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.     

Dynamics of energy transport in ternary molecular solids. II. Time evolution of naphthalene fluorescence

The spectrally resolved time-evolution of free and trapped singlet excitons was obtained at liquid-helium temperature for ternary crystals of perdeuteronaphthalene/naphthalene/betamethylnaphthalene (host/guest/supertrap). The naphthalene guest (donor) concentration varied between 0.30 and 0.99 mole fraction, while the supertrap (acceptor) concentrations were 10^?4–10^?5. At the lower guest concentrations (0.50 and below) the naphthalene-exciton decay time approaches the natural lifetime (≈ 122 ns). At higher concentrations, the decay is much shorter and extremely non-exponential. This behavior is inconsistent with simple homogeneous kinetics schemes that use a time-independent rate constant for energy transport. Above the percolation concentration (0.60 naphthalene) we fitted the experimental results with a random-flight-kinetic model, incorporating correlated random walks on the percolating guest cluster. The best fit was obtained for a “coherence length” (mean free path) of ≈ 10² lattice units. These results are in good agreement with previous steady-state studies on the same samples, and seem to indicate a partial coherence of the exciton transport in both pure and substitutionally disordered crystals at these low temperatures.     

Language time series analysis

We use the detrended fluctuation analysis (DFA) and the Grassberger–Proccacia analysis (GP) methods in order to study language characteristics. Despite that we construct our signals using only word lengths or word frequencies, excluding in this way huge amount of information from language, the application of GP analysis indicates that linguistic signals may be considered as the manifestation of a complex system of high dimensionality, different from random signals or systems of low dimensionality such as the Earth climate. The DFA method is additionally able to distinguish a natural language signal from a computer code signal. This last result may be useful in the field of cryptography.     

Stability and topology of scale-free networks under attack and defense strategies

We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an intentional attack with insufficient knowledge of the network. We determine, for all strategies, the critical fraction p(c) of nodes that must be removed for disintegrating the network. We find that, for an intentional attack, little knowledge of the well-connected sites is sufficient to strongly reduce p(c). At criticality, the topology of the network depends on the removal strategy, implying that different strategies may lead to different kinds of percolation transitions.     

Trapping without traps by correlated random walks

Correlated random walk of particles in the infinite cluster of percolating lattices in two dimensions is investigated. For infinitely strong forward correlations (no change of direction except at the boundaries) trapping of the particles in small regions of the infinite cluster is observed.