Multiscale laminar flows with turbulentlike properties

By applying fractal electromagnetic force fields on a thin layer of brine, we generate steady quasi-two-dimensional laminar flows with multiscale stagnation point topology. This topology is shown to control the evolution of pair separation (Delta) statistics by imposing a turbulentlike locality based on the sizes and strain rates of hyperbolic stagnation points when the flows are fast enough, in which case Delta(2) approximately t(gamma) is a good approximation with gamma close to 3. Spatially multiscale laminar flows with turbulentlike spectral and stirring properties are a new concept with potential applications in efficient and microfluidic mixing.     

Fractal structure of marine measuring networks

Summary This paper deals with the fractal character of several distribution points measuring the Earth's total magnetic field (ETMF) during some marine surveys that we carried out in the Gulf of Pozzuoli and around the island of Ischia (Naples, Italy). Previous studies evaluated the fractal dimension of networks constituted by fixed measuring stations. The examined distributions display a ?fractal scaling? regime on 3–4 decades of distances with fractal dimensions of 1.80 and 1.54. These values characterize the whole investigated area covered by the distribution of experimental data. Linked to fractal dimension is the possibility of reconstructing the field and the capacity to reveal sparse and intense phenomena (e.g. magnetic anomalies) with a low fractal dimension. In distributions with large areas without measuring points, Shannon's theorem is no longer applicable in 2D. The fractal evaluation enables a spatial limit to record the phenomena to be defined and therefore establishes the minimum wavelength recordable of the magnetic field.     

Statistics of resonances and of delay times in quasiperiodic Schrodinger equations

We study the distributions of the resonance widths P(gamma) and of delay times P(tau) in one-dimensional quasiperiodic tight-binding systems at critical conditions with one open channel. Both quantities are found to decay algebraically as gamma(-alpha) and tau(-gamma) on small and large scales, respectively. The exponents alpha and gamma are related to the fractal dimension D(E)(0) of the spectrum of the closed system as alpha = 1+D(E)(0) and gamma = 2-D(E)(0). Our results are verified for the Harper model at the metal-insulator transition and for Fibonacci lattices.     

KDP晶体单点金刚石车削表面形貌分形分析

 分别使用2维和3维分形方法对单点金刚石车削加工的KDP晶体表面形貌进行了分析，并对表面的3维分形维数和3维粗糙度表征参数进行了比较，分析了二者对表面形貌表征的差异。使用2维轮廓分形方法计算了KDP晶体表面圆周各方向上的分形维数。通过分析得出：3维分形维数与表面粗糙度值成反比关系；使用单点金刚石车削方法加工KDP晶体会形成各向异性特征明显的已加工表面，在一定程度上容易形成小尺度波纹；已加工表面是否具有明显的小尺度波纹特征与表面粗糙度值并无直接关系，但与其表面轮廓分形状态分布密切相关；KDP晶体表面2维功率谱密度与其分形状态具有相近的方向性特征。     

湍流大气中的准直激光束III.分形结构与相位不连续点饶瑞中

 利用数值方法研究了不同起伏条件下准直激光束在湍流大气中的传播，分析了光斑的分形维数以及相位不连续点数目的统计特征。结果表明：随着起伏条件的增大，光斑的分形维数以及相位不连续点数目增大；光斑的分形维数与锐度（描述光斑质量的参量）有一定的关系，但相位不连续点数目与光斑质量不存在确定的关系。在本文的计算条件下，分形维数一直随起伏条件的增大而增大，没有出现类似于闪烁饱和的现象。在一定的起伏条件下，相位不连续点数目具有一定的统计分布，而不是一个确定的值，并且具有相当的发散性。     

断裂表面自相似与自仿射复杂分形结构的研究

 按照分形理论研究了具有自相似和自仿射分形结构的复杂表面,并研究了其在Ⅰ型+Ⅱ型和Ⅰ型+Ⅲ型混合载荷下形成的断裂表面的应用。结果指出：分维D与粗糙度指数H之间的关系（D+H=2或D×H=1）只是粗略的近似。用分维D或粗糙度指数H测量断裂表面,在双对数图上得到的是实验曲线而不是直线并不说明没有分形结构,很可能是自相似和自仿射结构的混合。     

水分子凝聚体系的介孔结构分形学

透射电镜研究表明，4,40-双硬脂酰胺基二苯醚在水中聚集、自组装成缠绕细纤维状聚集体，进而使整个体系形成三维网络结构．水分子被包囊在这个网络结构中，形成一种新型的凝聚体系(水分子凝胶)．水分子凝胶是一种典型的纳米介孔物质，其复杂的微孔结构可以用分形维数D来表征，通过气体吸附方法(孔度法和比表面积法)计算，求得水分子凝胶体系的微孔结构的分形维数为2.1?2.2．对于纤维状三维网络结构的分形表征，通过粘度法和Cayley分形树模型得出分形维数为1.98．由此推测其分形网络形成的过程是一个初始成核-生长-枝化的循环过程．     

水分子凝胶中有机凝胶因子聚集体的分形结构研究

水分子凝胶是一种新型软凝聚体系.是凝胶因子在很低的浓度下在水中聚集、自组装，使水凝胶化形成的凝聚体系.透射电镜(TEM)表明凝胶因子在水中聚集、自组装成细纤维状结构.通过对TEM照片进行数字化处理，采用Sandbox法和密度-密度相关函数法计算的结果表明凝胶因子在聚集组装过程中具有典型的分形特征.根据C++程序计算出分形维数D＝1.814—1.977.以分形理论对凝胶因子的聚集过程以及由此形成的水分子凝聚体系的分形特征进行了讨论.利用小角x射线散射(SAXS)研究进一步表明，凝聚体系的分形结构存在于尺度α 关键词： 分形 凝胶因子 水分子凝聚体系 透射电镜(TEM) 小角x射线散射(SAXS)     

On obtaining global nonlinear system characteristics through interpolated cell mapping

Period doubling bifurcations and fractal basin boundaries are investigated by means of Interpolated Cell Mapping (ICM). ICM is a new method to determine the continuous time trajectory of a nonlinear system by spatially discretizing the system and employing an interpolation procedure to estimate the system's response at any arbitrary point in phase space. The parameter values at which period doubling occurs for a Duffing's oscillator is found by both conventional time integration and two mapping techniques and the results compared. The ICM method is shown to very accurately determine the points of bifurcation. The dimension of a fractal basin boundary is determined by ICM and compared to an exact determination. The ICM procedure produces the same fractal dimension determination as the exact analysis but only requires one thousandth of the computation time.     

Fractal properties of aggregates of metal nanoclusters on solid surface

AFM images are used to determine and analyze fractal characteristics (cluster fraction dimension and lacunarity) of aggregates of Au and Ag nanoclusters on metal films of the same metal produced with the aid of thermal vacuum deposition on mica surface. A fractal dimension of 1.6 that corresponds to typical samples with relatively uniform distribution of nanoclusters on the film surface is in agreement with the mean value calculated from experimental data of Belko et al., who studied the fractal dimension of Au nanoclusters on a different dielectric (quartz) surface. When a compact single aggregate of Au nanoclusters is formed on a certain active center or defect, the fractal cluster dimension decreases to 1.4. The experimental data are compared with the results of existing theoretical models of association of nanoclusters in 2D systems.     

Velocity Profiles of Slow Blood Flow in a Narrow Tube

A fractal model is introduced into the slow blood motion. When blood flows slowly in a narrow tube, red cell aggregation results in the formation of an approximately cylindrical core of red cells. By introducing the fractal model and using the power law relation between area fraction φ and distance from tube axis ρ, rigorous velocity profiles of the fluid ia and outside the aggregated core and of the core itself are obtained analytically for different fractal dimensions. It shows a blunted velocity distribution for a relatively large fractal dimension (D～2), which can be observed in normal blood; a pathological velocity profile for moderate dimension (D = 1), which is similar to the Segre-Silberberg effect; and a parabolic profile for negligible red cell concentration (D = 0), which likes in the Poiseuille flow.     

Characterization of Synthetic-Coal Char Particles using fractal dimension analysis

The development and change of surface ruggedness in chars was studied at conditions typical in a pulverized coal furnace. The fractal dimension, a measure of surface ruggedness, of chars was measured using physisorption techniques. By adjusting the temperature encountered (1173 to 1773 K) and residence time (0.1 to 1.5 s) of the synthetic coal (sized to 46–106 μm diameter), chars at different stages of combustion were prepared in a laminar flow (drop-tube) furnace. The particles were quickly cooled and quenched in an inert atmosphere. The samples were examined using a scanning electron microprobe, and their fractal dimensions were determined using gas physisorption. The adsorption data were used to test if the char surface was fractal on a molecular scale, to determine the fractal dimension, and to quantify changes in the fractal dimension during combustion. The fractal dimension of the unburned synthetic coal was approximately 2. The fractal dimension increased as high as 2.85 as the carbon matrix burned away and exposed mineral moieties. However, as combustion continued the carbon burned completely away leaving a mineral fly ash particle with a fractal dimension as low as 2.47.     

Comparison of fractal analysis methods in the study of fractals with independent branching

The notion of dimension as a quantitative characteristic of space geometry is discussed. It is supposed that hadrons created in interactions between particles and nuclei can be considered sets of points possessing fractal properties in the three-dimensional phase space (p _T , η, ?). The Hausdorff-Besicovich dimension D _F is considered the most natural characteristic for determining the fractal dimension. Different methods for determining the fractal dimension are compared: box counting (BC), P-adic coverage (PaC), and system of equations of P-adic coverage (SePaC). A procedure for choosing optimum values of parameters of the considered methods is presented. These parameters are shown to be able to reconstruct the fractal dimension D _F , number of levels N _lev, and fractal structure with maximal efficiency. The features of the PaC- and SePaC-methods in the analysis of fractals with independent branching are noted.     

Using Fractal Function Auto correlative Method to Confirm Fractal Dimension of Function Graph

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Thermodynamics of photons on fractals

A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PV(s) = U/d(s), where d(s) is the spectral dimension and V(s) defines the "spectral volume." For regular manifolds, V(s) coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.     

Time evolution of quantum fractals

We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential, and free particle. The box-counting dimension of the probability density P(t)(x) = |Psi(x,t)|(2) is shown not to change during the time evolution. We prove a universal relation D(t) = 1+Dx/2 linking the dimensions of space cross sections Dx and time cross sections D(t) of the fractal quantum carpets.     

Dimension of fractal growth patterns as a dynamical exponent

We consider a conformal theory of fractal growth patterns in two dimensions, including diffusion limited aggregation (DLA) as a particular case. In this theory the fractal dimension of the asymptotic cluster manifests itself as a dynamical exponent observable already at very early growth stages. Using a renormalization relation we show from early stage dynamics that the dimension D of DLA can be estimated, 1.69相似文献   

Analysis of fractals with dependent branching by box counting, P-adic coverages, and systems of equations of P-adic coverages

Concept of the dimension of space-time in the general relativity theory and quantum theory is discussed. It is emphasized that the dimension of a discrete space can be defined based on the Hausdorff measure. The noninteger dimension is a typical characteristic of a fractal. The process of hadron formation in interactions between high-energy particles and nuclei is supposed to possess fractal properties. The following methods for analyzing fractals are considered: box counting (BC), method of P-adic coverages (PaC), and method of systems of equations of P-adic coverages (SePaC), for determining the fractal dimension. A comparative analysis of fractals with dependent branching is performed using these methods. We determine the optimum values of parameters permitting one to determine the fractal dimension D _F , number of levels N _lev, and the fractal structure with maximal efficiency. It is noted that the SePaC method has advantages in analyzing fractals with dependent branching.     

Dimensionally frustrated diffusion towards fractal adsorbers

Diffusion towards a fractal adsorber is a well-researched problem with many applications. While the steady-state flux towards such adsorbers is known to be characterized by the fractal dimension (D{F}) of the surface, the more general problem of time-dependent adsorption kinetics of fractal surfaces remains poorly understood. In this Letter, we show that the time-dependent flux to fractal adsorbers (1相似文献   

Effects of Fractal Size Distributions on Velocity Distributions and Correlations of a Polydisperse Granular Gas

By the Monte Carlo method, the effect of dispersion of disc size distribution on the velocity distributions and correlations of a polydisperse granular gas with fractal size distribution is investigated in the same inelasticity. The dispersion can be described by a fractal dimension D, and the smooth hard discs are engaged in a two- dimensional horizontal rectangular box, colliding inelastically with each other and driven by a homogeneous heat bath. In the steady state, the tails of the velocity distribution functions rise more significantly above a Gaussian as D increases, but the non-Gaussian velocity distribution functions do not demonstrate any apparent universal form for any value of D. The spatial velocity correlations are apparently stronger with the increase of D. The perpendicular correlations are about half the parallel correlations, and the two correlations are a power-law decay function of dimensionless distance and are of a long range. Moreover, the parallel velocity correlations of postcollisional state at contact are more than twice as large as the precollisional correlations, and both of them show almost linear behaviour of the fractal dimension D.