Related papers: Area quasi-minimizing partitions with a graphical …
We study partitions on three dimensional manifolds which minimize the total geodesic perimeter. We propose a relaxed framework based on a $\Gamma$-convergence result and we show some numerical results. We compare our results to those…
In this paper we apply both the procedure of dimension reduction and the incorporation of structured deformations to a three-dimensional continuum in the form of a thinning domain. We apply the two processes one after the other, exchanging…
We study a 3D ternary system derived as a sharp-interface limit of the Nakazawa-Ohta density functional theory of triblock copolymers, which combines an interface energy with a long range interaction term. Although both the binary case in…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem…
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…
We minimise the Canham-Helfrich energy in the class of closed immersions with prescribed genus, surface area and enclosed volume. Compactness is achieved in the class of oriented varifolds. The main result is a lower-semicontinuity estimate…
In this paper, we study the statistical mechanics within the polymer quantization framework in the semiclassical regime. We apply a non-canonical transformation to the phase space variables. Then, we use this non-canonical transformation to…
In this paper, we prove a Poincar\'e-type inequality for any set of finite perimeter which is stable with respect to the free energy among volume-preserving perturbation, provided that the Hausdorff dimension of its singular set is at most…
We study the localization of sets with constant nonlocal mean curvature and prescribed small volume in a bounded open set with smooth boundary, proving that they are {\em sufficiently close} to critical points of a suitable non-local…
The existence of minimizers in the fractional isoperimetric problem with multiple volume constraints is proved, together with a partial regularity result.
We derive and analyze a novel approach for modeling and computing the mechanical relaxation of incommensurate 2D heterostructures. Our approach parametrizes the relaxation pattern by the compact local configuration space rather than real…
Geometrical arrangements of minimum energy of a system of identical repelling particles in two dimensions are studied for different forms of the interaction potential. Stability conditions for the triangular structure are derived, and some…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
Motivated by the construction of time-periodic solutions for the three-dimensional Landau-Lifshitz-Gilbert equation in the case of soft and small ferromagnetic particles, we investigate the regularity properties of minimizers of the…
In this paper, we develop regularized discrete least squares collocation and finite volume methods for solving two-dimensional nonlinear time-dependent partial differential equations on irregular domains. The solution is approximated using…
The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps…
We consider $L^2$ minimizing geodesics along the group of volume preserving maps $SDiff(D)$ of a given 3-dimensional domain $D$. The corresponding curves describe the motion of an ideal incompressible fluid inside $D$ and are (formally)…
Partial localization is the phenomenon of self-aggregation of mass into high-density structures that are thin in one direction and extended in the others. We give a detailed study of an energy functional that arises in a simplified model…
In this paper, we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a…