Coagulation dynamics under environmental noise: Scaling limit to SPDE

Dynamics of limit-cycle oscillators subject to general noise.

The phase description is a powerful tool for analyzing noisy limit-cycle oscillators. The method, however, has found only limited applications so far, because the present theory is applicable only to Gaussian noise while noise in the real world often has non-Gaussian statistics. Here, we provide the phase reduction method for limit-cycle oscillators subject to general, colored and non-Gaussian,...

Ja n 20 03 Scaling Limit , Noise , Stability

Linear functions of many independent random variables lead to classical noises (white, Poisson, and their combinations) in the scaling limit. Some singular stochastic flows and some models of oriented percolation involve very nonlinear functions and lead to nonclassical noises. Two examples are examined, Warren’s ‘noise made by a Poisson snake’ and the author’s ‘Brownian web as a black noise’. ...

The Scaling Attractor and Ultimate Dynamics for Smoluchowski's Coagulation Equations

We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski’s coagulation equation for the three simplest rate kernels K(x,y) = 2, x + y and xy. In another work, we classified all self-similar solutions and all universality classes (domains of attraction) for scaling limits under weak converg...

Dynamics and scaling in models of coarsening and coagulation

Clustering phenomena occur in numerous areas of science. This includes condensation at the nanoscale in condensed matter physics, smog and cloud formation in aerosol physics, processes of stellar and galactic clustering in astrophysics, random graph theory, and merging of lines of descent in ancestral trees. Some basic models of coagulation and aggregation take the form of rate equations for cl...

Extinction risk under coloured environmental noise