We report on recent developments concerning adaptive finite particle methods, which are used for the numerical simulation of multiscale phenomena in time-dependent evolution processes. The proposed concept relies on a finite volume approach, which we combine with WENO reconstruction from particle average values. In this method, polyharmonic splines are key tools for both the optimal recovery fr...

We investigate an N-particle Bose-Hubbard dimer with an additional effective decay term in one of the sites. A mean-field approximation for this non-Hermitian many-particle system is derived, based on a coherent state approximation. The resulting nonlinear, non-Hermitian two-level dynamics, in particular, the fixed point structures showing characteristic modifications of the self-trapping trans...

Particle filter algorithms are widely used for object tracking in video sequences, but the standard particle filter algorithm cannot solve the validity of particles ideally. To solve the problems of particle degeneration and sample impoverishment in a particle filter tracking algorithm, an improved object tracking algorithm is proposed, which combines ...

As a stochastic model for quantum mechanics we present a stationary quantum Markov process for the time evolution of the Wigner function on a lattice phase space Z N ×Z N with N odd. By introducing a phase factor extension to the phase space, each particle can be treated independently. This is an improvement on earlier methods that require the whole distribution function to determine the evolut...

This paper addresses optimal estimation for time varying autoregressive (TVAR) models. First, we propose a statistical model on the time evolution of the frequencies, moduli and real poles instead of a standard model on the AR coefficients as it makes more sense from a physical viewpoint. Second, optimal estimation involves solving a complex optimal filtering problem which does not admit any cl...

We study a general class of translation invariant quantum Markov evolutions for a particle on Z. We assume locality of the spatial jumps and exponentially fast relaxation in momentum space. It is shown that the particle position diffuses in the long time limit. We employ a fiber decomposition in momentum space of the evolution made possible by the translation invariance of the dynamics. A centr...

The dynamical evolution of a two-site Hubbard model is derived in the presence of an uniform external magnetic field for a general initial state. The time evolution of the half-filled (two-particle) case has a complex behaviour. Under certain initial conditions, the average number of fermions in one-particle state, in the half-filled case, is not necessarily periodic, even though the magnetizat...

First results from RHIC on charged multiplicities, evolution of multiplicities with central-ity, particle ratios and transverse momentum distributions in central and minimum bias collisions , are analyzed in a string model which includes hard collisions, collectivity in the initial state considered as string fusion, and rescattering of the produced secondaries. Multiplici-ties and their evoluti...

The evolution of beam phase space in ionization injection into plasma wakefields is studied using theory and particle-in-cell simulations. The injection process involves both longitudinal and transverse phase mixing, leading initially to a rapid emittance growth followed by oscillation, decay, and a slow growth to saturation. An analytic theory for this evolution is presented and verified throu...

The reactive power planning and dispatch problems have been solved using Genetic algorithm (GA), Differential evolution (DE) and Particle Swarm Optimization (PSO) technique in order to have a comparative study on the performance of these algorithms. It has been found that Differential evolution performs best followed by the Particle swarm optimization. Both DE and PSO can perform well even with...