Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.

Effects of Particle Size on Dilute Particle Dispersion in a Karman Vortex Street Flow

It is shown that in a Karman vortex street flow, particle size influences the dilute particle dispersion. Together with an increase of the particle size, there is an emergence of a period-doubling bifurcation to a chaotic orbit, as well as a decrease of the corresponding basins of attraction. A crisis leads the attractor to escape from the central region of flow. In the motion of dilute particles, a drag term and gravity term dominate and result in a bifurcation phenomenon.

A Constrained Particle Dynamics for Continuum-Particle Hybrid Method in Micro- and Nano-Fluidics

A hybrid method of continuum and particle dynamics is developed for micro- and nano-fluidics, where fluids are described by a molecular dynamics (MD) in one domain and by the Navier-Stokes (NS) equations in another domain. In order to ensure the continuity of momentum flux, the continuum and molecular dynamics in the overlap domain are coupled through a constrained particle dynamics. The constrained particle dynamics is constructed with a virtual damping force and a virtual added mass force. The sudden-start Couette flows with either non-slip or slip boundary condition are used to test the hybrid method. It is shown that the results obtained are quantitatively in agreement with the analytical solutions under the non-slip boundary conditions and the full MD simulations under the slip boundary conditions.

Modified Generalized Beam Lattice Model Associated With Fracture Of Reinforced Fiber/Particle Composites

Lattice-type model can simulate in a straightforward manner heterogeneous brittle media. Mohr-Coulomb failure criterion has recently been involved into the generalized beam (GB) lattice model, and as a result, numerical experiments on concrete under various loading conditions can be conducted. The GB lattice model is further used to investigate the reinforced fiber/particle composites instead of only particle composites as the model did before. Numerical examples are given to show the effectiveness of the modeling procedure, and influences of inclusions (particle, fiber and rebar) on the fracture processes are also discussed. (c) 2008 Elsevier Ltd. All rights reserved.

Experimental Investigation Of Particle Velocity Distributions In Windblown Sand Movement

With the PDPA (Phase Doppler Particle Analyzer) measurement technology, the probability distributions of particle impact and lift-off velocities on bed surface and the particle velocity distributions at different heights are detected in a wind tunnel. The results show that the probability distribution of impact and lift-off velocities of sand grains can be expressed by a log-normal function, and that of impact and lift-off angles complies with an exponential function. The mean impact angle is between 28 degrees and 39 degrees, and the mean lift-off angle ranges from 30 degrees to 44 degrees. The mean lift-off velocity is 0.81-0.9 times the mean impact velocity. The proportion of backward-impacting particles is 0.05-0.11, and that of backward-entrained particles ranges from 0.04 to 0.13. The probability distribution of particle horizontal velocity at 4 mm height is positive skew, the horizontal velocity of particles at 20 mm height varies widely, and the variation of the particle horizontal velocity at 80 mm height is less than that at 20 mm height. The probability distribution of particle vertical velocity at different heights can be described as a normal function.

An Efficient Front-Tracking Method For Fully Nonlinear Interfacial Waves

A fully nonlinear and dispersive model within the framework of potential theory is developed for interfacial (2-layer) waves. To circumvent the difficulties arisen from the moving boundary problem a viable technique based on the mixed Eulerian and Lagrangian concept is proposed: the computing area is partitioned by a moving mesh system which adjusts its location vertically to conform to the shape of the moving boundaries but keeps frozen in the horizontal direction. Accordingly, a modified dynamic condition is required to properly compute the boundary potentials. To demonstrate the effectiveness of the current method, two important problems for the interfacial wave dynamics, the generation and evolution processes, are investigated. Firstly, analytical solutions for the interfacial wave generations by the interaction between the barotropic tide and topography are derived and compared favorably with the numerical results. Furthermore simulations are performed for the nonlinear interfacial wave evolutions at various water depth ratios and satisfactory agreement is achieved with the existing asymptotical theories. (c) 2008 Elsevier Inc. All rights reserved.