Particle density distribution

The constraint of a finite volume requires that the one-particle density distribution satisfy the condition... 

The Laplace-Young equation refers to a spherical phase boundary known as the surface of tension which is located a distance from the center of the drop. Here the surface tension is a minimum and additional, curvature dependent, terms vanish (j ). The molecular origin of the difficulties, discussed in the introduction, associated with R can be seen in the definition of the local pressure. The pressure tensor of a spherically symmetric inhomogeneous fluid may be computed through an integration of the one and two particle density distributions. 

A uniform-irradiation technique is commonly used for ion beam applications in materials science and biotechnology, and for biomedical application such as cancer therapy. Uniformity of the irradiated-particle density distribution is essential to bring about the same... 

In these density profiles the latex particles, added before starting the experiment, migrate to that position in the cell where their density coincides with the density of the surrounding medium. The position of the particles can be recorded by schlieren optics or, if there is a particle density distribution, more precisely by scanning extinction measurements normally used for the characterization of proteins. Thus the density and extinction profile in the ultracentrifugation cell yield a criterion for the density distribution and hence, because of the correlation between chemical composition and particle density, a criterion for the composition distribution or heterogeneity of the latex particles. 

Particle density distribution of soil (density gradient tube)... 

This paper outlines the basic principles and theory of sedimentation field-flow fractionation (FFF) and shows how the method is used for various particle size measurements. For context, we compare sedimentation FFF with other fractionation methods using four criteria to judge effective particle characterization. The application of sedimentation FFF to monodisperse particle samples is then described, followed by a discussion of polydisperse populations and techniques for obtaining particle size distribution curves and particle densities. We then report on preliminary work with complex colloids which have particles of different chemical composition and density. It is shown, with the help of an example, that sedimentation FFF is sufficiently versatile to unscramble complex colloids, which should eventually provide not only particle size distributions, but simultaneous particle density distributions. 

The state-dependent nuclear charge density distribution, p r), can then be obtained from the particle density distributions through convolution with the charge density distributions of the single nucleons, Pp(r) and Pn(r) respectively ... 

The chemical potential p, = 6J f6p enters the respective Euler-Lagrange equation obtained by minimizing the grand ensemble thermodynamic potential — p J pd a , which defines the equilibrium particle density distribution... 

Due to the kinetic nature of LBE, phenomenon or physics that involves molecular interaction can easily be applied and hence makes LBM a good tool for micro-Znanofluidics simulation. Fewer sets of discrete velocities and particle density distribution function in phase space are used in LBM as opposed to a continuous velocity or distribution function in the complete functional phase space of the Boltzmann equation. 

We define the particle density distribution of the quantum mechanical state Y as... 

For the sake of brevity, we will usually drop the state index n and write simply p r) for the particle density distribution as it will be clear from the context whether this is a ground state density or the density of a state higher in energy. 

We have already encountered the particle density distribution in the context of the Bom interpretation in section 4.1. After what has been said about observables, it should be possible to assign an operator to this observable also. We can deduce the explicit form of the operator pr> which represents the particle density at a given position r in space, by relating its expectation value for an N-particle system,... 

The Hamiltonian of a multiple-chain system consisting of n chains is split into two parts H = H o -F W, where H o is the Hamiltonian of a reference (ideal) system composed of n noninteracting chains but with all the intramolecular interaction terms, while the intermolecular interactions are accounted for by the second term W that is assumed to be dependent on the particle positions only through the particle density distribution. One of the simplest expressions for this nonbonded interaction is as follows ... 

Fig. 1.2. Normalised frequency plots of number, surface, and volume (particle volume times particle density) distributions for the grand average 1969 Pasadena, California smog aerosol. Note the bimodal distribution of mass. Each weighting shows features of the distribution not shown by the other plots. From Whitby (1975, p. II-ll) in NRC (1979).

Glicksman LR, Piper GA. Particle density distribution in a freeboard of a fluidized bed. Powder Technol 53 179, 1987. 

Instead of specifying the discrete positions Vi of all particles, one can also use a continuum description and introduce the particle density distribution Cm r). First we write down the scattering amplitude for a single microstate, as represented by the associated density distribution... 

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