Issue No. 03 - May/June (2006 vol. 8)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/MCSE.2006.43
Grant Lythe , University of Leeds
Salman Habib , Los Alamos National Laboratory
Kinks are examples of "coherent structures": clearly identifiable localized features in a noisy, spatially-extended system that can be followed as they move about under the influence of fluctuations. The authors study kinks in stochastic partial differential equations, where a steady-state mean density is dynamically maintained: kinks and antikinks are nucleated in pairs, follow Brownian paths, and annihilate on meeting. Current computers can attain sufficient resolution to perform direct comparisons with predictions for the steady state, and work at sufficiently low temperatures to unambiguously locate kinks and identify nucleation events. In order to perform precise comparison between numerical and exact results at finite temperature, it is important to use the exact correlation length and not a low-temperature approximation. Numerical convergence of thermodynamic properties, where analytical results are available, makes it possible to proceed with confidence to an exploration of the fascinating stochastic dynamics of kinks.
noise, signal interaction, numerics, kinks, partial differential equations
G. Lythe and S. Habib, "Kink Stochastics," in Computing in Science & Engineering, vol. 8, no. , pp. 10-15, 2006.