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Understanding the functional dynamics of the mammalian brain is one of the central aims of modern neuroscience. Mathematical modeling and computational simulations of neural networks can help in this quest. In recent publications, a multilevel model has been presented to simulate the resting-state dynamics of the cortico-cortical connectivity of the mammalian brain. In the present work we investigate how much of the dynamical behavior of the multilevel model can be reproduced by a strongly simplified model. We find that replacing each cortical area by a single Rulkov map recreates the patterns of dynamical correlation of the multilevel model, while the outcome of other models and setups mainly depends on the local network properties, e. g. the input degree of each vertex. In general, we find that a simple simulation whose dynamics depends on the global topology of the whole network is far from trivial. A systematic analysis of different dynamical models and coupling setups is required.
A new approach for efficient second-harmonic generation using diode lasers is presented. The experimental setup is based on a tapered amplifier operated in a ring resonator that is coupled to a miniaturized enhancement ring resonator containing a periodically poled lithium niobate crystal. Frequency locking of the diode laser emission to the resonance frequency of the enhancement cavity is realized purely optically, resulting in stable, single-frequency operation. Blue light at 488 nm with an output power of 310 mW is generated with an optical-to-optical conversion efficiency of 18%.
The formation of different micro- and nanostructures during the chemical synthesis of polypyrrole is reviewed shortly based on the conceptions of hard- and soft-templating models. Contrary to other models that emphasize the role of micelles it is found here that during the oxidative polymerization of pyrole using sulfonic acid dopants a crystalline hard template is found in the first steps of the reaction before the addition of the oxidant. This template is formed by a complex consisting of 2,5-bis(pyrrole-2-yl)pyrrolidine and the sulfonic acid anion. The acid catalyzed formation of this specific tripyrrole is discussed. (C) 2009 Elsevier B.V. All rights reserved.
An effective dynamical description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by the stochastic phase oscillators invariant probability density or its first passage times. Using the first approach the effective phase exhibits the correct frequency and invariant distribution density, whereas the second approach models the proper phase resetting curve. The discrepancy of the effective models is most pronounced for noise-induced oscillations and is related to non-monotonicity of the stochastic phase variable due to fluctuations.
Human comment is studied using data from 'tianya' which is one of the most popular on-line social systems in China. We found that the time interval between two consecutive comments on the same topic, called inter-event time, follows a power-law distribution. This result shows that there is no characteristic decay time on a topic. It allows for very long periods without comments that separate bursts of intensive comments. Furthermore, the frequency of a different ID commenting on a topic also follows a power-law distribution. It indicates that there are some "hubs" in the topic who lead the direction of the public opinion. Based on the personal comments habit, a model is introduced to explain these phenomena. The numerical simulations of the model fit well with the empirical results. Our findings are helpful for discovering regular patterns of human behavior in on-line society and the evolution of the public opinion on the virtual as well as real society.
We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations.
Superexponential droplet fractalization as a hierarchical formation of dissipative compactons
(2010)
We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hilliard equation. The evolution leads to a fractalization into smaller and smaller scales. We demonstrate that a primitive element in the appearing hierarchical structure is a dissipative compacton. Both direct simulations and the analysis of a self-similar solution show that the compactons appear at superexponentially decreasing scales, which means vanishing dimension of the fractal.