Related papers: Multiphase quadrature domains (existence and uniqu…
For different phases to coexist in equilibrium at constant temperature $T$ and pressure $P$, the condition of equal chemical potential $\mu$ must be satisfied. This condition dictates that, for a single-component system, the maximum number…
The phase diagrams and transitions of nonequilibrium systems with multiplicative noise are studied theoretically. We show the existence of both strong and weak-coupling critical behavior, of two distinct active phases, and of a nonzero…
Multiphase estimation is a paradigmatic example of a multiparameter problem. When measuring multiple phases embedded in interferometric networks, specially-tailored input quantum states achieve enhanced sensitivities compared with both…
Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any…
The aim of this work is to prove existence and uniqueness of $L^{2}-$solutions of stochastic fractional partial differential equations in one spatial dimension. We prove also the equivalence between several notions of $L^{2}-$solutions. The…
In exact density functional theory (DFT) the total ground-state energy is a series of linear segments between integer electron points, a condition known as "piecewise linearity". Deviation from this condition is indicative of poor…
We prove a homogenization theorem for quadratic convolution energies defined in perforated domains. The corresponding limit is a Dirichlet-type quadratic energy, whose integrand is defined by a non-local cell-problem formula. The proof…
One of the crucial properties of a quantum system is the existence of bound states. While the existence of eigenvalues below zero, i.e., below the essential spectrum, is well understood, the situation of zero energy bound states at the edge…
The method of iterated conformal maps allows to study the harmonic measure of Diffusion Limited Aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of…
In pattern-forming systems, competition between patterns with different wave numbers can lead to domain structures, which consist of regions with differing wave numbers separated by domain walls. For domain structures well above threshold…
The computation of multiphase flows presents a subtle energetic equilibrium between potential (i.e., surface) and kinetic energies. The use of traditional interface-capturing schemes provides no control over such a dynamic balance. In the…
In this article, the energy stability of a one-field fictitious domain method is proved and validated by numerical tests in two and three dimensions. The distinguishing feature of this method is that it only solves for one velocity field…
We establish conditions to ensure the existence of minimizer for a class of mass-constrained functionals involving a nonattractive point interaction in three dimensions. The existence of minimizers follows from the compactness of minimizing…
In a series of papers on optimal control problems for the monodomain as well as for the bidomain equations of cardiac electrophysiology, the authors studied existence of minimizers and derived first-order necessary optimality conditions.…
This letter presents a dual quadrature phasemeter, an implementation of a phase-locked loop designed to track the phase of homodyne and heterodyne inter-satellite laser links. The dual quadrature phasemeters use dual quadrature optical…
Phase separation, i.e., the coexistence of two different phases, is observed in many systems away from the coexistence curve of a first-order transition, leading to a stable heterogeneous phase or region. Examples include various quantum…
This paper presents a detailed asymptotic and numerical investigation of the phase diagram for global minimizers to a Cahn-Hilliard functional with long-range interactions in two space dimensions. We introduce a small parameter measuring…
This article reveals an analysis of the quadratic systems that hold multiparametric families therefore, in the first instance the quadratic systems are identified and classified in order to facilitate their study and then the stability of…
While the scaling of entanglement in a quantum system can be used to distinguish many-body quantum phases, it is usually hard to quantify the amount of entanglement in mixed states of open quantum systems, while measuring entanglement…
The parametrisation method for invariant manifolds is a powerful technique for deriving reduced-order models in the context of nonlinear vibrating systems, allowing accurate computations of nonlinear normal modes. Thanks to arbitrary order…