On minimizing expected absorption times

A random walk with variable step size, depending on the location of the particle, is considered. Two cases are discussed: one with two absorbing boundaries, and another when one boundary is absorbing while the other cannot be reached. Generalization of the uniquess problem of a functional equation for the expected duration is proved. Also the optimal policy, i.e. step size for each location minimizing the expected duration, is discussed. The natural solution of the problem in case of two absorbing boundaries is verified, while for the case of one boundary a necessary and sufficient condition for the existence of optimal solution is developed, while specific policy still remains open.     

Solvent Relaxation in Phospholipid Bilayers: Principles and Recent Applications

Although there exist a number of methods, such as NMR, X-ray, e.g., which explore the hydration of phospholipid bilayers, the solvent relaxation (SR) method has the advantage of simple instrumentation, easy data treatment and possibility of measuring fully hydrated samples. The main information gained from SR by the analysis of recorded “time-resolved emission spectra” (TRES) is micro-viscosity and micro-polarity of the dye microenvironment. Based on these parameters, one can draw conclusions about water structure in the bilayer. In this review, we focus on physical background of this method, on all the procedures that are needed in order to obtain relevant parameters, and on the requirements on the fluorescence dyes. Furthermore, a few recent applications (the effect of curvature, binding of antibacterial peptides and phase transition) illustrating the versatility of this method are mentioned. Moreover, limitations and potential problems are discussed.     

Mechanism for flow-rate controlled breakup in confined geometries: a route to monodisperse emulsions

This Letter describes a quasistationary breakup of an immiscible, inviscid fluid at low capillary numbers. The breakup proceeds in a coflowing, viscous liquid, in a confined geometry of a long and narrow orifice. In contrast to the capillary instability in an unbounded fluid, the collapse proceeds through a series of equilibria, each yielding the minimum interfacial energy of the fluid-fluid interface. The process is slow in comparison to typical relaxation speeds of the interface, and it is reversible. Its quasistatic character of collapse forms the basis for controlled, high-throughput generation of monodisperse fluid dispersions.     

Critical behavior in vacuum gravitational collapse in 4 + 1 dimensions

We show that the (4 + 1)-dimensional vacuum Einstein equations admit gravitational waves with radial symmetry. The dynamical degrees of freedom correspond to deformations of the three-sphere orthogonal to the (t,r) plane. Gravitational collapse of such waves is studied numerically and shown to exhibit discretely self-similar type II critical behavior at the threshold of black hole formation.     

Global regular and singular solutions for a model of gravitating particles

The existence of solutions of a nonlinear parabolic equation describing the gravitational interaction of particles is studied for the initial data in spaces of (generalized) pseudomeasures. This approach permits us to relax regularity assumptions on the initial conditions and to prove asymptotic stability results for the above problem.Mathematics Subject Classification (2000):35B40, 35K15, 82C21     

Polymeric complexes of cornstarch and waxy cornstarch phosphates with milk casein and their performance as biodegradable materials

Complexes of phosphated cornstarch and waxy cornstarch with casein were prepared and characterised. They were prepared from casein in defatted milk and corn and waxy corn starches phosphated to degree of substitution values (DS) of 0.0637 and 0.0968, respectively. The components were blended in starch to casein ratios of 2:1, 1:1, and 1:2, then precipitated with hydrochloric acid. Aqueous solubility, water binding capacity, IR spectra, and thermal analysis (thermogravimetry, TG, and differential thermogravimetry, DTG) of the precipitates revealed that they were not simple physical mixtures of the components. The components interact with one another electrostatically with involvement of the starch phosphate groups and the peptide bonds of casein as documented by the IR spectra. Because of their insolubility in 7 M aqueous urea solution they might also be considered as complexes in which the components were chemically bound. Enzymatic studies showed that they are biodegradable materials.     

Properties of grafted amphiphilic chains. A computer simulation study

The model of a heteropolymer film formed by polypeptide chains was used for theoretical considerations. The linear chains consisting of amino acid residues were approximated by alpha carbon chains. Each chain was constructed on a very flexible [310] lattice. The inter- and intramolecular interactions consisted of the long-range contact potential between residues. The chains were built of hydrophilic and hydrophobic residues. Chains were terminally attached to an impenetrable surface with lateral motions possible. The Monte Carlo simulations of this model were carried out by using the Metropolis algorithm. The influence of the grafting density, the sequence of the amino acid residues, and the temperature on the static properties of the formed layer were studied and discussed. It was shown that homopolymer chains collapsed at higher temperature than the heteropolymers. The size of the polymers forming brush was smaller for homopolymers than for heteropolymers. The structure of the resulting polymer film and of its external surface was determined. The block copolymers formed well defined hydrophobic and hydrophilic layers, while for the amphiphilic case the composition of the brush layers changed continuously at high temperature. It was observed that the latter effect vanished at the collapsed amphiphilic copolymer.     

Fano versus Kondo resonances in a multilevel "semiopen" quantum dot

Linear conductance across a large quantum dot via a single level epsilon(0) with large hybridization to the contacts is strongly sensitive to quasibound states localized in the dot and weakly coupled to epsilon(0). The conductance oscillates with the gate voltage due to interference of the Fano type. At low temperature and Coulomb blockade, Kondo correlations damp the oscillations on an extended range of gate voltage values, by freezing the occupancy of the epsilon(0) level itself. As a consequence, the antiresonances of Fano origin are washed out. The results are in good correspondence with experimental data for a large quantum dot in the semiopen regime.     

Patterns of lepton-flavour violation motivated by decoupling and sneutrino inflation

We present predictions for flavour-violating charged-lepton decays induced by the seesaw mechanism implemented within the constrained minimal supersymmetric standard model (CMSSM) with universal input soft supersymmetry breaking terms. We assume that one heavy singlet neutrino almost decouples from the seesaw mechanism, as suggested by the pattern of light neutrino masses and mixing angles. This is suggested independently by sneutrino inflation with a low reheating temperature, T_RH10⁷ GeV, so as to avoid overproducing gravitinos. This requirement further fixes the mass of the weakly-coupled sneutrino, whose decays may lead to leptogenesis. We find that BR(μ→eγ)10⁻¹³ but BR(τ→μγ)10⁻⁹ in the bulk of the acceptable parameter space, apart from a few isolated points. The ratio BR(μ→eγ)/BR(τ→eγ) depends on only one complex parameter, and is particularly interesting to compare with experiment.     

Vortex fluctuations in underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) crystals

Vortex thermal fluctuations in heavily underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) (T(c)=69.4 K) are studied using Josephson plasma resonance. From the zero-field data, we obtain the c-axis penetration depth lambda(L,c)(0)=230+/-10 micrometer and the anisotropy ratio gamma(T). The low plasma frequency allows us to study phase correlations over the whole vortex solid state and to extract a wandering length r(w) of vortex pancakes. The temperature dependence of r(w) as well as its increase with dc magnetic field is explained by the renormalization of the vortex line tension by the fluctuations, suggesting that this softening is responsible for the dissociation of the vortices at the first order transition.