One-Dimensional Hard-Rod Caricature of Hydrodynamics: “Navier–Stokes Correction” for Local Equilibrium Initial States

A one-dimensional system, consisting of identical hard-rod particles of length $a$ is studied in the hydrodynamical limit. A “Navier–Stokes correction” to the Euler equation is found for an initial local equilibrium family of states , of constant density. The correction is given, at , by a non-linear second order differential operator acting on f(q,v), the hydrodynamical density at a point of the “species” of fluid with velocity . Received: 14 October 1996 / Accepted: 13 February 1997     

Comparing the Efficiencies of Stochastic Isothermal Molecular Dynamics Methods

Molecular dynamics typically incorporates a stochastic-dynamical device, a “thermostat,” in order to drive the system to the Gibbs (canonical) distribution at a prescribed temperature. When molecular dynamics is used to compute time-dependent properties, such as autocorrelation functions or diffusion constants, at a given temperature, there is a conflict between the need for the thermostat to perturb the time evolution of the system as little as possible and the need to establish equilibrium rapidly. In this article we define a quantity called the “efficiency” of a thermostat which relates the perturbation introduced by the thermostat to the rate of convergence of average kinetic energy to its equilibrium value. We show how to estimate this quantity analytically, carrying out the analysis for several thermostats, including the Nosé-Hoover-Langevin thermostat due to Samoletov et al. (J. Stat. Phys. 128:1321–1336, 2007) and a generalization of the “stochastic velocity rescaling” method suggested by Bussi et al. (J. Chem. Phys. 126:014101, 2007). We find efficiency improvements (proportional to the number of degrees of freedom) for the new schemes compared to Langevin Dynamics. Numerical experiments are presented which precisely confirm our theoretical estimates.     

Nearly spherical vesicles: Shape fluctuations

Isolated vesicles with “insufficient” area have a finite surface tension and spherical shapes, whereas vesicles with “excess” area are necessarily aspherical. We consider the crossover behavior between both kinds of vesicles occurring as the equilibrium area increases. In the mean field approximation it is a second-order phase transition from the spherical to aspherical shape. We demonstrate the fluctuations smear the transition. The critical behavior of the amplitudes of fluctuations and of their characteristic times is investigated. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 3, 203–208 (10 February 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Balanced Topological Field Theories

We describe a class of topological field theories called “balanced topological field theories”. These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of “iterated superspaces” that carry two differentials. We find the most general action for these theories, which turns out to define Morse theory on field space. We illustrate the constructions with numerous examples. Finally, we relate these theories to topological sigma-models twisted using an isometry of the target space. Received: 2 September 1996 / Accepted: 3 October 1996     

The role of photoelectronic processes in the formation of a fluorescent plume by 248-nm laser irradiation of single crystal NaNO3

 Visible fluorescent “plumes” are readily produced when nominally transparent ionic materials are exposed to pulsed UV laser irradiation. Over a wide range of laser fluences where plumes are observed, however, the photon and electron densities are inadequate to support multiphoton ionization and inverse bremsstrahlung, which are often used to explain plasma production and excitation of atomic spectral lines. We present evidence that the great majority of charged particles (electrons and positive ions) comprising the plume at the onset of formation in defect-laden NaNO₃ are emitted directly from the surface. A model is described wherein the required electron energy to excite and eventually ionize neutral atoms is provided by electrostatic interactions in the expanding plume. The time evolution of the “overlap” between the expanding charge cloud and thermally emitted neutrals accounts for the time evolution of the atomic line emissions after the laser pulse. Received: 15 August 1996/Accepted: 16 August 1996     

On the Stability of Realistic Three-Body Problems

We consider the system Sun—Jupiter—Ceres as an example of a planar, circular, restricted three-body problem and, after substituting the mass ratio of Jupiter/Sun (which is approximately 10^-3) with a parameter , we prove the existence of stable quasi-periodic motions with frequencies close to the observed (average) frequencies reported in “The Astronomical Almanac” for . The proof is “computer-assisted”. Received: 1 April 1996 / Accepted: 25 October 1996     

A neutron reflectometry study of polystyrene network interfaces

We have used neutron reflectometry to measure interfacial widths between two polystyrene films, where either one or both films are crosslinked. The observed interfacial width between two networks is larger than the size expected for “dangling ends”, which suggests motion of heterogeneous regions of the networks. In the case when one of the networks is replaced by a linear polymer, the interfacial profile can be asymmetric with a diffusion “front” of linear polymer penetrating the network to a length scale of up to 200 ?. In the case of a more densely crosslinked network and a high molecular weight linear polymer the interface is symmetric implying negligible penetration. Received: 4 December 1996 / Revised: 13 October 1997 / Accepted: 23 December 1997     

Total quantum-current yield in the soft x-ray region

The emission of slow secondary electrons excited in efficient photocathodes by fast internal x-ray electrons upon absorption of x-ray photons having energies in the range 1–10 keV is analyzed. Analytical expressions are derived for the quantum current yield of the x-ray photoelectric effect for a “point” model and a “non-point” model of energy exchange of fast internal x-ray electrons. We present some estimates for its parameters in a CsI photocathode. Fiz. Tverd. Tela (St. Petersburg) 40, 1042–1046 (June 1998)     

Nonequilibrium noise and instabilities in membranes with active pumps

We study the statistical properties and dynamics of flexible fluid membranes containing active transmembrane proteins and find that such active membranes can be either stable or unstable to small disturbances, depending on the signs of certain crucial parameters characterising the protein-membrane interaction. A major finding is that the shape-fluctuation spectrum in the stable case for a zero-tension active membrane has the same form over a large range of length scales as at equilibrium, but with a nonequilibrium “noise temperature” determined by the activity.     

Exponential Relaxation of Glauber Dynamics with Some Special Boundary Conditions

We consider attractive finite-range Glauber dynamics and show that if a certain mixing condition is satisfied, then the system evolving on arbitrary subsets of the lattice, with appropriate boundary conditions, converges to equilibrium exponentially fast, in the uniform sense, uniformly over the subsets of the lattice. This result applies, for instance, to the ferromagnetic nearest neighbor Ising model in the so-called “Basuev region,” where complete analyticity is expected to fail. Technically the result in this paper is an extension of a result of Martinelli and Olivieri, who proved that under a weaker form of mixing the infinite system approaches equilibrium exponentially fast. Conceptually this paper may be seen as a step towards developing and exploiting a restricted notion of complete analyticity in which the boundary conditions, rather than the shapes of the regions under consideration, are being restricted. Received: 24 May 1996 / Accepted: 24 May 1996     

The optical sum rule in strongly correlated systems

We discuss the problem of a possible “violation” of the optical sum rule in the normal (nonsuperconducting) state of strongly correlated electronic systems, using our recently proposed DMFT + Σ approach applied to two typical models: the “hot spot” model of the pseudogap state and the disordered Anderson-Hubbard model. We explicitly demonstrate that the general Kubo single-band sum rule is satisfied for both models, but the optical integral itself is in general dependent on temperature and characteristic parameters, such as the pseudogap width, correlation strength, and disorder scattering, leading to an effective “violation” of the optical sum rule, which may be observed in experiments. The text was submitted by the authors in English.     

QCD, conformal invariance and the two Pomerons

Using the solution of the BFKL equation including the leading and subleading conformal spin components, we show how the conformal invariance underlying the leading expansion of perturbative QCD leads to elastic amplitudes described by two effective Pomeron singularities. One Pomeron is the well-known “hard” BFKL leading singularity, while the new one appears from a shift of the higher conformal spin BFKL singularities from subleading to leading position. This new effective singularity is compatible with the “soft” Pomeron and thus, together with the “hard” Pomeron, meets at large the “double Pomeron” solution which has recently been conjectured by Donnachie and Landshoff. Received: 8 February 1999 / Revised version: 8 March 1999 / Published online: 18 June 1999     

Breathing solitons in optical fiber links

We introduce the concept of “breathing” solitons to describe the dynamics of optical pulses in transmission lines with passive compensation of fiber chromatic dispersion. The “breathing” pulse can be used as the information carrier. The theory presented is complimentary to the concept of the guiding-center soliton. It is shown that an average bright soliton can propagate in a system with large variations of the dispersion, including segments with high normal dispersion. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 10, 814–819 (25 May 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Reconstruction of the Fermi surface in the pseudogap state of cuprates

Reconstruction of the Fermi surface of high-temperature superconducting cuprates in the pseudogap state is analyzed within a nearly exactly solvable model of the pseudogap state, induced by short-range order fluctuations of the antiferromagnetic (AFM), spin-density wave (SDW), or a similar charge-density wave (CDW) order parameter, competing with the superconductivity. We explicitly demonstrate the evolution from “Fermi arcs” (on the “large” Fermi surface) observed in the ARPES experiments at relatively high temperatures (when both the amplitude and phase of the density waves fluctuate randomly) towards the formation of typical “small” electron and hole “pockets,” which are apparently observed in the de Haas-van Alphen and Hall resistance oscillation experiments at low temperatures (when only the phase of the density waves fluctuate and the correlation length of the short-range order is large enough). A qualitative criterion for the quantum oscillations in high magnetic fields to be observable in the pseudogap state is formulated in terms of the cyclotron frequency, the correlation length of fluctuations, and the Fermi velocity. The text was submitted by the authors in English.     

Thermal conductivity of pressure polymerized C60

60 polymerization in the temperature interval at pressures below by measurements of the time dependence of the thermal conductivity. It has been found at that the polymerization process at is slower than the reverse transformation from “polymeric” to “monomeric” phase at . The thermal conductivity of polymerized C₆₀ was measured in the temperature range and found to increase with increasing temperature, which reflects strong phonon scattering. Both the presence of non-bonded C₆₀ molecules and a high degree of structural disorder in the crystalline lattice of the polymeric phase might be responsible for the behaviour of . The results for are qualitatively similar to those reported previously for C₆₀ polymerized at higher , but an order of magnitude smaller. Received: 20 September 1996/Accepted: 11 November 1996     

VLBI studies of the solar-wind plasma irregularities at 18 and 92 CM wavelengths in 1994–1996

We discuss the capabilities of VLBI studies of irregularities of the solar-wind plasma using multi-element radio interferometric facilities. We analyze the data obtained during international VLBI experiments at decimeter wavelengths (92 and 18 cm) in 1994–1996 and supposed that the irregularities have a “stream” structure. The “streams” are strongly elongated in the solar-wind direction (longitudinal size of about a few hundred thousand kilometers) and have the transverse size of about 0.5–2.0 thousand kilometers. The irregularities inside a single “stream” are almost isotropic. We discuss the restrictions imposed on operation of decimeter VLBI systems due to effects of the interplanetary medium. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 3, pp. 197–206, March, 2000     

Multiplex H_2 CARS thermometry in a microwave assisted diamond CVD plasma

Rapid temperature measurements in a low pressure, microwave assisted, diamond CVD plasma are reported. By using a “modeless” laser as the Stokes source for H CARS, accurate single-shot and averaged temperatures were obtained which agreed with values obtained from laser induced fluorescence measurements. The speed of data acquisition afforded by multiplex CARS allowed variations of temperature to be monitored with changing plasma conditions induced by variations of pressure, gas composition and microwave power. The application of the technique for “on-line” monitoring of plasma processes is briefly discussed. Received: 13 February 1996 / Accepted: 12 June 1996     

Computer Simulations for Some One-Dimensional Models of Random Walks in Fluctuating Random Environment

We report some results of computer simulations for two models of random walks in random environment (rwre) on the one-dimensional lattice for fixed space–time configuration of the environment (“quenched rwre”): a “Markov model” with Markov dependence in time, and a “quasi stationary” model with long range space–time correlations. We compare with the corresponding results for a model with i.i.d. (in space time) environment. In the range of times available to us the quenched distributions of the random walk displacement are far from gaussian, but as the behavior is similar for all three models one cannot exclude asymptotic gaussianity, which is proved for the model with i.i.d. environment. We also report results on the random drift and on some time correlations which show a clear power decay