Enhancement of the backscattered intensity from fractal aggregates

Abstract

Comparative measurements were conducted for the backscattered intensities of light from uniform random and fractal aggregated media. Different features are found for the backscattered intensity peak shapes. A crossover between the θ^1?D and θ^?2 dependences of the backscattered intensity occurs in the case of fractal aggregated medium, where D indicates the fractal dimension.     

Far-field intensity of electromagnetic waves scattered from random,self-affine fractal metal surfaces

Abstract

By means of the rigorous Green theorem integral equation formulation, we study the far-field intensity of linearly polarized, monochromatic electromagnetic waves scattered from a one-dimensionally rough silver surface characterized by a self-affine fractal structure. These surface fractal properties are ensured for the entire range of relevant length scales, from the illuminated spot size down to a sufficiently small (in terms of the wavelength) lower cut-off length. A peak in the specular direction is found in the angular distribution of the diffuse component of the mean scattered intensity, which becomes broader and smaller with increasing fractal dimension. For large fractal dimensions, enhanced backscattering in the case of p-polarization is observed owing to the roughness-induced excitation of surface plasmon polaritons. The interplay of different length scales of the fractal surface in the scattering process is analysed for an intermediate fractal dimension.     

Deducing residual self-interference of inelastic photons in coherent backscattering of intense laser light from two atoms

A coherent backscattering of intense laser light by two isotropic atoms is studied in the helicity preserving polarization channel. It is demonstrated that single scattering has a non-negligible contribution to the background intensity L(θ) at small angles θ with respect to the backwards direction. This contribution can be subtracted from the total signal, and the value of L(0) necessary for evaluating the coherent backscattering enhancement factor – inferred from measurements of the backscattered light intensity beyond the interference peak.     

On the kinetic theory of energy losses in a randomly heterogeneous medium

The equation describing the distribution of energy losses of a particle propagating in a fractal medium with quenched and dynamic heterogeneities has been derived. It has been shown that in the case of the medium with fractal dimension 2 < D < 3, the losses Δ are characterized by the sublinear anomalous dependence Δ ∼ x ^α with a power-law dependence on the distance x from the surface and exponent α = D − 2.     

The scattering of electromagnetic waves in fractal media

Abstract

The scattering of electromagnetic waves in fractal media is studied. The fractal dimension is naturally involved in the formulation of two physical problems studied in this paper. The general theory of multiple scattering of electromagnetic wave in fractal media is developed by modifying Twersky's theory. Statistical quantities, such as the average field and average intensity of the multiple scattered wave, are studied for a wave propagating in a fractal medium. The scattering cross section of the medium is deduced. The backscattering of electromagnetic waves is also studied. The results showing the range of dependence of the backscattered signals are in agreement with numerical simulations by Rastogi and Scheucher (1990). It also suggests a method of measuring the fractal dimension of the fractal embedded media using radar sounding. The theory developed in this paper can also be used for problems related to multiple scattering of other kinds of waves, such as acoustic waves, elastic waves etc, in fractal media.     

基于分形多孔介质三维网络模型的非混溶两相流驱替数值模拟

提出了一个描述多孔介质孔隙尺寸分布的三维分形网络模型,利用该模型对多孔介质中的非混溶两相流驱替进行了数值模拟,研究了孔隙尺寸分布分维D_f和两相流黏滞比M对驱替前沿指进型的影响,结果表明指进型容量维数D_h随着孔隙尺寸分布分维D_f以及黏滞比M的增大而减少,并通过曲线拟合得到了它们之间的定量关系. 关键词： 多孔介质 三维网络 黏滞指进 非混溶两相流     

Proton-detected scalar coupling based assignment strategies in MAS solid-state NMR spectroscopy applied to perdeuterated proteins

Assignment of proteins in MAS (magic angle spinning) solid-state NMR relies so far on correlations among heteronuclei. This strategy is based on well dispersed resonances in the ¹⁵N dimension. In many complex cases like membrane proteins or amyloid fibrils, an additional frequency dimension is desirable in order to spread the amide resonances. We show here that proton detected HNCO, HNCA, and HNCACB type experiments can successfully be implemented in the solid-state. Coherences are sufficiently long lived to allow pulse schemes of a duration greater than 70 ms before incrementation of the first indirect dimension. The achieved resolution is comparable to the resolution obtained in solution-state NMR experiments. We demonstrate the experiments using a triply labeled sample of the SH3 domain of chicken α-spectrin, which was re-crystallized in H₂O/D₂O using a ratio of 1/9. We employ paramagnetic relaxation enhancement (PRE) using EDTA chelated Cu^II to enable rapid data acquisition.     

Diffusion on complex cellular automata patterns

We studied random walks on two-dimensional patterns formed by the sequence of configurations of complex elementary cellular automata (CA) with random initial configurations. The walkers are allowed to jump between nearest neighbours or next nearest neighbours 1 sites. On patterns of rules 22, 54, 90, 122, 126, 150 and 182, the diffusion is normal (ν=1/2). On patterns 18 and 146 the diffusion is anomalous, with ν=0.415±0.005, and the spectral dimension is D_s=1.25±0.1. From the analysis of the diffusion in the horizontal and vertical directions (space and time directions of the CA problem, respectively) of patterns 18 and 146, we obtained ν_x≈0.22 and ν_y≈0.42, because they have branches of 1 sites which are long in the vertical direction but narrow in the horizontal direction. Due to the anisotropic diffusion, the results do not satisfy the relation D_s=2D_F/D_w, with D_w=1/ν and fractal dimension D_F=2. Considering that the fractal dimension of the region visited by the walker is equal to the dimension of the substrate (D_F), we suggest the new scaling relation D_s=2(ν_x+ν_y). This relation is supported by our numerical results and may be generalized to other structures with anisotropic diffusion.     

Fractal model of the frequency dependence of electromagnetic wave attenuation by vegetation fragments

An approach to describing the earlier discovered power-type frequency dependence of microwave attenuation Y by vegetation fragments is developed. It is established that Y ∼ ω^3−D , where ω is the circular frequency, 3 is the dimension of the Euclidean space, and D is the fractal dimension of the structure related to vegetation fragments.     

Electrical conductivity improvement of strontium titanate doped lead vanadate glasses by nanocrystallization

The structural and electrical conductivity (σ) of annealed SrTiO₃–PbO₂–V₂O₅ glasses were studied. The annealing of initially glass samples leads to formation of nanocrystalline grains embedded in the glassy matrix. XRD patterns of the glass–ceramic samples show that nanocrystals were embedded in the glassy matrix with an average grain size of 32 nm. The glass–ceramic nanocrystals obtained by annealing at temperatures close to the crystallization temperature T_c exhibit enhancement of electrical conductivity up to four orders of magnitude than initially glasses. The enhancement of the electrical conductivity due to annealing was attributed to two interdependent factors: (i) an increase of concentration of V⁴⁺–V⁵⁺ pairs; and (ii) formation of defective, well-conducting regions along the glass–crystallites interfaces. From the conductivity temperature relation, it was found that small polaron hopping model was applicable at temperature above θ_D/2 (θ_D, the Debye temperature). The electrical conduction at T >θ_D/2 was due to non-adiabatic small polaron hopping (SPH) of electrons between vanadium ions. The parameters obtained from the fits of the experimental data to this model appear reasonable and are consistent with glass composition.     

Enhancement of the backscattered intensity from fractal aggregates

Comparative measurements were conducted for the backscattered intensities of light from uniform random and fractal aggregated media. Different features are found for the backscattered intensity peak shapes. A crossover between the θ^1-D and θ^-2 dependences of the backscattered intensity occurs in the case of fractal aggregated medium, where D indicates the fractal dimension.     

Frequency and spatial characteristics of the electrophysical parameters of a living tree trunk

The method of vertical electrical sounding is applied to derive the spatial characteristic of the dc resistivity ρ of a living pine trunk, ρ = L-0.85, and the frequency characteristic of the ac resistance R of the same pine trunk, R = f-0.053. The results are simulated by the methods of fractal geometry, according to which ρ = L ^{−h + 2} and $ R \sim f^{ - \tfrac{3} {h} + 1} $ R \sim f^{ - \tfrac{3} {h} + 1} , where h is the walk dimension of the electric current in the trunk. From comparison between the experimental and theoretical results, it follows that h = 2.85 and fractal dimension D = 1/h = 0.35. Since D = 1, conducting layers form a Cantor set.     

Electromagnetic radiation of charges with fractal distribution

The radiation of charges with fractal distributions is studied in the framework of classical electrodynamics. The properties of the form factork(x) of the density of the fractal distribution are investigated. It is shown that the nature of the decrease of the averaged square of the form factor modulus with increasing wave vectorx of the radiation is determined by the dimension D of the fractal distribution of the charge: ¦k(x)¦^2–D .Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 111–116, January, 1992.The author thanks Professor V. G. Bagrov for a helpful discussion of the questions considered in this paper.     

Catastrophes in the multi-fractal dynamics of social-economic systems

In the present paper, the concept of multi-fractal dynamics is developed. The problem concerning catastrophes in this dynamics is studied in detail. In the framework of the concept of fractal curve as a thick curve, it is proved that the cell approach to measuring the fractal dimension D is equivalent to measuring the dependence of the length L of the line on the scope δ. The introduction of a fractal scale of temperatures T ^f is suggested.     

Diffusion of silicon in titanium nitride films. Efficiency of TiN barrier layers

Two kinds of reactively evaporated titanium nitride films with columnar (B ₀ films) and fine-grained film structure (B ₊ films) have been examined as diffusion barriers, preventing the silicon diffusion in silicon devices. The silicon diffusion profiles have been investigated by 2 MeV ⁴He⁺ Rutherford backscattering spectrometry (RBS) after annealing at temperatures up to 900° C, in view of application of high-temperature processes. The diffusivity from 400 to 900° C: D (m² s^–1)=2.5×10^–18 exp[–31 kJ/mol/(RT)] in B ₀ layers and D (m² s^–1)=3×10^–19 exp[–26 kJ/mol/(RT) in B ₊ TiN layers. The diffusivities determined correspond to grain boundary diffusion, the difference being due to the different microstructure. The very low diffusivity of silicon in B ₊ TiN layer makes it an excellent high-temperature barrier preventing silicon diffusion.     

Enhancement Factor in the Light Backscattered by Fractal Aggregated Media

We investigate the phenomenon of the enhanced backscattering of light from soft sediments of fractal clusters. The clusters consist of spherical PMMA particles with the diameter of 0.4 μ, aggregated in aqueous solutions of NaCl. We found that the kinetics of aggregation, which determines the average cluster size in sediments, is controlled by the salt concentration and that the sediments are mutually self-similar media. In comparison to uniform random media, specific features for the enhancement peaks are revealed. It is found that the peak line-shape reflects the particularities of the density of scatterers in a fractal-like medium. It is shown experimentally that the enhancement factor in the light backscattered by fractal aggregated media is sensitive to the average cluster size. On this basis, we suggest a possible way to distinguish between mutually self-similar media.     

Aluminium diffusion in titanium nitride films. Efficiency of TiN barrier layers

Two kinds of reactively evaporated titanium nitride films with columnar (B ₀ films) and fine-grained (B ₊ films) film structures, respectively, have been examined as diffusion barriers for preventing aluminium diffusion. The aluminium diffusion profiles have been investigated by 2 MeV ⁴He⁺ Rutherford backscattering spectrometry (RBS) at temperatures up to 550° C. The diffusivity from 300° C to 550° C is: D[m²s^–1]=3×10^–18 exp[–30/(RT)] in B ₀ layers and D[m²s^–1]=1.4×10^–16 exp[–48/(RT)] in B ₊ TiN layers. The activation-energy values determined indicate a grain boundary diffusion mechanism. The difference between the diffusion values is determined implicitly by the microstructure of the layers. Thus, the porous B ₀ layers contain a considerable amount of oxygen absorbed in the intercolumnar voids and distributed throughout the film thickness. As found by AES depth profiling, this oxygen supply allows the formation of Al₂O₃ during annealing the latter preventing the subsequent diffusion of the aluminium atoms.     

Correlation between Curie temperature and system dimension

Curie temperature T_C of spin arrangement with arbitrary dimension was considered. We assumed that interaction of a spin with all other spins vary with a power-law decay rate in exchange integral on Heisenberg model. As a result, we found that T_C, which was obtained from T_C=λC (λ: mean-field coefficient and C: Curie constant), significantly depends on fractal dimension of spin arrangements D, the exchange integral and the decay constant. This semi-quantitatively explains how T_C depends on D (1≤D≤3) in a universal way and also the finite size effect on T_C in low-dimensional spin systems.     

表面分形球、柱的光散射

分形和分维是近些年才兴起的一门处理复杂事物的新方法￣［１］。本文主要研究具有表面分形的球、柱的光散射特征。我们首先利用几何光学近似研究了一种表面满足自仿射原理的分形均匀球的散射，其散射特性与分维存在一定的关系。我们还利用微扰法讨论了表面具有沟槽的分形柱的光散射的分形特征。     

Critical Slowing Down in One-Dimensional Maps and Beyond

This is a brief review on critical slowing down near the Feigenbaum period-doubling bifurcation points and its consequences. The slowing down of numerical convergence leads to an “operational” fractal dimension D=2/3 at a finite order bifurcation point. There is a cross-over to D ₀=0.538... when the order goes to infinity, i.e., to the Feigenbaum accumulation point. The problem of whether there exists a “super-scaling” for the dimension spectrum D _q ^W that does not depend on the primitive word W underlying the period-n-tupling sequence seems to remain open