Asymptotic theory of the reflection of electromagnetic radiation by moderately and highly conductive bodies

In this paper a method of deriving generalized impedance boundary conditions continuing tangential derivatives of high order is proposed. The case of reflection of an arbitrary electromagnetic wave by a curvilinear surface on which a generalized impedance condition holds is considered. The phenomenon of diffusion polarization dependent on the material and geometric properties of the reflecting surface is investigated. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 203, 1992, pp. 68–82. Translated by M. A. Lyalinov.     

A uniform dispersion equation in a multichannel problem

Uniform dispersion equations are obtained which make it possible to trace the transition of eigenvalues and eigenfunctions of two waveguides separated by an impermeable barrier into the eigenvalues and eigenfunctions of the composite waveguide.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 89, pp. 71–83, 1979.     

Potential of mean force between hydrophobic solutes in the Jagla model of water and implications for cold denaturation of proteins

Using the Jagla model potential we calculate the potential of mean force (PMF) between hard sphere solutes immersed in a liquid displaying water-like properties. Consistent estimates of the PMF are obtained by (a) umbrella sampling, (b) calculating the work done by the mean force acting on the hard spheres as a function of their separation, and (c) determining the position dependent chemical potential after calculating the void space in the liquid. We calculate the PMF for an isobar along which cold denaturation of a model protein has previously been reported. We find that the PMF at contact varies non-monotonically, which is consistent with the observed cold denaturation. The Henry constant also varies non-monotonically with temperature. We find, on the other hand, that a second (solvent separated) minimum of the PMF becomes deeper as temperature decreases. We calculate the solvent-solvent pair correlation functions for solvents near the solute and in the bulk, and show that, as temperature decreases, the two pair correlation functions become indistinguishable, suggesting that the perturbation of solvent structure by the solute diminishes as temperature decreases. The solvent-solute pair correlation function at contact grows as the temperature decreases. We calculate the cavity correlation function and show the development of a solvent-separated peak upon decrease of temperature. These observations together suggest that cold denaturation occurs when the solvent penetrates between hydrophobic solutes in configurations with favorable free energy. Our results thus suggest that cold denatured proteins are structured and that cold denaturation arises from strong solvent-solute interactions, rather than from entropic considerations as in heat denaturation.     

Aging in short-ranged attractive colloids: a numerical study

We study the aging dynamics in a model for dense simple liquids, in which particles interact through a hard-core repulsion complemented by a short-ranged attractive potential, of the kind found in colloidal suspensions. In this system, at large packing fractions, kinetically arrested disordered states can be created both on cooling (attractive glass) and on heating (repulsive glass). The possibility of having two distinct glasses, at the same packing fraction, with two different dynamics offers the unique possibility of comparing-within the same model-the differences in aging dynamics. We find that, while the aging dynamics of the repulsive glass is similar to the one observed in atomic and molecular systems, the aging dynamics of the attractive glass shows novel unexpected features.     

Correlated randomness and switching phenomena

One challenge of biology, medicine, and economics is that the systems treated by these serious scientific disciplines have no perfect metronome in time and no perfect spatial architecture—crystalline or otherwise. Nonetheless, as if by magic, out of nothing but randomness one finds remarkably fine-tuned processes in time and remarkably fine-tuned structures in space. Further, many of these processes and structures have the remarkable feature of “switching” from one behavior to another as if by magic. The past century has, philosophically, been concerned with placing aside the human tendency to see the universe as a fine-tuned machine. Here we will address the challenge of uncovering how, through randomness (albeit, as we shall see, strongly correlated randomness), one can arrive at some of the many spatial and temporal patterns in biology, medicine, and economics and even begin to characterize the switching phenomena that enables a system to pass from one state to another. Inspired by principles developed by A. Nihat Berker and scores of other statistical physicists in recent years, we discuss some applications of correlated randomness to understand switching phenomena in various fields. Specifically, we present evidence from experiments and from computer simulations supporting the hypothesis that water’s anomalies are related to a switching point (which is not unlike the “tipping point” immortalized by Malcolm Gladwell), and that the bubbles in economic phenomena that occur on all scales are not “outliers” (another Gladwell immortalization). Though more speculative, we support the idea of disease as arising from some kind of yet-to-be-understood complex switching phenomenon, by discussing data on selected examples, including heart disease and Alzheimer disease.     

Influence of disorder on superconductivity in non-magnetic rare-earth nickel borocarbides

The effect of substitutional disorder on the superconducting properties of YNi₂B₂C was studied by partially replacing yttrium and nickel by Lu and Pt, respectively. For the two series of (Y, Lu)Ni₂B₂C and Y(Ni, Pt)₂B₂C compounds, the upper critical field H _c2(T) and the specific heat c _p(T, H) in the superconducting mixed state have been investigated. Disorder is found to reduce several relevant quantities such as T _c, the upper critical field H _c2(0) at T=0 and a characteristic positive curvature of H _c2(T) observed for these compounds near T _c. The H _c2(T) data point to the clean limit for (Y, Lu) substitutions and to a transition to the quasi-dirty limit for (Ni, Pt) substitutions. The electronic specific heat contribution γ(H) exhibits significant deviations from the usual linear γ(H) law. These deviations reduce with growing substitutional disorder but remain even in the quasidirty limit which is reached in the Y(Ni_1−x , Pt _x )₂B₂C samples for x=0.1.     

Waterlike glass polyamorphism in a monoatomic isotropic Jagla model

We perform discrete-event molecular dynamics simulations of a system of particles interacting with a spherically-symmetric (isotropic) two-scale Jagla pair potential characterized by a hard inner core, a linear repulsion at intermediate separations, and a weak attractive interaction at larger separations. This model system has been extensively studied due to its ability to reproduce many thermodynamic, dynamic, and structural anomalies of liquid water. The model is also interesting because: (i) it is very simple, being composed of isotropically interacting particles, (ii) it exhibits polyamorphism in the liquid phase, and (iii) its slow crystallization kinetics facilitate the study of glassy states. There is interest in the degree to which the known polyamorphism in glassy water may have parallels in liquid water. Motivated by parallels between the properties of the Jagla potential and those of water in the liquid state, we study the metastable phase diagram in the glass state. Specifically, we perform the computational analog of the protocols followed in the experimental studies of glassy water. We find that the Jagla potential calculations reproduce three key experimental features of glassy water: (i) the crystal-to-high-density amorphous solid (HDA) transformation upon isothermal compression, (ii) the low-density amorphous solid (LDA)-to-HDA transformation upon isothermal compression, and (iii) the HDA-to-very-high-density amorphous solid (VHDA) transformation upon isobaric annealing at high pressure. In addition, the HDA-to-LDA transformation upon isobaric heating, observed in water experiments, can only be reproduced in the Jagla model if a free surface is introduced in the simulation box. The HDA configurations obtained in cases (i) and (ii) are structurally indistinguishable, suggesting that both processes result in the same glass. With the present parametrization, the evolution of density with pressure or temperature is remarkably similar to the corresponding experimental measurements on water. Our simulations also suggest that the Jagla potential may reproduce features of the HDA-VHDA transformations observed in glassy water upon compression and decompression. Snapshots of the system during the HDA-VHDA and HDA-LDA transformations reveal a clear segregation between LDA and HDA but not between HDA and VHDA, consistent with the possibility that LDA and HDA are separated by a first order transformation as found experimentally, whereas HDA and VHDA are not. Our results demonstrate that a system of particles with simple isotropic pair interactions, a Jagla potential with two characteristic length scales, can present polyamorphism in the glass state as well as reproducing many of the distinguishing properties of liquid water. While most isotropic pair potential models crystallize readily on simulation time scales at the low temperatures investigated here, the Jagla potential is an exception, and is therefore a promising model system for the study of glass phenomenology.     

Characterization of the branching structure of the lung from "macroscopic" pressure-volume measurements

We analyze the problem of fluid flow in a bifurcating structure containing random blockages that can be removed by fluid pressure. We introduce an asymmetric tree model and find that the predicted pressure-volume relation is connected to the distribution Pi(n) of the generation number n of the tree's terminal segments. We use this relation to explore the branching structure of the lung by analyzing experimental pressure-volume data from dog lungs. The Pi(n) extracted from the data using the model agrees well with experimental data on the branching structure. We can thus obtain information about the asymmetric structure of the lung from macroscopic, noninvasive pressure-volume measurements.     

Diffraction echo signal generated by the incidence of a plane wave on a prolate spheroid

The problem of the diffraction of a plane wave by a prolate spheroid placed in a fluid is considered in the high-frequency approximation. The spheroid is hereby either a solid body or a shell. The contribution to the echo signal, i.e., the back-reflected field, of diffraction waves of creep and break-off type is investigated. Computational formulas for the geometric divergences of surface rays and also of creep and break-off waves are obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituts im. V. A. Steklova AN SSSR, Vol. 140, pp. 18–35, 1984.