Related papers: Discrete Transformations in the Thomson Problem

In this paper we perform a refined blow up analysis of finite energy approximated solutions to a Nirenberg type problem on half spheres. The later consists of prescribing, under minimal boundary conditions, the scalar curvature to be a…

We give a description of numerical Newton algorithm on a constraint manifold using only the ambient coordinates (usually Euclidean coordinates) and the geometry of the constraint manifold. We apply the numerical Newton algorithm on a sphere…

Force fields uniquely assign interatomic forces for a given set of atomic coordinates. The underlying assumption is that electrons are in their quantum-mechanical ground state or in thermal equilibrium. However, there is an abundance of…

We study the Yamabe equation in the Euclidean half-space. We prove that any sign-changing solution has at least twice the energy of a standard bubble. Moreover, a sharper energy lower bound of the sign-changing solution set is also…

The Energy-Dissipation Principle provides a variational tool for the analysis of parabolic evolution problems: solutions are characterized as so-called null-minimizers of a global functional on entire trajectories. This variational…

We study the energy transfer process in quantum battery systems consisting of multiple central spins and bath spins. Here with "quantum battery" we refer to the central spins, whereas the bath serves as the "charger". For the single…

A cubic kilometer scale experiment has been proposed to detect cosmic neutrinos of energy from tens of GeV up to the highest energies observed for cosmic rays, around 10**20 eV, or possibly even beyond. Detection efficiencies depend…

Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem…

The use of quasi-elastic electron nucleus scattering is shown to provide significant constraints on models of the proton electromagnetic form factor of off-shell nucleons. Such models can be constructed to be consistent with constraints…

We study existence, regularity, and qualitative properties of solutions to the system \[ -\Delta u = |v|^{q-1} v\quad \text{ in }\Omega,\qquad -\Delta v = |u|^{p-1} u\quad \text{ in }\Omega,\qquad \partial_\nu u=\partial_\nu v=0\quad \text{…

Let $\Omega$ be a smooth bounded domain in $\mathbb{R}^{N}$, with $N\geq 5$, $a>0$, $\alpha\geq 0$ and $2^*=\frac{2N}{N-2}$. We show that the the exponent $q=\frac{2(N-1)}{N-2}$ plays a critical role regarding the existence of least energy…

In this work, we investigate the amount of energy that can be extracted or charged through unitary operations when only minimal information about the state is known. Assuming knowledge of only the mean energy of the state, we start by…

In this paper, we extend the analysis of the subcritical approximation of the Nirenberg problem on spheres recently conducted in \cite{MM19, MM}. Specifically, we delve into the scenario where the sequence of blowing up solutions exhibits a…

We consider an energy functional that arises in micromagnetic and liquid crystal theory on thin films. In particular, our energy comprises a non-convex term that models anti-symmetric exchange as well as an anisotropy term. We devise an…

We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…

We consider a model for a quantum battery consisting of a collection of $N$ two-level atoms driven by a classical field and decaying to a common reservoir. In the extensive regime, where the energy $E$ scales as $N$ and the fluctuations…

In this paper we consider the {\it Density Functional Theory} (DFT) framework, where a functional of the form $$F_\eps(\rho)=\eps T(\rho)+bC(\rho)-U(\rho)$$ has to be minimized in the class of non-negative measures $\rho$ which have a…

We present a topological mechanism of discretization, which gives for the fundamental electric charge a value equal to the square root of the Planck constant times the velocity of light, which is about 3.3 times the electron charge. Its…

We employ the chiral nucleon-nucleon potential derived using the method of unitary transformation up to next-to-next-to-leading order (NNLO) to study bound and scattering states in the two-nucleon system. The predicted partial wave phase…

The most challenging scenario for Kohn-Sham density functional theory, that is when the electrons move relatively slowly trying to avoid each other as much as possible because of their repulsion (strong-interaction limit), is reformulated…