Discrete random walk

This jump length distribution corresponds to the nearest neighbor, discrete random walk of jump length /. 

For a symmetric, nearest neighbor discrete random walk, we obtain... 

From a probabilistic point of view, S (t) is the attractor for the rescaled particle position X (t). To understand this, consider first a discrete random walk. The rescaled position of a particle with jumps Z that are symmetric with respect to zero is Y = / J2 i=i with 0 < a < 2. We are interested in the limit n oo, such that the sequence T converges toward a new random variable Z in distribution,... 

T.3.6 Integral-Difference Equation and Discrete Random Walk... 

For a uniform and symmetric channel with a steady-state flux J of particles impinging at the channel entrance, the dynamics of the tracer particle is then described by the discrete random walk model defined in Eq. (46), with the transition matrix =r l-n.j )M.j=-r(2- n -nj.fi and 0 otherwise [80]. The resulting analytical expressions are cumbersome, and the outcomes are summarized in Fig. 3. 

It is usually sufficient to update the DPM source terms during the calculation after every fiftieth continuous phase iteration. The parcels should be tracked for at most 100 000 steps, applying the discrete random walk model for stochastic tracking with 10 tries at a time scale constant of approximately 0.15. For the... 

In order to study the peripheral classification we injected a particle with zero velocity through the upper orifice near the chamber axis. For all our computations we used Discrete Random Walk Tracking (DRWT) option of Fluent code to take into account the influence of air velocity random component, caused by turbulence (k-e model), on particle trajectories. In Fig. 4, for example, one can see calculated trajectories for particles with various sizes. Large (200 pm ) particles move along the complex polygonal trajectory (Fig. 4-... 

Coppersmith et al. identified two distinctly different results from this model. The simplest case, which they termed the critical o,i limit, involved particles distributing either all or none of their load to a particular neighbor below. That is, the random variables were either 0 (no load transmitted) or 1 (all load transmitted). This is formally equivalent to a discrete random walk, with paths from particles above coalescing as they move downward. In this limit they did indeed find a power-law scaling of the weight distribution function with depth, with... 

In RANS-based simulations, the focus is on the average fluid flow as the complete spectrum of turbulent eddies is modeled and remains unresolved. When nevertheless the turbulent motion of the particles is of interest, this can only be estimated by invoking a stochastic tracking method mimicking the instantaneous turbulent velocity fluctuations. Various particle dispersion models are available, such as discrete random walk models (among which the eddy lifetime or eddy interaction model) and continuous random walk models usually based on the Langevin equation (see, e.g.. Decker and... 

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