相关论文: Shape optimisation for nonlocal anisotropic energi…
We study the existence and the properties of ground states at fixed mass for a focusing nonlinear Schr\"odinger equation in dimension two with a point interaction, an attractive Coulomb potential and a nonlinearity of power type. We prove…
We report Monte Carlo results for the fluid structure of a system of dimeric particles interacting via a core-softened potential. More specifically, dimers interact through a repulsive pair potential of inverse-power form, modified in such…
In this series of papers, we present a motion planning framework for planning comfortable and customizable motion of nonholonomic mobile robots such as intelligent wheelchairs and autonomous cars. In Part I, we presented the mathematical…
The paper is devoted to the relaxation and integral representation in the space of functions of bounded variation for an integral energy arising from optimal design problems. The presence of a perimeter penalization is also considered in…
We carry on our study of the connection between two shape optimization problems with spectral cost. On the one hand, we consider the optimal design problem for the survival threshold of a population living in a heterogenous habitat…
In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…
In this paper we consider a nonlocal energy $I_\alpha$ whose kernel is obtained by adding to the Coulomb potential an anisotropic term weighted by a parameter $\alpha\in \R$. The case $\alpha=0$ corresponds to purely logarithmic…
Elastic interaction of pressurized spherical cavities embedded in a three-dimensional hyperelastic medium is computationally analyzed. Using finite element analysis across several positive and negative pressure scenarios, we calculate the…
The paper deals with an eigenvalue problems possessing infinitely many positive and negative eigenvalues. Inequalities for the smallest positive and the largest negative eigenvalues, which have the same properties as the fundamental…
We establish the $\Gamma$-convergence of some energy functionals describing nonlocal attractive interactions in bounded domains. The interaction potential solves an elliptic equation (local or nonlocal) in the bounded domain and the primary…
We simulate ultra-central collisions of prolate uranium-uranium nuclei at intermediate energies using the isospin-dependent Boltzmann-Uehling-Uhlenbeck model to investigate the impact of momentum anisotropy on spatial geometric effects. By…
We study the critical points of Coulomb energy considered as a function on configuration spaces associated with certain geometric constraints. Two settings of such kind are discussed in some detail. The first setting arises by considering…
In the da Costa's thin-layer approach, a quantum particle moving in a 3D sample is confined on a curved thin interface. At the end, the interface effects are ignored and such quantum particle is localized on a curved surface. A geometric…
Since shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations, we show how shape optimization techniques can also be applied to an interface identification problem…
We investigate the shape of critical points for a free energy consisting of a nonlocal perimeter plus a nonlocal repulsive term. In particular, we prove that a volume-constrained critical point is necessarily a ball if its volume is…
In this paper we consider the volume-constrained minimization of a variant of the Ohta-Kawasaki functional with an anisotropic surface energy replacing the standard perimeter. Following and suitably adapting the second variation approach…
In this paper, we describe a way to construct a class of dark energy models that admit late time de Sitter attractor solution. In the canonical scalar and Born-Infeld scalar dark energy models, we show mathematically that a simple…
We study an intrinsic model for collective behaviour on the hyperbolic space $\bbh^\dm$. We investigate the equilibria of the aggregation equation (or equivalently, the critical points of the associated interaction energy) for interaction…
We study an isoperimetric problem the energy of which contains the perimeter of a set, Coulomb repulsion of the set with itself, and attraction of the set to a background nucleus as a point charge with charge $Z$. For the variational…
We study the efficiency of sliding locomotion for three-link bodies in the presence of dry (Coulomb) friction. Friction coefficient space can be partitioned into several regions, each with distinct types of efficient kinematics. These…