Generic dynamic scaling in kinetic roughening

We study the dynamic scaling hypothesis in invariant surface growth. We show that the existence of power-law scaling of the correlation functions (scale invariance) does not determine a unique dynamic scaling form of the correlation functions, which leads to the different anomalous forms of scaling recently observed in growth models. We derive all the existing forms of anomalous dynamic scaling from a new generic scaling ansatz. The different scaling forms are subclasses of this generic scaling ansatz associated with bounds on the roughness exponent values. The existence of a new class of anomalous dynamic scaling is predicted and compared with simulations.     

Anomalous scaling exponents in nonlinear models of turbulence

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We construct, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. The statistics of the auxiliary linear model are dominated by "statistically preserved structures" which are associated with exact conservation laws. The latter can be used, for example, to determine the value of the anomalous scaling exponent of the second order structure function. The approach is equally applicable to shell models and to the Navier-Stokes equations.     

含有广义守恒律的生长方程标度奇异性的直接标度分析

利用直接标度分析方法研究一个含有广义守恒律生长方程的标度奇异性,得到强弱耦合区域的奇异标度指数.作为其特殊情况,这个方程包含Kardar-Parisi-Zhang（KPZ）方程、 Sun-Guo-Grant（SGG）方程以及分子束外延（MBE）生长方程,并能对其进行统一的研究.研究发现, KPZ方程和SGG方程,无论在弱耦合还是在强耦合区域内都遵从自仿射Family -Vicsek正常标度规律;而MBE 方程在弱耦合区域内服从正常标度,在强耦合区域内能呈现内禀奇异标度行为.这里所得到生长方程的奇异标度性质与利用重正化群理论、数值模拟以及实验相符很好. 关键词： 标度奇异性 强耦合 弱耦合     

Scaling law of anomalous Hall effect in Fe/Cu bilayers

The scaling of anomalous Hall resistivity on longitudinal resistivity has been intensively studied in different magnetic systems, including multilayer and granular films, to examine whether a skew scattering or a side jump mechanism dominates in the origin of anomalous Hall effect (AHE). The scaling law is based on the premise that both resistivities are a consequence of electron scattering by the imperfections in the materials. By studying the anomalous Hall effect in the simple Fe/Cu bilayers, it was demonstrated that the measured anomalous Hall effect should not follow the scaling laws derived from skew scattering or side jump mechanism due to the short-circuit and shunting effects of the non-magnetic layers.     

On the scaling of three-dimensional homogeneous and isotropic turbulence

In this paper we investigate the scaling properties of three-dimensional isotropic and homogeneous turbulence. We analyze a new form of scaling (extended self-similarity) recently introduced in the literature. We found that anomalous scaling of the velocity structure functions is clearly detectable even at a moderate and low Reynolds number and it extends over a much wider range of scales with respect to the inertial range.     

Anomalous roughening of Hele-Shaw flows with quenched disorder

The kinetic roughening of a stable oil-air interface moving in a Hele-Shaw cell that contains a quenched columnar disorder (tracks) has been studied. A capillary effect is responsible for the dynamic evolution of the resulting rough interface, which exhibits anomalous scaling. The three independent exponents needed to characterize the anomalous scaling are determined experimentally. The anomalous scaling is explained in terms of the initial acceleration and subsequent deceleration of the interface tips in the tracks coupled by mass conservation. A phenomenological model that reproduces the measured global and local exponents is introduced.     

Distribution- versus correlation-induced anomalous transport in quenched random velocity fields

We study mechanisms of anomalous transport in quenched random media. Broad disorder point distributions and strong disorder correlations cause anomalous transport and can lead to the same anomalous scaling laws for the mean and variance of the particle displacements. The respective mechanisms, however, are fundamentally different. This difference is reflected in the spatial particle densities and first passage time distributions, which provide an indicator to identify the origins of anomalous transport.     

Anomalous dynamic scaling of the non-local growth equations

The anomalous dynamic scaling behavior of the d+1 dimensional non-local growth equations is investigated based on the scaling approach. The growth equations studied include the non-local Kardar-Parisi-Zhang (NKPZ), non-local Sun-Guo-Grant (NSGG), and non-local Lai-Das Sarma-Villain (NLDV) equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively. Our results show that non-local interactions can affect anomalous scaling properties of surface fluctuations.     

Influence of Velocity Shell Correlations on Anomalous Scaling Exponents of Passive Scalars in Shell Models

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of passive scalars of turbulence. Different to the original problem, the distribution function of the prescribed random velocity field is multi-dimensional normal and delta-correlated in time. Here, our random velocity field is spatially correlative. For comparison, we also give the result obtained by the Gaussian random velocity field without spatial correlation. The anomalous scaling exponents H(p) of passive scalar advected by two kinds of random velocity above are determined for structure function up to p=15 by numerical simulations of the random shell model with Runge-Kutta methods to solve the stochastic differential equations. We observed that the H(p)'s obtained by the multi-dimensional normal distribution random velocity are more anomalous than those obtained by the independent Gaussian random velocity.     

Scaling of the interface roughness in Fe-Cr superlattices: self-affine versus non-self-affine

We have analyzed kinetic roughening in Fe-Cr superlattices by energy-filtered transmission electron microscopy. The direct access to individual interfaces provides both static and dynamic roughness exponents. We find an anomalous non-self-affine scaling of the interface roughness with a time dependent local roughness at short length scales. While the deposition conditions affect strongly the long-range dynamics, the anomalous short-range exponent remains unchanged. The different short- and long-range dynamics outline the importance of long-range interactions in kinetic roughening.     

Pipe network model for scaling of dynamic interfaces in porous media

We present a numerical study on the dynamics of imbibition fronts in porous media using a pipe network model. This model quantitatively reproduces the anomalous scaling behavior found in imbibition experiments [Phys. Rev. E 52, 5166 (1995)]. Using simple scaling arguments, we derive a new identity among the scaling exponents in agreement with the experimental results.     

Foundations of electrodynamics: S.R. de Groot and L.G. Suttorp, (North-Holland Publishing Company,Amsterdam, 1972. xii-535 pages. Fl. 140.-)

We show that the anomalous dimension of the fundamental field is connected to the anomalous dimensions of the high spin bilinear operators. The dimensions of these operators can be determined by examining the violations of the Bjorken scaling law in deep-inelastic electron-proton scattering. The structure function at field ω near to one has a power dependence of q², the exponent being the anomalous dimension of the “parton” field.     

Asymptotic Scaling in a Model Class of Anomalous Reaction-Diffusion Equations

Abstract

We analyze asymptotic scaling properties of a model class of anomalous reaction-diffusion (ARD) equations. Numerical experiments show that solutions to these have, for large t, well defined scaling properties. We suggest a general framework to analyze asymptotic symmetry properties; this provides an analytical explanation of the observed asymptotic scaling properties for the considered ARD equations.     

Interference as a probe of spin incoherence in strongly interacting quantum wires

We show that interference experiments can be used to identify the spin-incoherent regime of strongly interacting one-dimensional conductors. Two qualitative signatures of spin incoherence are found: a strong magnetic field dependence of the interference contrast and an anomalous scaling of the interference contrast with the applied voltage, with a temperature and magnetic field dependent scaling exponent. The experiments distinguish the spin-incoherent from the spin-polarized regime, and so may be useful in deciding between alternative explanations proposed for the anomalous conductance quantization observed in quantum point contacts and quantum wires at low density.     

含时空关联噪声生长方程的标度奇异性分析

基于动力学重整化群理论研究表面界面生长动力学标度奇异性问题, 得到含时空关联噪声的表面生长方程标度奇异指数的一般结果,并将此方法应用于几种典型的局域生长方程——Kardar-Parisi-Zhang（KPZ）方程、线性生长方程、Lai-Das Sarma-Villain（LDV）方程.结果表明,在长波长极限下局域生长方程的动力学标度奇异性与最相关项、基底维数以及噪声有关,并且若出现标度奇异性,只会是超粗化（super rough）奇异标度行为,而不是内禀（intrinsically）奇异标度行为. 关键词： 标度奇异性 动力学重整化群理论 时空关联噪声     

Localized magnetic states in graphene

We examine the conditions necessary for the presence of localized magnetic moments on adatoms with inner shell electrons in graphene. We show that the low density of states at the Dirac point, and the anomalous broadening of the adatom electronic level, lead to the formation of magnetic moments for arbitrarily small local charging energy. As a result, we obtain an anomalous scaling of the boundary separating magnetic and nonmagnetic states. We show that, unlike any other material, the formation of magnetic moments can be controlled by an electric field effect.     

Lévy model for interstellar scintillations

Observations of radio signals from distant pulsars provide a valuable tool for investigation of interstellar turbulence. The time shapes of the signals are the result of pulse broadening by the fluctuating electron density in the interstellar medium. While the scaling of the shapes with the signal frequency is well understood, the observed anomalous scaling with respect to the pulsar distance has remained a puzzle for more than 30 years. We propose a new model for interstellar electron density fluctuations, which explains the observed scaling relations. We suggest that these fluctuations obey Lévy statistics rather than Gaussian statistics, as assumed in previous treatments of interstellar scintillations.     

Anomalous Scaling of Surface Growth Equations with Spatially and Temporally Correlated Noise

Based on the scaling idea of local slopes by López et al. [Phys. Rev. Lett. 94 (2005) 166103], we investigate anomalous dynamic scaling of (d+1)-dimensional surface growth equations with spatially and temporally correlated noise. The growth equations studied include the Kardar-Parisi-Zhang (KPZ), Sun-Guo-Grant (SGG), and Lai-Das Sarma-Villain (LDV) equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively.     

Correlations and aggregate statistics in granular packs

We study how the aggregate statistical properties for density fluctuations in granular aggregates scale with the sample size and how such a scaling is associated with the correlations between grains. Correlations are studied both between grain positions and between Vorono? cell volumes, showing distinct behaviors and properties. A non-linear scaling in the aggregate volume fluctuations as function of the sample size is discovered and the connection between such anomalous scaling and correlations is explained. It emerges that volume fluctuations might be described by means of a single universal equation for all samples at all cluster sizes.