Re-localization due to finite response times in a nonlinear Anderson chain

We study a disordered nonlinear Schr?dinger equation with an additional relaxation process having a finite response time ??. Without the relaxation term, ?? = 0, this model has been widely studied in the past and numerical simulations showed subdiffusive spreading of initially localized excitations. However, recently Caetano et al. [Eur. Phys. J. B 80, 321 (2011)] found that by introducing a response time ?? > 0, spreading is suppressed and any initially localized excitation will remain localized. Here, we explain the lack of subdiffusive spreading for ?? > 0 by numerically analyzing the energy evolution. We find that in the presence of a relaxation process the energy drifts towards the band edge, which enforces the population of fewer and fewer localized modes and hence leads to re-localization. The explanation presented here relies on former findings by Mulansky et al. [Phys. Rev. E 80, 056212 (2009)] on the energy dependence of thermalized states.     

Early Stages of Interchange Reactions in Polymer Blends

Summary: Simple models are studied for better understanding of the early stages of interchange reactions in polymer blends. For a homogeneous blend of homopolymers A and B, parameters of copolymer AB formed at the reaction beginning are explicitly calculated. It is shown that the analysis of the copolymer composition can help to establish the prevailing interchange mechanism. For a bilayer blend of immiscible homopolymers A and B, the reactive compatibilization through interchange is studied by continual Monte Carlo modeling. The analysis of the local distribution in block length shows that the interdiffusion of blend components may start only after the formation of rather short copolymer blocks in the course of interchange.     

Milnor numbers, spanning trees, and the Alexander–Conway polynomial

We study relations between the Alexander–Conway polynomial _L and Milnor higher linking numbers of links from the point of view of finite-type (Vassiliev) invariants. We give a formula for the first non-vanishing coefficient of _L of an m-component link L all of whose Milnor numbers μ_i1…ip vanish for pn. We express this coefficient as a polynomial in Milnor numbers of L. Depending on whether the parity of n is odd or even, the terms in this polynomial correspond either to spanning trees in certain graphs or to decompositions of certain 3-graphs into pairs of spanning trees. Our results complement determinantal formulas of Traldi and Levine obtained by geometric methods.     

Migration of salts in the unsaturated zone caused by heating

Heat-transfer phenomena as well as moisture movement in unsaturated soils due to thermal gradients, have been extensively studied during the last four decades. Less attention has been devoted to the transport and redistribution of solutes caused by heating.Solar radiation, radioactive waste repositories, underground energy storage, buried electric cables and steam pipes, disposal of waste heat from power plants are examples of heat sources in the soil.Soil-water properties, such as surface tension, viscosity, density, as well as the equilibrium composition of phases, depend on temperature. Hence, nonuniform heating of a soil partially saturated by saline water has an effect on such processes as water flow under capillary and gravitational forces, evaporation, condensation and diffusion of vapor and transport and precipitation of salts.A mathematical model is presented for the migration of salts in the vadoze zone in the soil under nonisothermal conditions, taking into account the above-mentioned phenomena. The physical assumptions underlying the model are briefly discussed.The study of a particular case shows that under certain conditions, a heat source may attract dissolved salts, and cause their precipitation in the hot area.     

Phase synchronization of chaotic oscillations in terms of periodic orbits

We consider phase synchronization of chaotic continuous-time oscillator by periodic external force. Phase-locking regions are defined for unstable periodic cycles embedded in chaos, and synchronization is described in terms of these regions. A special flow construction is used to derive a simple discrete-time model of the phenomenon. It allows to describe quantitatively the intermittency at the transition to phase synchronization. (c) 1997 American Institute of Physics.     

Syntheses and oxidation of methyloxorhenium(V) complexes with tridentate ligands

Four new methyloxorhenium(V) compounds were synthesized with these tridentate chelating ligands: 2-mercaptoethyl sulfide (abbreviated HSSSH), 2-mercaptoethyl ether (HSOSH), thioldiglycolic acid (HOSOH), and 2-(salicylideneamino)benzoic acid (HONOH). Their reactions with MeReO(3) under suitable conditions led to these products: MeReO(SSS), 1, MeReO(SOS), 2, MeReO(OSO)(PAr(3)), 3, and MeReO(ONO)(PPh(3)), 4. These compounds were characterized spectroscopically and crystallographically. Compounds 1 and 2 have a five-coordinate distorted square pyramidal geometry about rhenium, whereas 3 and 4 are six-coordinate compounds with distorted octahedral structures. The kinetics of oxidation of 2 and 3 in chloroform with pyridine N-oxides follow different patterns. The oxidation of 2 shows first-order dependences on the concentrations of 2 and the ring-substituted pyridine N-oxide. The Hammett analysis of the rate constants gives a remarkably large and negative reaction constant, rho = -4.6. The rate of oxidation of 3 does not depend on the concentration or the identity of the pyridine N-oxide, but it is directly proportional to the concentration of water, both an accidental and then a deliberate cosolvent. The mechanistic differences have been interpreted as reflecting the different steric demands of five- and six-coordinate rhenium compounds.     

Stereoselective preparation of functionalized acyclic alkenylmagnesium reagents using i-PrMgCl.LiCl

Acyclic functionalized alkenyl iodides are converted with high stereoselectivity to the corresponding functionalized alkenylmagnesium derivatives by the reaction with i-PrMgCl.LiCl between -40 and -20 degrees C. Functional groups such as a nitrile, chloride, iodide, and ester are readily tolerated. The conversion of an alkenyl iodide bearing a keto group to the corresponding silylated cyanohydrin allows preparation of the corresponding Grignard reagent affording, after acylation and deprotection, unsaturated 1,4-diketones.     

Selection of internal standards for quantitative analysis by matrix-assisted laser desorption-ionization (MALDI) time-of-flight mass spectrometry

The selection of an appropriate internal standard (IS) for quantification by matrix-assisted laser desorption/ionization (MALDI) mass spectrometry is critical for the successful application of quantitative MALDI. Selection of the IS depends on the chemical similarity of the analyte and IS and the mass separation of the analyte and IS as a function of instrumental peak resolution. For the quantification of bovine insulin, a series of internal standards including horse heart cytochrome C, bovine insulin chain B, des-pentapeptide human insulin, and des-octapeptide porcine insulin was investigated. Des-pentapeptide human insulin was found to be the most appropriate internal standard (relative standard deviation of the standard curve slope = 2.99%, correlation coefficient = 0.988 in the range of 0.5-0.4 μmol/L). Two methods for measuring of the MALDI signal intensity were evaluated, direct peak integration following subtraction of a linear background and non-linear least squares curve fitting. The results obtained with these methods were equivalent.     

International symposium on fundamental problems in quantum physics

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International symposium on fundamental problems in quantum physics