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The hitting time, which refers to the time required to find the marked element in the search algorithm, is one of the most interesting properties of quantum walk. In this paper we briefly analyze the hitting time on a finite 2D lattice in the classical case, focusing on the quantum version of the hitting time and give specific expressions for each. It is well known that the quantum hitting time has the same order as the square of the classical case, and our work also happens to verify this particular property. [ABSTRACT FROM AUTHOR]

The existing interacting multiple model (IMM) suffers from two problems when tracking an underwater maneuvering target: 1) the conventional nonlinear filters in IMM cannot work on the condition of delayed measurement, 2) the inefficiency of model switching in IMM may degrade the tracking performance. In order to handle the delayed measurement, a novel Bayesian filter framework under two Gaussian assumptions is proposed. The new extended Kalman filter (EKF) and unscented Kalman filter (UKF) are developed as two variations of the proposed filter. In addition, to solve the problem of low switching efficiency between IMM models, a transfer probability corrected function is designed to adaptively update the transfer probability matrix (TPM) in IMM. The simulation results show that the proposed algorithm outperforms the existing IMM-EKF and IMM-UKF. • This paper investigates the problem of underwater maneuvering target tracking with one-step randomly delayed measurements. • We construct a new augmented state vector including target state and measurement noise information. • Under Gaussian assumptions, a novel Bayesian filter framework with delayed measurement is proposed. • A new extended Klaman filter and unscented Kalman filter with randomly delayed measurements are evaluated. • A new function is proposed to update the transfer probability matrix in interacting multiple model. [ABSTRACT FROM AUTHOR]

A stochastic model was developed to describe the liquid radial dispersion in a trickle-bed reactor, which has conventionally been modeled by the effective diffusion model. To establish the stochastic model, the column was divided into some layers of particles in the axial direction and several annulus rings in each layer in the radial direction. The liquid spreading was regarded as a fluid transport process and the matrix of transfer probability was derived based on the coordinates of the particle network in the cross-section of the column. With this transfer probability matrix and the initial liquid distribution, the liquid distribution in the downstream was predicted. In order to evaluate the model parameters, experimental data of the liquid dispersion were obtained from electrical capacitance tomography images and tracer injection. Good agreement was obtained between the stochastic model and the experimental liquid distribution data. [ABSTRACT FROM AUTHOR]