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Mean medium approximation

The semianalytical model by Roichman et al. [42] is based on the mean medium approximation (MMA) and is probably the only one that shares the assumptions found in standard semiconductor models (for better or worse). A percolation-type model, which predicts that there are bottlenecks or small regions in which the current density is much larger than average, do not agree with the assumptions behind the semiconductor device model equations. The assumptions behind the MMA model include... [Pg.1322]

The physical properties of atoms and molecules embedded in polar liquids have usually been described in the frame of the effective medium approximation. Within this model, the solute-solvent interactions are accounted for by means of the RF theory [1-3], The basic quantity of this formalism is the RF potential. It is usually variationally derived from a model energy functional describing the effective energy of the solute in the field of an external electrostatic perturbation. For instance, if a singly negative or positive charged atomic system is considered, the RF potential is simply given by... [Pg.82]

If a singularity in the medium modified few-body T matrix is obtained, it may be taken to indicate the formation of a quantum condensates. Different kinds of quantum condensates are also considered [7, 8], They become obvious if the binding energy of nuclei is investigated [9], Correlated condensates are found to give a reasonable description of near-threshold states of na nuclei [10], The contribution of condensation energy to the nuclear matter EOS would be of importance and has to be taken into account not only in mean-field approximation but also considering correlated condensates. [Pg.77]

The modification of the three and four-particle system due to the medium can be considered in cluster-mean field approximation. Describing the medium in quasi-particle approximation, a medium-modified Faddeev equation can be derived which was already solved for the case of three-particle bound states in [9], as well as for the case of four-particle bound states in [10]. Similar to the two-particle case, due to the Pauli blocking the bound state disappears at a given temperature and total momentum at the corresponding Mott density. [Pg.86]

Chapter 15 - It was shown, that the reesterification reaction without catalyst can be described by mean-field approximation, whereas introduction of catalyst (tetrabutoxytitanium) is defined by the appearance of its local fluctuations. This effect results to fractal-like kinetics of reesterification reaction. In this case reesterification reaction is considered as recombination reaction and treated within the framework of scaling approaches. Practical aspect of this study is obvious-homogeneous distribution of catalyst in reactive medium or its biased diffusion allows to decrease reaction duration approximately twofold. [Pg.15]

A number of theoretical models for solvation dynamics that go beyond the simple Debye Onsager model have recently been developed. The simplest is an extension of Onsager model to include solvents with a non-Debye like (dielectric continuum and the probe can be represented by a spherical cavity. Newer theories allow for nonspherical probes [46], a nonuniform dielectric medium [45], a structured solvent represented by the mean spherical approximation [38-43], and other approaches (see below). Some of these are discussed in this section. Attempts are made where possible to emphasize the comparison between theory and experiment. [Pg.32]

The purpose of this chapter is to get a better insight of the first problem listed above, i.e., the polarization of interfaces (colloidal particles) during their interaction. Because of tutorial reasons, the electrolyte solution will be described using a rather simple, mean field approximation, that, however, allows to obtain an analytical solution of the problem. It is clear that this elaboration can easily be followed, and one can extend our model on more advanced situations. This model is identical with so-called weak-coupling theory for point ions treated in a course of the Debye-Hiickel approximation. Before going to make an elaboration for two interacting macrobodies immersed into an electrolyte solution, we would like to introduce a method, which is usually used to model this polarization, and to compute the electrical field next to a polarized medium. Then we will also discuss consequences of the polarization for the ion distribution at the particle-solution interface. [Pg.445]

In the mean-field approximation, the CEP occurs at mo = 0. Since thermal fluctuations play an important role both in the microemulsion and near a critical point, Monte Carlo (MC) simulations and a variational approach have been used to study the variation of the microemulsion structure as a function of mo [85]. The calculation is carried out for a value of go = (0) = — L2, which corresponds to a system with strong (medium-... [Pg.70]

The knowledge of both thermodynamic constants at zero ionic strength and of the specific interaction coefficients will allow the speciation diagram of the element in the considered medium to be established. At higher electrolyte concentrations, more sophisticated theories taking into account electrostatic or/and hydrodynamic interactions (Pitzer, Mean Spherical Approximation, etc., [35, 37])... [Pg.256]

The existence of yield stress Y at shear strains seems to be the most typical feature of rheological properties of highly filled polymers. A formal meaing of this term is quite obvious. It means that at stresses lower than Y the material behaves like a solid, i.e. it deforms only elastically, while at stresses higher than Y, like a liquid, i.e. it can flow. At a first approximation it may be assumed that the material is not deformed at all, if stresses are lower than Y. In this sense, filled polymers behave as visco-plastic media with a low-molecular and low-viscosity dispersion medium. This analogy is not random as will be stressed below when the values of the yield stress are compared for the systems with different dispersion media. The existence of yield stress in its physical meaning must be correlated with the strength of a structure formed by the interaction between the particles of a filler. [Pg.71]

Elutriation differs from sedimentation in that fluid moves vertically upwards and thereby carries with it all particles whose settling velocity by gravity is less than the fluid velocity. In practice, complications are introduced by such factors as the non-uniformity of the fluid velocity across a section of an elutriating tube, the influence of the walls of the tube, and the effect of eddies in the flow. In consequence, any assumption that the separated particle size corresponds to the mean velocity of fluid flow is only approximately true it also requires an infinite time to effect complete separation. This method is predicated on the assumption that Stokes law relating the free-falling velocity of a spherical particle to its density and diameter, and to the density and viscosity of the medium is valid... [Pg.510]


See other pages where Mean medium approximation is mentioned: [Pg.743]    [Pg.76]    [Pg.283]    [Pg.48]    [Pg.60]    [Pg.68]    [Pg.312]    [Pg.26]    [Pg.345]    [Pg.208]    [Pg.42]    [Pg.312]    [Pg.13]    [Pg.236]    [Pg.255]    [Pg.12]    [Pg.684]    [Pg.464]    [Pg.238]    [Pg.283]    [Pg.131]    [Pg.150]    [Pg.244]    [Pg.546]    [Pg.63]    [Pg.233]    [Pg.185]    [Pg.280]    [Pg.1143]    [Pg.426]    [Pg.57]    [Pg.1304]   
See also in sourсe #XX -- [ Pg.7 , Pg.8 , Pg.9 ]




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