Temperature dependent fractal dimension of magneto-conductance fluctuations in semiconductor billiards

We present investigations of the fractal behaviour of magneto-conductance fluctuations in semiconductor billiards as a function of temperature. The introduction of finite phase coherence by nonzero temperatures is found not to suppress fractal behaviour in the experimental data. Instead, we show that the fractal dimension decreases with increasing temperature and we present a remarkable similarity between the phase coherence time and the fractal dimension.     

The influence of confining wall profile on quantum interference effects in etched Ga0.25In0.75As/InP billiards

We present measurements of the potential profile of etched GaInAs/InP billiards and show that their energy gradients are an order of magnitude steeper than those of surface-gated GaAs/AlGaAs billiards. Previously observed in GaAs/AlGaAs billiards, fractal conductance fluctuations are predicted to be critically sensitive to the billiard profile. Here we show that, despite the increase in energy gradient, the fractal conductance fluctuations persist in the harder GaInAs/InP billiards.     

Fractal survival probability fluctuations

We study fluctuations of survival probability in an open quantum system classically described by a map with a mixed phase space. Our results provide the first numerical support to theoretical predictions that such fluctuations have a fractal structure, quantitatively related to the algebraic decay of the classical survival probability.     

Sound scattering by random fractal inhomogeneities in the ocean

Sound scattering by random volume inhomogeneities (fluctuations of the refraction index in a medium) with an arbitrary anisotropy is considered using the small perturbation method (Born’s approximation). Surfaces (boundaries) of the inhomogeneities are deemed to be fractal ones: the energy spectra of the refraction index fluctuations follow the power law with a nonintegral exponent. Formulas are obtained for the volume scattering coefficient. Frequency and angular dependences of the scattering coefficient and their relations to the fractal dimension of inhomogeneities with different kinds of anisotropy and different sizes (on the sound wavelength scale) are presented. The fractal dimension of the inhomogeneities is estimated.     

Fluctuational transitions through a fractal basin boundary

Fluctuational transitions between two coexisting chaotic attractors, separated by a fractal basin boundary, are studied in a discrete dynamical system. It is shown that the transition mechanism is determined by a hierarchy of homoclinic points. The most probable escape path from a chaotic attractor to the fractal boundary is found using both statistical analyses of fluctuational trajectories and the Hamiltonian theory of fluctuations.     

The scattering of flexural waves by random fractal inhomogeneities in a thin plate

The scattering of flexural waves by small statistical fractal inhomogeneities in a thin plate is considered. An expression for the average intensity of the fluctuations of the scattered wave field is obtained. A relation of the intensity to the plate parameters and to the fractal dimension of the inhomogeneities is determined. An expected frequency dependence of the attenuation of flexural waves in a plate due to the scattering by fractal inhomogeneities is discussed.     

Fractal structure of the acoustic signal excited in a liquid by an unstable laser radiation

Thermooptical excitation of sound in a liquid by a laser radiation with a harmonically modulated intensity randomly distributed over the beam cross-section is considered. The processes are considered to be statistically homogeneous. It is assumed that the spatial spectrum of the intensity fluctuations in a laser beam is described by a power (fractal) law. It is demonstrated that the acoustic field in a liquid has a fractal structure.     

Power spectrum of fluctuation for ultrasonic cavitation process in glycerin

Experiments were carried out on ultrasonic cavitation in glycerin. The zone near the emitter has a structure from interacting gas-vapor bubbles; this structure takes the form of fractal clusters. The photometry of passed laser emission was the tool for studying dynamics of fluctuations. In transitive mode, the power spectrum of fluctuation varies by the law inversely proportional to frequency. Distributions of local fluctuations are different from Gaussian and exhibit the property of scale invariance. The qualitative behavior of the frequency dependence of the spectral fluctuation density was tested while varying the power of the ultrasonic emitter. It was demonstrated that the growth of the high-frequency margin of flicker-type behavior evidences for growing instability and can be considered as a forerunner of possible large-scale outbursts. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 05-08-01320a).     

Some features of the fractal structure of the developed small-scale ionospheric turbulence

We present the results of the first studies of the fractal structure of the developed small-scale ionospheric turbulence (SSIT) during special experiments on radio-raying of the midlatitude ionosphere by signals from orbital satellites in 2005–2006. It is established that under conditions of developed turbulence, typical values of the fractal dimension of the space occupied by natural SSIT inhomogeneities are, as a rule, close to the topological dimension of their embedding space, and the true values of the spectral index of isotropic SSIT only slightly differ from the corresponding generally accepted nominal values in the embedding space. Nevertheless, even small differences in the mentioned parameters detected in the experiment witness a sharply nonuniform distribution of the local fractal structures of the developed SSIT in space. We propose a stochastic model of the nonstationary process for fast amplitude fluctuations of signals during their propagation in the ionosphere with nonuniform spatial distribution of small-scale electron-density fluctuations. Eventually, namely this nonuniform distribution of small-scale electron-density fluctuations leads to the specific multifractal structure of the amplitude records of received signals. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 4, pp. 287–294, April 2008.     

A GDP fluctuation model based on interacting firms

A distinctive feature of the market economies is the short-run fluctuations in output around the trend of long-run growth over time, and we regard this feature is internal to complex economic systems composed of interacting heterogeneous units. To explore such internal mechanisms of macroeconomic fluctuations, we present a multi-agent Keynesian theory-based model, which can provide a good approximation to the key empirical features of the western business cycles in the 20th Century, such as the structure of the autocorrelation function of overall output growth, correlations between the output growth of individual agents over time, the distribution of recessions, etc.     

Order-disorder transitions in atactic polystyrene films

The results of the electron microscopy investigation of the surface topology of the films obtained from solutions of linear atactic polystyrene in chloroform are presented. It has been shown that the distribution of density fluctuations in the films can be described using the model of a fractal percolation cluster of macromolecular coils. A decrease in the local packing density of particles upon going from θ-coils to blobs is associated with mutual penetration of the coils. An increase in density fluctuations and a decrease in the relative area and fractal surface of the cluster of the particles are associated with a decrease in the short-range order caused by the formation of the percolation cluster, which reflects portions of the chains not involved in the blobs.     

From 1/f noise to multifractal cascades in heartbeat dynamics

We explore the degree to which concepts developed in statistical physics can be usefully applied to physiological signals. We illustrate the problems related to physiologic signal analysis with representative examples of human heartbeat dynamics under healthy and pathologic conditions. We first review recent progress based on two analysis methods, power spectrum and detrended fluctuation analysis, used to quantify long-range power-law correlations in noisy heartbeat fluctuations. The finding of power-law correlations indicates presence of scale-invariant, fractal structures in the human heartbeat. These fractal structures are represented by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales. We then describe very recent work that quantifies multifractal features in these cascades, and the discovery that the multifractal structure of healthy dynamics is lost with congestive heart failure. The analytic tools we discuss may be used on a wide range of physiologic signals. (c) 2001 American Institute of Physics.     

Influence of nanoscale cutoff in random self-affine fractal silver surfaces on the excitation of localized optical modes

We report rigorous numerical calculations of the near field scattered from rough, one-dimensional self-affine fractal silver surfaces. We show that fractal lower-scale cutoff (decreased to the order of tens of nanometers) has a strong effect on excitation and strength of localized optical modes, leading to very large enhancements of the intensity (larger than 10(4)) and fluctuations of the electric field.     

Fractal structure of films deposited in a tokamak

The surface of amorphous films deposited in the T-10 tokamak was studied in a scanning tunnel microscope. The surface relief on a scale from 10 nm to 100 μm showed a stochastic surface topography and revealed a hierarchy of grains. The observed variety of irregular structures of the films was studied within the framework of the concept of scale invariance using the methods of fractal geometry and statistical physics. The experimental probability density distribution functions of the surface height variations are close in shape to the Cauchy distribution. The stochastic surface topography of the films is characterized by a Hurst parameter of H = 0.68–0.85, which is evidence of a nontrivial self-similarity of the film structure. The fractal character and porous structure of deposited irregular films must be considered as an important issue related to the accumulation of tritium in the ITER project. The process of film growth on the surface of tokamak components exposed to plasma has been treated within the framework of the general concept of inhomogeneous surface growth. A strong turbulence of the edge plasma in tokamaks can give rise to fluctuations in the incident flux of particles, which leads to the growth of fractal films with grain dimensions ranging from nano-to micrometer scale. The shape of the surface of some films found in the T-10 tokamak has been interpreted using a model of diffusion-limited aggregation (DLA). The growth of films according to the discrete DLA model was simulated using statistics of fluctuations observed in a turbulent edge plasma of the T-10 tokamak. The modified DLA model reproduces well the main features of the surface of some films deposited in tokamaks.     

Fluctuations of the local density of states probe localized surface plasmons on disordered metal films

We measure the statistical distribution of the local density of optical states (LDOS) on disordered semicontinuous metal films. We show that LDOS fluctuations exhibit a maximum in a regime where fractal clusters dominate the film surface. These large fluctuations are a signature of surface-plasmon localization on the nanometer scale.     

随机散射屏的原子力显微镜形貌分析及其光散射特性

用原子力显微镜对三种不同粗糙度的随机散射屏的表面形貌进行了测量分析,发现它们在短程范围内具有明显的分形特征.对于粗糙度较大和较小的散射屏,分形特征分别以无规则的 高度调制和无特征大小的小颗粒的形式存在.用自仿射分形表面模型对散射屏的统计特性进 行了描述和拟合.光散射测量发现,散射光强在远轴区域按负幂函数下降,理论分析证明这 源于表面的分形结构;在近轴区域有散射亮环存在,用自仿射分形表面模型尚不能给出理论解释. 关键词： 随机散射屏 光散射 自仿射分形表面     

Fractal dimension of the surface upon martensitic transformation in titanium nickelide

The fractal dimension of the residual deformation relief on the surface of titanium nickelide is shown to be sensitive to the deformation mechanism. It decreases under phase-transformation-induced inelasticity and increases under plasticity. At the time the basic deformation mechanism changes, fluctuations are maximal. The experimental dependence of the microstrain on the fractal dimension for the initial austenitic phase is not a single-valued function: it consists of two groups of data points that correspond to different deformation mechanisms.     

Fractal structures in turbulence

We present a qualitative overview of our work on the issue of fractal structures in turbulence. We explain why fully developed turbulence is not space filling and describe how its fractal dimension can be estimated theoretically. The implications of the fractal nature of turbulence on transport processes like turbulent diffusion and on fluctuations in passive scalars are discussed. The latter affect wave propagation in turbulent media and these effects are examined. In addition we consider clouds in the atmosphere which are claimed to have fractal perimeters (or surfaces) and outline the physical reasons for this phenomenon. The fractal dimension of clouds is tied to the theory of turbulent diffusion and is computed theoretically. Indications of the road ahead are given.     

具有幂次相互作用的磁性粒子凝聚过程的数值研究

在扩散限制凝聚模型的基础上引入粒子的自旋自由度(包括自旋向上和向下),并假设粒子间存在幂次Ising磁相互作用,采用Monte Carlo方法研究了在不同相互作用力程情况下磁性粒子的分形生长规律.模拟结果表明,当粒子间以反铁磁方式耦合时,凝聚体中的粒子自旋交替凝聚.当粒子间以铁磁方式耦合时,凝聚体中粒子的自旋分布与相互作用力程有关:对于短程作用系统,凝聚体中存在大小不同的自旋畴块,即为铁磁生长;而对于长程相互作用系统,凝聚体中的自旋出现反常分布,即中心区域是近似反铁磁生长的结构,其外围后续生长的粒子却保持 关键词： 幂次相互作用 扩散限制凝聚模型 自旋