Stratified random walks on the n-cube

In this paper we present a method for analyzing a general class of random walks on the n-cube (and certain subgraphs of it). These walks all have the property that the transition probabilities depend only on the level of the point at which the walk is. For these walks, we derive sharp bounds on their mixing rates, i.e., the number of steps required to guarantee that the resulting distribution is close to the (uniform) stationary distribution. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 199–222, 1997     

Graphene sensing an inhomogeneous strain due to the surface relief in FeNiCoTi shape memory alloy

In this paper, we present a novel method of using graphene for sensing the inhomogeneous strain due to the surface relief in FeNiCoTi shape memory alloy. In the experiment, a large sheet of graphene fabricated by chemical vapor deposition was transferred onto the FeNiCoTi substrate. The flat surface of the substrate would become wrinkled due to the surface relief formed during the FeNiCoTi substrate phase transformation, meanwhile loading a tensile strain on the surface graphene. It is found that the 2D Raman peak of graphene demonstrates a significant red shift due to the tensile strain. The different colors exhibited in the Raman mapping image of the graphene directly displayed the strain distribution information across the surface. In the future, we may alter to quantitatively analyze the surface relief by using Raman spectroscopy instead of the atomic force microscopy. Copyright © 2013 John Wiley & Sons, Ltd.