Related papers: Nonlocal Shape Optimization via Interactions of At…
In this paper we consider a competitive weakly coupled elliptic system in which each species is attracted to a small region and repelled from its complement. In this setting, we establish the existence of infinitely many solutions and of a…
During the last stage of collapse of a compact object into the horizon of events, the potential energy of its surface layer decreases to a negative value below all limits. The energy-conservation law requires an appearance of a…
We introduce and study certain variants of Gamow's liquid drop model in which an anisotropic surface energy replaces the perimeter. After existence and nonexistence results are established, the shape of minimizers is analyzed. Under…
Via numerical simulations and analytical calculations, depletion forces are studied in mixtures of small and big particles that interact via soft repulsive potentials. While big particles are spherical, small particles are nonspherical with…
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…
We consider a large class of interacting particle systems in 1D described by an energy whose interaction potential is singular and non-local. This class covers Riesz gases (in particular, log gases) and applications to plasticity and…
In this paper we consider the problem of characterizing the minimum energy configurations of a finite system of particles interacting between them due to attracting or repulsive forces given by a certain inter molecular potential. We limit…
We consider particles on a one-dimensional lattice whose evolution is governed by nearest-neighbor interactions where particles that have reached size zero are removed from the system. Concentrating on configurations with infinitely many…
We consider a shape optimization problem related to the persistence threshold for a biological species, the unknown shape corresponding to the zone of the habitat which is favorable to the population. Analytically, this translates in the…
Newton's problem of the body of minimal aerodynamic resistance is traditionally stated in the class of {\it convex} axially symmetric bodies with fixed length and width. We state and solve the minimal resistance problem in the wider class…
A new inequality for a nonlinear surface layer integral is proved for minimizers of causal variational principles. This inequality is applied to obtain a new proof of the positive mass theorem with volume constraint. Next, a positive mass…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of…
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…
Laboratory experiments on gravitation are usually performed with objects of constant density, so that the analysis of the forces concerns only the geometry of their shape. In an ideal experiment, the shapes of the constituent parts will be…
We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross-Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen…
Evaluating accessible conformational space is computationally expensive and thermal motions are partly neglected in computer models of molecular interactions. This produces error into the estimates of binding strength. We introduce a method…
We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and energy). We classify all special macroscopic modes…
We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of…
We show that heterogeneity in self-propulsion speed can lead to the emergence of a robust effective short-range repulsion among active particles interacting via long-range attractive potentials. Using the example of harmonically coupled…