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The splitting of quasi-Fermi levels (QFLs) represents a key concept utilized to describe finite-bias operations of semiconductor devices, but its atomic-scale characterization remains a significant challenge. Herein, the non-equilibrium QFL…

We construct a quasi-polynomial time deterministic approximation algorithm for computing the volume of an independent set polytope with restrictions. Randomized polynomial time approximation algorithms for computing the volume of a convex…

The starting point of our analysis is a class of one-dimensional interacting particle systems with two species. The particles are confined to an interval and exert a nonlocal, repelling force on each other, resulting in a nontrivial…

While in principle exact, Kohn-Sham density functional theory -- the workhorse of computational chemistry -- must rely on approximations for the exchange-correlation functional. Despite staggering successes, present-day approximations still…

Since the pioneering work of Canham and Helfrich, variational formulations involving curvature-dependent functionals, like the classical Willmore functional, have proven useful for shape analysis of biomembranes. We address minimizers of…

We consider the sharp interface limit of a coupled Stokes/Cahn\textendash Hilliard system in a two dimensional, bounded and smooth domain, i.e., we consider the limiting behavior of solutions when a parameter $\epsilon>0$ corresponding to…

This paper investigates a Cahn-Hilliard-Swift-Hohenberg system, focusing on a three-species chemical mixture subject to physical constraints on volume fractions. The resulting system leads to complex patterns involving a separation into…

The volume distance from a point p to a convex hypersurface M of the (N+1)-dimensional space is defined as the minimum (N+1)-volume of a region bounded by M and a hyperplane H through the point. This function is differentiable in a…

The aim of this paper is twofold: - To give an elementary and self-contained proof of an explicit formula for the free energy for a general class of polymer chains interacting with an environment through periodic potentials. This…

We consider the convergence of partition functions and endpoint density for the half-space directed polymer model in dimension $1+1$ in the intermediate disorder regime as considered for the full space model by Alberts, Khanin and Quastel…

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 show how the spectrum of normal discrete short-range infinite-volume operators can be approximated with two-sided error control using only data from finite-sized local patches. As a corollary, we prove the computability of the spectrum…

The ab initio simulation of charged interfaces in the framework of density functional theory (DFT) is heavily employed for the study of electrochemical energy conversion processes. The capacitance is the primary descriptor for the response…

This paper continues the study of the asymptotic development of order 2 by $\Gamma$ -convergence of the Cahn-Hilliard functional with Dirichlet boundary conditions initiated in [8]. While in the first paper, the Dirichlet data are assumed…

The Dirac equation for the Coulomb problem is restated by incorporating a nonlinear effective interaction into the Dirac Hamiltonian: one keeps the $1/r$ dependence for the Coulomb field, but the coupling constant is modified by a factor…

We introduce a new paradigm for finite and infinite strict-one-dimensional uniform electron gases. In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. In the high-density limit (small-$r_s$, where…

The local Casimir energy density and the global Casimir energy for a massless scalar field associated with a $\lambda\delta$-function potential in a 3+1 dimensional circular cylindrical geometry are considered. The global energy is examined…

We derive a macroscopic limit for a sharp interface version of a model proposed in [29] to investigate pattern formation due to competition of chemical and mechanical forces in biomembranes. We identify sub- and supercrital parameter…

The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit plays a crucial role in the understanding of the…

The interaction of optical fields sculpted on the nano-scale with matter may not be described by the dipole approximation since the fields vary appreciably across the molecular length scale. Rather than incrementally adding higher…