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Full-Text Articles in Physical Sciences and Mathematics
Extinction Transitions In Correlated External Noise, Alexander H. O. Wada, Matthew Small, Thomas Vojta
Extinction Transitions In Correlated External Noise, Alexander H. O. Wada, Matthew Small, Thomas Vojta
Physics Faculty Research & Creative Works
We analyze the influence of long-range correlated (colored) external noise on extinction phase transitions in growth and spreading processes. Uncorrelated environmental noise (i.e., temporal disorder) was recently shown to give rise to an unusual infinite-noise critical point [Europhys. Lett. 112, 30002 (2015)EULEEJ0295-507510.1209/0295-5075/112/30002]. It is characterized by enormous density fluctuations that increase without limit at criticality. As a result, a typical population decays much faster than the ensemble average, which is dominated by rare events. Using the logistic evolution equation as an example, we show here that positively correlated (red) environmental noise further enhances these effects. This means, the correlations accelerate …
Fractional Brownian Motion With A Reflecting Wall, Alexander H. O. Wada, Thomas Vojta
Fractional Brownian Motion With A Reflecting Wall, Alexander H. O. Wada, Thomas Vojta
Physics Faculty Research & Creative Works
Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. Whereas the mean-square displacement of the particle shows the expected anomalous diffusion behavior (x2) ~ tα, the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case α > 1, the particles accumulate at the barrier leading to a divergence of the …