Electric field driven fractal growth dynamics in polymeric medium

This paper reports the extension of earlier work (Dawar and Chandra, 2012) [27] by including the influence of low values of electric field on diffusion limited aggregation (DLA) patterns in polymer electrolyte composites. Subsequently, specified cut-off value of voltage has been determined. Below the cut-off voltage, the growth becomes direction independent (i.e., random) and gives rise to ramified DLA patterns while above the cut-off, growth is governed by diffusion, convection and migration. These three terms (i.e., diffusion, convection and migration) lead to structural transition that varies from dense branched morphology (DBM) to chain-like growth to dendritic growth, i.e., from high field region (A) to constant field region (B) to low field region (C), respectively. The paper further explores the growth under different kinds of electrode geometries (circular and square electrode geometry). A qualitative explanation for fractal growth phenomena at applied voltage based on Nernst–Planck equation has been proposed.     

Electrostatic forces in micromanipulation: Experimental characterization and simulation including roughness

Manipulation by contact of objects between 1 m and 1 mm are often disturbed by adhesion between the manipulated object and the gripper. Electrostatic forces are among the phenomena responsible for this adhesive effect. Analytical models have been developed in the literature to predict electrostatic forces. Most models have been developed within the framework of scanning probe microscopy, i.e. for a contact between a conducting tip and a metallic surface. In our study, we developed a simulation tool based on finite elements modeling. The strength of this model lies in the fact that it integrates roughness parameters. Measurements of electrostatic forces in function of roughness were conducted by atomic force microscopy. The experimental results were compared with the simulation results showing very good correlation. This demonstrates the influence of surface topography on electrostatic forces, especially for very small separation distances and proves the utility of the simulation tool in designing surfaces with controlled adhesion. Some application fields to which these results can be applied are drug delivery devices and micromanipulation tools.     

A lower bound for the symbolic multifractal spectrum of a self-similar multifractal with arbitrary overlaps

By now the multifractal structure of self-similar measures satisfying the so-called Open Set Condition is well understood. However, if the Open Set Condition is not satisfied, then almost nothing is known. In this paper we prove a nontrivial lower bound for the symbolic multifractal spectrum of an arbitrary self-similar measure. We emphasize that we are considering arbitrary self-similar measures (and sets) which are not assumed to satisfy the Open Set Condition or similar separation conditions. Our results also have applications to self-similar sets which do not satisfy the Open Set Condition (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Percolation in two-scale porous media

Two-scale porous media are generated by filtering a Gaussian random correlated field with a random correlated threshold field. The percolation threshold and the critical exponent ν are derived with the help of a finite-size scaling method. The percolation threshold for the three-dimensional media is a decreasing function of the variance and correlation length of the threshold field. A simplified model predicts these trends in 3d; moreover, it suggested some effects in 2d which were all numerically verified. Received 17 August 2000     

Temperature-dependent susceptibility in ALON

Herein, we propose a stochastic model of the complex susceptibility in aluminum nitride (ALON), a polycrystalline transparent ceramic. The proposed model yields an inverse power-law dependence of the dielectric loss tangent on frequency, in remarkably close agreement with data. In addition, the phenomenological parameters are found to be strongly temperature-dependent. This temperature dependence is determined, in the theoretical model, to be a consequence of the thermodynamic properties of the molecular dipoles in the material.     

Structure of gels and aggregates of disk-like colloids

The static structure factor (S(q)) of dispersions and gels of disk-like mineral colloids (Laponite) was investigated using time- and ensemble-averaged light scattering. The evolution of S(q) in time after increasing the ionic strength of well-dispersed Laponite suspensions shows that Laponite aggregates and forms fractal clusters. The structure of the aggregates does not depend on the ionic strength, but the rate of growth increases very strongly with the ionic strength. At concentrations below about 3 g/l (0.12% v/v) the aggregates sediment while at higher concentrations space-filling gels are formed. The gels are homogeneous on length scales larger than the correlation length which decreases strongly with decreasing ionic strength and increasing concentration. However, the local structure is the same, independent of the concentration and the ionic strength. Received 6 August 2000 and Received in final form 16 March 2001     

Analysis on Fractal Objects

Irregular objects are often modeled by fractals sets. In order to formulate partial differential equations on these nowhere differentiable sets the development of a “new analysis” is necessary. With the help of the model case of the Sierpinski gasket the definition of energy forms and Laplacians on self-similar finitely ramified fractals is explained. Moreover, some results for certain classes of non-self-similar fractals are presented. 2000 Math. Subj. Class.: Primary 28A80, 35J15; Secondary 31C25, 35P05     

Construction of recurrent bivariate fractal interpolation surfaces and computation of their box-counting dimension

Recurrent bivariate fractal interpolation surfaces (RBFISs) generalise the notion of affine fractal interpolation surfaces (FISs) in that the iterated system of transformations used to construct such a surface is non-affine. The resulting limit surface is therefore no longer self-affine nor self-similar. Exact values for the box-counting dimension of the RBFISs are obtained. Finally, a methodology to approximate any natural surface using RBFISs is outlined.