Direct evidence of the dependence of surface state density on the size of SnO2 nanoparticles observed by scanning tunnelling spectroscopy

In this work, we report a scanning tunnelling spectroscopy (STS) study of 30 and 10 nm tin dioxide nanoparticles. The STS spectra give a surface band gap of 2.5 eV for both samples and show that the density of surface states in the band gap is around 6 times higher for the 30 nm particles than for the 10 nm particles. This provides direct experimental evidence for our theoretical model, which predicts a decrease in the surface state density as the particle size decreases, and partly accounts for the improved sensitivity of gas sensing devices fabricated with nanoparticles.     

B(a)cklund Transformation and Multiple Soliton Solutions for (3+1)-Dimensional Potential-YTSF Equation

We study an approach to constructing multiple soliton solutions of the (3 1)-dimensional nonlinear evolu tion equation. We take the (3 1)-dimensional potential-YTSF equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3 1)-dimensional potential-YTSF equa tion into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3 1)-dimensional potential-YTSF equation are obtained by introducing a class of formal solutions.     

Effects of surface step on molecular propane adsorption

We have studied the effects of surface step on molecular propane adsorption using molecular-dynamics simulations and a model stepped surface, Pt(6 5 5). Incidences along the step edge (smooth azimuth) and perpendicular to the step edge with upstairs momentum (upstairs azimuth) and downstairs momentum (downstairs azimuth) are considered. In general, the surface step enhances the initial trapping probability of propane except for the downstairs incidences. The most efficient zone in facilitating adsorption is near the bottom of the surface step on the lower terrace where incident molecules experience stronger attraction and an “additional-layer” effect when crossing the step. The least efficient zone is the top of the surface step on the upper terrace due to an opposite “missing-layer” effect. Surface step also creates steric effects such that more incident molecules along the upstairs azimuth but significantly less molecules along the downstairs azimuth impact the step-bottom zone. The latter steric effect, a shadowing effect, undermines the high trapping efficiency of the step-bottom zone to cause the downstairs incidences to have the lowest trapping probabilities. While the shadowing effect can be enhanced by larger incident angles and lower incident energies, the other steric effect on the upstairs incidences is relatively insensitive to the incident energy. Overall, the influence of surface step on molecular adsorption diminishes at low incident energies and large incident angles because longer contact times and less normal momenta result in high trapping probability across the entire stepped surface.     

Backlund Transformations for the Initial Problems of Nizhnich and Nizhnich-Novikov-Veselov Equations

The homogeneous balance method is a method for solving general partial differential equations (PDEs). Inthis paper we solve a kind of initial problems of the PDEs by using the special Backlund transformations of the initialproblem. The basic Fourier transformation method and some variable-separation skill are used as auxiliaries. Two initialproblems of Nizhnich and the Nizhnich-Novikov-Veselov equations are solved by using this approach.     

New localized excitations in a (2+1)-dimensional Broer—Kaup system

Starting with the extended homogeneous balance method and a variable separation approach, a general variable separation solution of the Broer—Kaup system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakon and fractal localized solutions, some new types of localized excitations, such as compacton and folded excitations, are obtained by introducing appropriate lower-dimensional piecewise smooth functions and multiple-valued functions, and some interesting novel features of these structures are revealed.     

High‐order numerical methods for one‐dimensional parabolic singularly perturbed problems with regular layers

In this work we construct and analyze some finite difference schemes used to solve a class of time‐dependent one‐dimensional convection‐diffusion problems, which present only regular layers in their solution. We use the implicit Euler or the Crank‐Nicolson method to discretize the time variable and a HODIE finite difference scheme, defined on a piecewise uniform Shishkin mesh, to discretize the spatial variable. In both cases we prove that the numerical method is uniformly convergent with respect to the diffusion parameter, having order near two in space and order one or 3/2, depending on the method used, in time. We show some numerical examples which illustrate the theoretical results, in the case of using the Euler implicit method, and give better numerical behaviour than that predicted theoretically, showing order two in time and order N^?2log²N in space, if the Crank‐Nicolson scheme is used to discretize the time variable. Finally, we construct a numerical algorithm by combining a third order A‐stable SDIRK with two stages and a third‐order HODIE difference scheme, showing its uniformly convergent behavior, reaching order three, up to a logarithmic factor. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

Adatom concentration on GaAs(001) during MBE annealing

We study the concentration of adatoms on GaAs(001) during annealing under MBE conditions. By rapidly cooling the sample from typical growth temperatures and typical As overpressures, the thermal concentration of adatoms can be frozen into small islands on the terraces. The area of the resulting islands is measured with STM far from terrace steps, giving an estimate of the concentration of adatoms during equilibrium. We find that a surprisingly large concentration of adatoms is present for typical growth temperatures, e.g. 0.18 monolayer at 600°C. Possible consequences for current growth models are discussed.     

Markov chain model of mixed surfactant systems

A new model of mixed surfactant systems have been developed in the work presented. It includes two parameters only connected directly with the Gibbs free energy of the surfactant aggregation. They can be determined using both the aggregation equilibrium constant values or the phase composition data. It has been shown also the relation between these new parameters and the same of the regular solution approximation and the alternative models. The possibility to describe the available experimental information about the micelle composition as a function of the singly dispersed surfactant mixture composition better than by the other models has been shown also.     

Discrete symmetry groups of vertex models in statistical mechanics

We analyze discrete symmetry groups of vertex models in lattice statistical mechanics represented as groups of birational transformations. They can be seen as generated by involutions corresponding respectively to two kinds of transformations onq×q matrices: the inversion of theq×q matrix and an (involutive) permutation of the entries of the matrix. We show that the analysis of the factorizations of the iterations of these transformations is a precious tool in the study of lattice models in statistical mechanics. This approach enables one to analyze two-dimensionalq ⁴-state vertex models as simply as three-dimensional vertex models, or higher-dimensional vertex models. Various examples of birational symmetries of vertex models are analyzed. A particular emphasis is devoted to a three-dimensional vertex model, the 64-state cubic vertex model, which exhibits a polynomial growth of the complexity of the calculations. A subcase of this general model is seen to yield integrable recursion relations. We also concentrate on a specific two-dimensional vertex model to see how the generic exponential growth of the calculations reduces to a polynomial growth when the model becomes Yang-Baxter integrable. It is also underlined that a polynomial growth of the complexity of these iterations can occur even for transformations yielding algebraic surfaces, or higher-dimensional algebraic varieties.     

Scattering Parameters of FSS on Anisotropic Layers at Millimeter Wave Frequencies

The analysis of periodic structures on anisotropic substrates is presented for incident millimeter waves. Frequency selective surface structures composed by a periodic array of conducting crossed dipoles on anisotropic layers are analyzed. A full-wave analysis for the problem of scattering is performed. The formulation uses the moment method in combination with the immitance approach, in the Fourier domain, to determine the scattering parameters of the considered structures. A set of entire-domain type basis functions is used in the expansion for the unknown induced current. This analysis is computationally efficient, and its accuracy is verified by the agreement between results obtained in this work and those available in the literature, for particular cases.