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.     

Polarization Properties of the Enhanced Backscattering of Light from the Fractal Aggregate of Particles

The polarized intensity enhancement of the light backscattered multiply from a fractal aggregate of particles is numerically investigated using Monte Carlo simulations. It is confirmed only for the co-polarized intensity component that an effective mean free pathlength l_D defined for a fractal medium has the same physical meaning as a mean free pathlength l for a homogeneously random medium. Furthermore, co- and crosspolarized components of the backscattering intensity enhancement decrease in accordance with θ^2.16-1.03D and θ^4-1.8D in the far-field plane and with ζ^0.93D-3.94 and ζ^1.07D-3.98 in the boundary plane between the scattering medium and the air. Therefore, the two-dimensional Fourier transform relation is satisfied only between the co-polarized intensity distributions in the far-field and the boundary planes but not the cross-polarized ones with the accuracy of the numerical simulation. Finally, we notice the applicability of the enhanced backscattering light to estimating the dimension of the absorbent fractal medium on the basis of the result that the slope of the intensity decay of the intensity peak is directly proportional to the dimension of the medium but is independent of the absorption.     

Riccion from higher-dimensional space-time with D-dimensional sphere as a compact manifold and one-loop renormalization

Lagrangian density of riccions is obtained with the quartic self-interacting potential using higher-derivative gravitational action in (4 +D)-dimensional space-time withS ^D as a compact manifold. It is found that the resulting four-dimensional theory for riccions is one-loop multiplicatively renormalizable. Renormalization group equations are solved and its solutions yield many interesting results such as (i) dependence of extra dimensions on the enegy mass scale showing that these dimensions increase with the increasing mass scale up toD = 6, (ii) phase transition at 3.05 × 10¹⁶ GeV and (iii) dependence of gravitational and other coupling constants on energy scale. Results also suggest that space-time above 3.05 × 10¹⁶ GeV should be fractal. Moreover, dimension of the compact manifold decreases with the decreasing energy mass scale such thatD = 1 at the scale of the phase transition. Results imply invisiblity of S¹ at this scale (which is 3.05 × 10¹⁶ GeV).     

Evolution of the fractal surface of amorphous lead zirconate-titanate films during crystallization

The recrystallization kinetics of amorphous lead zirconate-titanate films prepared by sol-gel technology are investigated experimentally using elastic scattering of light. Sequences of elastic dependences of the scattered light intensity are recorded directly during thermal annealing. The evolution of the morphology of the film surface during annealing is described in terms of the variation of their fractal dimensionalities D _s. The experimental dependences D _s(t) are compared with the results of a computer simulation of the phase transition kinetics in a thin plate (film). Fiz. Tverd. Tela (St. Petersburg) 41, 306–309 (February 1999)     

The determination of surface debye temperatures from low-energy electron diffraction data

The temperature dependence of low-energy electron diffraction (LEED) intensities has often been interpreted with kinematic theory in terms of an effective Debye temperature θ_D^eff of the surface atoms. The validity of this procedure, often questioned in the literature, is tested with a computer experiment in which LEED spectra are calculated from dynamical theory (layer-KKR method) for a model of Ag{111} with a given value of θ_D^eff and then the usual kinematic formulae are used to re-extract the value of θ_D^eff. The results of the experiment indicate that this procedure yields rough values of the surface Debye temperature for electron energies higher than about 40 eV, which fluctuate substantially and tend to be somewhat smaller than that originally introduced into the model. At energies lower than about 40 eV the kinematically deduced values of θ_D^eff are too large by 10 to 15 %.     

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.     

Comment on the equivalence between fracton/spectral dimensionality,and the dimensionality of recurrence

The fracton/spectral dimensionality ^D fracton is an important characteristic of fractal processes. Until now, it has not been interpreted as the fractal dimensionality of any well-defined fractal set, and it has been claimed that ^D fracton is more intrinsic than the fractal dimensionality. In fact, ^D fractol, is best understood as an originaldynamical reinterpretation of a well-defined previously knownkinetic dimensionality: ^D fracton 's twice the fractal codimensionality of the time instants when a fractal process returns to a point it had previously visited.Presented at theThird Conference on Fractals: Fractals in the Physical Sciences, held at the National Bureau of Standards, Gaithersburg, Maryland, on November 20–23, 1983.While this talk has been widely discussed, its text was not available for inclusion in these proceedings.     

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.     

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.     

The crystal structure of Rb2CdCl4 in para- and ferroelastic phases

Abstract

The crystal structure of Rb₂CdCl₄ has been studied by X-ray diffraction at 295 and 160 K in the initial phase D ¹⁷ _4h as well as at 105 K in the ferroelastic phase. It was found that the phase transition D ¹⁷ _4h ? D ¹⁰ _2h takes place instead of D ¹⁷ _4h ? D ¹⁸ _2h as proposed earlier. The first of the transitions corresponds to unequal and the second to equal Φ-tilts of CdCl₆-octahedra around the a and b axes of the tetragonal unit cell.     

The structure of the glass phase of Rb1−x(ND4)xD2PO4

X-ray scattering techniques have been used to study the diffuse scattering from a single crystal of Rb_1–x(ND₄)_xD₂PO₄ withx=0.65. This system has a structural glass phase at low temperatures resulting from the competing ferroelectric interactions of RbD₂PO₄ and antiferroelectric interactions of (ND₄)D₂PO₄. The diffuse scattering shows a broad peak with a maximum occurring at a wavevector of about 0.3a ^*, and the intensity of these peaks is surprisingly different for wavevectorsq on opposite sides of the Bragg reflections. A model of the D bonding is developed which suggests that the diffuse scattering arises from the interaction between ferroelectric displacements alongc, ferroelectric displacements alongb, and transverse acoustic modes polarized alongb andc. The model accounts for the incommensurate wavevector and, qualitatively, for the intensity of the diffuse scattering around different Bragg reflections. The temperature dependence of the scattering is also measured.     

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.     

Random aggregation and random-walking center of mass

Two random aggregation models are used in demonstrating the properties of the random displacementsr _i of the center of mass of aggregating particles. It is found that r _i is a randomly decreasing sequence that scales with the cluster size (steps)s and _i ^=1/s r _i s ^1/D , whereD is the fractal dimension. The center-of-mass random walk is a consistent representation of the dynamics of aggregation.     

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     

Erbium electroluminescence excitation in amorphous hydrogenated silicon under thermally stimulated deep-center tunneling ionization

A study of the electroluminescence of erbium-doped, amorphous hydrogenated silicon, a-Si:H 〈Er〉, is reported. It has been found that the electroluminescence intensity at the wavelength λ=1.54 μm corresponding to the ⁴ I _13/2→⁴ I _15/2 intra-4f shell transition in Er passes through a maximum near room temperature. The unusual temperature and field dependences of the electroluminescence indicate electric-field induced multi-phonon tunneling emission of electrons from deep centers. The electroluminescence of Er³⁺ ions is due to their becoming excited as conduction-band electrons are captured by neutral dangling bonds (D ⁰ centers), which form when erbium is incorporated into the amorphous matrix. This Auger process transforms the center from its neutral state, D ⁰, to a negatively charged state, D ⁻, and the energy released in the capture is transferred by Coulomb interaction into the erbium-ion 4f shell. The steady-state current through the electroluminescent structure is supported by the reverse process of multi-phonon tunneling-electron emission from the D ⁻ center to the conduction band. The proposed theoretical model is in a good agreement with experimental data. Fiz. Tverd. Tela (St. Petersburg) 41, 210–217 (February 1999)     

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     

Topological orbifold models and quantum cohomology rings

We discuss the topological sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold ofCP ¹ by the dihedral groupD ₄, how to compute the complete ring of observables. Through this procedure, we compute all the rings of dihedralCP ¹ orbifolds. We then considerCP ²/D ₄, and show how the techniques of topologicalanti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds.Supported in part by Fannie and John Hertz Foundation     

Universal behaviour of scattering amplitudes for scattering from a plane in an average rough surface for small grazing angles

Abstract

It is shown that for scattering from a plane in an average rough surface, the scattering cross section of the range of small grazing angles of the scattered wave demonstrates a universal behaviour. If the angle of incidence is fixed (in general it should not be small), the diffusive component of the scattering cross section for the Dirichlet problem is proportional to θ² where θ is the (small) angle of elevation, and for the Neumann problem it does not depend on θ. For the backscattering case these dependences correspondingly become θ⁴ and θ°. The result is obtained from the structure of the equations that determine the scattering problem rather than by use of an approximation.     

Unitary equivalence between a spin 1/2 charged particle in a two-dimensional magnetic field and a spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electric field

We prove the unitary equivalence between the Dirac HamiltonianH _D for a relativistic spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electrostatic fieldE = (E ₁,E ₂) and the direct sum of the Dirac-Weyl operatorsD(±A) for a spin 1/2 charged particle in two-dimensional magnetic fields ±dA with the vector potentialA =E ₂ dx ¹ -E ₁ dx ², (x ¹,x ²) ². As applications, we investigate the ground state and the spectra ofH _D.     

Relation of Experimental Features of P-Even,T-Odd Asymmetries in Ternary Nuclear Fission Induced by Cold Polarized Neutrons to Triple and Quintuple Scalar Correlations

In employing the concept of the isotropy of space, the coefficients D of P-even, T-odd asymmetry in the angular distributions of prescission alpha particles emitted as third particles in the ternary fission of nonoriented target nuclei that is induced by polarized cold neutrons are expressed in the lowest orders of perturbation theory in the neutron polarization vector in terms of two P-even scalar coefficients D₃ and D₅ associated with, respectively, triple and quintuple correlations depending on the unit vectors k_α, k_LF, and σ_n, which determine the features of the coefficients being studied. On the basis of the above representation, the experimental values of the coefficients D₃ and D₅ are determined by using the experimental values of D and the angular distributions of alpha particles emitted in the analogous reaction induced by unpolarized neutrons. The resulting coefficients D₃ and D₅ are compared with the analogous coefficients found by means of the classical method of trajectory calculations and by means of quantum-mechanical fission theory relying on the concept that it is the rotational mechanism that is responsible for the appearance of the asymmetries being studied. It turns out that the classical method, which disregards the interference between fission amplitudes for different S-wave neutron resonances, leads to an irremovable contradiction between the calculated coefficient D₃ and the analogous experimental coefficient for the ²³³U target nucleus. In the case of employing the quantum-mechanical approach, it is concluded that three-body calculations of the Coriolis interaction—perturbed amplitude of the angular distributions of alpha particles moving in the Coulomb fields of fission fragments are required for the ²³³U target nucleus.