Related papers: Energy minimization, periodic sets and spherical d…
A two-dimensional bistable lattice is a periodic triangular network of non-linear bi-stable rods. The energy of each rod is piecewise quadratic and has two minima. Consequently, a rod undergoes a reversible phase transition when its…
We study finite-difference approximations of both Poisson and Poisson-Boltzmann (PB) electrostatic energy functionals for periodic structures constrained by Gauss' law and a class of local algorithms for minimizing the finite-difference…
In this paper, we prove a Fenchel theorem for Gauss maps by providing sharp lower bounds for the path length of Gauss maps of an embedding. By combining the Fenchel-type theorem with various techniques from the field of geometric analysis,…
A mechanism to modify the energy band structure is proposed by considering a chain of periodic scatterers forming a linear lattice around which an external cylindrical trapping potential is applied along the chain axis. When this trapping…
We consider point-to-point directed paths in a random environment on the two-dimensional integer lattice. For a general independent environment under mild assumptions we show that the quenched energy of a typical path satisfies a central…
Local Energy Communities (LECs) facilitate consumer involvement in local electricity generation and distribution, offering a significant opportunity for society to participate in the energy transition. This paper presents the optimization…
Using clover fermions on CP-PACS dynamical configurations, we consider a number of ways of measuring hadronic electric polarizability, an $|\mathbf{E}|^{2}$ effect in hadron masses, using lattice techniques. We consider the effects of…
The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit plays a crucial role in the understanding of the…
In this paper, we consider multi-valued graphs with a prescribed real analytic interface that minimize the Dirichlet energy. Such objects arise as a linearized model of area minimizing currents with real analytic boundaries and our main…
We introduce and study the unconstrained polarization (or Chebyshev) problem which requires to find an $N$-point configuration that maximizes the minimum value of its potential over a set $A$ in $p$-dimensional Euclidean space. This problem…
We derive general linear programming bounds for spherical $(k,k)$-designs. This includes lower bounds for the minimum cardinality and lower and upper bounds for minimum and maximum energy, respectively. As applications we obtain a universal…
Solving the Euler equation which corresponds to the energy minimum of a density functional expressed in orbital-free form involves related but distinct computational challenges. One is the choice between all-electron and pseudo-potential…
In this paper, we study a maximization and a minimization problem associated with a Poisson boundary value problem. Optimal solutions in a set of rearrangements of a given function define stationary and stable flows of an ideal fluid in two…
We analyze a nonlocal coupled system arising as the Euler--Lagrange equations of an energy functional involving regional fractional Laplacians of orders $s_1$ and $s_2$ ($ 0 < s_1,s_2 < 1$), each acting on a separate disjoint domain and…
A systematic first-principle study is performed to calculate the lattice parameters, electronic structure, and thermodynamic properties of UN using the local-density approximation (LDA)+\emph{U} and the generalized gradient approximation…
The goal of these lecture notes is to review the problem of free energy minimization as a unified framework underlying the definition of maximum entropy modelling, generalized Bayesian inference, learning with latent variables, statistical…
The paper deals with minimum energy problems in the presence of external fields with respect to the Riesz kernels $|x-y|^{\alpha-n}$, $0<\alpha<n$, on $\mathbb R^n$, $n\geqslant2$. For quite a general (not necessarily lower semicontinuous)…
We present a new expression for the energy of the lowest collective states in even-even nuclei throughout the entire periodic table. Our empirical formula is extremely valid and holds universally for all of the natural parity even multipole…
We prove lower bounds for energy functionals of mappings from real, complex and quaternionic projective spaces to Riemannian manifolds. For real and complex projective spaces, these lower bounds are sharp, and we characterize the family of…
We analyse an energy minimisation problem recently proposed for modelling smectic-A liquid crystals. The optimality conditions give a coupled nonlinear system of partial differential equations, with a second-order equation for the…