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Register a new userModeling self-organization of nano-size vacancy clusters in stochastic systems subjected to irradiation
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A study of the self-organization of vacancy clusters in irradiated materials is presented. Using a continuum stochastic model we take into account dynamics of point defects and their sinks with elastic interactions of vacancies. Dynamics of vacancy clusters formation is studied analytically and numerically under conditions related to irradiation in both reactors and accelerators. We have shown a difference in patterning dynamics and studied the external noise influence related to fluctuation in a defect production rate. Applying our approach to pure nickel irradiated under different conditions we have shown that vacancy clusters having a linear size 6 nm can arrange in statistical periodic structure with nano-meter range. We have found that linear size of vacancy clusters at accelerator conditions decreases down to 20%, whereas a period of vacancy clusters reduces to 6.5%.
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The occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with emphasis on the analytical formulation of the problem as well as a possible analytical derivation of key quantifiers of stochastic resonance. The nonlinear Fokker-Planck equation describing the system dynamics, together with the corresponding Ito-Langevin equation, are formulated. In the linear-response regime analytical expressions of the spectral amplification, of the signal-to-noise ratio and of the hysteresis loop area are derived as quantifiers of stochastic resonance. These quantifiers are found to be strongly dependent on the parameters controlling the type of diffusion, in particular the peak characterizing the signal-to-noise ratio occurs only in close ranges of parameters. Results introduce the relevant information that taking into consideration the interactions of anomalous diffusive systems with a periodic signal, can provide a better understanding of the physics of stochastic resonance in bistable systems driven by periodic forces.
A nonadditive generalization of Klimontovichs S-theorem [G. B. Bagci, Int.J. Mod. Phys. B 22, 3381 (2008)] has recently been obtained by employing Tsallis entropy. This general version allows one to study physical systems whose stationary distributions are of the inverse power law in contrast to the original S-theorem, which only allows exponential stationary distributions. The nonadditive S-theorem has been applied to the modified Van der Pol oscillator with inverse power law stationary distribution. By using nonadditive S-theorem, it is shown that the entropy decreases as the system is driven out of equilibrium, indicating self-organization in the system. The allowed values of the nonadditivity index $q$ are found to be confined to the regime (0.5,1].
A simple periodically driven system displaying rich behavior is introduced and studied. The system self-organizes into a mosaic of static ordered regions with three possible patterns, which are threaded by one-dimensional paths on which a small number of mobile particles travel. These trajectories are self-avoiding and non-intersecting, and their relationship to self-avoiding random walks is explored. Near $rho=0.5$ the distribution of path lengths becomes power-law like up to some cutoff length, suggesting a possible critical state.
We study the dynamics of exchange value in a system composed of many interacting agents. The simple model we propose exhibits cooperative emergence and collapse of global value for individual goods. We demonstrate that the demand that drives the value exhibits non Gaussian fat tails and typical fluctuations which grow with time interval with a Hurst exponent of 0.7.
Scale-free outbursts of activity are commonly observed in physical, geological, and biological systems. The idea of self-organized criticality (SOC), introduced back in 1987 by Bak, Tang and Wiesenfeld suggests that, under certain circumstances, natural systems can seemingly self-tune to a critical state with its concomitant power-laws and scaling. Theoretical progress allowed for a rationalization of how SOC works by relating its critical properties to those of a standard non-equilibrium second-order phase transition that separates an active state in which dynamical activity reverberates indefinitely, from an absorbing or quiescent state where activity eventually ceases. Here, we briefly review these ideas as well as a recent closely-related concept: self-organized bistability (SOB). In SOB, the very same type of feedback operates in a system characterized by a discontinuos phase transition, which has no critical point but instead presents bistability between active and quiescent states. SOB also leads to scale-invariant avalanches of activity but, in this case, with a different type of scaling and coexisting with anomalously large outbursts. Moreover, SOB explains experiments with real sandpiles more closely than SOC. We review similarities and differences between SOC and SOB by presenting and analyzing them under a common theoretical framework, covering recent results as well as possible future developments. We also discuss other related concepts for imperfect self-organization such as self-organized quasi-criticality and self-organized collective oscillations, of relevance in e.g. neuroscience, with the aim of providing an overview of feedback mechanisms for self-organization to the edge of a phase transition.
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