Experimental observations show that the random process of two-phase flow behind an aerator is an ergodic process and its amplitude distribution is similar to a normal distribution. The maximum pressure fluctuation is ...Experimental observations show that the random process of two-phase flow behind an aerator is an ergodic process and its amplitude distribution is similar to a normal distribution. The maximum pressure fluctuation is at the re-attachment point where the jet-trajectory flow over the aerator re-attaches to the bottom of the channel, and its amplitude is 2—3 times larger than when there is no aerator. There is a dominant frequency of 1.24 Hz in the model, but the coherence in the frequency domain is not obvious for other frequencies beside the dominant frequency. There is a large vortex at the re-attachment point behind the aerator but correlation among the measurement points is not obvious in the time domain.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Experimental observations show that the random process of two-phase flow behind an aerator is an ergodic process and its amplitude distribution is similar to a normal distribution. The maximum pressure fluctuation is at the re-attachment point where the jet-trajectory flow over the aerator re-attaches to the bottom of the channel, and its amplitude is 2—3 times larger than when there is no aerator. There is a dominant frequency of 1.24 Hz in the model, but the coherence in the frequency domain is not obvious for other frequencies beside the dominant frequency. There is a large vortex at the re-attachment point behind the aerator but correlation among the measurement points is not obvious in the time domain.
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.
