Sharif Digital Repository

A generalized form of the Hastings and Levitov algorithm for the simulation of diffusion-limited aggregation (DLA) restricted in a sector geometry is studied. It is found that this generalization with uniform measure produces 'wedge-like' fractal patterns in the physical space, whose fractal dimension and anisotropy exponent depend significantly on the opening angle β of the sector. The morphological properties and the overall shape of the patterns are analyzed by computing the angular two-point density correlation function of the patterns. We also find that the fractal dimension of the patterns with sinusoidal distributed measure depends weakly on β with almost the same dimension as the... 

We study (2+1)-dimensional single step model for crystal growth including both deposition and evaporation processes parametrized by a single control parameter p. Using extensive numerical simulations with a relatively high statistics, we estimate various interface exponents such as roughness, growth and dynamic exponents as well as various geometric and distribution exponents of height clusters and their boundaries (or iso-height lines) as function of p. We find that, in contrary to the general belief, there exists a critical value at which the model undergoes a roughening transition from a rough phase with in the Kardar-Parisi-Zhang universality to a smooth phase with , asymptotically in... 

In this paper, we analyze the scaling behavior of a diffusion-limited aggregation (DLA) simulated by the Hastings-Levitov method. We obtain the fractal dimension of the clusters by direct analysis of the geometrical patterns, in good agreement with one obtained from an analytical approach. We compute the two-point density correlation function and we show that, in the large-size limit, it agrees with the obtained fractal dimension. These support the statistical agreement between the patterns and DLA clusters. We also investigate the scaling properties of various length scales and their fluctuations, related to the boundary of the cluster. We find that all of the length scales do not have a... 

We investigate some aspects of the c = -2 logarithmic conformal field theory (LCFT). At first, we calculate some correlators of logarithmic conformal fields which have third order singular OPE with the energymomentum tensor. Then, we argue about the fields in the c = -2 model which are associated with this kind of more general logarithmic primary fields. We go on to find fermionic representations for all the fields in the extended Kac table, in particular the untwisted sector. Moreover, we calculate the various OPEs of the fields, especially for the logarithmic energy-momentum tensor and by using these OPEs we find the exact finite transformation of this field. We briefly discuss about the... 

We have studied the effect of annealing temperature on the statistical properties of WO3 surface using atomic force microscopy (AFM) techniques. We have applied both level crossing and structure function methods. Level crossing analysis indicates an optimum annealing temperature of around 400°C at which the effective area of the WO3 thin film is maximum, whereas the composition of the surface remains stoichiometric. The complexity of the height fluctuation of surfaces was characterized by roughness, the roughness exponent and the lateral size of surface features. We have found that there is a phase transition at around 400°C from one set to two sets of roughness parameters. This happens due... 

Correlations between electrical and thermal conduction in polymer composites are blurred due to the complex contribution of charge and heat carriers at the nanoscale junctions of filler particles. Conflicting reports on the lack or existence of thermal percolation in polymer composites have made it the subject of great controversy for decades. Here, we develop a generalized percolation framework that describes both electrical and thermal conductivity within a remarkably wide range of filler-to-matrix conductivity ratios (Y f / Y m), covering 20 orders of magnitude. Our unified theory provides a genuine classification of electrical conductivity with typical Y f / Y m ≥ 10 10 as...