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Biological cells estimate concentration gradients of signaling molecules with a precision that is limited not only by sensing noise, but additionally by the cell's own stochastic motion. We ask for the theoretical limits of gradient…
The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with…
A nonlinear Poisson--Boltzmann equation with transmission boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic…
Using time-dependent density matrix renormalization group calculations we study the transport properties ($I-V$ curves and shot noise) of the interacting resonant level model (IRLM) in a large range of the interaction parameter $U$, in the…
In this paper we investigate the behavior of a family of steady state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a $\epsilon$-neighborhood of a portion $\Gamma$ of the…
We consider charge transport across a finite graphene flake with a circular antidot defined in its center. The flake is connected to thin metallic armchair nanoribbons and the study covers the energy range within the neighborhood of the…
Conductivity of the defectless, perfect crystal graphene is found at the neutrality point at zero temperature and in the limit of large dielectric constant of the substrate. The steady state of the graphene with weak current is assumed to…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
Many types of cells are able to accurately sense shallow gradients of chemicals across their diameters, allowing the cells to move towards or away from chemical sources. This chemotactic ability relies on the remarkable capacity of cells to…
The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including size exclusion and their effect on the behaviour of…
The general problem of two-phase transport in phase-field models is analyzed: the flux of a conserved quantity is driven by the gradient of a potential through a medium that consists of domains of two distinct phases which are separated by…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
We consider perturbation defects obtained by perturbing a 2D conformal field theory (CFT) by a relevant operator on a half-plane. If the perturbed bulk theory flows to an infrared fixed point described by another CFT, the defect flows to a…
We discuss the limit of small width for the Laplacian defined on a waveguide with Robin boundary conditions. Under suitable hypothesis on the scaling of the curvature, we prove the convergence of the Robin Laplacian to the Laplacian on the…
We consider the vacuum wave function of a free scalar field theory in space partitioned into two regions, with the field obeying Robin conditions (of parameter $\kappa$) on the interface. A direct integration over fields in a subregion is…
The behavior of a conductive membrane in a static (DC) electric field is investigated theoretically. An effective zero-thickness model is constructed based on a Robin-type boundary condition for the electric potential at the membrane,…
We compute the Coulomb correction $\mathcal{C}$ to the a. c. conductivity of interacting massless Dirac particles in graphene in the collisionless limit using the polarization tensor approach in a regularization independent framework.…
We study the gradient flow of the Allen-Cahn equation with fixed boundary contact angle in Euclidean domains for initial data with bounded energy. Under general assumptions, we establish both interior and boundary convergence properties for…
A robust field-only boundary integral formulation of electromagnetics is derived without the use of surface currents that appear in the Stratton-Chu formulation. For scattering by a perfect electrical conductor (PEC), the components of the…
We construct a unique global-in-time solution to the two species Vlasov-Poisson-Boltzmann system in convex domains with the diffuse boundary condition, which can be viewed as one of the ideal scattering boundary model. The construction…