相关论文: 2D Theta Functions and Crystallization among Brava…

We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic…

By means of extensive equilibrium molecular dynamics simulations we have investigated, the behavior of the interfacial tension $\gamma$ of two immiscible symmetrical Lennard-Jones fluids. This quantity is studied as function of reduced…

Using classical density functional theory, we study the behavior of dimers, i.e. hard rods of length $L=2$, on a two-dimensional cubic lattice. For deriving a free energy functional, we employ Levy's prescription which is based on the…

We consider a constrained minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures on a locally compact space. The components are positive measures (charges) that are constrained from…

We consider the numerical approximation of a continuum model of antiferromagnetic and ferrimagnetic materials. The state of the material is described in terms of two unit-length vector fields, which can be interpreted as the magnetizations…

The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of {\Gamma}-convergence, in the framework of finite plasticity. Denoting by {\epsilon} the thickness of the plate, we analyse the case where…

We use the method of $\Gamma$-convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film in the limit of vanishing thickness. In this asymptotic regime, surface energy plays a greater role and we…

Particles interacting through long-range attraction and short-range repulsion given by power-laws have been widely used to model physical and biological systems, and to predict or explain many of the patterns they display. Apart from rare…

Proving the universal optimality of the hexagonal lattice is one of the big open challenges of nowadays mathematics. We show that the hexagonal lattice outperforms certain "natural" classes of periodic configurations. Also, we rule out the…

For the Landau-de Gennes functional modeling nematic liquid crystals in dimension three, we prove that, if the energy is bounded by $C(\log\frac{1}{\varepsilon}+1)$, then the sequence of minimizers…

We study existence and qualitative properties of the minimizers for a Thomas--Fermi type energy functional defined by $$E_\alpha(\rho):=\frac{1}{q}\int_{\mathbb{R}^d}|\rho(x)|^q…

For an old problem of Euler's elastica we prove the novel global property that every planar elastica with non-constant monotone curvature is uniquely minimal subject to the clamped boundary condition. We also partly extend this unique…

We make some remarks on the Euler-Lagrange equation of energy functional $I(u)=\int_\Omega f(\det Du)\,dx,$ where $f\in C^1(\mathbb R).$ For certain weak solutions $u$ we show that the function $f'(\det Du)$ must be a constant over the…

We study a two-dimensional ternary inhibitory system derived as a sharp-interface limit of the Nakazawa-Ohta density functional theory of triblock copolymers. This free energy functional combines an interface energy favoring micro-domain…

We provide a compactness criterion for the set of laws $\mathfrak{P}^{ac}_{sem}(\Theta)$ on the Skorokhod space for which the canonical process $X$ is a semimartingale having absolutely continuous characteristics with differential…

Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state…

We study a two parameter family of energy minimization problems for interaction energies $\mathcal{E}_{\alpha,\beta}$ with attractive-repulsive potential $W_{\alpha,\beta}$. We develop a concavity principle, which allows us to provide a…

We create low-entropy states of neutral atoms by utilizing a conceptually new optical-lattice technique that relies on a high-precision, high-bandwidth synthesis of light polarization. Polarization-synthesized optical lattices provide two…

Several authors have suggested that the surfaces of vanishing potential generated by the electrostatic fields from a distribution of point charges resemble triply periodic minimal surfaces (TPMS) corresponding to the positions of the point…

In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…