We consider some basic properties of random walks on a simple ladder including the first and the second moments, the probability of returning to the starting site, the probability of ever reaching a given site, the conditional mean first-passage time to a given site and the expected number of distinct sites visited. These basic properties provide us a great deal of information about mobility, diffusivity and exploration of the random walker. We study these properties by using two different approaches, i.e., the Roerdink and Shuler’s approach and the direct generating function approach. Most of the results are identical to those for one-dimensional lattice except for a renormalization of coefficients.
In this paper, we study phase-ordering dynamics of 2d Ising model under influence of oscillatory shear by computer simulation. We focus on the time evolution of the equal-time correlation functions to test the dynamical scaling hypothesis and to determine the governing growth laws. We find that at late times the system has two different behaviours which are a non-shear behaviour and a uniformly sheared behaviour. Initial phases and frequencies of oscillatory shear determine the behaviour of the system. On one hand, if the frequency is high, the system behaves as if it is not under shear. On the other hand, if the frequency is approached zero, the behaviour of the system will be determined by the initial phase of oscillatory shear. At the initial phase of 90 degree (or 270 degree), the system also behaves as if it is not under shear. Otherwise, the system behaves as if it is under uniform shear (Oscillatory shear is in the form of cosine function).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.