相关论文: Nonlocal Shape Optimization via Interactions of At…
A polymer repelled by unfavorable interactions with a uniform flat surface may still be pinned to attractive edges and corners. This is demonstrated by considering adsorption of a two-dimensional ideal polymer to an attractive corner of a…
Repulsion between individuals within a finite radius is encountered in numerous applications, including cell exclusion, i.e. avoidance of overlapping cells, bird flocks, or microscopic pedestrian models. We define such individual based…
We prove the stability of the ball as global minimizer of an attractive shape functional under volume constraint, by means of mass transportation arguments. The stability exponent is $1/2$ and it is sharp. Moreover, we use such stability…
We consider the mass-critical nonlinear Schr\"odinger equation on non-compact metric graphs. A quite complete description of the structure of the ground states, which correspond to global minimizers of the energy functional under a mass…
In this work, we study a new notion involving convergence of microstructures represented by matrices $B^\epsilon$ related to the classical $H$-convergence of $A^\epsilon$. It incorporates the interaction between the two microstructures.…
We are interested in a kinetic equation intended to describe the interaction of particles with their environment. The environment is modeled by a collection of local vibrational degrees of freedom. We establish the existence of weak…
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…
A classic feature of gravity is that it is an attractive force. If a source mass is prepared in a localized (classical- like) state, it will cause another probe mass to move towards it. Here we consider the situation in which a source mass…
In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or…
We consider a shape optimization problem written in the optimal control form: the governing operator is the $p$-Laplacian in the Euclidean space $\R^d$, the cost is of an integral type, and the control variable is the domain of the state…
We study the {\it quasi-classical limit} of a quantum system composed of finitely many non-relativistic particles coupled to a quantized field in Nelson-type models. We prove that, as the field becomes classical and the corresponding…
We study a multi--particle model including a kinetic energy and a non linear local self-interaction, both in the bosonic and fermionic cases. In both cases, we prove that the model is well-posed if the number of particles is large enough.…
The goal of this paper is to improve the performance of an electric motor by modifying the geometry of a specific part of the iron core of its rotor. To be more precise, the objective is to smooth the rotation pattern of the rotor. A shape…
We introduce \emph{contact interactions hamiltonians} (self-adjointoperators defined by boundary conditions) between $N$ massive particles in $R^3$, $N \geq 3$. We prove that they are limits (in strong resolvent sense) when $ \epsilon \to…
We solve explicitly a certain minimization problem for probability measures in one dimension involving an interaction energy that arises in the modelling of aggregation phenomena. We show that in a certain regime minimizers are absolutely…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
In the supersymmetric quantum mechanics formalism, the shape invariance condition provides a sufficient constraint to make a quantum mechanical problem solvable; i.e., we can determine its eigenvalues and eigenfunctions algebraically. Since…
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…
We consider the shape-topological control of a singularly perturbed variational inequality. The geometry-dependent state problem that we address in this paper concerns a heterogeneous medium with a micro-object (defect) and a macro-object…
In this paper, we are interested in the analysis of a well-known free boundary/shape optimization problem motivated by some issues arising in population dynamics. The question is to determine optimal spatial arrangements of favorable and…