Universality in the critical dynamics of fluids: ultrasonic attenuation

In contrast to the binary liquids, the order-parameter relaxation rates in the pure fluids are greatly affected by a large non-critical component. With the appropriate crossover correction to dynamic scaling, we restore universality and demonstrate that the ultrasonic data for both the one- and two-component fluids fall on the same scaling plot.     

Universal behavior of crossover scaling functions for continuous phase transitions

We consider two different systems exhibiting a continuous phase transition into an absorbing state. Both models belong to the same universality class; i.e., they are characterized by the same scaling functions and the same critical exponents. Varying the range of interactions, we examine the crossover from the mean-field-like to the non-mean-field scaling behavior. A phenomenological scaling form is applied in order to describe the full crossover region, which spans several decades. Our results strongly support the hypothesis that the crossover function is universal.     

A general isomorphism approach to thermodynamic and transport properties of binary fluid mixtures near critical points

A general isomorphism approach to critical phenomena in binary fluid mixtures that may exhibit complex critical-line behavior is developed by relating the two relevant scaling fields to linear combinations of three physical field variables. These physical field variables are related to the temperature and chemical potentials of the two components. The proposed approach includes crossover from vapor-liquid critical behavior to liquid-liquid critical behavior and incorporates also the critical behavior near other special points on critical loci. It is shown that the key factor which determines the apparent behavior of the thermodynamic and transport properties of near-critical mixtures is the shape of the critical locus. The number of system-dependent coefficients that determine the asymptotic critical behavior is elucidated. The choice of zero-points of entropy and energy in binary mixtures is also discussed. The approach provides a powerful tool for predicting thermodynamic and transport properties of fluid mixtures in the critical region.     

Crossover scaling of wavelength selection in directional solidification of binary alloys

We simulate cellular and dendritic growth in directional solidification in dilute binary alloys using a phase-field model solved with adaptive-mesh refinement. The spacing of primary branches is examined for a wide range of thermal gradients and alloy compositions and is found to undergo a maximum as a function of pulling velocity, in agreement with experimental observations. We demonstrate that wavelength selection is unambiguously described by a nontrivial crossover scaling function from the emergence of cellular growth to the onset of dendritic fingers. This result is further validated using published experimental data, which obeys the same scaling function.     

Scaling law in the ordering process of quenched thermodynamically unstable systems

The dynamics of phase separation in quenched thermodynamically unstable systems is studied. The scaling law exhibited in the late stage of the ordering process is investigated by the interface model. In the kinetics of the order-disorder transition the motion of random interfaces is shown to be responsible for the scaling law. The scaling form of the scattering function is obtained with particular attention to the fluctuating thermal noises. A droplet picture is used to discuss spinodal decomposition of off-critically quenched binary fluids. The sealing function is calculated explicitly in the region where the Brownian coagulation is most dominant for the phase separation. It is shown that the thermal noises are relevant to the scaling law in the ordering process driven by the Brownian coagulation whereas they are negligible in the kinetics of order-disorder transition.     

Scaling relationship between effective critical exponents throughout the crossover region in thin Ising films

The Monte Carlo (MC) approach is used to check the validity of the scaling relationship for the effective critical exponents in thin Ising films. We investigate this relationship not just in the critical region but throughout the crossover to the expected two-dimensional behavior. Our results indicate that this scaling relationship is very well-fulfilled throughout the entire crossover temperature region, as predicted by a previous renormalization group analysis. The two-dimensional universality class of Ising films is confirmed by means of data collapsing plots for plates with increasing L, up to L=100. The evolution of the maximum value of the effective critical exponents with film thickness is discussed. Received 22 April 1999     

Scaling behaviour of the Hellmann potential with different strength parameters

We are reporting the scaling behaviour of the bound state energies associated with the Hellmann potential, with different strength parameters, using the Laguerre basis. We show the existence of a crossover phenomenon for the energy spectrum; the scaling laws for bound states as we approach the continuum are calculated. Close to the bound–resonance phase transition region, state energies and wavefunctions for the Hellmann potential, with different strength parameters, have been studied.     

Effects of encounters on phase separation dynamics from diffusion-controlled growth to coarsening

We investigate the dynamics of phase separations in quenched binary mixtures, such as binary alloys and polymer blends with low mobilities, at higher volume fractions. Computer simulations are performed using simple model equations in the presence of encounters of droplets. Four characteristics stages with three crossovers, including dynamical scaling behavior and temporal power laws, are found beyond a volume fraction of approximately 0.14, where each crossover is attributed to a transition from one growth mechanism to the other. The encounter effect is thus shown to strongly influence a transition from the diffusion-controlled (t^1/2) stage to the coarsening (t^1/3) stage. A simple analytical argument for the simulation results is also presented.     

Periodic orbits in a two-variable coupled map

Periodic orbits are calculated for a linear transformation composed of two coupled tent maps using a symbolic dynamics defined as the direct product of the single-map symbols {0,1,2}. As the coupling strength is increased orbits are pruned and a crossover to one-dimensional behavior is observed. The disallowed binary orbits containing only symbols {0,1} form a connected region in a binary symbol plane. Stable orbits may appear for strong couplings.     

Non-linear characteristics and long-range correlations in Asian stock markets

We test several non-linear characteristics of Asian stock markets, which indicates the failure of efficient market hypothesis and shows the essence of fractal of the financial markets. In addition, by using the method of detrended fluctuation analysis (DFA) to investigate the long range correlation of the volatility in the stock markets, we find that the crossover phenomena exist in the results of DFA. Further, in the region of small volatility, the scaling behavior is more complicated; in the region of large volatility, the scaling exponent is close to 0.5, which suggests the market is more efficient. All these results may indicate the possibility of characteristic multifractal scaling behaviors of the financial markets.     

Free energy of multiple overlapping chains

How accurate is pair additivity in describing interactions between soft polymer-based nanoparticles? Using numerical simulations we compute the free energy cost required to overlap multiple chains in the same region of space, and provide a quantitative measure of the effectiveness of pair additivity as a function of chain number and length. Our data suggest that pair additivity can indeed become quite inadequate as the chain density in the overlapping region increases. We also show that even a scaling theory based on polymer confinement can only partially account for the complexity of the problem. In fact, we unveil and characterize an isotropic to star-polymer crossover taking place for large number of chains, and propose a revised scaling theory that better captures the physics of the problem.     

New universal scaling laws of diffusion and Kolmogorov-Sinai entropy in simple liquids

A new universal scaling law relating the self-diffusivities of the components of a binary fluid mixture to their excess entropies is derived using mode coupling theory. These scaling laws yield numerical results, for a hard sphere as well as Lennard-Jones fluid mixtures, in excellent agreement with simulation results even at a low density region, where the empirical scaling laws of Dzugutov [Nature (London) 381, 137 (1996)]] and Hoyt, Asta, and Sadigh [Phys. Rev. Lett. 85, 594 (2001)]] fail completely. A new scaling law relating the Kolmogorov-Sinai entropy to the excess entropy is also obtained.     

Flux front penetration in disordered superconductors

We investigate flux front penetration in a disordered type-II superconductor by molecular dynamics simulations of interacting vortices and find scaling laws for the front position and the density profile. The scaling can be understood by performing a coarse graining of the system and writing a disordered nonlinear diffusion equation. Integrating numerically the equation, we observe a crossover from flat to fractal front penetration as the system parameters are varied. The value of the fractal dimension indicates that the invasion process is described by gradient percolation.     

Collective modes and ballistic expansion of a fermi gas in the BCS-BEC crossover

We evaluate the frequencies of collective modes and the anisotropic expansion rate of a harmonically trapped Fermi superfluid at varying coupling strengths across a Feshbach resonance driving a BCS-BEC crossover. The equations of motion for the superfluid are obtained from a microscopic mean-field expression for the compressibility and are solved within a scaling ansatz. Our results confirm nonmonotonic behavior in the crossover region and are in quantitative agreement with current measurements of the transverse breathing mode by Kinast et al. [Phys. Rev. Lett. 92, 150402 (2004)]] and of the axial breathing mode by Bartenstein et al. [Phys. Rev. Lett. 92, 203201 (2004)]].     

Power spectrum crossover in sediments of a paleolake disturbed by volcanism

We study density fluctuations from sediments of a paleolake in central Mexico that was subjected to volcanic perturbations by means of computed tomography (CT) measurements on blocks chiselled out of mines at the lake's bed. The mine walls show laminations corresponding to the alternation of low density diatom sediments and high density volcanic ash depositions. We have previously shown that there is a range of scales where these fluctuations present a self-similar behavior [1]. Here we relate density correlation calculations to the power spectrum of the fluctuations. We show that a scaling region in the power spectrum coincides with the scaling region in the correlations produced by relaxation from intense volcanic perturbations to steady state fluctuations. There appears to be a kink-like crossover in the power spectrum from mid range scaling to a shorter range scale invariance. This, together with the density probability distribution of the fluctuations, draws attention to the dominant role of rare events. We believe that our analysis may be useful for the understanding of other phenomena with similar power spectrum properties, in which a scale invariance in the unperturbed system is altered by external perturbations that induce an additional scaling behavior.     

Role of disorder in the size scaling of material strength

We study the sample-size dependence of the strength of disordered materials with a flaw, by numerical simulations of lattice models for fracture. We find a crossover between a regime controlled by the disorder and another controlled by stress concentrations, ruled by continuum fracture mechanics. The results are formulated in terms of a scaling law involving a statistical fracture process zone. Its existence and scaling properties are revealed only by sampling over many configurations of the disorder. The scaling law is in good agreement with experimental results obtained from notched paper samples.     

The electrical conductivity of binary disordered systems,percolation clusters,fractals and related models

We review theoretical and experimental studies of the AC dielectric response of inhomogeneous materials, modelled as bond percolation networks, with a binary (conductor-dielectric) distribution of bond conductances. We first summarize the key results of percolation theory, concerning mostly geometrical and static (DC) transport properties, with emphasis on the scaling properties of the critical region around the percolation threshold. The frequency-dependent (AC) response of a general binary model is then studied by means of various approaches, including the effective-medium approximation, a scaling theory of the critical region, numerical computations using the transfer-matrix algorithm, and several exactly solvable deterministic fractal models. Transient regimes, related to singularities in the complex-frequency plane, are also investigated. Theoretical predictions are made more explicit in two specific cases, namely R-C and RL-C networks, and compared with a broad variety of experimental results, concerning, for example, granular composites, thin films, powders, microemulsions, cermets, porous ceramics and the viscoelastic properties of gels.     

Mean-field and anomalous behavior on a small-world network

We consider various equilibrium statistical mechanics models with combined short- and long-range interactions and identify the crossover to mean-field behavior, finding anomalous scaling in the width of the mean-field region, as well as in the mean-field amplitudes. We then show that this model enables us, in many cases, to determine the universal critical properties of systems on a small-world network. Finally, we consider nonequilibrium processes.     

Flux noise near the Berezinski\overset{\lower0.5em\hbox{-Kosterlitz-Thouless transition

The flux noise in Josephson junction arrays is studied in the critical regime above the Berezinskii-Kosterlitz-Thouless transition. In proximity-coupled arrays a local Ohmic damping for the phases is relevant, giving rise to anomalous vortex diffusion and a dynamic scaling of the flux noise in the critical region. The flux noise exhibits a crossover from white to 1/f noise at a frequency ω_ξ∝ξ^?z with a dynamic exponent z=2.