Computer particles

One of the recent advances in magnetic studies is that it enables not only the estimation of the average volume v of clusters from the LF and HF approximations of the Langevln function, but also enables to compute particle size distribution based on an assumed function. By judiciously combining the parameters of the Langevln and of the "log normal function, we obtained a particle (cluster) size distribution of Y Fe203 in ZSM-5. The essential features of such computation are shown in Fig. 6. 

A complete model for the description of plasma deposition of a-Si H should include the kinetic properties of ion, electron, and neutral fluxes towards the substrate and walls. The particle-in-cell/Monte Carlo (PIC/MC) model is known to provide a suitable way to study the electron and ion kinetics. Essentially, the method consists in the simulation of a (limited) number of computer particles, each of which represents a large number of physical particles (ions and electrons). The movement of the particles is simply calculated from Newton s laws of motion. Within the PIC method the movement of the particles and the evolution of the electric field are followed in finite time steps. In each calculation cycle, first the forces on each particle due to the electric field are determined. Then the... 

In the second method, i.e., th particle method 546H5471 a spray is discretized into computational particles that follow droplet characteristic paths. Each particle represents a number of droplets of identical size, velocity, and temperature. Trajectories of individual droplets are calculated assuming that the droplets have no influence on surrounding gas. A later method, 5481 that is restricted to steady-state sprays, includes complete coupling between droplets and gas. This method also discretizes the assumed droplet probability distribution function at the upstream boundary, which is determined by the atomization process, by subdividing the domain of coordinates into computational cells. Then, one parcel is injected for each cell. 

Transport control of flocculation is realized in an especially direct way in the process known as diffusion-limited cluster-cluster aggregation5 (aggregation as used in this term means flocculation in the present chapter). In this process, which is straightforward to simulate and visualize on a computer, particles undergo Brownian motion (i.e., diffusion) until they come together in close proximity, after which they coalesce instantaneously and irreversibly to form floccules (or clusters ). The clusters then diffuse until they contact one another and combine to form larger clusters, and so on, until gravitational... 

Fig. 17. Flow model study for a three-stage fluidized leacher—comparison of computed particle size (solid lines) with experimental results (open circles). [After Kwauk and Wang, 1981.]...

Methods that calculate average polymer properties without the DRI are significant because they circumvent complications that arise from the measurement of the interdetector volume between the light-scattering and concentration detectors 10, 11). It is necessary, however, that each local signal,, be divided by the computed particle scattering function, P 6)i. 

A list of typical dependent and independent variables for a furnace simulation is shown in Table VI. Coal particles typically are treated in a procedure that couples the continuum (Eulerian or fixed reference fame) gas-phase grid and the discrete (Lagrangian or moving reference frame) particles. Numerical solutions are repeated until the gas flow field is converged for the computed particle source terms, radiative fluxes, and gaseous reactions. Lagrangian particle trajectories are then calculated. After solving all particle-class trajectories, the new source terms... 

In their original work, O Rourke and coworkers [17, 20] injected parcels from the injector, resulting in a much fewer number of tracked computational particles. In this work, the parcel model is further extended to a hybrid particle-parcel scheme [33]. The basic idea behind the hybrid approach is as follows. At every... 

Basciano CA (2010) Computational particle-hemodynamics analysis applied to an abdominal aortic aneurysm with thrombus and microspheretargeting of liver tumors. Ph.D. dissertation. North Carolina State University, Department of Mechanical and Aerospace Engineering, Raleigh... 

Computed particle tracking in the CRD mixer with a high Ap simulated across the mixing section... 

Figure 12.52 Computed particle tracking in one repeating unit of the SMX static mixer...

Figure 12.55 Computed particle tracking in one module of the Dispersive/ Distributive Static Mixer using BEM...

Figure 6 Diagram of the Microtrac UFA light path, data collection, and analysis. As with diffraction, the computer plays a vital role in controlling the measurement, collecting the signals and performing specialized analysis of the raw signals to provide a particle size distribution. Computed particle size distributions are printed and/or communicated to computer data storage media.

Interestingly, Rajamani and Milin found no need to iterate for feed concentrations up to 20% by weight where clean water velocity profiles were used and the separation results compared well with experiments (limestone in water, in a 75 mm hydrocyclone). This is due to the fast dilution process taking place in the flow as pointed out in section 1.4. Only for concentrations above 20% by weight the authors needed to iterate the computations the first iteration of particle trajectories is done with the values of water viscosity and density, from which particle concentrations (and slurry viscosities and densities) are computed at each point. For this the authors use computed particle trajectories and assume that the concentration is proportional to particle residence time in each computational cell. 

In a lattice gas, computational particles are allowed to move on a lattice according to certain rules. The lattice may be either two or three dimensional. By considering a hexagonal lattice, Frisch et al. [109] showed that one could obtain solutions of the two-dimensional Navier-Stokes equation by suitable averaging of the lattice gas solutions for appropriate collision rules. Their work was extended to three dimensions by d Humieres et al [110] who considered a projection of the four-dimensional face-centered-hyper-cubic (FCHC) lattice. 

The LBM is similar to the LGA in that one performs simulations for populations of computational particles on a lattice. It differs from the LGA in that one computes the time evolution of particle distribution functions. These particle distribution functions are a discretized version of the particle distribution function that is used in Boltzmann s kinetic theory of dilute gases. There are, however, several important differences. First, the Boltzmann distribution function is a function of three continuous spatial coordinates, three continuous velocity components, and time. In the LBM, the velocity space is truncated to a finite number of directions. One popular lattice uses 15 lattice velocities, including the rest state. The dimensionless velocity vectors are shown in Fig. 66. The length of the lattice vectors is chosen so that, in one time step, the population of particles having that velocity will propagate to the nearest lattice point along the direction of the lattice vector. If one denotes the distribution function for direction i by fi x,t), the fluid density, p, and fluid velocity, u, are given by... 

As a newly emerging field, e-textiles impose new challenges not only on modeling and analysis but also on simulation tools used for validation. The issue of concurrency is the fundamental problem in order to effieiently map complex apphcations onto e-textiles. As e-textiles contain many computational particles distributed on large surfaces, it is of crucial importance to expose the entire eonemrenc available at application level. 

To perform a computation, particles are injected by an outside agent at different speeds at the ends of the lattice, propagating along the lattice, colliding with other... 

---