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Direct correlation functions (DCFs), linked to the second functional derivative of the free energy with respect to the one-particle density, play a fundamental role in a statistical mechanics description of matter. This holds, in particular, for the ordered phases: DCFs contain information about the local structure including defects and encode the thermodynamic properties of crystalline solids; they open a route to the elastic constants beyond low temperature expansions. Via a demanding numerical approach, we have explicitly calculated for the first time the DCF of a solid: based on the fundamental measure concept, we provide results for the DCF of a hard sphere crystal. We demonstrate that this function differs at coexistence significantly from its liquid counterpart—both in shape as well as in its order of magnitude—because it is dominated by vacancies. We provide evidence that the traditional use of liquid DCFs in functional Taylor expansions of the free energy is conceptually wrong and show that the emergent elastic constants are in good agreement with simulation-based results. published

We numerically study the structure of the interactions occurring in three-dimensional systems of hard spheres at jamming, focusing on the large-scale behavior. Given the fundamental role they play in the configuration of jammed packings, we analyze the propagation through the system of the weak forces and of the variation of the coordination number with respect to the isostaticity condition $\Delta Z$. We show that these correlations can be successfully probed by introducing a correlation function weighted on the density-density fluctuations. The results of this analysis can be further improved by introducing a representation of the system based on the contact points between particles. In particular, we find evidence that the weak forces and the $\Delta Z$ fluctuations support the hypothesis of randomly jammed packings of spherical particles being hyperuniform by exhibiting an anomalous long-range decay. Moreover, we find that the large-scale structure of the density-density correlation exhibits a complex behavior due to the superimposition of two exponentially damped oscillating signals propagating with linearly depending frequencies., Comment: Main: 5 pages, 4 figures; Supp. Info.: 2 pages, 1 figure

Using a framework of partial differential equation-constrained optimization, we demonstrate that multiple constitutive relations can be extracted simultaneously from a small set of images of pattern formation. Examples include state-dependent properties in phase-field models, such as the diffusivity, kinetic prefactor, free energy, and direct correlation function, given only the general form of the Cahn-Hilliard equation, Allen-Cahn equation, or dynamical density functional theory (phase-field crystal model). Constraints can be added based on physical arguments to accelerate convergence and avoid spurious results. Reconstruction of the free energy functional, which contains nonlinear dependence on the state variable and differential or convolutional operators, opens the possibility of learning nonequilibrium thermodynamics from only a few snapshots of the dynamics.

The bulk viscosity determines dissipation during hydrodynamic expansion. It vanishes in scale invariant fluids, while a nonzero value quantifies the deviation from scale invariance. For the dilute Fermi gas the bulk viscosity is given exactly by the correlation function of the contact density of local pairs. As a consequence, scale invariance is broken purely by pair fluctuations. These fluctuations give rise also to logarithmic terms in the bulk viscosity of the high-temperature nondegenerate gas. For the quantum degenerate regime I report numerical Luttinger-Ward results for the contact correlator and the dynamical bulk viscosity throughout the BEC-BCS crossover. The ratio of bulk to shear viscosity $\zeta/\eta$ is found to exceed the kinetic theory prediction in the quantum degenerate regime. Near the superfluid phase transition the bulk viscosity is enhanced by critical fluctuations and has observable effects on dissipative heating, expansion dynamics and sound attenuation., Comment: 6+4 pages, 4 figures; published version

The de Gennes narrowing phenomenon is frequently observed by neutron or x-ray scattering measurements of the dynamics of complex systems, such as liquids, proteins, colloids, and polymers. The characteristic slowing down of dynamics in the vicinity of the maximum of the total scattering intensity is commonly attributed to enhanced cooperativity. In this Letter, we present an alternative view on its origin through the examination of the time-dependent pair correlation function, the van Hove correlation function, for a model liquid in two, three, and four dimensions. We find that the relaxation time increases monotonically with distance and the dependence on distance varies with dimension. We propose a heuristic explanation of this dependence based on a simple geometrical model. This finding sheds new light on the interpretation of the de Gennes narrowing phenomenon and the α-relaxation time.

In this letter we present a measurement of the phase-space density distribution (PSDD) of ultra-cold \Rb atoms performing 1D anomalous diffusion. The PSDD is imaged using a direct tomographic method based on Raman velocity selection. It reveals that the position-velocity correlation function $C_{xv}(t)$ builds up on a timescale related to the initial conditions of the ensemble and then decays asymptotically as a power-law. We show that the decay follows a simple scaling theory involving the power-law asymptotic dynamics of position and velocity. The generality of this scaling theory is confirmed using Monte-Carlo simulations of two distinct models of anomalous diffusion., Comment: 5 pages, 4 figures in main text. 13 pages, 8 figures in supplementary Accepted for publication in PRL

We measured the power spectrum and two-point correlation function for the randomly fluctuating free surface on the downstream side of a stationary flow with a maximum Froude number $F_{\rm max} \approx 0.85$ reached above a localised obstacle. On such a flow the scattering of incident long wavelength modes is analogous to that responsible for black hole radiation (the Hawking effect). Our measurements of the noise show a clear correlation between pairs of modes of opposite energies. We also measure the scattering coefficients by applying the same analysis of correlations to waves produced by a wave maker., Comment: 11 pages, 14 figures. several points clarified; two new subsections in the Supplemental Material on the wave equation and the links with experiments in BECs

Single point measurement turbulence cannot distinguish variations in space and time. We employ an ensemble of one- and two-point measurements in the solar wind to estimate the space-time correlation function in the comoving plasma frame. The method is illustrated using near Earth spacecraft observations, employing ACE, Geotail, IMP-8, and Wind data sets. New results include an evaluation of both correlation time and correlation length from a single method, and a new assessment of the accuracy of the familiar frozen-in flow approximation. This novel view of the space-time structure of turbulence may prove essential in exploratory space missions such as Solar Probe Plus and Solar Orbiter for which the frozen-in flow hypothesis may not be a useful approximation. Fil: Matthaeus, W. H.. Bartol Research Institute; Reino Unido Fil: Weygand, J. M.. University Of California, Los Angeles, Institute Of Geophysics And Planetary Physics; Estados Unidos Fil: Dasso, Sergio Ricardo. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina

International audience; Supramolecular self-assembly is a multiple length-scale and time-dependent process involving many coexisting components. Such complexity requires suitable strategies to extract quantitative dynamical and structural information on all involved species. Here, we detail an original light scattering method to study the kinetics of tailored triarylamine molecules capable of self-assembling in supramolecular highly conductive nanowires upon light exposure. These micrometric assemblies cause the emergence of intermittences in the scattered intensity and the construction of a predominant slow mode in the correlation function making separation between small-and large-size species impossible using conventional treatments. Our strategy is based on the time monitoring of intermittences and allows us to determine the fraction of nanowires as well as those of small critical nuclei and triarylamine building blocks as a function of time and light exposure, in good agreement with recent theoretical predictions.

We examine correlations of transverse particle displacements and their relationship to the shear modulus of a glass and the viscosity of a fluid. To this end we use computer simulations to calculate a correlation function of the displacements, $S_4(q;t)$, which is similar to functions used to study heterogeneous dynamics in glass-forming fluids. We show that in the glass the shear modulus can be obtained from the long-time, small-q limit of $S_4(q;t)$. By using scaling arguments, we argue that a four-point correlation length $\xi_4(t)$ grows linearly in time in a glass and grows as $\sqrt{t}$ at long times in a fluid, and we verify these results by analyzing $S_4(q;t)$ obtained from simulations. For a viscoelastic fluid, the simulation results suggest that the crossover to the long-time $\sqrt{t}$ growth of $\xi_4(t)$ occurs at a characteristic decay time of the shear stress autocorrelation function. Using this observation, we show that the amplitude of the long-time $\sqrt{t}$ growth is proportional to $\sqrt{\eta}$ where $\eta$ is the viscosity of the fluid., Comment: 5 pages of main article and two pages of supplemental material. Accepted for publication in Physical Review Letters

Using the transfer matrix method, we numerically compute the precise position of the mobility edge of atoms exposed to a laser speckle potential, and study its dependence vs. the disorder strength and correlation function. Our results deviate significantly from previous theoretical estimates using an approximate self-consistent approach of localization. In particular we find that the position of the mobility edge in blue-detuned speckles is much lower than in the red-detuned counterpart, pointing out the crucial role played by the asymmetric on-site distribution of speckle patterns., 5 pages, 3 figures, plus Supplemental Material (3 pages, 3 figures)

Using the newly developed Matrix Product State (MPS) formalism for non-abelian Fractional Quantum Hall (FQH) states, we address the question of whether a FQH trial wave function written as a correlation function in a non-unitary Conformal Field Theory (CFT) can describe the bulk of a gapped FQH phase. We show that the non-unitary Gaffnian state exhibits clear signatures of a pathological behavior. As a benchmark we compute the correlation length of Moore-Read state and find it to be finite in the thermodynamic limit. By contrast, the Gaffnian state has infinite correlation length in (at least) the non-Abelian sector, and is therefore gapless. We also compute the topological entanglement entropy of several non-abelian states with and without quasiholes. For the first time in FQH the results are in excellent agreement in all topological sectors with the CFT prediction for unitary states. For the non-unitary Gaffnian state in finite size systems, the topological entanglement entropy seems to behave like that of the Composite Fermion Jain state at equal filling., Comment: 5 pages, 5 figures, and supplementary material. Published version

The two-dimensional (2D) melting transition is analyzed on the basis of the long-time behavior of a modified Lindemann parameter in 2D gamma(L)(t) and the bond-angular correlation function g(6)(t). Using video microscopy complete positional data are obtained over five decades in time for an ensemble of superparamagnetic colloidal particles confined to an air-water interface. We find that each of the three phases (solid/hexatic/isotropic liquid) is uniquely characterized by the long-time behavior of gamma(L)(t), g(6)(t), and the non-Gaussian parameter of the relative neighbor-neighbor displacement.

The polarization of light scattered by oxide films thermally grown on photolithographically generated microrough silicon surfaces was measured as functions of scattering angle. Using the predictions of first-order vector perturbation theory for scattering from interfacial roughness to interpret the results, the roughness of each interface and the correlation function between the two interfaces can be determined. The results show the spatial frequency dependence of the SiO (2)/Si interface smoothening.

We investigate aging in glassy systems based on a simple model, where a point in configuration space performs thermally activated jumps between the minima of a random energy landscape. The model allows us to show explicitly a subaging behavior and multiple scaling regimes for the correlation function. Both the exponents characterizing the scaling of the different relaxation times with the waiting time and those characterizing the asymptotic decay of the scaling functions are obtained analytically by invoking a `partial equilibrium' concept., 4 pages, 3 figures

We present an Instantaneous Normal Modes analysis of liquid HF aimed to clarify the origin of peculiar dynamical properties which are supposed to stem from the arrangement of molecules in linear hydrogen-bonded network. The present study shows that this approach is an unique tool for the understanding of the spectral features revealed in the analysis of both single molecule and collective quantities. For the system under investigation we demonstrate the relevance of hydrogen-bonding ``stretching'' and fast librational motion in the interpretation of these features., Comment: REVTeX, 7 pages, 5 eps figures included. Minor changes in the text and in a figure. Accepted for publication in Phys. Rev. Lett

We define a correlation function that quantifies the spatial correlation of single-particle displacements in liquids and amorphous materials. We show that for an equilibrium liquid this function is related to fluctuations in a bulk dynamical variable. We evaluate this function using computer simulations of an equilibrium glass-forming liquid, and show that long range spatial correlations of displacements emerge and grow on cooling toward the mode coupling critical temperature. [S0031-9007(99)09452-1] Liquids cooled toward their glass transition exhibit remarkable dynamical behavior [1]. The initial slowing of transport processes for liquids at temperatures T well above their glass transition temperature Tg is described by the mode coupling theory (MCT) [2], which predicts diverging relaxation times at a dynamical critical temperature Tc (in real and simulated liquids, this divergence is only apparent). The dynamical singularity of MCT occurs without a corresponding growing static correlation length associated with density or composition fluctuations [3]. Yet recent studies show that in the range of T described by MCT, simulated glass-forming liquids exhibit spatially heterogeneous dynamics [4 ‐6]. In this Letter, we define a correlation function that quantifies the spatial correlation of particle displacements and evaluate this function for a Lennard-Jones liquid. We find that spatial correlations of displacement arise and become long ranged on cooling toward Tc. First, we briefly review the conventional static correla

We report observations of the dynamics of the exact structure factor (speckle pattern) during phase separation in a sodium borosilicate glass, measured using intensity fluctuation spectroscopy with a coherent x-ray beam. Nonequilibrium fluctuations in the structure factor are analyzed using a two-time correlation function to extract the time-dependent and wave-number-dependent correlation time. The behavior of the correlation time is in agreement with a scaling law previously found in simulations. {copyright} {ital 1998} {ital The American Physical Society }

The aging effects of a 'diffusing glass', a single elastic string diffusing in a two-dimensional disordered media assisted by thermal noise are studied by Monte Carlo (MC) simulations. We find for the first time convincing numerical evidence of non-trivial aging effects both in the linear response against transverse force and the associated correlation function. Our results retain some important predictions of the conventional dynamical mean-field theory (MFT) but also reveal remarkable differences from it.

Statistical properties of energy levels and eigenfunctions in a ballistic system with diffusive surface scattering are investigated. The two-level correlation function, the level number variance, the correlation function of wavefunction intensities, and the inverse participation ratio are calculated., 4 pages REVTEX, two figures included as eps files

The dynamics of a polymer network are studied by direct view observation of the motion of a single point within a single polymer. Taking advantage of rather rigid biological microtubules as a case study, we expand the space and time scales of the system to those accessible by optical microscopy and standard video tools. Tracking is achieved by chemically attaching an optically resolved microsphere to a single point on the filament. We study the time dynamics of this point, without spatial averaging inherent in scattering methods. It is shown that the mean square displacement of the individual point is sensitive to local filament and network properties. [S0031-9007(97)05158-2] PACS numbers: 83.10.Nn An essential physical question in the study of polymer dynamics is how to relate the bulk rheological response of a network to the molecular-scale motions executed by an individual monomer. The latter are driven by random thermal collisions with the surrounding solvent molecules, and constrained at two levels: the embedding of the monomer within the polymer and the entanglement of the polymer within the network. In conventional chemical polymers the relevant length scales are on the order of 1 nm, far too small to be resolved by direct imaging techniques. Typical methods of study include light and neutron scattering, which are sensitive to local fluctuations in the density of the bulk sample. Light scattering can provide superb time resolution, while the few-angstrom wavelength of neutrons offers much improved spatial sensitivity. Nonetheless, these methods make a spatial averaging of the fluctuations taking place in a large volume of the sample. Attention is typically focused on the time domain, with use of fluctuation-dissipation arguments to relate modes of response to the thermally generated fluctuations. Recently, there have been a number of attempts to investigate local dynamics by direct imaging methods. The main trend has been to exploit biological polymers for their relative stiffness compared to simple synthetic ones, and also for their intrinsic biophysical interest. One approach has been to fluorescently label an entire polymer and watch its motion using video microscopy. The polymer is analyzed by measuring the wave vector [1] or the cosine correlation function [2]. In these methods the dynamics of a monomer is studied implicitly by measuring the dynamics of the entire polymer. Another method has been to implant a large bead in a network and investigate its restricted diffusion due to collisions with the surrounding filaments [3]. In this method, interpretation in terms of single filament dynamics must involve some a priori assumption. The approach described here is to prepare a system in which it is possible to image monomer motion directly, and to study the polymer network via the dynamics of a single monomer [4]. To this end, we expand the size and time scales of the system by exploiting biological polymers known as microtubules. These self-assembling filaments are stiff enough to maintain an average direction from end to end, yet sufficiently flexible to display thermally driven undulations. We “tag” a single monomer by attaching to it an optically resolvable bead (Fig. 1) and trace the bead’s position by video analysis. The motion of the bead displays the thermally driven motion of the microtubule itself. Using the clock provided by the video frame rate, we measure the mean square displacement (MSD) vs time interval of the bead. Classical random walk diffusion predicts that the MSD grows linearly in time, and our results lie in the deviations from this familiar situation. We interpret the data to probe the internal state of the network, e.g., to detect entanglement or quenched stress. Background for this experiment is set by considering a bead attached to a single microtubule whose dynamics are governed by thermally driven bending fluctuations. The important parameters governing the MSD at a point

A new method for investigating dynamic processes in transmission electron microscopy is proposed and demonstrated for Lorentz microscopy measurement of vortex motion in a Nb thin film. A selected portion of the electron beam current, modulated by the dynamics of the specimen, is led through the probe aperture at the image plane and measured as sequential counts of electrons or as a correlation function. The free energy barrier of the vortex hopping and the local creeping velocity are determined. In addition, the feasibility of observing the elastic flow of vortices is shown. {copyright} {ital 1997} {ital The American Physical Society}

Onsager reaction-field approach which corrects Weiss mean-field theory has been very successful in localized magnetism. We generalize this approach to the finite-temperature magnetism of the Hubbard model and calculate the N\'eel temperature ${T}_{N}$, the magnetic susceptibility, and the spin-spin correlation function. The results compare well with the available quantum Monte Carlo simulations.

An ab initio theoretical expression for the $N$-body Lyapunov exponent of a dilute gas is derived. It shows the Lyapunov exponent to be a function of the time integral of the correlation function for the second derivative of the interparticle potential (approximately a power $\frac{1}{3}$ law). This establishes a link between the Lyapunov exponent and the transport coefficients. We compare the theory with numerical simulations of a one component plasma.

We study a dynamically generated pattern in height gradients, centered around the active growth site, in the steady state of a self-organized interface depinning model. The pattern has a power-law tail and depends on the interface slope. An approximate integral equation relates the profile to local interface readjustments and long-ranged jumps of the active site. The pattern results in a two-point correlation function saturating to a finite value which depends on system size. Pattern formation is generic to systems in which the dynamics leads to correlated motion of the active site.

Experimentally measured velocities are used to obtain the one- and two-particle distribution functions f(1) and f(2) and the two-particle correlation function g(2)≡f(2)-f(1)f(1). The fluctuating velocities of interacting charged microparticles were recorded by tracking their motion while they were immersed in a dusty plasma. The phase space was reduced by having only two particles in a harmonic one dimensional confining potential. In statistical theory, g(2) is usually said to be dominated by the randomness of collisions, but here we find that it is dominated by collective oscillatory modes.

The ring angular correlation function is a characteristic feature determined by the particle structure. Averaging over a large number of ring angular correlation functions calculated from x-ray diffraction patterns will cancel out the cross correlations between different particles and converge to the autocorrelation functions of single particles. Applied on heterogeneous disordered ensembles, the retrieved function is a linear combination of a single-particle autocorrelation function multiplied by the molar ratios in a heterogeneous system. Using this relation, the ring angular correlation functions of the individual component particles in the heterogeneous system can be retrieved through the high throughput fluctuation x-ray scattering technique. This method is demonstrated with a simulated heterogeneous system composed of nanorods, nanoprism, and nanorice.

Multifragment decays of central collisions in 84Kr + 197Au at E/A = 35, 55, and 70 MeV are studied. The dependence of the extracted emission time on the velocity of the fragment pair is investigated. More energetic pairs manifest a stronger Coulomb interaction indicating emission from a source of smaller spatial-temporal extent than less-energetic pairs. This trend can be understood in the context of a statistical model which allows the source characteristics to evolve as the fragments are emitted.

We report x-ray photon correlation spectroscopy studies of the static structure factor and dynamic correlation function of a gold colloid dispersed in the viscous liquid glycerol. We find a diffusion coefficient for Brownian motion of the gold colloid which agrees well with that extrapolated from measurements made with visible light, but which was determined on an optically opaque sample and in a wave-vector range inaccessible to visible light.

We present an exact diagonalization study of the dynamical spin and density correlation function of the 2D t-J model for hole doping < 25%. Both correlation functions show a remarkably regular, but completely different scaling behaviour with both hole concentration and parameter values: the density correlation function is consistent with that of bosons corresponding to the doped holes and condensed into the lowest state of the noninteracting band of width 8t, the spin correlation function is consistent with Fermions in a band of width J. We show that the spin bag picture gives a natural explanation for this unusual behaviour.

There is currently no experimental technique available to probe spatially resolved rotational diffusion of nanoparticles in the vicinity of a wall. We present the first experimental study of rotational diffusion of small spherical colloids, using dynamic evanescent wave scattering. A setup is used where the wave vector components parallel and perpendicular to the wall can be varied independently, and an expression is derived for the first cumulant of the intensity correlation function in VH evanescent wave geometry for optically anisotropic spheres. The experimental results are in agreement with theoretical predictions that take particle-wall hydrodynamic interactions into account.

Ultrafast two-dimensional infrared (2D-IR) spectroscopy is used to study the picosecond dynamics of a vibrational probe molecule dissolved in a fragile glass former. The spectral dynamics are observed as the system is cooled to within a few degrees of the glass transition temperature (T(g)). We observe nonexponential relaxation of the frequency-frequency correlation function, similar to what has been reported for other dynamical correlation functions. In addition, we see evidence for α-like relaxation, typically associated with long-time, cooperative molecular motion, on the ultrafast time scale. The data suggests that the spectral dynamics are sensitive to cooperative motion occurring on time scales that are necessarily longer than the observation time.

In the past few years, coupling strengths between light and mechanical motion in optomechanical setups have improved by orders of magnitude. Here we show that, in the standard setup under continuous laser illumination, the steady state of the mechanical oscillator can develop a non-classical, strongly negative Wigner density if the optomechanical coupling is large at the single-photon level. Because of its robustness, such a Wigner density can be mapped using optical homodyne tomography. These features are observed near the onset of the instability towards self-induced oscillations. We show that there are also distinct signatures in the photon-photon correlation function $g^{(2)}(t)$ in that regime, including oscillations decaying on a time scale not only much longer than the optical cavity decay time, but even longer than the \emph{mechanical} decay time., 6 pages including 1 appendix. 6 Figures. Corrected

The spatial fluctuations of the dynamics of a colloidal system composed of nanoparticles are probed by a novel experimental setup, which combines homodyne and heterodyne dynamic light scattering focused onto a micron-sized volume via a microscope objective. The technique is used to measure the four-point susceptibility of an aging colloidal suspension, revealing a breakdown of the Gaussian approximation for the correlation function of the scattered electromagnetic field. The deviation from the Gaussian approximation increases with waiting time as the system evolves toward an arrested phase, signaling the gradual emergence of higher-order nontrivial dynamic correlations.

We derive a simple formula for the fluctuations of the time average around the thermal mean for overdamped Brownian motion in a binding potential U(x). Using a backward Fokker-Planck equation, introduced by Szabo, et al. in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large non-ergodic fluctuations and show how they are related to a super-aging correlation function., 5 pages, 3 figures

One of the most important experimental results for proton-proton scattering at the LHC is the observation of a so-called "ridge" structure in the two particle correlation function versus the pseudorapidity difference $\Delta\eta$ and the azimuthal angle difference $\Delta\phi$. One finds a strong correlation around $\Delta\phi=0$, extended over many units in $\Delta\eta$. We show that a hydrodynamical expansion based on flux tube initial conditions leads in a natural way to the observed structure. To get this result, we have to perform an event-by-event calculation, because the effect is due to statistical fluctuations of the initial conditions, together with a subsequent collective expansion. This is a strong point in favour of a fluid-like behavior even in $pp$ scattering, where we have to deal with length scales of the order of 0.1 fm., Comment: 5 pages, 4 figures

Information on the temperature dependence of the atomic correlation functions in quasicrystals has been obtained from M\"ossbauer and high resolution neutron spectroscopies. A pronounced nonlinear decrease is observed at high temperature for the purely elastic contribution. This indicates localized vibrational states within a length scale of about 10 \AA{}.

Proton-proton correlations at small relative momenta were measured for [sup 40]Ar+[sup 197]Au reactions at [ital E]/[ital A]=200 MeV. Comparing the correlation functions to predictions based on single-particle phase space distributions from microscopic Boltzmann-Uehling-Uhlenbeck and quantum-molecular-dynamics (QMD) simulations, no satisfactory agreement could be established. Calculations utilizing two-particle emission probabilities predicted by the QMD model differ significantly from the single-particle calculations and are much closer to the experimental observations at [ital E]/[ital A]=200 MeV, potentially signaling the importance of the two-particle density for the proton-proton correlation function.

The structure of the Cu(110) surface is studied at high temperatures using a combination of lattice-gas Monte Carlo and molecular dynamics methods with identical many-atom interactions derived from the effective medium theory. The anisotropic six-vertex model is used in the interpretation of the lattice-gas results. We find a clear roughening transition around T_R=1000K and T_R/T_M=0.81. Molecular dynamics reveals the clustering of surface defects as the atomistic mechanism of the transition and allows us to estimate characteristic time scales. For the system of size 50x50, the time scale of the local roughening at 1150 K of an initially smooth surface is of the order of 100 ps., Comment: 24 pages (12 figs available upon request), REVTEX, to be published in PRB, JYFL Preprint 16/93

Dense self-avoiding polymer chains in strictly two dimensions are compact objects with fractal contours. Using scaling arguments and molecular dynamics simulations (with negligible momentum conservation) it is shown that correlated amoebalike fluctuations of the (sub)chain contours dominate the relaxation dynamics on all scales. The incompressibility of the melt and the compactness of (sub)chains impose a scale-free constraint on the contour fluctuations. This leads to strong long range spatiotemporal correlations of the displacement field as shown, e.g., by the (negative) algebraic decay of the center-of-mass velocity correlation function C(t) ∼ -1/t 6/5 with time t.

Rotating convection near onset is studied using a three mode model but with the inclusion of spatial dependence. An apparently chaotic dynamics is found, consistent with experiment, without the necessity of adding ad hoc noise terms as in previous models. There is no phase transition approaching the point of linear instability of straight rolls from the disordered side, and the characteristic domain size and switching time remain finite here. This behavior is discussed in terms of the velocity of walls between the different domains.

We present Monte Carlo simulations of binary mixtures of hard parallel spherocylinders with length-to-width ratios L 1 /D=1.0 and L 2 /D ranging from 1.3 to 2.1. The composition is such that the partial volume fractions are equal. For L 2 /D>1.6, we observe a thermodynamically stable columnar phase which is not formed by the monodisperse components separately

We show that the classical Heisenberg antiferromagnet on a Kagom\'e lattice is an example of a spin nematic. By calculating the effects of thermal fluctuations around ground states, and by Monte Carlo simulations, we find entropically driven, local spin-nematic order at low temperature T with a correlation length which is divergent in the limit T\ensuremath{\rightarrow}0. Dynamical correlations are also studied, within the harmonic approximation, in the nematically ordered states.

Bond-energy correlation functions are calculated exactly for a planar Ising model in finite-size strip geometry for subcritical temperatures with surface fields of either equal or opposite sign applied to opposite edges. We show that the Wulff construction (surface free-energy minimization) applied to the bubble model for the 2-point energy correlation function gives exact results and demonstrates the significance of wetting phenomena.

The current correlation function is determined from dynamic light scattering measurements of a suspension of particles with hard spherelike interactions. For suspensions in thermodynamic equilibrium we find scaling of the space and time variables of the current correlation function. This finding supports the notion that the movement of suspended particles can be described in terms of uncorrelated Brownian encounters. However, in the metastable fluid, at volume fractions above freezing, this scaling fails.

We encode periodic spatiotemporal patterns in Ising-spin neural networks, using the simple learning rule inspired by the spike-timing-dependent synaptic plasticity. It is then found that periodically oscillating spin neurons successfully reproduce phase differences of the encoded periodic patterns. The storage capacity of this associative memory neural network is enhanced with an adequate level of asymmetry in synapse connections. To understand the properties of these nonequilibrium retrieval states of the neural network, we carry out an analysis based on a path integral method. The relation of a dynamic crosstalk term to time-persistent oscillation of a correlation function well explains the enhancement of the storage capacity in spite of our approximation on nonpersistent terms. We investigate the accuracy of this approximation further by detailed comparison with numerical simulations.

Measurements of the correlation function below the electrohydrodynamic instability in a thin layer of a nematic liquid crystal reveal fluctuating convection patches. Their amplitude {ital {bar A}}, correlation length {xi}, and correlation time {tau} can be desribed by a stochastic mean-field model. The amplitude agrees with the expected fluctuations due to thermal noise.

For equilibrium systems with Ising symmetry, the three-point correlation function is always zero above criticality. When a lattice-gas version of this system is driven to a nonequilibrium steady state, this correlation becomes nontrivial. Its dominant large-scale behavior is found to be a consequence of both the manifest breaking of Ising symmetry by the driving force and the more subtle violation of the fluctuation-dissipation theorem

We present a microscopic model of a granular pile submitted to vibration, emphasizing the competing roles of collective and single-particle excitations which lead to specific characteristics of the resulting state. The erect of vibration on a powder is next investigated by a novel computer-simulation approach in three dimensions, which enables us to probe cooperative erects in the bulk; satisfying agreement with the predictions of the model is obtained