相关论文: The Phase Transition in 5 Point Energy Minimizatio…

The goal of the present paper is to establish some kind of regularity of an energy minimizer map between Riemannian polyhedra. More precisely, we will show the h\"{o}lder continuity of local energy minimizers between Riemannian polyhedra…

We consider a nonlinear Schr\"odinger equation with focusing nonlinearity of power type on a star graph ${\mathcal G}$, written as $ i \partial_t \Psi (t) = H \Psi (t) - |\Psi (t)|^{2\mu}\Psi (t)$, where $H$ is the selfadjoint operator…

Using dimensional reduction we construct an effective 3D theory of the Minimal Supersymmetric Standard Model at finite temperature. The final effective theory is obtained after three successive stages of integration out of massive…

We study measures and point configurations optimizing energies based on multivariate potentials. The emphasis is put on potentials defined by geometric characteristics of sets of points, which serve as multi-input generalizations of the…

In this paper an iterative minimization method is proposed to approximate the minimizer to the double-well energy functional arising in the phase-field theory. The method is based on a quadratic functional posed over a nonempty closed…

We provide numerical evidence for the existence of phase transitions with respect to the temperature in the one-dimensional Riesz gases with non-singular pair interaction, that is particles on the line interacting via the potential…

We consider $\mathbb{S}^2$-valued maps on a domain $\Omega\subset\mathbb{R}^N$ minimizing a perturbation of the Dirichlet energy with vertical penalization in $\Omega$ and horizontal penalization on $\partial\Omega$. We first show the…

We compute the one-loop Casimir energy of gravity and matter fields, obeying various boundary conditions, in 5-dimensional S^1/Z_2 and 6-dimensional T^2/Z_k orbifolds. We discuss the role of the Casimir energy in possible radius…

We consider the minimal discrete and continuous energy problems on the unit sphere $\mathbb{S}^d$ in the Euclidean space $\mathbb{R}^{d+1}$ in the presence of an external field due to finitely many localized charge distributions on…

The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional defined on the space of vector fields $H^1(S,T)$, where $S$ and $T$ are surfaces of revolution. The energy functional we consider is closely related…

We investigate the Riesz energy minimization problem on a $d$-dimensional ball in the presence of an external field created by a point charge above the ball in $\R^{d+1}$, $d\geq1$. Both cases of an attractive charge and a repulsive charge…

We study minimal energy problems for strongly singular Riesz kernels on a manifold. Based on the spatial energy of harmonic double layer potentials, we are motivated to formulate the natural regularization of such problems by switching to…

Sandier and Serfaty studied the one-dimensional Log-gas model, in particular they gave a crystallization result by showing that the one-dimensional lattice $\mathbb{z}$ is a minimizer for the so-called renormalized energy which they…

Using $\Gamma$-convergence, we study the Cahn-Hilliard problem with interface width parameter $\varepsilon > 0$ for phase transitions on manifolds with conical singularities. We prove that minimizers of the corresponding energy functional…

We study a large family of axisymmetric Riesz-type singular interaction potentials with anisotropy in three dimensions. We generalize some of the results of our recent work in two dimensions to the present setting. For potentials with…

Following Brown[1], we construct composite operators for the scalar $\phi^3$ theory in six dimensions using renormalisation group methods with dimensional regularisation. We express bare scalar operators in terms of renormalised composite…

We study the Riesz and logarithmic energies on the Grassmannian $\operatorname{Gr}_{2,4}$ of $2$-dimensional subspaces of $\mathbb{R}^4$. We prove that the continuous Riesz and logarithmic energies are uniquely minimized by the uniform…

This paper discusses the regularity of multiple-valued Dirichlet minimizing maps into the sphere. It shows that even at branched point, as long as the normalized energy is small enough, we have the energy decay estimate. Combined with the…

We prove existence and regularity of minimisers for the Canham-Helfrich energy in the class of weak (possibly branched and bubbled) immersions of the $2$-sphere. This solves (the spherical case) of the minimisation problem proposed by…

To maximize the received power at a user equipment, the problem of optimizing a reconfigurable intelligent surface (RIS) with a limited phase range R < 2{\pi} and nonuniform discrete phase shifts with adjustable gains is addressed.…