MONTE CARLO SIMULATION OF MULTIFOCAL STOCHASTIC SCANNING SYSTEM

Multifocal multiphoton microscopy(MMM)has greatly improved the utilization of excitationlight and imaging speed due to parallel multiphoton excitation of the samples and simultaneousdetection of the signals,which allows it to perform three-dimensional fast fuorescence imaging.Stochastic scanming can provide continuous,uniform and high-speed excitation of the sample,which makes it a suitable scanning scheme for MMM.In this paper,the graphical programminglanguage,LabVIEW is used to achieve stochastic scanning of the two-dimensional galvo scanmers by using white noise signals to control the a and y mirrors independently.Moreover,thestochastic scanning process is simulated by using Monte Carlo method.Our results show that MMM can avoid oversampling or subsampling in the scanning area and meet the requirements of uniform sampling by stochastically scanning the individual units of the N×N foci array.Therefore,continuous and umiform scaning in the whole field of view is implemented.

COUPLING EFFECT BETWEEN RELIABILITY OF BEDDING LAYER AND STABILITY OF DOWNSTREAM CONCRETE SLAB OF OVERFLOW EARTH-ROCK COFFERDAM

The protection of downstream concrete slab is a key issue for the stability of overflow earth-rock cofferdam. The coupling effect between bedding layer and concrete slab was taken into account when the stability of downstream concrete slab was researched. The characteristics of overflow and seepage over the downstream concrete slab were investigated when floodwater passes over the cofferdam. Firstly a limit equation of seepage failure for the bedding layer was derived with the consideration of geometric and mechanical factors, and a reliability model was established and numerically simulated. Then based on the reliability calculation for the bedding layer, the coupling effect between bedding layer and downstream concrete slab was analyzed. Under the most unfavorable pressure condition for the concrete slab, its instability criterion was put forward, which offers a structural design tool of downstream concrete slab for overflow earth-rock cofferdam. Compared with model tests, it shows that the model of reliability calculation of bedding layer and the stability analysis of downstream concrete slab are effective.

WEAK APPROXIMATION OF OBLIQUELY REFLECTED DIFFUSIONS IN TIME-DEPENDENT DOMAINS

In an earlier paper, we proved the existence of solutions to the Skorohod problem with oblique reflection in time-dependent domains and, subsequently, applied this result to the problem of constructing solutions, in time-dependent domains, to stochastic differential equations with oblique reflection. In this paper we use these results to construct weak approximations of solutions to stochastic differential equations with oblique reflection, in time-dependent domains in Rd, by means of a projected Euler scheme. We prove that the constructed method has, as is the case for normal reflection and time-independent domains, an order of convergence equal to 1/2 and we evaluate the method empirically by means of two numerical examples. Furthermore, using a well-known extension of the Feynman-Kac formula, to stochastic differential equations with reflection, our method gives, in addition, a Monte Carlo method for solving second order parabolic partial differential equations with Robin boundary conditions in time-dependent domains.

An Implicit Algorithm of Solving Nonlinear Filtering Problems

Nonlinear filter problems arise in many applications such as communications and signal processing.Commonly used numerical simulation methods include Kalman filter method,particle filter method,etc.In this paper a novel numerical algorithm is constructed based on samples of the current state obtained by solving the state equation implicitly.Numerical experiments demonstrate that our algorithm is more accurate than the Kalman filter and more stable than the particle filter.