Thermal diffusion of envelope solitons on anharmonic atomic chains

We study the motion of envelope solitons on anharmonic atomic chains in the presence of dissipation and thermal fluctuations. We consider the continuum limit of the discrete system and apply an adiabatic perturbation theory which yields a system of stochastic integro-differential equations for the collective variables of the ansatz for the perturbed envelope soliton. We derive the Fokker-Planck equation of this system and search for a statistically equivalent system of Langevin equations, which shares the same Fokker-Planck equation. We undertake an analytical analysis of the Langevin system and derive an expression for the variance of the soliton position Var[x _s ] which predicts a stronger than linear time dependence of Var[x _s ] (superdiffusion). We compare these results with simulations for the discrete system and find they agree well. We refer to recent studies where the diffusion of pulse solitons were found to exhibit a superdiffusive behaviour on longer time scales.Received: 28 June 2004, Published online: 26 November 2004PACS: 05.10.Gg Stochastic analysis methods - 05.45.Yv Solitons - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.50. + q Lattice theory and statistics     

Determination of low dose concentration profiles in solids by means of (n,p) and (n, α) reactions

The isotopes³He,⁶Li,⁷Be and¹⁰B exhibit extremely large cross sections, between 1 and 48 kilobarn, for (n, p) or (n, α) reactions with thermal neutrons. Together with now available extracted thermal neutron fluxes of 10⁽ n·cm⁻²·sec⁻¹ or more, these reactions present a highly sensitive method of detecting the mentioned light elements in any heavy matrix material. Through the experimentally determined energy losses of the emitted protons or α-particles, also well resolved depth profiles can be obtained, as demonstrated here for some relevant examples from semiconductor and fusion technology.     

Characterization of Carbohydrates in Paper and Paper Pulps Using Anion Exchange Chromatography and Principal Component Analysis

In the course of this investigation, a method for the characterization and differentiation of paper pulps was developed. After hydrolyzation of the papers and the respective raw pulps with trifluoroacetic acid, the hydrolyzates were analyzed with respect to their carbohydrate composition using ion exchange chromatography. The variations in carbohydrate composition mainly arise from the various hemicelluloses of the papers and pulps. The chromatographic results were then further processed using principal component analysis which allows correlating the various papers to different pulp materials.     

Classification of the CD. Spectra of carotenoids

The CD. spectra of carotenoids in the 220-500 nm region may by inspection be classified as (a) essentially Conservative, (b) intermediate, or (c) essentially nonconservative. A conservative spectrum shows in that spectral region a sequence of 5-6 relatively sharp Cotton effects of alternating sign, the rotatory strengths of which roughly add to zero. In a non-conservative spectrum Δ? has the same sign over the whole region and its absolute value is in general somewhat smaller. In general, typical conservative spectra invert upon isomerization of the molecule from all-trans to mono-cis. Non-conservative spectra do not invert. The model of a chiral polyene of the length of the conjugated carotene chromophore reproduces well the main features of the conservative spectra. The theoretical predictions and the experimental data are shown to conform to the C₂-rule [43] [44]. The particular nature of the longest-wavelength transition is interpreted. Based on a summary of the chiroptic data on about 50 naturally occurring compounds, the question is discussed of when conservative spectra arise and when not.