Angle-Resolved Photoemission of Solvated Electrons in Sodium-Doped Clusters

Angle-resolved photoelectron spectroscopy of the unpaired electron in sodium-doped water, methanol, ammonia, and dimethyl ether clusters is presented. The experimental observations and the complementary calculations are consistent with surface electrons for the cluster size range studied. Evidence against internally solvated electrons is provided by the photoelectron angular distribution. The trends in the ionization energies seem mainly determined by the degree of hydrogen bonding in the solvent and the solvation of the ion core. The onset ionization energies of water and methanol clusters do not level off at small cluster sizes, but decrease slightly with increasing cluster size

Tightness for a stochastic Allen--Cahn equation

We study an Allen-Cahn equation perturbed by a multiplicative stochastic noise which is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive uniform energy bounds and prove tightness of of solutions in the sharp interface limit, and show convergence to phase-indicator functions.Comment: 27 pages, final Version to appear in "Stochastic Partial Differential Equations: Analysis and Computations". In Version 4, Proposition 6.3 is new. It replaces and simplifies the old propositions 6.4-6.

Particle approximation of the one dimensional Keller-Segel equation, stability and rigidity of the blow-up

We investigate a particle system which is a discrete and deterministic approximation of the one-dimensional Keller-Segel equation with a logarithmic potential. The particle system is derived from the gradient flow of the homogeneous free energy written in Lagrangian coordinates. We focus on the description of the blow-up of the particle system, namely: the number of particles involved in the first aggregate, and the limiting profile of the rescaled system. We exhibit basins of stability for which the number of particles is critical, and we prove a weak rigidity result concerning the rescaled dynamics. This work is complemented with a detailed analysis of the case where only three particles interact

On a linear programming approach to the discrete Willmore boundary value problem and generalizations

We consider the problem of finding (possibly non connected) discrete surfaces spanning a finite set of discrete boundary curves in the three-dimensional space and minimizing (globally) a discrete energy involving mean curvature. Although we consider a fairly general class of energies, our main focus is on the Willmore energy, i.e. the total squared mean curvature Our purpose is to address the delicate task of approximating global minimizers of the energy under boundary constraints. The main contribution of this work is to translate the nonlinear boundary value problem into an integer linear program, using a natural formulation involving pairs of elementary triangles chosen in a pre-specified dictionary and allowing self-intersection. Our work focuses essentially on the connection between the integer linear program and its relaxation. We prove that: - One cannot guarantee the total unimodularity of the constraint matrix, which is a sufficient condition for the global solution of the relaxed linear program to be always integral, and therefore to be a solution of the integer program as well; - Furthermore, there are actually experimental evidences that, in some cases, solving the relaxed problem yields a fractional solution. Due to the very specific structure of the constraint matrix here, we strongly believe that it should be possible in the future to design ad-hoc integer solvers that yield high-definition approximations to solutions of several boundary value problems involving mean curvature, in particular the Willmore boundary value problem

Combined treatment with memantine and galantamine-CR compared with galantamine-CR only in antidementia drug naive patients with mild-to-moderate Alzheimer's disease

Introduction: Several studies have tested the N-methyl-D-aspartate–receptor antagonist memantine as an add-on to pre-existing treatment with acetylcholinesterase inhibitors. The objective of this study was to evaluate the efficacy and safety of a combined memantine and galantamine-CR de novo regimen compared with galantamine-CR only treatment in never treated patients with mild-to-moderate Alzheimer's disease (AD). Methods: Antidementia drug–naïve participants (n = 232) with probable, mild-to-moderate AD, and mini-mental state examination scores between 15 and 26 (inclusive) were randomized to receive either 20 mg/day memantine plus 24 mg/day galantamine-CR or 24 mg/day galantamine-CR plus placebo in a 52-week, prospective, double-blind, controlled trial. The primary outcome measurement was the change on the Alzheimer's disease assessment scale-cognition score. Secondary measures comprised the Alzheimer's Disease Cooperative Study-activities of daily living inventory and the clinical dementia rating. Results: At the end of the trial, there were no statistically significant differences between the galantamine-CR/memantine combination and galantamine-CR only group in primary and secondary outcome measurements. The incidence and the severity of adverse events were similar between the groups. Discussion: In this trial, memantine in combination with galantamine-CR did not show an advantage with respect to cognition, function, and behavior in previously never treated patients with mild-to-moderate AD. There were no significant differences in tolerability and safety between the groups. Thus, a de novo combination treatment results in no significant improvement in disease progression (current controlled trials number: NCT01921972)

The sharp-interface limit for the Navier--Stokes--Korteweg equations

We investigate the sharp-interface limit for the Navier--Stokes--Korteweg model, which is an extension of the compressible Navier--Stokes equations. By means of compactness arguments, we show that solutions of the Navier--Stokes--Korteweg equations converge to solutions of a physically meaningful free-boundary problem. Assuming that an associated energy functional converges in a suitable sense, we obtain the sharp-interface limit at the level of weak solutions

On Vanishing Theorems For Vector Bundle Valued p-Forms And Their Applications

Let $F: [0, \infty) \to [0, \infty)$ be a strictly increasing $C^2$ function with $F(0)=0$. We unify the concepts of $F$-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce $F$-Yang-Mills fields, $F$-degree, $F$-lower degree, and generalized Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on manifolds. When $F(t)=t, \frac 1p(2t)^{\frac p2}, \sqrt{1+2t} -1,$ and $1-\sqrt{1-2t},$ the $F$-Yang-Mills field becomes an ordinary Yang-Mills field, $p$-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the plus sign, and a generalized Yang-Mills-Born-Infeld field with the minus sign on a manifold respectively. We also introduce the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) and derive the first variational formula of the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) with applications. In a more general frame, we use a unified method to study the stress-energy tensors that arise from calculating the rate of change of various functionals when the metric of the domain or base manifold is changed. These stress-energy tensors, linked to $F$-conservation laws yield monotonicity formulae. A "macroscopic" version of these monotonicity inequalities enables us to derive some Liouville type results and vanishing theorems for $p-$forms with values in vector bundles, and to investigate constant Dirichlet boundary value problems for 1-forms. In particular, we obtain Liouville theorems for $F-$harmonic maps (e.g. $p$-harmonic maps), and $F-$Yang-Mills fields (e.g. generalized Yang-Mills-Born-Infeld fields on manifolds). We also obtain generalized Chern type results for constant mean curvature type equations for $p-$forms on $\Bbb{R}^m$ and on manifolds $M$ with the global doubling property by a different approach. The case $p=0$ and $M=\mathbb{R}^m$ is due to Chern.Comment: 1. This is a revised version with several new sections and an appendix that will appear in Communications in Mathematical Physics. 2. A "microscopic" approach to some of these monotonicity formulae leads to celebrated blow-up techniques and regularity theory in geometric measure theory. 3. Our unique solution of the Dirichlet problems generalizes the work of Karcher and Wood on harmonic map