Reduced-order modeling of three-dimensional unsteady partial cavity flows

An efficient reduced-order modeling to analyze three-dimensional unsteady partial cavity flows is proposed. The proposed approach is based on the boundary element method along with the potential flow assumption. To this end, a novel non-iterative method based on the flow eigenmodes of three-dimensional partial cavity flows is applied. Eigenanalysis and reduced-order modeling for unsteady flows over a three-dimensional hydrofoil with various sections are performed. The results obtained from the present analysis are compared with those reported in the literature to verify the strength of the proposed approach. In order to examine the performance of the introduced algorithm for unsteady cavitating flows, various simulations for several reduced frequencies, hydrofoil geometries and different cavitation numbers are also investigated. Comparison between the obtained results using the novel and conventional methods indicates that the present algorithm works very well with sufficient accuracy. Moreover, it is shown that the proposed method is computationally more efficient than the conventional ones for unsteady sheet cavitation analysis on three-dimensional hydrofoils.     

An eigenanalysis-based bifurcation indicator proposed in the framework of a reduced-order modeling technique for non-linear structural analysis

The Koiter–Newton method is a reduced order modeling technique which allows us to trace efficiently the entire equilibrium path of a non-linear structural analysis. In the framework of buckling the method is capable to handle snap-back and snap-through phenomena but may fail to predict reliably bifurcation branches along the equilibrium path. In this contribution we extend the original Koiter–Newton approach with a reliable and accurate bifurcation indicator which is based on an eigenanalysis of the reduced order tangent stiffness matrix. The proposed indicator has a negligible numerical effort since all computations refer to the reduced order model which is typically of very small dimension. The extension allows the identification of bifurcation points and a tracing of corresponding bifurcation branches in each sector of the equilibrium path. The performance of the method in terms of reliability, accuracy and computational effort is demonstrated with several examples.     

First Hitting Time Analysis of the Independence Metropolis Sampler

In this paper, we study a special case of the Metropolis algorithm, the Independence Metropolis Sampler (IMS), in the finite state space case. The IMS is often used in designing components of more complex Markov Chain Monte Carlo algorithms. We present new results related to the first hitting time of individual states for the IMS. These results are expressed mostly in terms of the eigenvalues of the transition kernel. We derive a simple form formula for the mean first hitting time and we show tight lower and upper bounds on the mean first hitting time with the upper bound being the product of two factors: a “local” factor corresponding to the target state and a “global” factor, common to all the states, which is expressed in terms of the total variation distance between the target and the proposal probabilities. We also briefly discuss properties of the distribution of the first hitting time for the IMS and analyze its variance. We conclude by showing how some non-independence Metropolis–Hastings algorithms can perform better than the IMS and deriving general lower and upper bounds for the mean first hitting times of a Metropolis–Hastings algorithm.     

Automatic mapping and modeling of human networks

Mobile telephones, company ID badges, and similar common devices form a sensor network which can be used to map human activity, and especially human interactions. The most informative sensor data seem to be measurements of person-to-person proximity, and statistics of vocalization and body movement measurements. Using this data to model individual behavior as a stochastic process allows prediction of future activity, with the greatest predictive power obtained by modeling the interactions between individual processes. Experiments show that between 40% and 95% of the variance in human behavior may be explained by such models.