Showing papers on "Correlation function (statistical mechanics) published in 2004"

On the Structure and Dynamics of Ionic Liquids

Abstract: The structure and dynamics of the ionic liquid 1-ethyl-3-methylimidazolium nitrate is studied by molecular dynamics simulations. We find long-range spatial correlations between the ions and a three-dimensional local structure that reflects the asymmetry of the cations. The main contribution to the configurational energy comes from the electrostatic interactions which leads to charge-ordering effects. Radial screening and three-dimensional distribution of charge are also analyzed. The motion of a single ion is studied via velocity and reorientational correlation functions. It is found that ions “rattle” in a long-lived cage, while the orientational structure relaxes on a time scale longer than 200 ps. As in a supercooled liquid, the mean square displacements reveal a subdiffusive dynamics. In addition, the presence of dynamic heterogeneities can be detected by analyzing the non-Gaussian behavior of the van Hove correlation function and the spatial arrangement of the most mobile ions. The short-time collect...

Exact Scaling Functions for One-Dimensional Stationary KPZ Growth

Abstract: We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann–Hilbert problem related to the Painleve II equation. We solve these equations numerically with very high precision and compare our, up to numerical rounding exact, result with the prediction of Colaiori and Moore(1) obtained from the mode coupling approximation.

Cosmic evolution of quasar clustering: implications for the host haloes

Abstract: We present detailed clustering measurements from the 2dF Quasi-Stellar Object Redshift Survey (2QZ) in the redshift range 0.8 < z < 2.1. Using a flux-limited sample of ∼14 000 objects with effective redshift z eff = 1.47, we estimate the quasar projected correlation function for separations 1 < r/ h −1 Mpc < 20. We find that the two-point correlation function in real space is well approximated by a power law with slope γ = 1.5 ± 0.2 and comoving correlation length r 0 = 4.8 +0.9 h −1 Mpc. Splitting the sample into three subsets based on redshift, we find evidence for an increase of the clustering amplitude with look-back time. For a fixed γ ,e v olution of r0 is detected at the 3.6σ confidence level. The ratio between the quasar correlation function and the mass autocorrelation function (derived adopting the concordance cosmological model) is found to be scale-independent. For a linear mass-clustering amplitude σ 8 = 0.8, the ‘bias parameter’ decreases from b � 3.9 at z eff = 1.89 to b � 1.8 at z eff = 1.06. From the observed abundance and clustering, we infer how quasars populate dark matter

Modeling inhomogeneous van der Waals fluids using an analytical direct correlation function.

Abstract: Rosenfeld's perturbative method [J. Chem. Phys. 98, 8126 (1993)] for constructing the Helmholtz energy functional of classical systems is applied to studying inhomogeneous Lennard-Jones fluids, in which the key input---the bulk direct correlation function---is obtained from the first-order mean-spherical approximation (FMSA) [J. Chem. Phys. 118, 4140 (2003)]. Preserving its high fidelity at the bulk limit, the FMSA shows stable and satisfactory performance for a variety of inhomogeneous Lennard-Jones fluids including those near hard walls, inside slit pores, and around colloidal particles. In addition, the inhomogeneous FMSA reproduces reliably the radial distribution function at its bulk limit. The FMSA is found, in particular, much better than the mean-field theory for fluids near hard surfaces. Unlike alternative non-mean-field approaches, the FMSA is computationally as efficient as the mean-field theory, free of any numerical determination of structure information, weight functions, or empirical parameters.

Line edge roughness and critical dimension variation: Fractal characterization and comparison using model functions

Abstract: Line edge (or width) roughness (LER or LWR) of photoresists lines constitutes a serious issue in shrinking the critical dimensions (CD) of the gates to dimensions of a few tens of nanometers. In this article, we address the problem of the reliable LER characterization as well as the association of LWR with the CD variations. The complete LER characterization requires more parameters than the rms value σ since the latter neglects the spatial aspects of LER and does not predict the dependence on the length of the measured line. The further spatial LER descriptors may be the correlation length ξ and the roughness exponent α, which can be estimated through various methods. One aim of the present work is to perform a systematic comparative study of these methods using model edges generated by a roughness algorithm, in order to show their advantages and disadvantages for a reliable and accurate determination of the spatial LER parameters. In particular, we compare the results from (a) the study of the height–height correlation function (HHCF), (b) the Fourier [or power spectrum (PS)] analysis, and (c) the variation of rms value σ with measured line edge L [σ(L) curve]. It is found that the HHCF can be considered approximately a rescaled version of σ(L) and that the value of σ becomes almost independent of the measured edge length for lengths larger than ten times the correlation length. As regards the PS, it is shown that the finite length of the edge may harmfully affect the reliable estimation of α and ξ. Finally, we confirm theoretically and generalize an experimental observation [Leunissen et al., Microelectron. Eng. (to be published)] regarding the relationship between LWR and the σ of the CD variations within a die of a wafer. It is shown that they behave in a complimentary way as line length increases so that the sum of their squares remains constant and equal to the square of the LWR σ of the infinite line.

Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition

Abstract: We show that the glass transition predicted by the Mode-Coupling Theory (MCT) is a critical phenomenon with a diverging length and time scale associated to the cooperativity of the dynamics. We obtain the scaling exponents nu and z that relate space and time scales to the distance from criticality, as well as the scaling form of the critical four-point correlation function. However, both these predictions and other well known MCT results are mean-field in nature and are thus expected to change below the upper critical dimension dc=6, as suggested by different forms of the Ginzburg criterion.

Static and dynamic properties of tethered chains at adsorbing surfaces: a Monte Carlo study.

Abstract: We present extensive Monte Carlo simulations of tethered chains of length N on adsorbing surfaces, considering the dilute case in good solvents, and analyze our results using scaling arguments. We focus on the mean number M of chain contacts with the adsorbing wall, on the chain’s extension (the radius of gyration) perpendicular and parallel to the adsorbing surface, on the probability distribution of the free end and on the density profile for all monomers. At the critical adsorption strength ec one has Mc∼Nφ, and we find (using the above results) as best candidate φ to equal 0.59. However, slight changes in the estimation of ec lead to large deviations in the resulting φ; this might be a possible reason for the difference in the φ values reported in the literature. We also investigate the dynamical scaling behavior at ec, by focusing on the end-to-end correlation function and on the correlation function of monomers adsorbed at the wall. We find that at ec the dynamic scaling exponent a (which describes the relaxation time of the chain as a function of N) is the same as that of free chains. Furthermore, we find that for tethered chains the modes perpendicular to the surface relax quicker than those parallel to it, which may be seen as a splitting in the relaxation spectrum.

Aging Correlation Functions for Blinking Nano-Crystals, and Other On - Off Stochastic Processes

Abstract: Following recent experiments on power law blinking behavior of single nano-crystals, we calculate two-time intensity correlation functions for these systems. We use a simple two state (on and off) stochastic model to describe the dynamics. We classify possible behaviors of the correlation function and show that aging, e.g., dependence of the correlation function on age of process t, is obtained for classes of the on time and off time distributions relevant to experimental situation. Analytical asymptotic scaling behaviors of the intensity correlation in the double time t and t' domain are obtained. In the scaling limit --> h(x), where four classes of behaviors are found: (i) finite averaged on and off times x=t' (standard behavior) (ii) on and off times with identical power law behaviors x=t/t' (case relevant for capped nano-crystals). (iii) exponential on times and power law off times x=tt' (case relevant for uncapped nano-crystals). (iv) For defected off time distribution we also find x=t+t' . Origin of aging behavior is explained based on simple diffusion model. We argue that the diffusion controlled reaction A+B AB, when followed on a single particle level exhibits aging behavior.

α-relaxation processes in binary hard-sphere mixtures

Abstract: Molecular-dynamics simulations are presented for two correlation functions formed with the partial density fluctuations of binary hard-sphere mixtures in order to explore the effects of mixing on the evolution of glassy dynamics upon compressing the liquid into high-density states. Partial-density-fluctuation correlation functions for the two species are reported. Results for the $\alpha$-relaxation process are quantified by parameters for the strength, stretching, and time scale, where the latter varies over almost four orders of magnitude upon compression. The parameters exhibit an appreciable dependence on the wave vector, and this dependence is different for the correlation function referring to the smaller and that for the larger species. These features are shown to be in semiquantitative agreement with those calculated within the mode-coupling theory for ideal liquid-glass transitions.

Aging correlation functions for blinking nanocrystals, and other on–off stochastic processes

Abstract: Following recent experiments on power law blinking behavior of single nanocrystals, we calculate two-time intensity correlation functions I(t)I(t+t') for these systems. We use a simple two state (on and off) stochastic model to describe the dynamics. We classify possible behaviors of the correlation function and show that aging, e.g., dependence of the correlation function on age of process t, is obtained for classes of the on time and off time distributions relevant to experimental situation. Analytical asymptotic scaling behaviors of the intensity correlation in the double time t and t' domain are obtained. In the scaling limit I(t)I(t+t('))-->h(x), where four classes of behaviors are found: (i) finite averaged on and off times x=t' (standard behavior); (ii) on and off times with identical power law behaviors x=t/t' (case relevant for capped nanocrystals); (iii) exponential on times and power law off times x=tt' (case relevant for uncapped nanocrystals); (iv) for defected off time distribution we also find x=t+t'. Origin of aging behavior is explained based on simple diffusion model. We argue that the diffusion controlled reaction A+B AB, when followed on a single particle level exhibits aging behavior.

Temperature dependence of spatially heterogeneous dynamics in a model of viscous silica.

Abstract: Molecular dynamics simulations are performed to study spatially heterogeneous dynamics in a model of viscous silica above and below the critical temperature of the mode coupling theory, ${T}_{\mathit{MCT}}$. Specifically, we follow the evolution of the dynamic heterogeneity as the temperature dependence of the transport coefficients shows a crossover from non-Arrhenius to Arrhenius behavior when the melt is cooled. It is demonstrated that, on intermediate time scales, a small fraction of oxygen and silicon atoms are more mobile than expected from a Gaussian approximation. These highly mobile particles form transient clusters larger than that resulting from random statistics, indicating that the dynamics are spatially heterogeneous. An analysis of the clusters reveals that the mean cluster size is maximum at times intermediate between ballistic and diffusive motion, and the maximum size increases with decreasing temperature. In particular, the growth of the clusters continues into the crossover to Arrhenius behavior for the transport coefficients. These findings imply that the structural relaxation in silica cannot be understood as a statistical bond breaking process. Although the mean cluster sizes for silica are at the lower end of the spectrum of values reported in the literature for other model liquids, we find that spatially heterogeneous dynamics in models of strong and fragile glass formers are similar on a qualitative level. However, unlike the results for fragile liquids, we show that correlated particle motion along quasi-one-dimensional, stringlike paths is of little importance for the structural relaxation in this model of silica, suggesting that stringlike motion is suppressed by the presence of a network structure. To study transient clusters of localized particles, we calculate a generalized susceptibility corresponding to the self-part of a four-point time dependent density correlation function. We find that this generalized susceptibility is maximum on the time scale of the structural relaxation, where a strong increase of the peak height indicates a growing length of spatial correlations between localized particles upon cooling. Characterizing the local structural environments of the most mobile and the most immobile particles, respectively, we show that high particle mobility is facilitated by, but not limited to, the vicinity of defects in the network structure.

Nonunitary Spin-Charge Separation in a One-Dimensional Fermion Gas

Abstract: In this Letter we report exact results on the infrared asymptotics of the one-particle dynamical correlation function of the gas of impenetrable spin 1/2 fermions at infinitesimal temperature. The correlation function shows signs of spin-charge separation with scaling behavior in the charge part and exponential decay as a function of the space coordinate in the spin part. Surprisingly, the anomalous dimensions in the charge part do not correspond to any unitary conformal field theory. We find that the fermion spectral weight has a power law divergency at low energy with the anomalous exponent -1/2.

Validation of an analytical solution for depth of correlation in microscopic particle image velocimetry

Abstract: Because the entire flowfield is generally illuminated in microscopic particle image velocimetry (microPIV), determining the depth over which particles will contribute to the measured velocity is more difficult than in traditional, light-sheet PIV. This paper experimentally and computationally measures the influence that volume illumination, optical parameters, and particle size have on the depth of correlation for typical microPIV systems. First, it is demonstrated mathematically that the relative contribution to the measured velocity at a given distance from the object plane is proportional to the curvature of the local cross-correlation function at that distance. The depth of correlation is then determined in both the physical experiments and in computational simulations by directly measuring the relative contribution to the correlation function of particles located at a known separation from the object plane. These results are then compared with a previously derived analytical model that predicts the depth of correlation from the basic properties of the imaging system and seed particles used for the microPIV measurements. Excellent agreement was obtained between the analytical model and both computational and physical experiments, verifying the accuracy of the previously derived analytical model.

Correlation amplitudes for the spin- 1 2 XXZ chain in a magnetic field

Abstract: We present accurate numerical estimates for the correlation amplitudes of leading and main subleading terms of the two- and four-spin correlation functions in the one-dimensional spin-$1/2$ $\mathrm{XXZ}$ model under a magnetic field. These data are obtained by fitting the correlation functions, computed numerically with the density-matrix renormalization-group method, to the corresponding correlation functions in the low-energy effective theory. For this purpose we have developed the Abelian bosonization approach to the spin chain under the open-boundary conditions. We use the numerical data of the correlation amplitudes to quantitatively estimate spin gaps induced by a transverse staggered field and by exchange anisotropy.

Correlation potentials for a multiconfigurational-based density functional theory with exact exchange

Abstract: A density functional theory based on a complete active space self consistent field (CASSCF) reference function with exact exchange is discussed. It is first shown that such a theory may be formulated with a correlation potential dependent on the density function and on the active space used. Auxiliary functions, such as the on-top two-particle density, are used to define uniquely the potential for different active spaces. The paper also analyses the correlation functional for some atomic and molecular cases. Large ab initio calculations are performed to obtain accurate density functions. A correlation potential is then fitted such that the reference CASSCF function gives the same density. The correlation potential values are saved in a data base for future analysis.

Multi-particle correlations in qp-Bose gas model

Abstract: The approach based on a multimode system of q-deformed oscillators and the related picture of an ideal gas of q-bosons enables us to effectively describe the observed non-Bose-type behaviour, in experiments on heavy-ion collisions, of the intercept (or the 'strength') λ of the two-particle correlation function of identical pions or kaons. In this paper we extend the main results of that approach in two aspects: first, we derive in explicit form the intercepts of n-particle correlation functions in the case of the q-Bose gas model and, second, provide their explicit two-parameter (or qp-) generalization.

Azimuthal harmonic coefficients of the microwave backscattering from a non-Gaussian ocean surface with the first-order SSA model

Abstract: In this paper, the first-order small slope approximation is applied to a rough sea surface with non-Gaussian statistics, for which the third- and the fourth-order statistics are taken into account in the calculation of the radar cross section. From the Cox and Munk slope distribution, the higher order statistic moments are derived, and behaviors of the corresponding correlation functions are assumed. We show that the fourth order (related to the peakedness or kurtosis) is isotropic, whereas the third order (related to the skewness) has a behavior as cos(/spl psi/), where /spl psi/ is the wave direction along the wind direction. Thus, using the Elfouhaily et al. sea height spectrum, related to the second-order statistics, we show that the normalized radar backscattering cross section (NRBCS) can be expanded as an even Fourier series in cos(n/spl phi/) (where n is a positive integer), for which the harmonic coefficients require only a single integration over the radial distance. This result is consistent with experimental data done for microwave frequencies. In addition, we show for microwave frequencies (like C- and Ku-bands) that the Fourier series can be truncated up to the second order, since the higher order harmonic coefficients vanish. The NRBCS is also compared with empirical backscattering models CMOD2-I3 and SASS-II, valid in C- and Ku-bands, according to the scattering angle and the wind direction. The first-order harmonic coefficient predicts the surface asymmetry along the upwind and downwind directions, whereas the second-order harmonic coefficient describes the surface asymmetry along the upwind and crosswind directions.

Evaluation of scaling laws derived from Lie group symmetry methods in zero-pressure-gradient turbulent boundary layers

Abstract: New scaling laws for turbulent boundary layers recently derived (see Oberlack 2000) using Lie group symmetry methods have been tested against experimental data from the KTH database for zero-pressure-gradient turbulent boundary layers. The most significant new law predicts an exponential variation of the mean velocity defect in the outer (wake) region. It was shown to fit the experimental data very well over a large part of the boundary layer, from the outer part of the overlap region to about half the boundary layer thickness ( $\delta_{99}$ ). In the outermost part of the boundary layer the velocity defect falls more rapidly than predicted by the exponential law. This can partly be attributed to intermittency in that region but the main cause stems from non-parallel effects that are not accounted for in the derivation of the exponential law. The two-point correlation function behaviour in the outer region, where an exponential velocity defect law is observed, was found to be very different from that derived under the assumption of parallel flow. It is found to be plausible that this indeed can be attributed to non-parallel effects. A small modification of the innermost part of the log-layer in the form of an additive constant within the log-function is predicted by the Lie group symmetry method. A qualitative agreement with such a behaviour just below the overlap region was found. The derived scaling law behaviour in the overlap region for the two-point correlation functions was also verified by the experimental data.

Decay of correlations in Fermi systems at nonzero temperature.

Abstract: The locality of correlation functions is considered for Fermi systems at nonzero temperature. We show that for all short-range, lattice Hamiltonians, the correlation function of any two fermionic operators decays exponentially with a correlation length which is of order the inverse temperature for small temperature. We discuss applications to numerical simulation of quantum systems at nonzero temperature.

Emissivity simulations in passive microwave remote sensing with 3-D numerical solutions of Maxwell equations

Abstract: In the numerical Maxwell-equation model (NMM3D) of rough-surface scattering, we solve Maxwell equations in three dimensions to calculate emissivities for applications in passive microwave remote sensing of soil and ocean surfaces. The difficult cases for soil surfaces are with exponential correlation functions when the surfaces have fine-scale structures of large slopes. The difficulty for ocean surfaces is that because the emissivities are close to that of a flat surface, the emissivities have to be calculated accurately to correctly assess the rough-surface effects. In this paper, the accuracies of emissivity calculations are improved by using Rao-Wilton-Glisson basis functions. We further use sparse matrix canonical method to solve the matrix equation of Poggio-Miller-Chang-Harrington-Wu integral equations. Energy conservation checks are provided for the simulations. Comparisons are made with results from the pulse basis function. Numerical results are illustrated for soil and ocean surfaces respectively with exponential correlation function and ocean spectrum. The emissivities of soil are illustrated at both L- and C-bands and at multiple incidence angles for the same physical roughness parameters. The brightness temperatures for ocean surfaces are illustrated for cases with various wind speeds. We compare results with those from the sparse matrix methods. Comparisons are also made with experimental emissivity measurements of soil surfaces. Parallel computation is also implemented. Lookup tables of emissivities based on NMM3D are provided.

Scattering Functions of Semidilute Solutions of Polymers in a Good Solvent

Abstract: Expressions for analyzing small-angle scattering data from semidilute solutions of polymers in a good solvent over a broad range of scattering vectors are examined. Three different scattering function expressions are derived from Monte Carlo simulations. The expressions are similar to those of polymer reference interaction site models, with a scattering-vector-dependent direct correlation function. In the most advanced model, the screening of excluded-volume interactions beyond the overlap concentration is taken into account. Two simpler expressions, in which the screening of excluded-volume interactions is not included, are also applied. The three models are tested against small-angle neutron scattering (SANS) experiments on polystyrene in deuterated toluene for a broad range of molar masses and concentrations over a wide range of scattering vectors. For each model, simultaneous fits to all the measured scattering data are performed. The most advanced model excellently reproduces the SANS data over the full range of the parameters. The two simpler models fit the data almost equally well. On the basis of an extensive study, an optimal fitting strategy can be recommended for experimentalists, who want to analyze small-angle scattering data from polymers at any concentration. For data sets that do not contain data on the single-chain scattering function, the simpler model is recommended; it uses a direct correlation function equal to the form factor of an infinitely thin rod, which is independent of the concentration and molar mass. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3081–3094, 2004

Next Nearest-Neighbor Correlation Functions of the Spin-1/2 XXZ Chain at Massive Region

Abstract: The second neighbor correlation functions of the spin-\(\frac{1}{2}\) X X Z chain in the ground state are expressed in the form of three dimensional integrals. We show that these integrals can be reduced to one-dimensional ones and thereby evaluate the values of the next nearest-neighbor correlation functions for Δ>1.

General solutions for multispin two-time correlation and response functions in the Glauber–Ising chain

Abstract: The kinetic Glauber–Ising spin chain is one of the very few exactly solvable models of non-equilibrium statistical mechanics. Nevertheless, existing solutions do not yield tractable expressions for two-time correlation and response functions of observables involving products of more than one or two spins. We use a new approach to solve explicitly the full hierarchy of differential equations for the correlation and response functions. From this general solution follow closed expressions for arbitrary multispin two-time correlation and response functions, for the case where the system is quenched from equilibrium at Ti > 0 to some arbitrary T ≥ 0. By way of application, we give the results for two- and four-spin two-time correlation and response functions. From the standard mapping, these also imply new exact results for two-time particle correlation and response functions in one-dimensional diffusion limited annihilation.

The Clustering of XMM-Newton Hard X-Ray Sources

Abstract: This Letter presents the clustering properties of hard (2-8 keV) X-ray-selected sources detected in a wide-field (?2 deg2), shallow [fX(2-8 keV) ? 10-14 ergs cm-2 s-1], and contiguous XMM-Newton survey. We perform an angular correlation function analysis using a total of 171 sources to the above flux limit. We detect an ~4 ? correlation signal out to 300'' with w(? < 300'') 0.13 ? 0.03. Modeling the two-point correlation function as a power law of the form w(?) = (?0/?)?-1, we find ?0 = 48.9 arcsec and ? = 2.2 ? 0.30. Fixing the correlation function slope to ? = 1.8, we obtain ?0 = 22.2 arcsec. Using Limber's integral equation and a variety of possible luminosity functions of the hard X-ray population, we find a relatively large correlation length, ranging from r0 ~ 9 to 19 h-1 Mpc (for ? = 1.8 and the concordance cosmological model), with this range reflecting also different evolutionary models for the source luminosities and clustering characteristics. The relatively large correlation length is comparable to that of extremely red objects and luminous radio sources.

Internal versus external conductivity of a dense plasma: many-particle theory and simulations.

Abstract: In the long-wavelength limit k=0, the response function has been investigated with respect to the external and internal fields which is expressed by the external and internal conductivity, respectively. Molecular dynamics simulations are performed to obtain the current-current correlation function and the dynamical collision frequency which are compared with analytical expressions. Special attention is given to the dynamical collision frequency and the description of plasma oscillations in the case of k=0. The relation between the external and internal conductivity and the current-current correlation function is analyzed.

Depolarization volume and correlation length in the homogenization of anisotropic dielectric composites

Abstract: In conventional approaches to the homogenization of random particulate composites, both the distribution and size of the component phase particles are often inadequately taken into account. Commonly, the spatial distributions are characterized by volume fraction alone, while the electromagnetic response of each component particle is represented as a vanishingly small depolarization volume. The strong-permittivity-fluctuation theory (SPFT) provides an alternative approach to homogenization wherein a comprehensive description of distributional statistics of the component phases is accommodated. The bilocally-approximated SPFT is presented here for the anisotropic homogenized composite which arises from component phases comprising ellipsoidal particles. The distribution of the component phases is characterized by a two-point correlation function and its associated correlation length. Each component phase particle is represented as an ellipsoidal depolarization region of nonzero volume. The effects o...

Angular Dependence of Scattered Light from Hyperbranched Structures in a Good Solvent. A Fractal Approach

Abstract: The neglect of excluded volume interaction in light scattering from randomly branched macromolecules leads to misinterpretation of the angular dependence. With a space correlation function of general fractal behavior γ(r) = Ae-(r/ξ)/(r/ξ)3-d Feltoft et al. (Phys. Rev. B 1986, 33, 269) derived the corresponding particle scattering factor P(qRg) of the angular dependence of scattered light, where q = (4πn0/λ0) sin θ/2 is the value of the scattering vector, Rg is the radius of gyration, and ξ is a correlation length which is correlated to Rg. Complete agreement between theory and three sets of chemically different randomly branched clusters was obtained (Macromolecules 1997, 30, 2365) with a fractal dimension of d = 1.76 (renormalization group theory: dRG = 1.70). In the present contribution, the Feltoft et al. approach is extended to hyperbranched and star-branched macromolecules. In contrast to randomly branched samples these structures are not selfsimilar objects. However, the angular dependence of these...

Grad’s equations and hydrodynamics for weakly inelastic granular flows

Abstract: We introduce and discuss Grad’s moment equations for dilute granular systems of hard spheres with dissipative collisions and variable coefficient of restitution, under the assumption of weak inelasticity. An important by-product is that in this way we obtain the hydrodynamic description of a system of nearly elastic particles by a direct procedure from the Boltzmann equation, without resorting to any homogeneous cooling state assumption. Several crucial results of the pertinent literature are recovered in the present physical context in which deviation from elastic scattering is of the same order as the Knudsen number. In particular, the correlation function plays a fundamental role in the decay of the temperature, and the latter is described asymptotically, in space homogeneous conditions, by a corrected Haff’s law.

Dynamics in colloidal liquids near a crossing of glass- and gel-transition lines.

Abstract: Within the mode-coupling theory for ideal glass transitions, the mean-squared displacement and the correlation function for density fluctuations are evaluated for a colloidal liquid of particles interacting with a square-well potential for states near the crossing of the line for transitions to a gel with the line for transitions to a glass. It is demonstrated how the dynamics is ruled by the interplay of the mechanisms of arrest due to hard-core repulsion and due to attraction-induced bond formation as well as by a nearby higher-order glass-transition singularity. Application of the universal relaxation laws for the slow dynamics near glass-transition singularities explains the qualitative features of the calculated time dependence of the mean-squared displacement, which are in accord with the findings obtained in molecular-dynamics simulation studies by Zaccarelli et al. [Phys. Rev. E 66, 041402 (2002)]. Correlation functions found by photon-correlation spectroscopy in a micellar system by Mallamace et al. [Phys. Rev. Lett. 84, 5431 (2000)] can be interpreted qualitatively as a crossover from gel to glass dynamics.