Angle‐resolved photoemission spectroscopy and imaging with a submicrometre probe at the SPECTROMICROSCOPY‐3.2L beamline of Elettra

The extensive upgrade of the experimental end‐station of the SPECTROMICROSCOPY‐3.2L beamline at Elettra synchrotron light source is reported. After the upgrade, angle‐resolved photoemission spectroscopy from a submicrometre spot and scanning microscopy images monitoring the photoelectron signal inside selected acquisition angle and energy windows can be performed. As a test case, angle‐resolved photoemission spectroscopy from single flakes of highly oriented pyrolitic graphite and imaging of the flakes with image contrast owing to rotation of the band dispersion of different flakes are presented.     

Action Spectroscopy on Dense Samples of Photosynthetic Reaction Centers of Rhodobacter sphaeroides WT Based on Nanosecond Laser-Flash 13C Photo-CIDNP MAS NMR

Photochemically induced dynamic nuclear polarization magic-angle spinning nuclear magnetic resonance (photo-CIDNP MAS NMR) allows for the investigation of the electronic structure of the photochemical machinery of photosynthetic reaction centers (RCs) at atomic resolution. For such experiments, either continuous radiation from white xenon lamps or green laser pulses are applied to optically dense samples. In order to explore their optical properties, optically thick samples of isolated and quinone-removed RCs of the purple bacteria of Rhodobacter sphaeroides wild type are studied by nanosecond laser-flash ¹³C photo-CIDNP MAS NMR using excitation wavelengths between 720 and 940 nm. Action spectra of both the transient nuclear polarization as well as the nuclear hyperpolarization, remaining in the electronic ground state at the end of the photocycle, are obtained. It is shown that the signal intensity is limited by the amount of accessible RCs and that the different mechanisms of the photo-CIDNP production rely on the same photophysical origin, which is the photocycle induced by one single photon.     

Nanosecond-Flash 15N Photo-CIDNP MAS NMR on Reaction Centers of Rhodobacter sphaeroides R26

Photochemically induced dynamic nuclear polarization (photo-CIDNP) is observed with time-resolved ¹⁵N magic-angle spinning (MAS) nuclear magnetic resonance (NMR) in uniformly ¹⁵N-labeled reaction centers (RCs) of the purple bacterium Rhodobacter (Rb.) sphaeroides R26 under illumination with nanosecond laser flashes. The ¹⁵N NMR signals enhanced by the solid-state photo-CIDNP effect are related to electron spin densities in the primary radical pair and allow for reconstruction of the electronic structure at atomic scale. New assignments for the photochemically active nitrogens are proposed based on simulations of the intensities. The ratio of electron spin densities between cofactors P _L and P _M is observed to be about 4:1. The origin of the high asymmetry is discussed.     

Frames of exponentials and sub-multitiles in LCA groups

In this note, we investigate the existence of frames of exponentials for $L^2(\mathrm{\Omega })$ in the setting of LCA groups. Our main result shows that sub-multitiling properties of $\mathrm{\Omega }?\stackrel{?}{G}$ with respect to a uniform lattice Γ of $\stackrel{?}{G}$ guarantee the existence of a frame of exponentials with frequencies in a finite number of translates of the annihilator of Γ. We also prove the converse of this result and provide conditions for the existence of these frames. These conditions extend recent results on Riesz bases of exponentials and multitilings to frames.     

Optical mercury sensing using a benzothiazolium hemicyanine dye

[structure: see text] The selectivity and sensitivity of a benzothiazolium hemicyanine dye toward mercury(II) in aqueous solutions are described. Mercury ions coordinate to the dye forming a 1:1 complex. This interaction induces a color change in the dye at micromolar concentrations of mercury. Furthermore, the color change and quenching of the dye emission are selective for mercury when compared with other ions such as lead(II), cadmium(II), zinc(II), or iron(II).     

Central limit theorems for solutions of the Kac equation: speed of approach to equilibrium in weak metrics

This paper is part of our efforts to show how direct application of probabilistic methods, pertaining to central limit general theory, can enlighten us about the convergence to equilibrium of the solutions of the Kac equation. Here, we consider convergence with respect to the following metrics: Kolmogorov’s uniform metric; 1 and 2 Gini’s dissimilarity indices (widely known as 1 and 2 Wasserstein metrics); χ-weighted metrics. Our main results provide new bounds, or improvements on already well-known ones, for the corresponding distances between the solution of the Kac equation and the limiting Gaussian (Maxwellian) distribution. The study is conducted both under the necessary assumption that initial data have finite energy, without assuming existence of moments of order greater than 2, and under the condition that the (2 + δ)-moment of the initial distribution is finite for some δ > 0.     

Mathematical models for the elastic beam with structural damping

In this paper the existence, regularity and sharp estimates for the solutions of an abstract second order evolution equation are proved and applications to models of a (possibly non homogeneous) elastic beam with a frequency-proportional damping are given.     

A new optimal electricity market bid model solved through perspective cuts

On current electricity markets the electrical utilities are faced with very sophisticated decision making problems under uncertainty. Moreover, when focusing in the short-term management, generation companies must include some medium-term products that directly influence their short-term strategies. In this work, the bilateral and physical futures contracts are included into the day-ahead market bid following MIBEL rules and a stochastic quadratic mixed-integer programming model is presented. The complexity of this stochastic programming problem makes unpractical the resolution of large-scale instances with general-purpose optimization codes. Therefore, in order to gain efficiency, a polyhedral outer approximation of the quadratic objective function obtained by means of perspective cuts (PC) is proposed. A set of instances of the problem has been defined with real data and solved with the PC methodology. The numerical results obtained show the efficiency of this methodology compared with standard mixed quadratic optimization solvers.     

Electrically Switchable Magnetic Molecules: Inducing a Magnetic Coupling by Means of an External Electric Field in a Mixed‐Valence Polyoxovanadate Cluster

Herein we evaluate the influence of an electric field on the coupling of two delocalized electrons in the mixed‐valence polyoxometalate (POM) [GeV₁₄O₄₀]^8? (in short V₁₄) by using both a t‐J model Hamiltonian and DFT calculations. In absence of an electric field the compound is paramagnetic, because the two electrons are localized on different parts of the POM. When an electric field is applied, an abrupt change of the magnetic coupling between the two delocalized electrons can be induced. Indeed, the field forces the two electrons to localize on nearest‐neighbors metal centers, leading to a very strong antiferromagnetic coupling. Both theoretical approaches have led to similar results, emphasizing that the sharp spin transition induced by the electric field in the V₁₄ system is a robust phenomenon, intramolecular in nature, and barely influenced by small changes on the external structure.     

Some characterizations of magnetic Sobolev spaces

ABSTRACT

The aim of this note is to survey recent results contained in Nguyen H-M, Squassina M. [On anisotropic Sobolev spaces. Commun Contemp Math, to appear. DOI:10.1142/S0219199718500177]; Nguyen H-M, Pinamonti A, Squassina M, et al. [New characterizations of magnetic Sobolev spaces. Adv Nonlinear Anal. 2018;7(2):227–245]; Pinamonti A, Squassina M, Vecchi E. [Magnetic BV functions and the Bourgain-Brezis-Mironescu formula. Adv Calc Var, to appear. DOI:10.1515/acv-2017-0019]; Pinamonti A, Squassina M, Vecchi E. [The Maz'ya-Shaposhnikova limit in the magnetic setting. J Math Anal Appl. 2017;449:1152–1159] and Squassina M, Volzone B. [Bourgain-Brezis-Mironescu formula for magnetic operators. C R Math Acad Sci Paris. 2016;354:825–831], where the authors extended to the magnetic setting several characterizations of Sobolev and BV functions.