Nonlinear Hydrodynamics of a Hard Sphere Fluid Near the Glass Transition

We conduct a numerical study of the dynamic behavior of a dense hard sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free energy functional of the Ramakrishnan-Yussouff form. We find that the system exhibits glassy behavior as evidenced through stretched exponential decay and two-stage relaxation of the density correlation function. The characteristic times grow with increasing density according to the Vogel-Fulcher law. The wavenumber dependence of the kinetics is extensively explored. The connection of our results with experiment, mode coupling theory, and molecular dynamics results is discussed.Comment: 34 Pages, Plain TeX, 12 PostScript Figures (not included, available on request

Free Energy Landscape Of Simple Liquids Near The Glass Transition

Properties of the free energy landscape in phase space of a dense hard sphere system characterized by a discretized free energy functional of the Ramakrishnan-Yussouff form are investigated numerically. A considerable number of glassy local minima of the free energy are located and the distribution of an appropriately defined ``overlap'' between minima is calculated. The process of transition from the basin of attraction of a minimum to that of another one is studied using a new ``microcanonical'' Monte Carlo procedure, leading to a determination of the effective height of free energy barriers that separate different glassy minima. The general appearance of the free energy landscape resembles that of a putting green: deep minima separated by a fairly flat structure. The growth of the effective free-energy barriers with increasing density is consistent with the Vogel-Fulcher law, and this growth is primarily driven by an entropic mechanism.Comment: 10 pages, 6 postscript figures, uses iopart.cls and iopart10.clo (included). Invited talk at the ICTP Trieste Conference on "Unifying Concepts in Glass Physics", September 1999. To be published in J. Phys. Cond. Ma

Time Scales for transitions between free energy minima of a hard sphere system

Time scales associated with activated transitions between glassy metastable states of a free energy functional appropriate for a dense hard sphere system are calculated by using a new Monte Carlo method for the local density variables. We calculate the time the system,initially placed in a shallow glassy minimum of the free energy, spends in the neighborhood of this minimum before making a transition to the basin of attarction of another free energy minimum. This time scale is found to increase with the average density. We find a crossover density near which this time scale increases very sharply and becomes longer than the longest times accessible in our simulation. This scale shows no evidence of dependence on sample size.Comment: 25 pages, Revtex, 6 postscript figures. Will appear in Phys Rev E, March 1996 or s

Supra-oscillatory critical temperature dependence of Nb-Ho bilayers

We investigate the critical temperature Tc of a thin s-wave superconductor (Nb) proximity coupled to a helical rare earth ferromagnet (Ho). As a function of the Ho layer thickness, we observe multiple oscillations of Tc superimposed on a slow decay, that we attribute to the influence of the Ho on the Nb proximity effect. Because of Ho inhomogeneous magnetization, singlet and triplet pair correlations are present in the bilayers. We take both into consideration when solving the self consistent Bogoliubov-de Gennes equations, and we observe a reasonable agreement. We also observe non-trivial transitions into the superconducting state, the zero resistance state being attained after two successive transitions which appear to be associated with the magnetic structure of Ho.Comment: Main article: 5 pages, 4 figures; Supplementary materials: 4 pages, 5 figure

Superconducting gap node spectroscopy using nonlinear electrodynamics

We present a method to determine the nodal structure of the energy gap of unconventional superconductors such as high $T_c$ materials. We show how nonlinear electrodynamics phenomena in the Meissner regime, arising from the presence of lines on the Fermi surface where the superconducting energy gap is very small or zero, can be used to perform ``node spectroscopy'', that is, as a sensitive bulk probe to locate the angular position of those lines. In calculating the nonlinear supercurrent response, we include the effects of orthorhombic distortion and $a-b$ plane anisotropy. Analytic results presented demonstrate a systematic way to experimentally distinguish order parameters of different symmetries, including cases with mixed symmetry (for example, $d+s$ and $s+id$). We consider, as suggested by various experiments, order parameters with predominantly $d$-wave character, and describe how to determine the possible presence of other symmetries. The nonlinear magnetic moment displays a distinct behavior if nodes in the gap are absent but regions with small, finite, values of the energy gap exist.Comment: 18 pages, Revtex, 9 postscript figures. Submitted to Phys. Rev

Multiresonant Layered Acoustic Metamaterial (MLAM) solution for broadband low-frequency noise attenuation through double-peak sound transmission loss response (preprint)

The problem of noise control and attenuation is of interest in a broad range of applications, especially in the low-frequency range, below 1000 Hz. Acoustic metamaterials allow us to tackle this problem with solutions that do not necessarily rely on high amounts of mass, however most of them still present two major challenges: they rely on complex structures making them difficult to manufacture, and their attenuating capabilities are limited to narrow frequency bandwidths. Here we propose the Multiresonant Layered Acoustic Metamaterial (MLAM) concept as a novel kind of acoustic metamaterial based on coupled resonances mechanisms. Their main advantages hinge on providing enhanced sound attenuation capabilities in terms of a double-peak sound transmission loss response by means of a layered configuration suitable for large scale manufacturing

Molecular Dynamics Simulation of Spinodal Decomposition in Three-Dimensional Binary Fluids

Using large-scale molecular dynamics simulations of a two-component Lennard-Jones model in three dimensions, we show that the late-time dynamics of spinodal decomposition in concentrated binary fluids reaches a viscous scaling regime with a growth exponent $n=1$, in agreement with experiments and a theoretical analysis for viscous growth.Comment: 4 pages, 3 figure

Mode-coupling theory of the stress-tensor autocorrelation function of a dense binary fluid mixture

We present a generalized mode-coupling theory for a dense binary fluid mixture. The theory is used to calculate molecular-scale renormalizations to the stress-tensor autocorrelation function (STAF) and to the long-wavelength zero-frequency shear viscosity. As in the case of a dense simple fluid, we find that the STAF appears to decay as $t^{-3/2}$ over an intermediate range of time. The coefficient of this long-time tail is more than two orders of magnitude larger than that obtained from conventional mode-coupling theory. Our study focuses on the effect of compositional disorder on the decay of the STAF in a dense mixture.Comment: Published; withdrawn since ordering in the archive gives misleading impression of new publicatio

Metastable Dynamics above the Glass Transition

The element of metastability is incorporated in the fluctuating nonlinear hydrodynamic description of the mode coupling theory (MCT) of the liquid-glass transition. This is achieved through the introduction of the defect density variable $n$ into the set of slow variables with the mass density $\rho$ and the momentum density ${\bf g}$. As a first approximation, we consider the case where motions associated with $n$ are much slower than those associated with $\rho$. Self-consistently, assuming one is near a critical surface in the MCT sense, we find that the observed slowing down of the dynamics corresponds to a certain limit of a very shallow metastable well and a weak coupling between $\rho$ and $n$. The metastability parameters as well as the exponents describing the observed sequence of time relaxations are given as smooth functions of the temperature without any evidence for a special temperature. We then investigate the case where the defect dynamics is included. We find that the slowing down of the dynamics corresponds to the system arranging itself such that the kinetic coefficient $\gamma_v$ governing the diffusion of the defects approaches from above a small temperature-dependent value $\gamma^c_v$.Comment: 38 pages, 14 figures (6 figs. are included as a uuencoded tar- compressed file. The rest is available upon request.), RevTEX3.0+eps

Dynamics of Weak First Order Phase Transitions

The dynamics of weak vs. strong first order phase transitions is investigated numerically for 2+1 dimensional scalar field models. It is argued that the change from a weak to a strong transition is itself a (second order) phase transition, with the order parameter being the equilibrium fractional population difference between the two phases at the critical temperature, and the control parameter being the coefficient of the cubic coupling in the free-energy density. The critical point is identified, and a power law controlling the relaxation dynamics at this point is obtained. Possible applications are briefly discussed.Comment: 11 pages, 4 figures in uuencoded compressed file (see instructions in main text), RevTeX, DART-HEP-94/0