Related papers: Finite-Difference Approximations and Local Algorit…

We consider Riesz-type nonlocal energies with general interaction kernels and their discretizations related to particle systems. We prove that the discretized energies $\Gamma$-converge in the weak-$*$ topology to the Riesz functional…

This paper investigates the existence and qualitative properties of minimizers for a class of nonlocal micromagnetic energy functionals defined on bounded domains. The considered energy functional consists of a symmetric exchange…

We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…

In this note, we show that the Local Molecular Field theory of Weeks et. al. can be re-derived as an extremum problem for an approximate Helmholtz free energy. Using the resulting free energy as a classical, fluid density functional yields…

In order to perform physically faithful particle-in-cell (PIC) simulations, the Gauss's law stands as a critical requirement, since its violation often leads to catastrophic errors in long-term plasma simulations. This work proposes a novel…

For solving the Poisson equation it is usually possible to discretize it into solving the corresponding linear system $Ax=b$.Variational quantum algorithms (VQAs) for the discreted Poisson equation have been studied before. We give a VQA…

Imposing the Born rule as a fundamental principle of quantum mechanics would require the existence of normalizable wave functions also for relativistic particles. Indeed, the Fourier transforms of normalized k-space amplitudes yield…

Accurately solving PDEs with localised features requires refined meshes that adapt to the solution. Traditional numerical methods, such as finite elements, are linear in nature and often ineffective for such problems, as the mesh is not…

This paper generalizes the entropy maximization problem leading to the Boltzmann-Gibbs distribution through the nonadditive entropy $S_{q,s}(p)=k_{s}\sum^{W}_{i\geq1}p_{i}\ln_{q}1/p_{i}$, $q\in(0,1)$, which is a rescaled version of $S_{q}$…

Building on existing $hp$-adaptive algorithms driven by equilibrated-flux estimators from [ESAIM Math. Model. Numer. Anal. 57 (2023), 329--366] and the references therein, we propose a novel $h$-adaptive algorithm for a fixed polynomial…

In this paper we prove discrete to continuum convergence rates for Poisson Learning, a graph-based semi-supervised learning algorithm that is based on solving the graph Poisson equation with a source term consisting of a linear combination…

We establish local existence and a quasi-optimal error estimate for piecewise cubic minimizers to the bending energy under a discretized inextensibility constraint. In previous research a discretization is used where the inextensibility…

This paper focuses on the analysis of a free energy functional, that models a dilute suspension of magnetic nanoparticles in a two-dimensional nematic well. The {\it first part} of the article is devoted to the asymptotic analysis of global…

Optimization algorithms can see their local convergence rates deteriorate when the Hessian at the optimum is singular. These singularities are inescapable when the optima are non-isolated. Yet, under the right circumstances, several…

Under low-collisionality conditions the isotropic part of the electron velocity distribution function in a plasma becomes non-local and the electrons can be described by a single global distribution function . This is also the regime…

We diagonalize the second-quantized Hamiltonian of a one-dimensional Bose gas with a nonpoint repulsive interatomic potential and zero boundary conditions. At weak coupling the solutions for the ground-state energy $E_{0}$ and the…

We formulate a generalized self-consistent stochastic quantum kinetic theory for finite-temperature ultracold Bose gases interacting via a generic long-range interaction, applicable to a broad range of systems, by means of Keldysh…

We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…

We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we…

We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume the density of states function is not…