A computational study of cation-π interactions in polycyclic systems: exploring the dependence on the curvature and electronic factors

Density functional theory (B3LYP) calculations with double and triple-ζ quality basis sets were performed on the Li⁺ and Na⁺ π-complexes of corannulene 2, sumanene 3CH₂, heterosumanenes 3X, triphenylene 4 and heterotrindenes 5X. The metal ions bind to both convex and concave faces of buckybowls, with a consistent preference to bind to the convex surface by about 1-4 kcal/mol. The metal ion complexation with the π-framework of the central six-membered ring span wider range compared to benzene, indicating the control of size, curvature and electronic perturbations over the strength of cation-π interactions. Computations show that the bowl-to-bowl inversion barriers are only slightly altered upon metal complexation, indicating the continuity of bowl-to-bowl inversion despite metal complexation. We have calculated the binding energies of model systems, triphenylene (4) and heterotrindenes (5X), which indicate that the interaction energies are controlled by electronic factors. While the inversion barrier is dependent mainly on the size of the heteroatom, the extent of binding is independent of the size of the atom or the bowl depth.     

Equivalence Principle Measurements

Over the centuries there have been many experimental tests of the universality of free-fall. To date, these measurements have established the equivalence between inertial and gravitational mass to high precision, justifying its use as a foundation stone of general relativity by Einstein. There is a surprising richness in the variety of techniques and choice of test bodies which have been used so far, and a brief review is presented. However, future space experiments promise much better precision in this measurement and STEP is presented in some detail as one of a number of such missions. Using pairs of concentric free-falling proof-masses, STEP will be able to test the Equivalence Principle (EP) to a sensitivity at least five orders of magnitude better than currently achievable on ground. The EP is a founding principle of general relativity and STEP is the most sensitive experiment of this type planned so far, aiming at 1 part in 10¹⁸.     

High order accurate,one-sided finite-difference approximations to concentration gradients at the boundaries,for the simulation of electrochemical reaction-diffusion problems in one-dimensional space geometry

Accurate calculation of concentration gradients at the boundaries is crucial in electrochemical kinetic simulations, owing to the frequent occurrence of gradient-dependent boundary conditions, and the importance of the gradient-dependent electric current. By using the information about higher spatial derivatives of the concentrations, contained in the time-dependent, kinetic reaction-diffusion partial differential equation(s) in one-dimensional space geometry, under appropriate assumptions it is possible to increase the accuracy orders of the conventional, one-sided n-point finite-difference formulae for the concentration gradients at the boundaries, without increasing n. In this way a new class of high order accurate gradient approximations is derived, and tested in simulations of potential-step chronoamperometric and current-step chronopotentiometric transients for the Reinert-Berg system. The new formulae possess advantages over the conventional gradient approximations. For example, they allow one to obtain a third order accuracy by using two space points only, or fourth order accuracy by using three points, and yet they yield smaller errors than the conventional four-point, or five-point formulae, respectively. Needing fewer points, for approximating the gradients with a given accuracy, simplifies also the solution of the linear algebraic equations arising from the application of implicit time integration schemes.     

The Universality of Zeta-Functions

The first part of the paper contains a survey on the universality of zeta-functions. Zeta-functions with Euler's product as well as zeta-functions without Euler's product are discussed. Also, the joint universality theorems are considered. In the second part of the paper the universality of zeta-functions of finite Abelian groups of rank 3 is proved.     

Behavioral and computational aspects of language and its acquisition

One of the greatest challenges facing the cognitive sciences is to explain what it means to know a language, and how the knowledge of language is acquired. The dominant approach to this challenge within linguistics has been to seek an efficient characterization of the wealth of documented structural properties of language in terms of a compact generative grammar—ideally, the minimal necessary set of innate, universal, exception-less, highly abstract rules that jointly generate all and only the observed phenomena and are common to all human languages. We review developmental, behavioral, and computational evidence that seems to favor an alternative view of language, according to which linguistic structures are generated by a large, open set of constructions of varying degrees of abstraction and complexity, which embody both form and meaning and are acquired through socially situated experience in a given language community, by probabilistic learning algorithms that resemble those at work in other cognitive modalities.     

Prediction of Γ-L and L-X crossovers in Ga<Subscript>x</Subscript>Al<Subscript>1-x</Subscript>Sb alloys by empirical pseudopotential method

Using empirical pseudopotential method Γ-L crossover is found for the Ga_0.74Al_0.26Sb. The conduction band minimum is observed to switch at the (0.87, 0, 0) point for Ga_0.51Al_0.49Sb which shifts to the X point for Ga_0.21Al_0.79Sb and remains at X leading finally to indirect band gap in AlSb. Band structure calculations for a large number of alloys are performed and bowing parameters b_X and b_L are proposed for the E_X and E_L respectively. Our findings may serve as directive to select the materials in a range of composition to examine the bowing parameters and thereby effective mass experimentally for the Ga_xAl_1-xSb alloys.     

Quasi-equilibrium lattice Boltzmann method

A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is developed. Lattice Boltzmann models for isothermal binary mixtures with a given Schmidt number, and for a weakly compressible flow with a given Prandtl number are derived and validated.     

Dynamics of a Tagged Particle in the Asymmetric Exclusion Process with the Step Initial Condition

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in the TASEP with the step initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of the TASEP to the Schur process, we show that the function is represented as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources.     

Resolution of computational aeroacoustics problems on unstructured grids with a higher-order finite volume scheme

Computational fluid dynamics (CFD) has become increasingly used in the industry for the simulation of flows. Nevertheless, the complex configurations of real engineering problems make the application of very accurate methods that only work on structured grids difficult. From this point of view, the development of higher-order methods for unstructured grids is desirable. The finite volume method can be used with unstructured grids, but unfortunately it is difficult to achieve an order of accuracy higher than two, and the common approach is a simple extension of the one-dimensional case. The increase of the order of accuracy in finite volume methods on general unstructured grids has been limited due to the difficulty in the evaluation of field derivatives. This problem is overcome with the application of the Moving Least Squares (MLS) technique on a finite volume framework. In this work we present the application of this method (FV-MLS) to the solution of aeroacoustic problems.