Rapid roughening in thin film growth of an organic semiconductor (diindenoperylene)

The scaling exponents alpha, beta, and 1/z in thin films of the organic molecule diindenoperylene deposited on SiO2 under UHV conditions are determined. Atomic-force microscopy, x-ray reflectivity, and diffuse x-ray scattering were employed. The surface width displays power law scaling over more than 2 orders of magnitude in film thickness. We obtained alpha = 0.684+/-0.06, beta = 0.748+/-0.05, and 1/zeta = 0.92+/-0.20. The derived exponents point to an unusually rapid growth of vertical roughness and lateral correlations. We suggest that they could be related to lateral inhomogeneities arising from the formation of grain boundaries between tilt domains in the early stages of growth.     

Surface dynamics and breakdown patterns of a random solid subject to a biased 3D etching

We propose a selective disaggregation model in three dimensions with a mixed Brownian-deterministic motion of the etchant particle driven by a tuning parameter taking into account the presence of an external field. The width of the surface sites in saturation is described by the Edwards-Wilkinson scaling law as in a ballistic selective decay process. Besides, we consider the surfaces resulting when the solid substrate is completely eroded up to the electrical breakdown. In this situation, we analyse the effects of the etchant particle motion on the topology and conductivity of the residual substrate and we compare the relevant patterns with the ones related to the classical percolation theory. These results may interpret some recent experimental findings in electrochemical nanotechnology.     

Equilibrium concentration profiles and sedimentation kinetics of colloidal gels under gravitational stress

We study the sedimentation of colloidal gels by using a combination of light scattering, polarimetry and video imaging. The asymptotic concentration profiles (z,t → ∞) exhibit remarkable scaling properties: profiles for gels prepared at different initial volume fractions and particle interactions can be superimposed onto a single master curve by using suitable reduced variables. We show theoretically that this behavior stems from a power law dependence of the compressive elastic modulus versus , which we directly test experimentally. The sedimentation kinetics comprises an initial latency stage, followed by a rapid collapse where the gel height h decreases at constant velocity and a final compaction stage characterized by a stretched exponential relaxation of h toward a plateau. Analogies and differences with previous works are briefly discussed.     

Critical adsorption in the weak surface field limit

We study critical adsorption in the small surface field (h(1)) limit using a homologous series of critical liquid mixtures. The experiment data, in the one-phase regime, is accurately described by a universal surface scaling function G+(z/xi(+),z/l(h)) at distance z from the interface with correlation length xi(+) and surface field length l(h) approximately absolute value of (h(1))(-nu/Delta(1)), where h(1) approximately Deltasigma, the surface energy difference between the two components.     

Kinetic roughening in polymer film growth by vapor deposition

The growth front roughness of linear poly( p-xylylene) films grown by vapor deposition polymerization has been investigated using atomic force microscopy. The interface width w increases as a power law of film thickness d, w approximately d(beta), with beta = 0. 25+/-0.03, and the lateral correlation length xi grows as xi approximately d(1/z), with 1/z = 0.31+/-0.02. This novel scaling behavior is interpreted as the result of monomer bulk diffusion, and belongs to a new universality class that has not been discussed previously.     

Quantum critical dynamics simulation of dirty boson systems

Recently, the scaling result z=d for the dynamic critical exponent at the Bose glass to superfluid quantum phase transition has been questioned both on theoretical and numerical grounds. This motivates a careful evaluation of the critical exponents in order to determine the actual value of z. We study a model of quantum bosons at T=0 with disorder in 2D using highly effective worm Monte?Carlo simulations. Our data analysis is based on a finite-size scaling approach to determine the scaling of the quantum correlation time from simulation data for boson world lines. The resulting critical exponents are z=1.8±0.05, ν=1.15±0.03, and η=-0.3±0.1, hence suggesting that z=2 is not satisfied.     

The Universality of the Critical Dynamics of the Kinetic Ising Model on the Regular Fractals

The form of the universal scaling law of the critical dynamic exponent, z = D_ƒ + 2/υ, is found on a family of regular fractals by the exact TDRG method. Here, we generate a regular fractal by an anisotropic growing process. Identifying the growing probabilities as the interactions between Ising spins on the fractals, we map the growing probability clouds as a group of the anisotropic Ising Hamiltonians. Applying the RG transformations, we find that the systems of this group of Ising Hamiltonians can be described by two universal static correlation exponents υ₀ = ∞ and υ = 1. So, the growing processes proposed by us capture the essential features in the directed DLA simulations. The studies about their critical dynamic behaviours reveal that unlike the one-dimensional chain the critical dynamics of the kinetic Ising model on the regular fractals is universal. The further discussions show that there is a universal scaling law form of the critical dynamic exponent of the kinetic Ising model, z = D_ƒ + R_max/2υ, on the site models of the regular fractals with R_min = 2. Meanwhile, we discuss Daniel Kandal's correction to the formula of the,critical dynamic exponent in the TDRG method and show that our TDRG calculations are exact.     

Turbulent-like diffusion in complex quantum systems

We study a quantum particle propagating through a “quantum mechanically chaotic” background, described by parametric random matrices with only short range spatial correlations. The particle is found to exhibit turbulent-like diffusion under very general situations, without the a priori introduction of power law noise or scaling in the background properties.     

Study of compound particle production in 84Kr-emulsion interactions at 1.7 A GeV

The characteristics of compound particle multiplicity distribution and multiplicity correlations between the compound particle and the grey particle, black particle, shower particle and heavily ionized track particle are investigated in this paper. It is found that the average multiplicities of the grey particle, black particle, shower particle and heavily ionized track particle increase with an increase in the number of compound particles, which can be explained by the impact geometrical model. The compound multiplicity distribution is observed to obey a Koba-Nielson-Olesen (KNO) type of scaling law.     

Dynamic scaling approach to glass formation

Experimental data for the temperature dependence of relaxation times are used to argue that the dynamic scaling form, with relaxation time diverging at the critical temperature T(c) as (T-T(c))(-nuz), is superior to the classical Vogel form. This observation leads us to propose that glass formation can be described by a simple mean-field limit of a phase transition. The order parameter is the fraction of all space that has sufficient free volume to allow substantial motion, and grows logarithmically above T(c). Diffusion of this free volume creates random walk clusters that have cooperatively rearranged. We show that the distribution of cooperatively moving clusters must have a Fisher exponent tau=2. Dynamic scaling predicts a power law for the relaxation modulus G(t) approximately t(-2/z), where z is the dynamic critical exponent relating the relaxation time of a cluster to its size. Andrade creep, universally observed for all glass-forming materials, suggests z=6. Experimental data on the temperature dependence of viscosity and relaxation time of glass-forming liquids suggest that the exponent nu describing the correlation length divergence in this simple scaling picture is not always universal. Polymers appear to universally have nuz=9 (making nu=3 / 2). However, other glass-formers have unphysically large values of nuz, suggesting that the availability of free volume is a necessary, but not sufficient, condition for motion in these liquids. Such considerations lead us to assert that nuz=9 is in fact universal for all glass- forming liquids, but an energetic barrier to motion must also be overcome for strong glasses.     

Two interacting particles in a random potential

We study the scaling of the localization length of two interacting bosons in a one-dimensional random lattice with the single particle localization length. We consider the short-range interaction assuming that the particles interact when located both on the same site. We discuss several regimes, among them one interesting weak Fock space disorder regime. In this regime we obtain a weak logarithmic scaling law. Numerical benchmark data support the absence of any strong enhancement of the two particle localization length.     

Scaling Law for Ablation of a Hydrogen Pellet in a Plasma

A scaling law is derived which gives the rate of ablation of a frozen hydrogen pellet immersed in a plasma without the presence of a magnetic field or space charge. Plasma particles penetrate the ablating gas-plasma cloud to the evaporating pellet surface and deliver power to the cloud to drive its expansion. The evaporation rate is determined by a "self-regulating" mechanism. The ablation time is shown to be proportional to a5/3?o-2/3?o-1/3 where a is the pellet radius, ?o is the effective penetration depth of the incident particle into solid hydrogen and ?o is the power flux density of the incident particles. It is found that for ablation in a thermonuclear plasma, the alpha particles significantly affect the ablation rate. For thermonuclear plasma electrons and alpha particles, the energy required to ablate one molecule is shown to be of the order of 10 eV or less. The scaling law is applied to presently available experimental results, and reasonable agreement is found.     

Anomalous roughening of viscous fluid fronts in spontaneous imbibition

We report experiments on spontaneous imbibition of a viscous fluid by a model porous medium in the absence of gravity. The average position of the interface satisfies Washburn's law. Scaling of the interface fluctuations suggests a dynamic exponent z approximately 3, indicative of global dynamics driven by capillary forces. The complete set of exponents clearly shows that interfaces are not self-affine, exhibiting distinct local and global scaling, both for time (beta = 0.64 +/- 0.02, beta(*) = 0.33 +/- 0.03) and space (alpha = 1.94 +/- 0.20, alpha(loc) = 0.94 +/- 0.10). These values are compatible with an intrinsic anomalous scaling scenario.     

Complete condensation in a zero range process on scale-free networks

We study a zero range process on scale-free networks in order to investigate how network structure influences particle dynamics. The zero range process is defined with the rate p(n) = n(delta) at which particles hop out of nodes with n particles. We show analytically that a complete condensation occurs when delta < or = delta(c) triple bond 1/(gamma-1) where gamma is the degree distribution exponent of the underlying networks. In the complete condensation, those nodes whose degree is higher than a threshold are occupied by macroscopic numbers of particles, while the other nodes are occupied by negligible numbers of particles. We also show numerically that the relaxation time follows a power-law scaling tau approximately L(z) with the network size L and a dynamic exponent z in the condensed phase.     

Exact short time dynamics for steeply repulsive potentials

The autocorrelation functions for the force on a particle, the velocity of a particle and the transverse momentum flux are studied for the power law potential v(r)=ε(σr)^ν (soft spheres). The latter two correlation functions characterize the Green–Kubo expressions for the self-diffusion coefficient and shear viscosity. The short-time dynamics is calculated exactly as a function of ν. The dynamics is characterized by a universal scaling function S(τ), where τ=t/τ_ν and τ_ν is the mean time to traverse the core of the potential divided by ν. In the limit of asymptotically large ν this scaling function leads to delta function in time contributions in the correlation functions for the force and momentum flux. It is shown that this singular limit agrees with the special Green–Kubo representation for hard-sphere transport coefficients. The domain of the scaling law is investigated by comparison with recent results from molecular dynamics simulation for this potential.     

Photon-burst correlation techniques for atmospheric crosswind measurements

With a cw visible laser, the method of photon-burst correlation is used measure atmospheric crosswinds. A scaling law, including the effects of atmospheric turbulence, for performance evaluation of both laser Doppler (LDV) and laser time-of-flight (LTV) velocimeters, is introduced theoretically and established experimentally with field experiments. Crosswind measurements in the night at a range of 500 m with a low-power argon-ion laser are reported. The measured signal particle arrival rate is consistent with the predicted arrival rate based on the scaling law. In addition to the use of higher laser power, it is suggested that with proper inclusion of signal photon bursts resulting from the simultaneous arrival of several particles, routine operation of this type of laser velocimeter for long ranges, up to 1000m, should be feasible.     

Direct observation of nonlocal effects in a superconductor

We have used the technique of low energy muon spin rotation to measure the local magnetic field profile B(z) beneath the surface of a lead film maintained in the Meissner state (z depth from the surface, z less, similar 200 nm). The data unambiguously show that B(z) clearly deviates from an exponential law and represent the first direct, model independent proof for a nonlocal response in a superconductor.     

Finite-size scaling for the mean spherical model with inverse power law interaction

A new analytical technique based on integral transformations with Mittag-Leffler-type kernels is used to derive the finite-size scaling function for the free energy per particle of the mean spherical model with inverse power law asymptotics of the interaction potential. The asymptotic formation of the singularities in the specific heat and magnetic susceptibility at the bulk critical point is studied.     

Non-LTE transfer with complete redistribution. Scaling laws for a slab

Scaling laws for conservative scattering in a finite slab are extracted from an asymptotic analysis of the integral equation for the source function. The solution is separated into an interior and a surface boundary layer part. The matching between the two parts provides a scaling law for the surface value of the source function. When expressed in terms of a mean number of scatterings, this scaling law is generalizable to non-conservative scattering and the empirical formula of Jones and Skumanich is recovered.     

Critical Behavior of Ising Model with Long Range Correlated Quenched Impurities

The theoretic renormalization-group approach is applied to the study of the critical behavior of the ddimensional Ising model with long-range correlated quenched impurities, which has a power-like correlations r^-(d-p). The asymptotic scaling law is studied in the framework of the expansion in e = 4 - d. In d ~ 4, the dynamic exponent z .is calculated up to the second order in p with ρ= O(ε^1/2). The shape function is obtained in one-loop calculation. When d = 4, the logarithmic corrections to the critical behavior are found. The finite size effect on the order parameter relaxation rate is also studied.