Algebraic Dirichlet-to-Neumann mapping for linear elasticity problems with extreme contrasts in the coefficients

The convergence of iterative based domain decomposition methods is linked with the absorbing boundary conditions defined on the interface between the sub-domains. For linear elasticity problems, the optimal absorbing boundary conditions are associated with non-local Dirichlet-to-Neumann maps. Most of the methods to approximate these non-local maps are based on a continuous analysis. In this paper, an original algebraic technique based on the computation of local Dirichlet-to-Neumann maps is investigated. Numerical experiments are presented for linear elasticity problems with extreme contrasts in the coefficients.     

A new class of long-tailed pausing time densities for the CTRW

We present some asymptotic results for the family of pausing time densities having the asymptotic (t) property(t) [t ln¹⁺(t/T)]^–1. In particular, we show that for this class of pausing time densities the mean-squared displacement r ²(t) is asymptotically proportional to ln(t/T), and the asymptotic distribution of the displacement has a negative exponential form.     

The velocity correlation function for the Lorentz gas

The results of variational solutions of the repeated ring and self-consistent repeated ring equations for the two-and three-dimensional overlapping Lorentz gas (LG), as formulated in a previous report, are presented. Calculations of the full velocity correlation function (VCF) for the 2D LG, including long-time tails, are compared with those from molecular dynamics. The trial functions chosen lead to predictions for the long-time tails that improve as the density of the scatterers is increased. At a value of 0.24 for* (= ², where is the density and the radius of scatterers), the self-consistent amplitudes of the long-time tail are within 40% of the molecular dynamics. A limited number of 3D results for the short-time behavior of the repeated ring VCF are presented. The 3D solutions agree with the molecular dynamics to within 10%.     

Reactions of esters of tetracoordinated phosphorus acids with nucleophilic reagents in highly organized media

Characteristic features of reactions involving esters of phosphorus-containing acids in highly organized media (micelles, liquid crystals, vesicles, and emulsions) are surveyed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 298–312, February, 1996.     

Qualitative properties of pulsating fronts for reaction–advection–diffusion equations in periodic excitable media

In this paper, we study the pulsating fronts of reaction–advection-diffusion equations with two types of nonlinear term in periodic excitable media. Firstly, for the case with combustion nonlinearity, the unique front is proved to decay exponentially when it approaches the unstable limiting state. Secondly, for the degenerate monostable type nonlinearity, it is shown that the front with critical speed is unique, monotone and decays exponentially at negative end, while the fronts of noncritical speeds decay to zero non-exponentially.     

Polymer diffusion in quenched disorder: A renormalization group approach

We study the diffusion of polymers through quenched short-range correlated random media by renormalization group (RG) methods, which allow us to derive universal predictions in the limit of long chains and weak disorder. We take local quenched random potentials with second momentv and the excluded-volume interactionu of the chain segments into account. We show that our model contains the relevant features of polymer diffusion in random media in the RG sense if we focus on the local entropic effects rather than on the topological constraints of a quenched random medium. The dynamic generating functional and the general structure of its perturbation expansion inu andv are derived. The distribution functions for the center-of-mass motion and the internal modes of one chain and for the correlation of the center of mass motions of two chains are calculated to one-loop order. The results allow for sufficient cross-checks to have trust in the one-loop renormalizability of the model. The general structure as well as the one-loop results of the integrated RG flow of the parameters are discussed. Universal results can be found for the effective static interactionwu–v0 and for small effective disorder coupling on the intermediate length scalel. As a first physical prediction from our analysis, we determine the general nonlinear scaling form of the chain diffusion constant and evaluate it explicitly as for .     

Steady flux in a continuous-space Sinai chain

We examine the steady-state flux of particles diffusing in a one-dimensional finite chain with Sinai-type disorder, i.e., the system in which in addition to the thermal noise, particles are subject to a stationary random-correlated in space Gaussian force. For this model we calculate the disorder average (over configurations of the random force) flux exactly for arbitrary values of system's parameters, such as chain lengthN, strength of the force, and temperature. We prove that within the limitN1 the average flux decreases withN as J(N)=C/N and thus confirm our recent predictions that the flux in the discrete-space Sinai model is anomalous.     

“Statistical” symmetry with applications to phase transitions

Hermann proposed that mesomorphic media should be classified by assigning certain statistical symmetry groups to each possible partially ordered array. Two translational groups introduced were called superordinate and subordinate. We find that the average density in such a partially ordered medium has the superordinate symmetry ₁, while the pair correlation function has the subordinate symmetry ₂. A complete listing is made of all compatible combinations of ₁ and ₂ in two and three dimensions. This leads to more possible symmetries than Hermann obtained, e.g., also to nonstoichiometric crystals. The order parameter space for the systems is found to be the quotient space ₁/₂. In most cases it is identical to the order parameter space of low-dimensionalXY spin systems. The Landau free energy is expanded as functional of the two-particle correlation functionK; the translation group is found to be ₁×₂. A Landau mean-field theory can then be carried out by expanding the system free energy into a series of invariants of the active irreducible representations ofK and mapping the free energy onto that for anXY planar spin system. We predict novel critical behavior for transitions between mesomorphic phases and go nogo selection rules for continuous transitions. We give the structure factors for X-ray scattering so changes in all such phase transitions are observable. The statistical symmetry groups, which describe point and translational symmetries of the mesophases, are classified. Proposals are made to include quasi-long-range or topological order in the classification scheme.This work supported in part by National Science Foundation (Division of International Programs), the PSC-BHE—Faculty Research Award CUNY and Deutsche Forschungsgemeinschaft.     

Thermodynamics of natural selection

It is shown that biological-natural-selection-like behavior can occur, as a general type of time evolution, in a statistical system where detailed balance is violated owing to the presence of metastable energy states. A model of a non-equilibrium phase transition corresponding to the spontaneous origin of self-reproduction in the system is suggested. After a phase transition, the system passes from one quasistationary distribution of self-reproducing subsystems to another, with an increase in the total organization, as long as the growth of the energy flow through the system or a reduction of energy dissipation in the system is possible. The entropy production is calculated for this process in terms of selective values of Eigen's theory for self-organization in autocatalytic systems. Correspondence of the extremal principle of Eigen's theory with the criterion of evolution in Prigogine's thermodynamics is established.     

Mixed hybrid bilayer lipid membrane incorporating valinomycin: improvements in preparation and functioning

The paper deals with the reconstruction of lipid bilayer membranes on a Au-covered polycarbonate membrane. Such a kind of like-biomembranes (namely mixed hybrid bilayer lipid membrane (MHBLM)) are characterised by appreciable long-term stability. Here we describe changes that have been made in the geometry of the experimental device in order to avoid artefacts and render membrane reproduction easier. Incorporation of valinomycin was performed to check the membrane and its stability: conductance and membrane potential following the changes of ion concentration were recorded. This new approach permits increase of successful trials and renders possible, when it breaks, easily formation of a new MHBLM on the same Au-covered polycarbonate membrane support. Finally, the stability shown by the MHBLM renders this system a promising tool for use under flowing conditions.