Reflection absorption infrared spectroscopy and temperature programmed desorption investigations of the interaction of methanol with a graphite surface

Reflection absorption infrared spectroscopy (RAIRS) and temperature programmed desorption (TPD) have been used to investigate the adsorption of methanol (CH3OH) on the highly oriented pyrolytic graphite (HOPG) surface. RAIRS shows that CH3OH is physisorbed at all exposures and that crystalline CH3OH can be formed, provided that the surface temperature and coverage are high enough. It is not possible to distinguish CH3OH that is closely associated with the HOPG surface from CH3OH adsorbed in multilayers using RAIRS. In contrast, TPD data show three peaks for the desorption of CH3OH. Initial adsorption leads to the observation of a peak assigned to the desorption of a monolayer. Subsequent adsorption leads to the formation of multilayers on the surface and two TPD peaks are observed which can be assigned to the desorption of multilayer CH3OH. The first of these shows a fractional order desorption, assigned to the presence of hydrogen bonding in the overlayer. The higher temperature multilayer desorption peak is only observed following very high exposures of CH3OH to the surface and can be assigned to the desorption of crystalline CH3OH. (C) 2005 American Institute of Physics

A law of the iterated logarithm for Grenander's estimator

In this note we prove the following law of the iterated logarithm for the Grenander estimator of a monotone decreasing density: If $f(t_0) > 0$, $f'(t_0) < 0$, and $f'$ is continuous in a neighborhood of $t_0$, then \begin{eqnarray*} \limsup_{n\rightarrow \infty} \left ( \frac{n}{2\log \log n} \right )^{1/3} ( \widehat{f}_n (t_0 ) - f(t_0) ) = \left| f(t_0) f'(t_0)/2 \right|^{1/3} 2M \end{eqnarray*} almost surely where $M \equiv \sup_{g \in {\cal G}} T_g = (3/4)^{1/3}$ and T_g \equiv \mbox{argmax}_u \{ g(u) - u^2 \} ; here ${\cal G}$ is the two-sided Strassen limit set on $R$. The proof relies on laws of the iterated logarithm for local empirical processes, Groeneboom's switching relation, and properties of Strassen's limit set analogous to distributional properties of Brownian motion.Comment: 11 pages, 3 figure

Numerical simulations of a two-dimensional lattice grain boundary model

We present detailed Monte Carlo results for a two-dimensional grain boundary model on a lattice. The effective Hamiltonian of the system results from the microscopic interaction of grains with orientations described by spins of unit length, and leads to a nearest-neighbour interaction proportional to the absolute value of the angle between the grains. Our analysis of the correlation length xi and susceptibility chi in the high-temperature phase favour a Kosterlitz-Thouless-like (KT) singularity over a second-order phase transition. Unconstrained KT fits of chi and xi confirm the predicted value for the critical exponent nu, while the values of eta deviate from the theoretical prediction. Additionally we apply finite-size scaling theory and investigate the question of multiplicative logarithmic corrections to a KT transition. As for the critical exponents our results are similar to data obtained from the XY model, so that both models probably lie in the same universality class.Comment: 13 pages, Latex, 7 figures, to appear in Physica

Scattering of surface and volume spin waves in a magnonic crystal

The operational characteristics of a magnonic crystal, which was fabricated as an array of shallow grooves etched on a surface of a magnetic film, were compared for magnetostatic surface spin waves and backward volume magnetostatic spin waves. In both cases the formation of rejection frequency bands was studied as a function of the grooves depth. It has been found that the rejection of the volume wave is considerably larger than of the surface one. The influences of the nonreciprocity of the surface spin waves as well as of the scattering of the lowest volume spin-wave mode into higher thickness volume modes on the rejection efficiency are discussed

A Polyhedral Homotopy Algorithm For Real Zeros

We design a homotopy continuation algorithm, that is based on numerically tracking Viro's patchworking method, for finding real zeros of sparse polynomial systems. The algorithm is targeted for polynomial systems with coefficients satisfying certain concavity conditions. It operates entirely over the real numbers and tracks the optimal number of solution paths. In more technical terms; we design an algorithm that correctly counts and finds the real zeros of polynomial systems that are located in the unbounded components of the complement of the underlying A-discriminant amoeba.Comment: some cosmetic changes are done and a couple of typos are fixed to improve readability, mathematical contents remain unchange