We prove strong crystallization results in two dimensions for an energy that arises in the theory of block copolymers. The energy is defined on sets of points and their weights, or equivalently on the set of atomic measures. It consists of two terms; the first term is the sum of the square root of the weights, and the second is the quadratic optimal transport cost between the atomic measure and the Lebesgue measure. We prove that this system admits crystallization in several different ways: (1) the energy is bounded from below by the energy of a triangular lattice (called T); (2) if the energy equals that of T, then the measure is a rotated and translated copy of T; (3) if the energy is close to that of T, then locally the measure is close ...
We study the homogenized energy densities of periodic ferromagnetic Ising systems. We prove that, fo...
We identified the effect of the geometry imposed by the shape of the Wigner-Seitz cell or confinemen...
Dans cette thèse, nous étudions des problèmes de minimisation d'énergies discrètes et nous cherchons...
We prove strong crystallization results in two dimensions for an energy that arises in the theory of...
Abstract. We prove strong crystallization results in two dimensions for an energy that arises in the...
We prove strong crystallization results in two dimensions for an energy that arises in the theory of...
We prove strong crystallization results in two dimensions for an energy that arises in the theory of...
In this paper we derive a new model for diblock copolymer melts with a dominant phase that is simple...
In this paper we derive a new model for diblock copolymer melts with a dominant phase that is simple...
<p>In this paper we derive a new model for diblock copolymer melts with a dominant phase that ...
In this thesis, we study minimization problems for discrete energies and we search to understand why...
In this paper we study a new model for patterns in two dimensions, inspired by diblock copolymer mel...
Many materials have a crystalline phase at low temperatures. The simplest example where this fundame...
We show that the emerging field of discrete differential geometry can be usefully brought to bear on...
36 pages. 10 figures. 2 tables.In this paper, we study minimization problems among Bravais lattices ...
We study the homogenized energy densities of periodic ferromagnetic Ising systems. We prove that, fo...
We identified the effect of the geometry imposed by the shape of the Wigner-Seitz cell or confinemen...
Dans cette thèse, nous étudions des problèmes de minimisation d'énergies discrètes et nous cherchons...
We prove strong crystallization results in two dimensions for an energy that arises in the theory of...
Abstract. We prove strong crystallization results in two dimensions for an energy that arises in the...
We prove strong crystallization results in two dimensions for an energy that arises in the theory of...
We prove strong crystallization results in two dimensions for an energy that arises in the theory of...
In this paper we derive a new model for diblock copolymer melts with a dominant phase that is simple...
In this paper we derive a new model for diblock copolymer melts with a dominant phase that is simple...
<p>In this paper we derive a new model for diblock copolymer melts with a dominant phase that ...
In this thesis, we study minimization problems for discrete energies and we search to understand why...
In this paper we study a new model for patterns in two dimensions, inspired by diblock copolymer mel...
Many materials have a crystalline phase at low temperatures. The simplest example where this fundame...
We show that the emerging field of discrete differential geometry can be usefully brought to bear on...
36 pages. 10 figures. 2 tables.In this paper, we study minimization problems among Bravais lattices ...
We study the homogenized energy densities of periodic ferromagnetic Ising systems. We prove that, fo...
We identified the effect of the geometry imposed by the shape of the Wigner-Seitz cell or confinemen...
Dans cette thèse, nous étudions des problèmes de minimisation d'énergies discrètes et nous cherchons...