Pseudo-particles

In the classical picture developed above, the wavepacket is modeled by pseudo-particles moving along uncorrelated Newtonian trajectories, taking the electrons with them in the form of the potential along the Uajectory. In this spirit, a classical wavepacket can be defined as an incoherent (i.e., noninteracting) superposition of confignrations, X/(, t)tlt,(r, t)... 

In computer science, advances have been made on several forefronts. These include the study by Crutchfield and colleagues of the emergence of pseudo-particles in cellular automata, where the particle interactions can carry out computations. 

Ge, W. and Li, J., Pseudo-particle approach to hydrodynamics of gas/solid two-phase flow, in "Circulating Fluidized Bed Technology V" (J. Li, M. Kwauk, Eds.), pp. 260-265. Science Press, Beijing (1996). 

H is the Hamiltonian for the motion of a pseudo-particle in the potential field V ( A, 4>) in the two-dimensional space with coordinates A, [Pg.346]

A complete understanding of the conduction processes has not yet been obtained. It is clear that at least two types of processes are required charge transport along the chains and charge transport between the chains. Transport along the chains may be possible because of the formation of various kinds of pseudo-particles, such as solitons and polarons, which are localised but mobile excitations (Bower, 2002). 

For the H system and its isotopomers after separating the CM motion from the Schrodinger equation, the problem is reduced to a two pseudo-particle problem. In the basis functions defined in eqn.40 r = (r[, r 2) is the 6x1 vector of relative coordinates defined above. The ground state spatial wave function (symmetric with respect to exchange of electrons) is then given as the symmetry projected linear combination of the 0, ... 

Koelman and Hoogerbrugge (1993) have developed a particle-based method that combines features from molecular dynamics (MD) and lattice-gas automata (LGA) to simulate the dynamics of hard sphere suspensions. A similar approach has been followed by Ge and Li (1996) who used a pseudo-particle approach to study the hydrodynamics of gas-solid two-phase flow. In both studies, instead of the Navier-Stokes equations, fictitious gas particles were used to represent and model the flow behavior of the interstial fluid while collisional particle-particle interactions were also accounted for. The power of these approaches is given by the fact that both particle-particle interactions (i.e., collisions) and hydrodynamic interactions in the particle assembly are taken into account. Moreover, these modeling approaches do not require the specification of closure laws for the interphase momentum transfer between the particles and the interstitial fluid. Although these types of models cannot yet be applied to macroscopic systems of interest to the chemical engineer they can provide detailed information which can subsequently be used in (continuum) models which are suited for simulation of macroscopic systems. In this context improved rheological models and boundary condition descriptions can be mentioned as examples. 

A large class of currently used CG models employs what some researchers call particle-based coarse-graining, in which a finite number of atoms of the molecular system are grouped into a single point mass (a CG particle, sometimes called a mesoparticle or a pseudo-particle). In the simulations of biomolecules, most commonly only a few heavy atoms (between 3 and 5) are replaced by a CG particle. 

The quanta of lattice vibrations, phonons, are the result of the interactions of the ions in the crystal lattice or, in other words, the vibrations of an atom in the lattice as its individual property and not of the whole cluster. However, most of them are not treated as interacting particles but as noninteracting particles (pseudo particles). In the case of phonons, one of the movements is associated to an acoustic horizontal and symmetrical motion and the other to an optical asymmetrical (forward and backward motion) process. The latter vibrates in the infrared portion of the spectrum, and since they exhibit a weak interaction with the rest of the particles, they can be treated independently. 

The first term only involves the X, Y and Z coordinates, and the operator is obviously separable in terms of X, Y and Z. Solution of the XYZ part gives translation of the whole system in three dimensions relative to the laboratory-fixed coordinate system. The xyz coordinates describe the relative motion of the two particles in terms of a pseudo-particle with a reduced mass /x relative to the centre of mass. 

The state of the art in understanding and describing droplet formation processes is divided into two different perspectives flie cmitinuum mechanics or fluid dynamics approach and the particle-based approach. Whilst the cmitinuum mechanics approach is based usually on the Navier-Stokes equation, the continuum equation and the energy equation, the particle-based approach is based on the interconnecting forces between neighboring particles like molecules or pseudo particles. 

The originality of this paper lies in applying a combination of Fourier and wavelets transform to a surface inspection. In this paper, pseudo particle images are processed by Fourier-wavelets transform to extract the defective feature to classify the inferior particles as a first step. Also, IEEE standard image is analyzed with the method. 

The instanton theory was invented in the field theory by introducing imaginary time to Minkowski space-time. The instanton is the classical object in the Euclidean space-time that gives a finite action. The instanton is also called pseudo-particle. Here the theory is explained by following Coleman [2]. See also References [17,39,43,46]. 

Pooling was one of the many possibilities imagined in early work, but its importance for MALDI requires more than excited neighbor pairs randomly created by the laser. These are not sufficiently numerous except at very high intensities." However, excitations can be mobile in the solid state, greatly increasing their interaction probability. " Mobile excitations can be treated as pseudo-particles and are denoted excitons. ... 

Lattice Fluid Mode/ The Lattice Fluid model developed by Sanchez and Lacombe (15,16) introduces vacancies into the classical incompressible Flory-Huggins model. The lattice vacancy is treated as a pseudo particle in the system. The free energy of an incompressible binary polymer solution is then converted to that of the bulk polymer. The equation of state for a polymer is given below ... 

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