Nature of segregation of reactants in diffusion controlled A+B reactions: Role of mobility in forming compact clusters

We investigate the A+B=0 bimolecular chemical reaction taking place in low-dimensional spaces when the mobilities of the two reacting species are not equal. While the case of different reactant mobilities has been previously reported as not affecting the scaling of the reactant densities with time, but only the pre-exponential factor, the mechanism for this had not been explained before. By using Monte-Carlo simulations we show that the nature of segregation is very different when compared to the normal case of equal reactant mobilities. The clusters of the mobile species are statistically homogeneous and randomly distributed in space, but the clusters of the less mobile species are much more compact and restricted in space. Due to the asymmetric mobilities, the initial symmetric random density fluctuations in time turn into asymmetric density fluctuations. We explain this trend by calculating the correlation functions for the positions of particles for the several different cases

Fracture mechanics analysis of arc shaped specimens for pipe grade polymers

Accepted versio

Percolation of randomly distributed growing clusters

We investigate the problem of growing clusters, which is modeled by two dimensional disks and three dimensional droplets. In this model we place a number of seeds on random locations on a lattice with an initial occupation probability, $p$. The seeds simultaneously grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The probability that such a system will result in a percolating cluster depends on the density of the initially distributed seeds and the dimensionality of the system. For very low initial values of $p$ we find a power law behavior for several properties that we investigate, namely for the size of the largest and second largest cluster, for the probability for a site to belong to the finally formed spanning cluster, and for the mean radius of the finally formed droplets. We report the values of the corresponding scaling exponents. Finally, we show that for very low initial concentration of seeds the final coverage takes a constant value which depends on the system dimensionality.Comment: 5 pages, 7 figure

Percolation of randomly distributed growing clusters: Finite Size Scaling and Critical Exponents

We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The model exhibits a discontinuous transition for very low values of the seed concentration $p$ and a second, non-trivial continuous phase transition for intermediate $p$ values. Here we study in detail this continuous transition that separates a phase of finite clusters from a phase characterized by the presence of a giant component. Using finite size scaling and large scale Monte Carlo simulations we determine the value of the percolation threshold where the giant component first appears, and the critical exponents that characterize the transition. We find that the transition belongs to a different universality class from the standard percolation transition.Comment: 5 two-column pages, 6 figure

Single and multiple random walks on random lattices: Excitation trapping and annihilation simulations

Random walk simulations of exciton trapping and annihilation on binary and ternary lattices are presented. Single walker visitation efficiencies for ordered and random binary lattices are compared. Interacting multiple random walkers on binary and ternary random lattices are presented in terms of trapping and annihilation efficiencies that are related to experimental observables. A master equation approach, based on Monte Carlo cluster distributions, results in a nonclassical power relationship between the exciton annihilation rate and the exciton density.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45145/1/10955_2005_Article_BF01012307.pd

Finite-Size Scaling Studies of Reaction-Diffusion Systems Part III: Numerical Methods

The scaling exponent and scaling function for the 1D single species coagulation model $(A+A\rightarrow A)$ are shown to be universal, i.e. they are not influenced by the value of the coagulation rate. They are independent of the initial conditions as well. Two different numerical methods are used to compute the scaling properties: Monte Carlo simulations and extrapolations of exact finite lattice data. These methods are tested in a case where analytical results are available. It is shown that Monte Carlo simulations can be used to compute even the correction terms. To obtain reliable results from finite-size extrapolations exact numerical data for lattices up to ten sites are sufficient.Comment: 19 pages, LaTeX, 5 figures uuencoded, BONN HE-94-0

Filtering of complex systems using overlapping tree networks

We introduce a technique that is capable to filter out information from complex systems, by mapping them to networks, and extracting a subgraph with the strongest links. This idea is based on the Minimum Spanning Tree, and it can be applied to sets of graphs that have as links different sets of interactions among the system's elements, which are described as network nodes. It can also be applied to correlation-based graphs, where the links are weighted and represent the correlation strength between all pairs of nodes. We applied this method to the European scientific collaboration network, which is composed of all the projects supported by the European Framework Program FP6, and also to the correlation-based network of the 100 highest capitalized stocks traded in the NYSE. For both cases we identified meaningful structures, such as a strongly interconnected community of countries that play important role in the collaboration network, and clusters of stocks belonging to different sectors of economic activity, which gives significant information about the investigated systems.Comment: 6 pages, 4 figure