researchers from the national university of singapore (nus) have developed an efficient numerical method, called the string method, for the study of complex energy landscapes and noise-induced rare events, according to a report from the university.

figure 1 shows the isotropic phase (left) and the nematic phase (right) of
liquid crystal. (w. ren/national university of singapore)

rare events are transitions from one state to another, which are limited by energy barriers existing between metastable states. when rare events happen, they are generally quick and important and there is typically a small amount of noise in the system that drives the events.

the idea behind this new mathematical model is “to evolve a string, which is a curve parameterized by its arc-length, in the path space by steepest descent-like dynamics. after the dynamics reach the steady state, the string converges to the minimum energy path, i.e. the transition path of maximum likelihood, and locates the transition state and the energy barriers.”

scientists have applied the method successfully to micro-magnetics, conformational changes of bio-molecules, dislocation dynamics in crystalline solids, the wetting transition on solid surfaces patterned with microstructures and more.

most recently, the researchers applied string method to study the isotropic-nematic phase transition in liquid crystals.

“they computed the minimum free energy path using the string method and studied the structure of the transition state,” according to the article. “their results revealed the multilayer structure of the critical nucleus. the nucleus grows further and evolves to the nematic phase after it crosses the energy barrier.”

the latest research has been accepted for publication in communications in computational physics. previous research on the subject was published in the journal of chemical physics in 2007. that article can be found at http://aip.scitation.org/doi/10.1063/1.2720838.