Structure and diffusion in mixtures of ionic liquids

The properties of ionic mixtures of LiBr-KBr are investigated on the basis of molecular dynamics calculations, using the Tosi-Fumi pair-potentials. The determination of the excess internal energy of mixing indicates the predominant negative contribution of the coulomb energy. The position of the first peak of the anion-cation radial distribution function depends strongly on the size of the ions and its height is much influenced by the strength of the coulomb forces. It is shown that the equivalent coordination numbers vary from about 4 for the Li-Br pair to 6 for the K-Br pair. These numbers do not change very much when the composition is varied.

The ionic dynamics is analysed through the brownian-like formalism which gives a useful connection between the structure and the particle motion. Two mechanisms are involved in the diffusion process: an oscillation of the particle in the force field of the neighbouring particles and a collective mode of motion which has a longer relaxation time. The strong anion-cation correlation, which mainly affects the smallest cation, dominates when the charge ordering (quasi-lattice structure) vanishes.     

Finding largest small polygons with GloptiPoly

A small polygon is a convex polygon of unit diameter. We are interested in small polygons which have the largest area for a given number of vertices n. Many instances are already solved in the literature, namely for all odd n, and for n = 4, 6 and 8. Thus, for even n ≥ 10, instances of this problem remain open. Finding those largest small polygons can be formulated as nonconvex quadratic programming problems which can challenge state-of-the-art global optimization algorithms. We show that a recently developed technique for global polynomial optimization, based on a semidefinite programming approach to the generalized problem of moments and implemented in the public-domain Matlab package GloptiPoly, can successfully find largest small polygons for n = 10 and n = 12. Therefore this significantly improves existing results in the domain. When coupled with accurate convex conic solvers, GloptiPoly can provide numerical guarantees of global optimality, as well as rigorous guarantees relying on interval arithmetic.     

An Algorithm for Nonlinear,Nonparametric Model Choice and Prediction

We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, aims to choose those combinations of vector components that provide best prediction. The algorithm is constructed specifically so that it devotes attention to components that might be of relatively little predictive value by themselves, and so might be ignored by more conventional methodology for model choice, but which, in combination with other difficult-to-find components, can be particularly beneficial for prediction. The design of the algorithm is also motivated by a desire to choose vector components that become redundant once appropriate combinations of other, more relevant components are selected. Our theoretical arguments show these goals are met in the sense that, with probability converging to 1 as sample size increases, the algorithm correctly determines a small, fixed number of variables on which the regression mean, g say, depends, even if dimension diverges to infinity much faster than n. Moreover, the estimated regression mean based on those variables approximates g with an error that, to first order, equals the error which would arise if we were told in advance the correct variables. In this sense, the estimator achieves oracle performance. Our numerical work indicates that the algorithm is suitable for very high dimensional problems, where it keeps computational labor in check by using a novel sequential argument, and also for more conventional prediction problems, where dimension is relatively low.     

The effect of solvent additives on morphology and excited-state dynamics in PCPDTBT:PCBM photovoltaic blends

The dependence of the thin film morphology and excited-state dynamics for the low-bandgap donor-acceptor copolymer poly[2,6-(4,4-bis-(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b']-dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] (PCPDTBT) in pristine films and in blends (1:2) with [6,6]-phenyl-C(61)-butyric acid methyl ester (PCBM) on the use of the solvent additive 1,8-octanedithiol (ODT) is studied by solid-state nuclear magnetic resonance (NMR) spectroscopy and broadband visible and near-infrared pump-probe transient absorption spectroscopy (TAS) covering a spectral range from 500-2000 nm. The latter allows monitoring of the dynamics of excitons, bound interfacial charge-transfer (CT) states, and free charge carriers over a time range from femto- to microseconds. The broadband pump-probe experiments reveal that excitons are not only generated in the polymer but also in PCBM-rich domains. Depending on the morphology controlled by the use of solvent additives, polymer excitons undergo mainly ultrafast dissociation (<100 fs) in blends prepared without ODT or diffusion-limited dissociation in samples prepared with ODT. Excitons generated in PCBM diffuse slowly to the interface in both samples and undergo dissociation on a time scale of several tens of picoseconds up to hundreds of picoseconds. In both samples a significant fraction of the excitons creates strongly bound interfacial CT states, which exhibit subnanosecond geminate recombination. The total internal quantum efficiency loss due to geminate recombination is estimated to be 50% in samples prepared without ODT and is found to be reduced to 30% with ODT, indicating that more free charges are generated in samples prepared with solvent additives. In samples prepared with ODT, the free charges exhibit clear intensity-dependent recombination dynamics, which can be modeled by Langevin-type recombination with a bimolecular recombination coefficient of 6.3 × 10(-11) cm(3) s(-1). In samples prepared without ODT, an additional nanosecond recombination of polaron pairs is observed in conjunction with an increased intensity-independent trap-assisted nongeminate recombination of charges. Furthermore, a comparison of the triplet-induced absorption spectra of PCPDTBT with the charge-induced absorption in PCPDTBT:PCBM blends reveals that triplets have a very similar excited-state absorption spectrum compared to the free charge carriers, however, in contrast have a distinct intensity-independent lifetime. Overall, our results suggest that whether free charges or strongly bound CT states are created upon dissociation of excitons at the PCPDTBT:PCBM interface is determined instantaneously upon exciton dissociation and that once formed strongly bound CT states rapidly recombine and thus are unlikely to dissociate into free charges. The observation of a significantly larger bimolecular recombination coefficient than previously determined for poly(3-hexylthiophen-2,5-diyl):PCBM (P3HT:PCBM) and PCDTBT:PCBM samples indicates that nongeminate recombination of free charges considerably competes with charge extraction in PCPDTBT:PCBM photovoltaic devices.     

Global stability for a model of competition in the chemostat with microbial inputs

We propose a model of competition of n species in a chemostat, with constant input of some species. We mainly emphasize the case that can lead to coexistence in the chemostat in a non-trivial way, i.e., where the n−1 less competitive species are in the input. We prove that if the inputs satisfy a constraint, the coexistence between the species is obtained in the form of a globally asymptotically stable (GAS) positive equilibrium, while a GAS equilibrium without the dominant species is achieved if the constraint is not satisfied. This work is round up with a thorough study of all the situations that can arise when having an arbitrary number of species in the chemostat inputs; this always results in a GAS equilibrium that either does or does not encompass one of the species that is not present in the input.     

Detecting high-dimensional determinism in time series with application to human movement data

We numerically investigate the ability of a statistic to detect determinism in time series generated by high-dimensional continuous chaotic systems. This recently introduced statistic (denoted V_E2) is derived from the averaged false nearest neighbors method for analyzing data. Using surrogate data tests, we show that the proposed statistic is able to discriminate high-dimensional chaotic data from their stochastic counterparts. By analyzing the effect of the length of the available data, we show that the proposed criterion is efficient for relatively short time series. Finally, we apply the method to real-world data from biomechanics, namely postural sway time series. In this case, the results led us to exclude the hypothesis of nonlinear deterministic underlying dynamics for the observed phenomena.     

Modeling basic components of solid oxide fuel cells using density functional theory: Bulk and surface properties of CeO2

In this paper, the structural and electronic properties of CeO₂ are studied using conventional and hybrid density functional theory. A computational protocol, based on the parameter-free hybrid functional PBE0 coupled with a 4f in-valence basis set for Ce atoms based on a 28 electrons small core pseudopotential is able to reasonably reproduce both structural and electronic experimental data. Such a protocol is then applied to the modeling of true 2-D periodic CeO₂ slabs of non polar low-index surfaces. The obtained results show that the (111) surface is more stable than the (110) one (0.73 vs 0.81 J/m²), with a substantial rumbling in the outermost planes of this latter. Finally, as a first step toward reactivity at CeO₂ surfaces involved in solid oxide fuel cells, the importance of electrostatic effects in the adsorption of chemical species such as CO is presented. These results will allow for a detailed study of catalytic reactions at ceria surface.     

Highly efficient broadband double-sided Fresnel lens for THz range

Modern passive THz setups require effective optical elements with a large numerical aperture. Here we propose a new type of the optical element for THz applications, which is a broadband double-sided Fresnel-like lens with an optimized thickness. The optimization is performed to obtain a very low attenuation, low material cost, and small weight in the element media. It also provides achromatic properties for the assumed wavelength range. The experimental evaluation of the proposed diffractive lens by means of time-domain spectroscopy is presented and discussed.     

An addition theorem and maximal zero-sum free sets in ℤ/<Emphasis Type="Italic">p</Emphasis>ℤ

Using the polynomial method in additive number theory, this article establishes a new addition theorem for the set of subsums of a set satisfying A ∩ (−A) = ∅ in ℤ/pℤ: