Investigation of the layer-by-layer transition near the bulk smectic-A-crystal-B transition in thick free-standing films

Highly sensitive optical reflectivity measurements are used to investigate the layer-by-layer transition in extremely thin and thick N-(4-n-hexyloxybenzylidene)-4-n-hexylaniline (6O.6) films. The simple power-law form, N=N ₀ t ^−1/3, for the penetration of the crystal-B order is found to describe the transitions only near the surface. A deviation from the power law is observed for the interior layers. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 4, 266–269 (25 February 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Experimental investigation and numerical simulation of the influence of resonator-length detuning on the output power,pulse duration and spectral width of a cw mode-locked picosecond optical parametric oscillator

We report on a cw mode-locked non-critically phase matched KTP optical parametric oscillator synchronously pumped by a picosecond Ti:Sapphire laser. High average signal output power of up to 950 mW over a large tuning range has been achieved. For this OPO the influence of resonator-length detuning on the output power, pulse duration and spectral bandwidth has been investigated. The measured data are in good agreement with the results of a numerical simulation using a split-step Fourier method which considers the group-velocity mismatch, the group-velocity dispersion and the self-phase modulation. The numerical simulation also describes the measured strong pump depletion and its influence on the OPO output and efficiency.     

Bounds for rectilinear crossing numbers

A rectilinear drawing of a graph is one where each edge is drawn as a straight-line segment, and the rectilinear crossing number of a graph is the minimum number of crossings over all rectilinear drawings. We describe, for every integer k ≥ 4, a class of graphs of crossing number k, but unbounded rectilinear crossing number. This is best possible since the rectilinear crossing number is equal to the crossing number whenever the latter is at most 3. Further, if we consider drawings where each edge is drawn as a polygonal line segment with at most one break point, then the resulting crossing number is at most quadratic in the regular crossing number. © 1993 John Wiley & Sons, Inc.     

129Xe NMR study of the homogeneity and the size distribution of small sodium metal particles in NaY zeolite

NaY zeolite samples loaded with sodium metal by vapor phase deposition have been investigated using¹²⁹Xe NMR spectroscopy. At low sodium concentration, the¹²⁹Xe NMR spectrum showed three resonance lines which clearly indicate the existence of distinct domains in the zeolite sample. Such an observation suggests that the diffusion of the xenon atoms into each domain only occurs with respect to the NMR time scale (2.9 ms). As the sodium concentration increases, observation of a single broad line indicate a macroscopic homogenization of the system. The shift of this line is explained in part due to a paramagnetic interaction between the xenon atoms and the unpaired electrons of particles containing an odd number of sodium atoms. The linewidth is due to the distribution of the local magnetic fields partially averaged by the rapid motion of the xenon atoms and to the statistical distribution of the sodium particles in the supercage cavities. The paramagnetic interaction vanishes with the oxidation of the sample leading to a narrowing and a shift of the line to higher magnetic fields.     

Spectra and Transport in Almost Periodic Dimers

We study spectral properties of discrete Schrödinger operators with potentials obtained via dimerization of a class of aperiodic sequences. It is shown that both the nature of the autocorrelation measure of a regular sequence and the presence of generic (full probability) singular continuous spectrum in the hull of primitive and palindromic (four block substitution) potentials are robust under dimerization. Generic results also hold for circle potentials. We illustrate these results with numerical studies of the quantum mean square displacement as a function of time. The numerical techniques provide a very fast algorithm for the time evolution of wave packets.     

Wavelet Collocation Methods for a First Kind Boundary Integral Equation in Acoustic Scattering

In this paper we consider a wavelet algorithm for the piecewise constant collocation method applied to the boundary element solution of a first kind integral equation arising in acoustic scattering. The conventional stiffness matrix is transformed into the corresponding matrix with respect to wavelet bases, and it is approximated by a compressed matrix. Finally, the stiffness matrix is multiplied by diagonal preconditioners such that the resulting matrix of the system of linear equations is well conditioned and sparse. Using this matrix, the boundary integral equation can be solved effectively.     

A STRASSEN LAW OF THE ITERATED LOGARITHM FOR PROCESSES WITH INDEPENDENT INCREMENT

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