Dynamic fractal structure of emulsions due to motion and interaction of the particles: Numerical simulation

The method of numerical simulation is used to study the geometrical structure of micro-emulsions in the plane. It is found that the interaction between the particles leads to the formation of a dynamic homogeneous fractal structure of the micro-emulsion. In the absence of any interaction between the particles the structure of the emulsion is homogeneous. The interaction energy of the particles at which the fractal inhomogeneity arises is close in magnitude to the interaction energy of the particles in real (e.g., aqueous) micro-emulsions. It is also found that the size of the inhomogeneities (correlation radius) depends on the particle density in the system and is largest for the density of the percolation transition. The numerical simulation data qualitatively coincide with the results of measurements in real micro-emulsions. Zh. éksp. Teor. Fiz. 111, 1314–1319 (April 1997)     

The metal-insulator transition and the phase transition in metal-ammonia solutions

The ground state of impurity metal (sodium) atoms in liquid ammonia close to the solvated state of the free electrons is considered. It is shown that the critical solubility point lying on the metal side of the metal-insulator transition is determined by the Coulomb interaction between the ions and electrons in the overlapping impurity states, classically accessible spheres of which form an infinite percolation cluster. The percolation conductivity via the impurity states is estimated. The estimate agrees with the experimental data near the critical solubility point. Zh. éksp. Teor. Fiz. 111, 938–948 (March 1997)     

Negative Poisson coefficient of fractal structures

On the basis of a fractal model the macroscopic elastic properties of an inhomogeneous medium with random structure have been determined. It is shown that if the ratio of the bulk moduli of the phases K ₂/K ₁→0, then the percolation threshold p _c the Poisson coefficient is equal to 0.2. A study of the behavior of a two-phase medium with negative Poisson coefficient is carried out. Fiz. Tverd. Tela (St. Petersburg) 41, 2147–2153 (December 1999)     

Giant nonlinear optical activity in an aggregated silver nanocomposite

Nonlinear optical activity due to spatial dispersion is observed in a colloidal solution of silver. It is shown experimentally that the effect is substantially enhanced (by a factor of ∼10²) when the silver particles aggregate into fractal clusters. The self-rotation angle of the plane of polarization is 2 mrad at an intensity of 2 MW/cm² for λ=0.532 μm and a pulse duration of 11 ns. A method of separating the contributions of the local and nonlocal effects to the rotation of the plane of polarization is proposed and implemented. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 8, 618–622 (25 October 1998)     

Nonlinear percolation near a metal-insulator transition in regular textures

Current percolation in weakly nonlinear two-dimensional periodic structures near a metal-insulator transition is studied. It is shown that the nonlinear conductivity exhibits critical behavior as a function of the density of the insulating and superconducting inclusions. The possibility of experimentally observing the effects predicted is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 521–524 (10 April 1997)     

Lévy-flight spreading of epidemic processes leading to percolating clusters

We consider two stochastic processes, the Gribov process and the general epidemic process, that describe the spreading of an infectious disease. In contrast to the usually assumed case of short-range infections that lead, at the critical point, to directed and isotropic percolation respectively, we consider long-range infections with a probability distribution decaying in d dimensions with the distance as . By means of Wilson's momentum shell renormalization-group recursion relations, the critical exponents characterizing the growing fractal clusters are calculated to first order in an -expansion. It is shown that the long-range critical behavior changes continuously to its short-range counterpart for a decay exponent of the infection . Received: 17 July 1998 / Revised: 20 July 1998 / Accepted: 28 July 1998     

燃烧过程中煤焦颗粒的逾渗特性变化

本论文根据分形理论及测定得到的准格尔褐煤在燃烧过程中颗粒的物性参数建立表征煤焦颗粒的分形体模型。 通过分形体上突入逾渗和普通逾渗模拟,研究在燃烧过程中由于颗粒内部分形体结构的改变造成的传输特性和反应特性 的变化情况。结果表明,建立的分形体模型能够很好的表征煤焦颗粒结构特征,逾渗模拟的结果与实际情况基本相符。     

Percolation model of ion transport in channel structures

Using the results of two-dimensional simulation and the analogy with diffusion it is shown that during the flux of a direct current the dynamic volume charge having a fractal geometry is formed at the electrode/superionic conductor interface. With the methods of percolation theory it is shown that the time dependence of the conductivity of volume charge region follows a fractal power law. In this case Fourier transformation leads to a frequency response with constant phase element (CPE) at low frequencies. Paper presented at the 1st Euroconference on Solid State Ionics, Zakynthos, Greece, 11 – 18 September 1994.     

Cluster description of water-in-oil microemulsions near the critical and percolation points

The three-component ionic microemulsion system consisting of AOT/water/decane shows an unusual phase behavior in the vicinity of room temperature. The phase diagram in the temperature-volume fraction (of the dispersed phase) plane exhibits a lower consolute critical point at about 40 degrees centigrades and 10% volume fraction. A percolation line, starting from the vicinity of the critical point, cuts across the plane, extending to high volume fraction side at progressively lower temperatures. In this paper we review the evidence that allows to interpret the phase behavior of our system in terms of interacting spherical droplets. We also investigate the dynamics of droplets, below and approaching the critical point by dynamic light scattering. The first cumulant and time evolution of the droplet density correlation function can be quantitatively calculated by assuming the existence of polydispersed fractal clusters formed by the microemulsion droplets due to attraction. The relaxation phenomena observed in an extensive set of measurements of electrical conductivity and permittivity close to percolation is also reviewed and interpreted through the same cluster-forming mechanism, which reproduces the most relevant features of the frequency-dependent complex dielectric constant of this system. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Fractal structure of high-temperature graphs of O(N) models in two dimensions

The critical behavior of the two-dimensional O(N) model close to criticality is shown to be encoded in the fractal structure of the high-temperature graphs of the model. Based on Monte Carlo simulations and with the help of percolation theory, de Gennes' results for polymer rings, corresponding to the limit N-->0, are generalized to random loops for arbitrary -2相似文献   

Fractal clusters and self-propagating high-temperature synthesis in thin Al/Ge films

Fractal clusters in amorphous thin films are examples of growth models. The main models are the Witten-Sander model and its modifications. It is believed that fractal patterns are formed in the course of the crystallization of an amorphous phase. It is shown that self-propagating high-temperature synthesis can be initiated in an Al/Ge film system and fractal patterns are formed in the reaction products. It is conjectured that the transition of an amorphous phase to a crystalline phase does not play a substantial role in the appearance of such patterns, while the formation of fractal clusters is determined by self-propagating high-temperature synthesis. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 317–321 (10 March 1998)     

Quasi-one-dimensional transport of nondegenerate electrons in two-dimensional systems with a fluctuation potential

A threshold vanishing of the Hall emf with decreasing gate voltage is observed at ≈ 77 K in semiconductor systems which are disordered as a result of a high built-in charge density near the plane of the 2D-electron channel. The effect is observed at a channel conductivity σ ≈e ²/h and is due to a transition to nondegenerate-electron transport via a 2D percolation cluster having a quasi-1D character of the conduction. We have established that the conductance of “short” structures, having a length of the order of the correlation length of a percolation cluster, equals ≈e ²/h per electron and is determined by isolated percolation paths having a lowered percolation threshold. These phenomena are a general property of disordered 2D systems. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 10, 633–638 (25 November 1997)     

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.     

Trivial, Critical and Near-critical Scaling Limits of?Two-dimensional Percolation

It is natural to expect that there are only three possible types of scaling limits for the collection of all percolation interfaces in the plane: (1) a trivial one, consisting of no curves at all, (2) a critical one, in which all points of the plane are surrounded by arbitrarily large loops and every deterministic point is almost surely surrounded by a countably infinite family of nested loops with radii going to zero, and (3) an intermediate one, in which every deterministic point of the plane is almost surely surrounded by a largest loop and by a countably infinite family of nested loops with radii going to zero. We show how one can prove this using elementary arguments, with the help of known scaling relations for percolation. The trivial limit corresponds to subcritical and supercritical percolation, as well as to the case when the density p approaches the critical probability, p _c , sufficiently slowly as the lattice spacing is sent to zero. The second type corresponds to critical percolation and to a faster approach of p to p _c . The third, or near-critical, type of limit corresponds to an intermediate speed of approach of p to p _c . The fact that in the near-critical case a deterministic point is a.s. surrounded by a largest loop demonstrates the persistence of a macroscopic correlation length in the scaling limit and the absence of scale invariance.     

Statistical theory of the propagation of optical radiation in turbulent media

The problem of the propagation of a plane light wave in a turbulent medium is studied on the basis of the ideas of statistical topography. A cluster (caustic) structure of the intensity of the wave field in a plane perpendicular to the direction of propagation of the wave is analyzed both in the region of weak intensity fluctuations and in the region of saturated fluctuations. The specific (per unit area) values of the total area of the regions where the intensity is greater than a fixed level, the fraction of the power confined in these regions, and the total perimeter and average number of such regions are estimated. It is shown that estimates of this kind can be made on the basis of a knowledge of the joint one-point probability distribution of the intensity and transverse gradient of the wave field. Zh. éksp. Teor. Fiz. 111, 2044–2058 (June 1997)     

Fractal structure of ultradisperse-diamond clusters

Ultradisperse-diamond clusters are shown to be fractal objects, and the character of variation of the fractal dimension in the course of the diamond-graphite phase transition under annealing in an inert atmosphere is studied. Fiz. Tverd. Tela (St. Petersburg) 40, 776–780 (April 1998)     

Conical refraction of elastic waves in absorbing crystals

The absorption-induced acoustic-axis splitting in a viscoelastic crystal with an arbitrary anisotropy is considered. It is shown that after “switching on” absorption, the linear vector polarization field in the vicinity of the initial degeneracy point having an orientation singularity with the Poincaré index n = ±1/2, transforms to a planar distribution of ellipses with two singularities n = ±1/4 corresponding to new axes. The local geometry of the slowness surface of elastic waves is studied in the vicinity of new degeneracy points and a self-intersection line connecting them. The absorption-induced transformation of the classical picture of conical refraction is studied. The ellipticity of waves at the edge of the self-intersection wedge in a narrow interval of propagation directions drastically changes from circular at the wedge ends to linear in the middle of the wedge. For the wave normal directed to an arbitrary point of this wedge, during movement of the displacement vector over the corresponding polarization ellipse, the wave ray velocity s runs over the same cone describing refraction in a crystal without absorption. In this case, the end of the vector moves along a universal ellipse whose plane is orthogonal to the acoustic axis for zero absorption. The areal velocity of this movement differs from the angular velocity of the displacement vector on the polarization ellipse only by a constant factor, being delayed by π/2 in phase. When the wave normal is localized at the edge of the wedge in its central region, the movement of vector s along the universal ellipse becomes drastically nonuniform and the refraction transforms from conical to wedge-like.     

Computer simulations of two-phase flow with surface tension in the percolation cluster

Percolation clusters with varying occupation probability were constructed. Viscous fingering (VF) in the percolation cluster, based on the assumption that throat radii are Rayleigh distributed, is investigated by means of a successive over-relaxation technique. The fractal dimension and the sweep efficiency of VF in the percolation cluster when surface tension is considered are larger than when surface tension is neglected. The fractal dimension of VF will increase as the percolation probability increases or the viscous ratio decreases. VF's fractal dimension of porous media in the limit viscous ratio → ∞ is found to be identical with the DLA. The topology and the geometry of the porous medium have a strong effect on the displacement processes and the structure of the VF.     

Raman scattering spectra and electrical conductivity of thin silicon films with a mixed amorphous-nanocrystalline phase composition: Determination of the nanocrystalline volume fraction

Raman spectra and electrical conductivity of thin films of hydrogenated silicon with mixed amorphous-nanocrystalline phase composition have been studied. It is shown that interpretation of experimental data in terms of percolation theory permits one to determine the integrated Raman-scattering cross-section ratio of the nanocrystalline to amorphous phase and to obtain a quantitative estimate of the volume fraction of each phase. Fiz. Tverd. Tela (St. Petersburg) 39, 1348–1353 (August 1997)     

Fractal magnetic microstructure in the (Co<Subscript>41</Subscript>Fe<Subscript>39</Subscript>B<Subscript>20</Subscript>)<Subscript>x</Subscript>(SiO<Subscript>2</Subscript>)<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript> nanocomposite films

Magnetostructural methods are applied to determine the exchange bond percolation limit in (Co₄₁Fe₃₉B₂₀)_x(SiO₂)_1?x nanocomposites (x _c = 0.30 ± 0.02), which separates the phase plane along the metal concentration axis into a superparamagnetic region and a ferromagnetic region. It is shown that, with respect to the singularities of the magnetization up to the magnetization saturation curves, the ferromagnetic region is further subdivided into three regions differing in the character of the spatial propagation of the magnetization ripples or in the magnetic correlation function characteristics. The fractal dimension of the nanocomposite magnetic microstructure near the percolation threshold is determined.