80 research outputs found
Characteristics of reaction-diffusion on scale-free networks
We examine some characteristic properties of reaction-diffusion processes of
the A+A->0 type on scale-free networks. Due to the inhomogeneity of the
structure of the substrate, as compared to usual lattices, we focus on the
characteristics of the nodes where the annihilations occur. We show that at
early times the majority of these events take place on low-connectivity nodes,
while as time advances the process moves towards the high-connectivity nodes,
the so-called hubs. This pattern remarkably accelerates the annihilation of the
particles, and it is in agreement with earlier predictions that the rates of
reaction-diffusion processes on scale-free networks are much faster than the
equivalent ones on lattice systems
Absence of kinetic effects in reaction-diffusion processes in scale-free networks
We show that the chemical reactions of the model systems of A+A->0 and A+B->0
when performed on scale-free networks exhibit drastically different behavior as
compared to the same reactions in normal spaces. The exponents characterizing
the density evolution as a function of time are considerably higher than 1,
implying that both reactions occur at a much faster rate. This is due to the
fact that the discerning effects of the generation of a depletion zone (A+A)
and the segregation of the reactants (A+B) do not occur at all as in normal
spaces. Instead we observe the formation of clusters of A (A+A reaction) and of
mixed A and B (A+B reaction) around the hubs of the network. Only at the limit
of very sparse networks is the usual behavior recovered.Comment: 4 pages, 4 figures, to be published in Physical Review Letter
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 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
A model for dislocation creep in polycrystalline Ni-base superalloys at intermediate temperatures
A model for creep at intermediate temperatures in polycrystalline Ni-based superalloys is presented. The model is based on describing stacking fault nucleation, propagation and subsequent shear within the
matrix and
precipitates. The critical energy for stacking fault nucleation is obtained by minimising the energy to form a stacking fault from dislocation partials, which is promoted by local stress concentrations. The extent of stacking fault shear at a
precipitate is estimated using a force balance at the
interface to determine the critical shear distance The model results are validated against creep experimental data in several polycrystalline superalloys showing good agreement. Individual contributions to creep from key microstructural features, including grain size and
distribution, are studied to identify which ones are more significant. Similarly, it is shown that one of the main factors controlling the creep rate is the stacking fault energy in the
as it dictates the stacking fault nucleation and shear rates. Parameter analysis on alloying additions typically used in commercial superalloys demonstrates which elements have the strongest effect on creep, highlighting how the present model can be used as tool for alloy and microstructure design against dislocation creep
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
Trapping in complex networks
We investigate the trapping problem in Erdos-Renyi (ER) and Scale-Free (SF)
networks. We calculate the evolution of the particle density of
random walkers in the presence of one or multiple traps with concentration .
We show using theory and simulations that in ER networks, while for short times
, for longer times exhibits a more
complex behavior, with explicit dependence on both the number of traps and the
size of the network. In SF networks we reveal the significant impact of the
trap's location: is drastically different when a trap is placed on a
random node compared to the case of the trap being on the node with the maximum
connectivity. For the latter case we find
\rho(t)\propto\exp\left[-At/N^\frac{\gamma-2}{\gamma-1}\av{k}\right] for all
, where is the exponent of the degree distribution
.Comment: Appendix adde
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
Dynamic correlations in an ordered c(22) lattice gas
We obtain the dynamic correlation function of two-dimensional lattice gas
with nearest-neighbor repulsion in ordered c(22) phase
(antiferromagnetic ordering) under the condition of low concentration of
structural defects. It is shown that displacements of defects of the ordered
state are responsible for the particle number fluctuations in the probe area.
The corresponding set of kinetic equations is derived and solved in linear
approximation on the defect concentration. Three types of strongly correlated
complex jumps are considered and their contribution to fluctuations is
analysed. These are jumps of excess particles, vacancies and flip-flop jumps.
The kinetic approach is more general than the one based on diffusion-like
equations used in our previous papers. Thus, it becomes possible to adequately
describe correlations of fluctuations at small times, where our previous theory
fails to give correct results. Our new analytical results for fluctuations of
particle number in the probe area agree well with those obtained by Monte Carlo
simulations.Comment: 10 pages, 7 figure
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