Fourier images of fractal objects

Fourier images corresponding to diffraction patterns in the Fraunhofer zone were obtained for a set of fractal objects by means of computer simulation with the use of net functions. The fractal dimensions of the objects being investigated were determined on the basis of the intensity distribution in the diffraction patterns.     

Output functions and fractal dimensions in dynamical systems

We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method. We call it the output function evaluation (OFE) method. We show analytically that the OFE method is much more efficient than the uncertainty method for boundaries with D<0.5, where D is the dimension of the intersection of the boundary with a one-dimensional manifold. We apply the OFE method to a scattering system, and compare it to the uncertainty method. We use the OFE method to study the behavior of the fractal dimension as the system's dynamics undergoes a topological transition.     

傅里叶望远镜大气湍流模拟实验

傅里叶望远术是一种能对深空暗弱目标进行高分辨率成像的技术.为了验证大气湍流对傅里叶望远镜系统的影响,进行了实验室环境下大气湍流模拟实验研究.在三束光傅里叶望远镜实验系统上,通过控制射频驱动器的输出功率来模拟光强抖动,改变射频驱动器的瞬时频率来模拟相位抖动.给出了实验理论依据,推导了湍流强度与实验变量的关系.实验在弱湍流闪烁和相位抖动两种情况下,分别给单束光和三束光加随机扰动并计算其Strehl比.结果表明,只在单束光上加扰动时重建图像影响不大;在三束光上加扰动时,弱湍流光强抖动对傅里叶望远镜系统的成像效果影响具有较大的随机性,而相位抖动会严重影响系统成像质量.因此,消除光强抖动和相位抖动影响是图像重建算法改进应该考虑的一个关键因素.     

气体吸附法测定二氧化硅干凝胶的分形维数

提出了一种方便、科学有效的利用气体吸附法测定二氧化硅干凝胶等多孔材料分形维数（表面分形维数和孔分布分形维数）的方法，不需要进行一系列的吸附/脱附实验，只需要利用单一气体的一次吸附/脱附实验得出的样品孔分布、比表面数据，与不同的标尺进行关联，即可同时获得表面分形维数和孔分布分形维数.通过误差分析和校正，保证了结果的可靠性.用上述方法测定了二氧化硅干凝胶的分形维数，以FHH法和SAXS法对所得结果进行了比较和验证，并对吸附/脱附过程所得结果的差异进行了初步分析. 关键词： 分形维数 气体吸附 二氧化硅 干凝胶     

Fourier transform and theory of fractal multilayer mirrors

A new type of non periodic interferential mirrors are proposed. These mirrors, built according to the pattern of a Cantor set, are autosimilar and are characterized by a fractional Hausdorff dimension. It is shown that such mirrors are able to reflect different radiations whose wavelengths are not harmonic.     

Phase separation on regular and fractal lattices in two dimensions

A stochastic reorganization model is simulated on a two-dimensional square lattice, where we investigate finite size effects, and on clusters generated by diffusion limited aggregation. We propose a simple mean-field model, which accounts well for the data.     

Some fractal properties of the percolating backbone in two dimensions

A new algorithm is presented, based on elements of artificial intelligence theory, to determine the fractal properties of the backbone of the incipient infinite cluster. It is found that the fractal dimensionality of the backbone isd _f ^BB =1.61±0.01, the chemical dimensionality isd _t=1.40±0.01, and the fractal dimension of the minimum pathd _min=1.15 ± 0.02 for the two-dimensional triangular lattice.     

Entanglement entropy of highly degenerate States and fractal dimensions

We consider the bipartite entanglement entropy of ground states of extended quantum systems with a large degeneracy. Often, as when there is a spontaneously broken global Lie group symmetry, basis elements of the lowest-energy space form a natural geometrical structure. For instance, the spins of a spin-1/2 representation, pointing in various directions, form a sphere. We show that for subsystems with a large number m of local degrees of freedom, the entanglement entropy diverges as d/2 logm, where d is the fractal dimension of the subset of basis elements with nonzero coefficients. We interpret this result by seeing d as the (not necessarily integer) number of zero-energy Goldstone bosons describing the ground state. We suggest that this result holds quite generally for largely degenerate ground states, with potential applications to spin glasses and quenched disorder.     

Influence of noise on dynamics with fractal Fourier spectra

In deterministic dynamics, the processes with fractal power spectra occupy the intermediate position between ordered and chaotic temporal behavior. We study numerically the influence of different kinds of noise upon these processes. In general, under the action of noise the spectral measure becomes absolutely continuous and the correlations decay. However, during the certain intermediate period the autocorrelation retains the pattern which is typical for dynamics with fractal spectra. Duration of this period is related to the noise intensity by the power law.     

Analysis of fractal dimensions in the express diagnostics of bacterial colonies

The features of the formation of speckle structures under irradiation of a model fractal (Sierpinski carpet) have been investigated. The relationship between the fractal properties of the diffraction pattern and the scattering structure parameters (model fractal geometrical sizes, fractal depth) has been analyzed for the irradiation by a focused light beam, whose size is comparable with that of the irradiated object. The results of the computer simulation of the Gaussian beam scattering in bacterial colonies are compared with the experimental data.     

Helical structures,fractal dimensions and renormalization-group approach in homogeneous turbulence

The concept of helicity-fluctuation hierarchy as generating the fractal structure of turbulence in conjunction with the renormalization-group theory are utilized to renormalize the iterative solution of the Navier-Stokes equation in all orders of perturbation theory. This solution produces the value of the intermittency exponent μ = 0.4 for both the lognormal and the β model of homogeneous turbulence.     

Lyapunov exponent, generalized entropies and fractal dimensions of hot drops

We calculate the maximal Lyapunov exponent, the generalized entropies, the asymptotic distance between nearby trajectories and the fractal dimensions for a finite two-dimensional system at different initial excitation energies. We show that these quantities have a maximum at about the same excitation energy. The presence of this maximum indicates the transition from a chaotic regime to a more regular one. In the chaotic regime the system is composed mainly of a liquid drop while the regular one corresponds to almost freely flowing particles and small clusters. At the transitional excitation energy the fractal dimensions are similar to those estimated from the Fisher model for a liquid-gas phase transition at the critical point. Received: 16 March 2001 / Accepted: 12 July 2001     

Diffusion by Turbulence

The turbulent diffusivity K of the atmosphere has first been studied by Richardson 1926 who empirically found that K depends on the scale l, K = Al^α, with α = 4/3 and A = 0.6 cm^2/3 s^?1. This empirical scaling law is derived here from a unified theory (based on the Navier-Stokes equation) together with an explicit result for the prefactor, A = 2.4 ?^1/3. The mean atmospheric dissipation rate compatible with this is ? = 0.016 cm² s^?3. For windtunnels with typical dissipation rates ? ? 1 m² s^?3 the turbulent diffusion coefficient should be K/cm² s^?1 = 52 (l/cm)^4/3.     

Event structure investigation of AuAu interactions from HIJING model using fractal dimensions

This work presents an implementation of fractal geometry methods in the study of event structure for AuAu interactions at collision energies √s _NN = 9.2, 62 and 200 GeV for different interaction dynamics. The events are generated by using the HIJING model. It is shown, that the fractal dimension of events in phase space projections rapidity-transverse momentum (y - p_t) and azimuthal angle-transverse momentum (φ - p_t) are sensitive to the interaction dynamics.