Related papers: Sharp interface limit of an energy modelling nanop…
Nanoscale fabrication techniques, computational inverse design, and fields from silicon photonics to metasurface optics are enabling transformative use of an unprecedented number of structural degrees of freedom in nanophotonics. A critical…
A vectorial Modica--Mortola functional is considered and the convergence to a sharp interface model is studied. The novelty of the paper is that the wells of the potential are not constant, but depend on the spatial position in the domain…
This paper is concerned with equilibrium configurations of one-dimensional particle system with non-convex nearest-neighbour and next-to-nearest-neighbour interactions and its passage to the continuum. The goal is to derive compactness…
For an Ising spin glass on a hierarchical lattice, we show that the energy barrier to be overcome during the flip of a domain of size L scales as L to the power d-1 for all dimensions d. We do this by investigating appropriate lower bounds…
We consider Riesz-type nonlocal energies with general interaction kernels and their discretizations related to particle systems. We prove that the discretized energies $\Gamma$-converge in the weak-$*$ topology to the Riesz functional…
The ability to tailor the energy distribution of plasmons at the nanoscale has many applications in nanophotonics, such as designing plasmon lasers, spasers, and quantum emitters. To this end, we analytically study the energy distribution…
We examine the problem of two particles confined in an isotropic harmonic trap, which interact via a finite-ranged Gaussian-shaped potential in two spatial dimensions. We derive an approximative transcendental equation for the energy and…
We consider a mean-field model of a polymer with a spherically-symmetric finitely supported potential. We describe how the typical size of the polymer depends on the two parameters: the temperature, which approaches the critical value, and…
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…
The jamming transition of particles with finite-range interactions is characterized by a variety of critical phenomena, including power law distributions of marginal contacts. We numerically study a recently proposed simple model of…
We consider electrostatic interactions in two classes of nanostructures embedded in a three dimensional space: (1) helical nanotubes, and (2) thin films with uniform bending (i.e., constant mean curvature). Starting from the atomic scale…
We investigate the singular limit, as $\ep \to 0$, of the Fisher equation $\partial_t u=\ep \Delta u + \ep ^{-1}u(1-u)$ in the whole space. We consider initial data with compact support plus, possibly, perturbations very small as $\Vert x…
We consider a directed polymer of length $N$ interacting with a linear interface. The monomers carry i.i.d. random charges $(\omega_i)_{i=1}^N$ taking values in $\mathbb{R}$ with mean zero and variance one. Each monomer $i$ contributes an…
We analyze the localized phase of a general model of a directed polymer in the proximity of an interface that separates two solvents. Each monomer unit carries a charge, $\omega_n$, that determines the type (attractive or repulsive) and the…
A free boundary problem arising from materials science is studied in one-dimensional case. The problem studied here is an obstacle problem for the non-convex energy consisting of a bending energy, tension and an adhesion energy. If the…
We present some long-range interaction models for phase coexistence which have recently appeared in the literature, recalling also their relation to classical interface and capillarity problems. In this note, the main focus will be on the…
The degenerate de Gennes-Cahn-Hilliard (dGCH) equation is a model for phase separation which may more closely approximate surface diffusion than others in the limit when the thickness of the transition layer approaches zero. As a first step…
We introduce a class of models of semiflexible polymers. The latter are characterized by a strong rigidity, the correlation length associated to the gradient-gradient correlations, called the persistence length, being of the same order as…
A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The…
This article is concerned with the problem of minimising the Willmore energy in the class of \emph{connected} surfaces with prescribed area which are confined to a small container. We propose a phase field approximation based on De Giorgi's…