Related papers: Approximation of the relaxed perimeter functional …
In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of…
The aim of this paper is to investigate the quality of approximation of almost time and band limited functions by its expansion in the Hermite and scaled Hermite basis. As a corollary, this allows us to obtain the rate of convergence of the…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
This paper concludes a three-part effort aimed at developing a consistent and unified framework for the phase-field modeling of cohesive fracture. Building on the theoretical foundations established in the first two parts, which included a…
We present a construction of a mean-field theory for thermodynamic and spectral properties of correlated electrons reliable in the strong-coupling limit. We introduce an effective interaction determined self-consistently from the reduced…
In two-phase image segmentation, convex relaxation has allowed global minimisers to be computed for a variety of data fitting terms. Many efficient approaches exist to compute a solution quickly. However, we consider whether the nature of…
In this paper, we present a new mathematical foundation for image-based lighting. Using a simple manipulation of the local coordinate system, we derive a closed-form solution to the light integral equation under distant environment…
In this article, we consider and analyse a small variant of a functional originally introduced in \cite{BLS,LS} to approximate the (geometric) planar Steiner problem. This functional depends on a small parameter $\varepsilon>0$ and…
In the present manuscript we give a structure condition that allows for energy approximation in the vectorial case and we provide two examples, enjoying such a condition.
The interaction Hamiltonian of an electron and a quasi-monochromatic pulse of a strong quantized electromagnetic field is examined. Canonical transformations of the field variables are found that allow the division of the system's…
The determination of the two-body density functional from its one-body density is achieved for Moshinsky's harmonium model, using a phase-space formulation, thereby resolving its phase dilemma. The corresponding sign rules can equivalently…
We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The method we…
A version of Gabor expansion over a lattice of critical density is shown to converge to an arbitrary function that belongs to domain of the oscillator operator. This expansion is used for approximation of an arbitrary function concentrated…
We provide the integral representation formula for the relaxation in $BV(\Omega; \mathbb{R}^M)$ with respect to strong convergence in $L^1(\Omega; \mathbb{R}^M)$ of a functional with a boundary contact energy term. This characterization is…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
The seminal results of Bourgain, Brezis, Mironescu and D\'avila show that the classical perimeter can be approximated by a family of nonlocal perimeter functionals. We consider a corresponding second order expansion for the nonlocal…
We demonstrate that a mean field approximation can be confidently employed in quasiperiodic moir\'e systems to treat interactions and quasiperiodicity on equal footing. We obtain the mean field phase diagram for an illustrative…
A general procedure is established to calculate the quantum phase diagrams for finite matter-field Hamiltonian models. The minimum energy surface associated to the different symmetries of the model is calculated as a function of the…
We prove a Lipschitz approximation with superlinear error terms for integral currents $\omega$-minimizing the area functional, where $\omega$ is a modulus of continuity satisfying a Dini condition. We also present an almost monotonicity…
We show that the entanglement of purification and the critical distance between the two mixed systems is a powerful measure in probing the phase structures of QCD and confining backgrounds, as it can distinguish the scale of chiral symmetry…