Related papers: Multiphase quadrature domains (existence and uniqu…
We investigate the effect of linear diffusion and interactions with the domain boundary on swarm equilibria by analyzing critical points of the associated energy functional. Through this process we uncover two properties of energy…
In this paper we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique…
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…
We study a quadratic nonlocal variational problem on a hybrid domain formed by a compact interval and finitely many discrete points. The associated energy splits into continuous, discrete, and interface contributions. Our main estimate…
We devise a new technique to prove two-dimensional crystallization results in the square lattice for finite particle systems. We apply this strategy to energy minimizers of configurational energies featuring two-body short-ranged particle…
Phase synchronization was proved to be unbounded in quantum level, but the witness of phase synchronization is always expensive in terms of the quantum resource and non-local measurements involved. Based on the quantum uncertainty relation,…
Many complex systems share two characteristics: 1) they are stochastic in nature, and 2) they are characterized by a large number of factors. At the same time, various natural complex systems appear to have two types of intertwined…
In this work we prove some abstract results about the existence of a minimizer for locally Lipschitz functionals, without any assumption of homogeneity, over a set which has its definition inspired in the Nehari manifold. As applications we…
Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets…
We present a novel approach which aims at high-performance uncertainty quantification for cardiac electrophysiology simulations. Employing the monodomain equation to model the transmembrane potential inside the cardiac cells, we evaluate…
Given a compact Riemannian manifold $(M^n,g)$ and a fixed cohomology class, $[\alpha^*] \in H^k(M)$, we consider the existence of a minimizer $\alpha \in [\alpha^*]$ of the generalized minimal surface energy $\int_M \sqrt{1+|\alpha|^2}…
We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. In contrast to Young's interference characterized by path lengths,…
In this paper, we develop a general framework for multicontinuum homogenization in perforated domains. The simulations of problems in perforated domains are expensive and, in many applications, coarse-grid macroscopic models are developed.…
The classification of the ground-state phases of complex one-dimensional electronic systems is considered in the context of a fixed-point strategy. Examples are multichain Hubbard models, the Kondo-Heisenberg model, and the one-dimensional…
We analytically study the critical phase of a mixed system of the U(2) gauge fields and global symmetry on the boundary using gauge/gravity. A variational minimization problem has been formulated. The numerical results pertinently show that…
Quantification of coherence lies at the heart of quantum information processing and fundamental physics. Exact evaluation of coherence measures generally needs a full reconstruction of the density matrix, which becomes intractable for…
We consider volume-constrained minimizers of the fractional perimeter with the addition of a potential energy in the form of a volume inte- gral. Such minimizers are solutions of the prescribed fractional curvature problem. We prove…
We consider the problem of rigorously computing periodic minimizers to the Ohta-Kawasaki energy. We develop a method to prove existence of solutions and determine rigorous bounds on the distance between our numerical approximations and the…
This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or…
In this note we provide a self-contained proof of an existence and uniqueness result for a class of Banach space valued evolution equations with an additive forcing term. The framework of our abstract result includes, for example, finite…