Scaling of the Euler characteristic, surface area, and curvatures in the phase separating or ordering systems

We present robust scaling laws for the Euler characteristic and curvatures applicable to any symmetric system undergoing phase separating or ordering kinetics. We apply it to the phase ordering in a system of the nonconserved scalar order parameter and find three scaling regimes. The appearance of the preferred nonzero curvature of an interface separating +/- domains marks the crossover to the late stage regime characterized by the Lifshitz-Cahn-Allen scaling.     

Maximal height scaling of kinetically growing surfaces

The scaling properties of the maximal height of a growing self-affine surface with a lateral extent L are considered. In the late-time regime its value measured relative to the evolving average height scales like the roughness: h*(L) approximately L alpha. For large values its distribution obeys logP(h*(L)) approximately (-)A(h*(L)/L(alpha))(a). In the early-time regime where the roughness grows as t(beta), we find h*(L) approximately t(beta)[lnL-(beta/alpha)lnt+C](1/b), where either b = a or b is the corresponding exponent of the velocity distribution. These properties are derived from scaling and extreme-value arguments. They are corroborated by numerical simulations and supported by exact results for surfaces in 1D with the asymptotic behavior of a Brownian path.     

Hydrodynamic coarsening of binary fluids

By suitable interpretation of results from the linear analysis of interface dynamics, it is found that the hydrodynamic growth of the size L of domains that follow spinodal decomposition in fluid mixtures scales with time as L approximately t(alpha), with alpha = 4/7 in the inertial regime. The previously proposed exponent alpha = 2/3 is shown to indicate only the scaling of the oscillatory frequency omega(-2/3) approximately L of the largest structures of the system. The viscous dissipation in the system occurs within a layer of thickness L(d) that also follows a power law of the form L(d) approximately L3/4 in the inertial regime. In the viscous regime the growth is linear in time L approximately t and the dissipative region remains constant L(d) approximately L0.     

Long-term fluctuations in globally coupled phase oscillators with general coupling: finite size effects

We investigate the diffusion coefficient of the time integral of the Kuramoto order parameter in globally coupled nonidentical phase oscillators. This coefficient represents the deviation of the time integral of the order parameter from its mean value on the sample average. In other words, this coefficient characterizes long-term fluctuations of the order parameter. For a system of N coupled oscillators, we introduce a statistical quantity D, which denotes the product of N and the diffusion coefficient. We study the scaling law of D with respect to the system size N. In other well-known models such as the Ising model, the scaling property of D is D～O(1) for both coherent and incoherent regimes except for the transition point. In contrast, in the globally coupled phase oscillators, the scaling law of D is different for the coherent and incoherent regimes: D～O(1/N(a)) with a certain constant a>0 in the coherent regime and D～O(1) in the incoherent regime. We demonstrate that these scaling laws hold for several representative coupling schemes.     

Experimental measures of affine and nonaffine deformation in granular shear

Through 2D granular Couette flow experiments, we probe failure and deformation of disordered solids under shear. Shear produces a mean azimuthal flow, smooth affine deformations, and irreversible so-called nonaffine particle displacements. We find that these processes are all of comparable magnitude and depend on the local shear rate. We compute the parameter of Falk and Langer characterizing nonaffine motion, Dmin2, and find that it is reasonably well described in terms of collections of single particles making locally nearly isotropic random steps, delta ri. Distributions for single particle nonaffine displacements, delta ri, satisfy P1(delta ri) proportional, variantexp[-|delta ri/Delta r|alpha] (alpha < or approximately 2).     

Current relaxation in nonlinear random media

We study the current relaxation of a wave packet in a nonlinear random sample coupled to the continuum and show that the survival probability decays as P(t) approximately 1/t(alpha). For intermediate times tt(*) and chi>chi(cr) we find a universal decay with alpha=2/3 which is a signature of the nonlinearity-induced delocalization. Experimental evidence should be observable in coupled nonlinear optical waveguides.     

Transport properties of saturated and unsaturated porous fractal materials

Inviscid, irrotational flow through fractal porous materials is studied. The key parameter is the variation of tortuosity with the filling fraction phi of fluid in the porous material. Altering the filling fraction provides a way of probing the effect of the fractal structure over all its length scales. The variation of tortuosity with phi is found to follow a power law of the form alpha approximately phi (-E) for deterministic and stochastic fractals in two and three dimensions. A phenomenological argument for the scaling of tortuosity alpha with filling fraction phi is presented and is given by alpha approximately phi(D_{w}-2/D_{f}-d_{E}), where D_{f} is the fractal dimension, D_{w} is the random walk dimension, and d_{E} is the Euclidean dimension. Numerically calculated values of the exponents show good agreement with those predicted from the phenomenological argument for both the saturated and the unsaturated model.     

Spin-wave contribution to the nuclear spin-lattice relaxation in triplet superconductors

We discuss collective spin-wave excitations in triplet superconductors with an easy axis anisotropy for the order parameter. Using a microscopic model for interacting electrons, we estimate the frequency of such excitations in Bechgaard salts and ruthenate superconductors to be 1 and 20 GHz, respectively. We introduce an effective bosonic model to describe spin-wave excitations and calculate their contribution to the nuclear spin-lattice relaxation rate. We find that, in the experimentally relevant regime of temperatures, this mechanism leads to the power law scaling of 1/T1 with temperature. For two- and three-dimensional systems, the scaling exponents are 3 and 5, respectively. We discuss experimental manifestations of the spin-wave mechanism of the nuclear spin-lattice relaxation.     

Aeolian transport layer

We investigate the airborne transport of particles on a granular surface by the saltation mechanism through numerical simulation of particle motion coupled with turbulent flow. We determine the saturated flux q(s) and show that its behavior is consistent with classical empirical relations obtained from wind tunnel measurements. Our results also allow one to propose and explain a new relation valid for small fluxes, namely, q(s) = a(u*-u(t))alpha, where u* and u(t) are the shear and threshold velocities of the wind, respectively, and the scaling exponent is alpha approximately 2. We obtain an expression for the velocity profile of the wind distorted by the particle motion due to the feedback and discover a novel dynamical scaling relation. We also find a new expression for the dependence of the height of the saltation layer as a function of the wind velocity.     

过渡流区钝锥体Linear桥函数调节参数研究

由于过渡区域流动的物理现象的复杂性和流动控制方程的非线性, 航天飞行器设计所需要的气动加热特性目前主要由工程计算方法得到. 为了使计算过渡流区热流的Linear桥函数方法能适用于广泛应用的钝锥体外形, 拟合得到了相应的调节参数, 使用DSMC方法对计算结果进行验证. 验证结果表明该调节参数适用于钝锥体外形, 使得Linear桥函数在过渡流区能比较准确地计算钝锥体物面热流.     

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.     

Traveling time and traveling length in critical percolation clusters

We study traveling time and traveling length for tracer dispersion in two-dimensional bond percolation, modeling flow by tracer particles driven by a pressure difference between two points separated by Euclidean distance r. We find that the minimal traveling time t(min) scales as t(min) approximately r(1.33), which is different from the scaling of the most probable traveling time, t* approximately r(1.64). We also calculate the length of the path corresponding to the minimal traveling time and find l(min) approximately r(1.13) and that the most probable traveling length scales as l* approximately r(1.21). We present the relevant distribution functions and scaling relations.     

Anti-de sitter/conformal-field-theory calculation of screening in a hot wind

One of the challenges in relating experimental measurements of the suppression in the number of J/psi mesons produced in heavy ion collisions to lattice QCD calculations is that whereas the lattice calculations treat J/psi mesons at rest, in a heavy ion collision a cc[over ] pair can have a significant velocity with respect to the hot fluid produced in the collision. The putative J/psi finds itself in a hot wind. We present the first rigorous nonperturbative calculation of the consequences of a wind velocity v on the screening length L(s) for a heavy quark-antiquark pair in hot N=4 supersymmetric QCD. We find L(s)(v,T)=f(v)[1-v(2)](1/4)/piT with f(v) only mildly dependent on v and the wind direction. This L(s)(v,T) approximately L(s)(0,T)/sqrt[gamma] velocity scaling, if realized in QCD, provides a significant additional source of J/psi suppression at transverse momenta which are high but within experimental reach.     

Reacting particles in open chaotic flows

We study the collision probability p of particles advected by open flows with chaotic advection. We show that p scales with the particle size (or, alternatively, reaction distance) δ as a power law whose coefficient is determined by the fractal dimensions of the invariant sets defined by the advection dynamics. We also argue that this same scaling also holds for the reaction rate of active particles in the low-density regime. These analytical results are compared to numerical simulations, and they are found to agree very well.     

Numerical Study on Depinning Dynamics of Fluids Interacting with Disorder

We investigate the depinning of two-dimensional fluids interacting with quenched disorder, based on Langevin simulations. For weak disorder the fluids depin elastically and flow in an ordered state. A power-law scaling lit between velocity and driving force can be obtained for the onset of motion in the elastic regime. This is in good agreement with that of colloid, charge density wave, and superconducting vortex systems. With an increasing strength of the disorder, we find a sharp crossover to plastic de. Pinning, accompanied by a substantial increase in the depinning force. The scaling fit obtained in the elastic regime becomes invalid when plastic flow occurs. In the plastic regime, the fluids flow in channels and the hexatic order decays exponentially with drives.     

Numerical Study on Depinning Dynamics of Fluids Interacting with Disorder

We investigate the depinning of two-dlmensional fluids interacting with quenched disorder, based on Langevin simulations. For weak disorder the fluids depin elastically and flow in an ordered state. A power-law scaling fit between velocity and driving force can be obtained for the onset of motion in the elastic regime. This is in good agreement with that of colloid, charge density wave, and superconducting vortex systems. With an increasing strength of the disorder, we find a sharp crossover to plastic depinning, accompanied by a substantial increase in the depinning force. The scaling fit obtained in the elastic regime becomes invalid when plastic flow occurs. In the plastic regime, the fluids flow in channels and the hexatic order decays exponentially with drives.     

Cluster size distribution and scaling for spherical particles and red blood cells in pressure-driven flows at small Reynolds number

The clustering characteristic of purely hydrodynamically interacting particles suspended in pressure-driven flow in a circular cylinder is studied using direct numerical simulation based on the solution of the lattice-Boltzmann equation. We find a universal scaling relation for the cluster size distribution in the subcritical regime for all of the cases considered in this study. This scaling relation is independent of particle shape and concentration.     

Harmonic measure and winding of conformally invariant curves

The exact joint multifractal distribution for the scaling and winding of the electrostatic potential lines near any conformally invariant scaling curve is derived in two dimensions. Its spectrum f(alpha,lambda) gives the Hausdorff dimension of the points where the potential scales with distance r as H approximately r(alpha) while the curve logarithmically spirals with a rotation angle phi=lambdalnr. It obeys the scaling law f(alpha,lambda)=(1+lambda(2))f(alpha)-blambda(2) with alpha=alpha/(1+lambda(2)) and b=(25-c)/12, and where f(alpha) identical with f(alpha,0) is the pure harmonic measure spectrum, and c the conformal central charge. The results apply to O(N) and Potts models, as well as to stochastic L?wner evolution.     

Charge transport transitions and scaling in disordered arrays of metallic dots

We examine the charge transport through disordered arrays of metallic dots using numerical simulations. We find power law scaling in the current-voltage curves for arrays containing no voids, while for void-filled arrays charge bottlenecks form and a single scaling is absent, in agreement with recent experiments. In the void-free case we also show that the scaling exponent depends on the effective dimensionality of the system. For increasing applied drives we find a transition from 2D disordered filamentary flow near threshold to a 1D smectic flow which can be identified experimentally using characteristics in the transport curves and conduction noise.