This paper shows an analysis ofMEM S （micro electro mechanical systems） due to Lorentz force and mechanical shock. The formulation is based on a modified couple stress theory, the von Karman geometric nonlinearity a...This paper shows an analysis ofMEM S （micro electro mechanical systems） due to Lorentz force and mechanical shock. The formulation is based on a modified couple stress theory, the von Karman geometric nonlinearity and Reynolds equation as well. The model contains a silicon microbeam, which is encircled by a stationary plate. The non-dimensional governing equations and associated boundary conditions are then solved iteratively through the Galerkin weighted method. The results show that pull-in voltage is dependent on the geometry nonlinearity. It is also demonstrated that by increasing voltage between the silicon microbeam and stationary plate, the pull-in instability happens.展开更多
In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple proof of the conclusion that every stationary Markov process is a generalized convex combinatio...In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple proof of the conclusion that every stationary Markov process is a generalized convex combination of stationary ergodic Markov processes. A direct consequence is that a stationary distribution of a Markov process is extremal if and only if the corresponding stationary Markov process is time ergodic and every stationary distribution is a generalized convex combination of such extremal ones. We then consider space ergodicity for spin flip particle systems. We prove space shift ergodicity and mixing for certain extremal invariant measures for a class of spin systems, in which most of the typical models, such as the Voter Models and the Contact Models, are included. As a consequence of these results we see that for such systems, under each of those extremal invariant measures, the space and time means of an observable coincide, an important phenomenon in statistical physics. Our results provide partial answers to certain interesting problems in spin systems.展开更多
文摘This paper shows an analysis ofMEM S （micro electro mechanical systems） due to Lorentz force and mechanical shock. The formulation is based on a modified couple stress theory, the von Karman geometric nonlinearity and Reynolds equation as well. The model contains a silicon microbeam, which is encircled by a stationary plate. The non-dimensional governing equations and associated boundary conditions are then solved iteratively through the Galerkin weighted method. The results show that pull-in voltage is dependent on the geometry nonlinearity. It is also demonstrated that by increasing voltage between the silicon microbeam and stationary plate, the pull-in instability happens.
基金the National Natural Science Foundation of China (Grant No. 10071008).
文摘In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple proof of the conclusion that every stationary Markov process is a generalized convex combination of stationary ergodic Markov processes. A direct consequence is that a stationary distribution of a Markov process is extremal if and only if the corresponding stationary Markov process is time ergodic and every stationary distribution is a generalized convex combination of such extremal ones. We then consider space ergodicity for spin flip particle systems. We prove space shift ergodicity and mixing for certain extremal invariant measures for a class of spin systems, in which most of the typical models, such as the Voter Models and the Contact Models, are included. As a consequence of these results we see that for such systems, under each of those extremal invariant measures, the space and time means of an observable coincide, an important phenomenon in statistical physics. Our results provide partial answers to certain interesting problems in spin systems.
