Related papers: Connected Coulomb Columns: Analysis and Numerics
We present a computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model of diblock copolymers. The model is a fourth-order parabolic partial differential equation subject to homogeneous Neumann boundary…
When a Coulombic fluid is confined between two parallel charged plates, an exact relation links the difference of ionic densities at contact with the plates, to the surface charges of these boundaries. It no longer applies when the…
The quasi-harmonic model proposes that a crystal can be modeled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss' law shows that the ion-ion potential for a cubic Coulomb…
We present a personal view on the current state of statistical mechanics of Coulomb fluids with special emphasis on the interactions between macromolecular surfaces, concentrating on the weak and the strong coupling limits. Both are…
The purpose of this paper is to investigate the Cahn-Hillard approximation for entire minimal hypersurfaces in the hyperbolic space. Combining comparison principles with minimization and blow-up arguments, we prove existence results for…
Motivated by recent developments on the fabrication and control of semiconductor-based quantum dot qubits, we theoretically study a finite system of tunnel-coupled quantum dots with the electrons interacting through the long-range Coulomb…
The relativistic quantum motion of scalar bosons under the influence of a full vector (minimal $A^{\mu}$ and nonminimal $X^{\mu}$) and scalar ($V_{s}$) interactions embedded in the background of a cosmic string is explored in the context of…
Inspired by previous work of Kusner and Bauer-Kuwert, we prove a strict inequality between the Willmore energies of two surfaces and their connected sum in the context of isoperimetric constraints. Building on previous work by…
We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that part of the…
In this paper, we consider a microscopic semilinear elliptic equation posed in periodically perforated domains and associated with the Fourier-type condition on internal micro-surfaces. The first contribution of this work is the…
We introduce a random interaction matrix model (RIMM) for finite-size strongly interacting fermionic systems whose single-particle dynamics is chaotic. The model is applied to Coulomb blockade quantum dots with irregular shape to describe…
Using the specific model of a system of like charged ions confined between two planar like charged surfaces, we compare the predictions for the energy and density profile of four simulation methods available to treat the long range Coulomb…
We investigate an ensemble of systems formed by a ring enclosing a magnetic flux. The ring is coupled to a side stub via a tunneling junction and via Coulomb interaction. We generalize the notion of level hybridization due to the hopping,…
We study a class of Landau-de Gennes energy functionals with a sextic bulk energy density in a three-dimensional domain. We examine the asymptotic behavior of uniformly bounded minimizers in two distinct scenarios: one where their energy…
We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the…
The quantum dimer model, relevant for short-range resonant valence bond physics, is rigorously shown to have long range order in a crystalline phase in the attractive case at low temperature and not too large flipping term. This term flips…
First principles methods based on periodic boundary conditions are used extensively by materials theorists. However, applying these methods to systems with confined electronic states entails the use of large unit cells in order to avoid…
Deviations from the uniform oscillator spacing, related to the shape of the confining potential, have a strong influence on few-electron states in quantum dots when Coulomb effects are included. Distinct signatures are found for level…
Using area-preserving curve shortening flow, and a new inequality relating the potential generated by a set to its curvature, we study a non-local isoperimetric problem which arises in the study of di-block copolymer melts, also referred to…
Density functionals with a range-separated treatment of the exchange energy are known to improve upon their semilocal forerunners and fixed-fraction hybrids. The conversion of a given semilocal functional into its short-range analog is not…