homogeneous media and the physically motivated…
Semiconductor Bloch equations, which microscopically describe the dynamics of a Coulomb interacting, spin-unpolarized electron-hole plasma, can be solved in two limits: the coherent and the quasi-equilibrium regime. These equations have…
Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…
This is the first paper of a series of our works on the self-similar orbit-averaged Fokker-Planck (OAFP) equation for distribution function of stars in dense isotropic star clusters. At the late stage of relaxation evolution of the…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
We consider a well known model for lipid-bilayer membrane vesicles exhibiting phase separation, incorporating a phase field with finite curvature elasticity. We prove the existence of a plethora of equilibria, corresponding to…
Recently, the theory of symmetric teleparallel equivalent of general relativity (STEGR) has gained much interest in the cosmology and astrophysics community. Within this theory, we discuss the method of deriving a stellar isotropic model.…
This paper introduces a new method for discretizing and solving integral equation formulations of Maxwell's equations which achieves spectral accuracy for smooth surfaces. The approach is based on a hybrid Nystr\"om-collocation method using…
We present a novel staggered semi-implicit hybrid FV/FE method for the numerical solution of the shallow water equations at all Froude numbers on unstructured meshes. A semi-discretization in time of the conservative Saint-Venant equations…
This work extends the concepts of algebraic flux correction and convex limiting to continuous high-order Bernstein finite element discretizations of scalar hyperbolic problems. Using an array of adjustable diffusive fluxes, the standard…
We first give an abstract framework to show the uniqueness of Ground State Solutions (GSS) for a large class of PDEs. To the best of our knowledge, all the existing results in the literature only addressed particular cases. Moreover, our…
In this paper we find a solution for a quasi-isotropic inflationary Universe which allows to introduce in the problem a certain degree of inhomogeneity. We consider a model which generalize the (flat) FRW one by introducing a first order…