Effective media simulation

The model has been treated analytically employing the effective medium approach [58] and by Monte Carlo simulation. It makes the following predictions A dilute ensemble of non-interacting charge carriers, initially generated at random within the DOS, lends to relax toward the tail slates and ultimately equilibrates at... 

The TEM data have been used to simulate, in the frame of the Mie theory and Maxwell-Garnett effective medium approximation [15], the optical absorption spectra of the sample implanted with 5 x lO Au /cm. The results are reported in Figure 8(c). In the first model used to describe... 

Ritz G, Schmid M, Varga P, Borg A, Ronning M. 1997. Pt(lOO) quasihexagonal reconstruction A comparison between scanning tunneling microscopy data and effective medium theory simulation calculations. Phys Rev B 56 10518-10525. 

This model, when applied to Nation as a function of water content, indicated a so-called quasi-percolation effect, which was verified by electrical impedance measurements. Quasi-percolation refers to the fact that the percolation threshold calculated using the single bond effective medium approximation (namely, x = 0.58, or 58% blue pore content) is quite larger than that issuing from a more accurate computer simulation. This number does not compare well with the threshold volume fraction calculated by Barkely and Meakin using their percolation approach, namely 0.10, which is less than the value for... 

Monte Carlo simulations [54], analytical effective medium theory [64], and stochastic hopping theory [46] predict a dependence of the charge carrier mobility as a function of temperature and electric field given in (3) ... 

Fig. 14 A comparison of different approaches to describe the charge carrier mobility in a Gaussian-type hopping system as a function of the normalized concentration of the charge carriers, (a) Full curves are the result of effective medium calculations [100] while symbols are computer simulations [96], (b) Full curves are calculated using the variable range hopping concept [101], symbols are the computer simulations. From [100] with permission. Copyright (2007) by the American Institute of Physics...

Quantitative simulation of spectra as outlined above is complicated for particle films. The material within the volume probed by the evanescent field is heterogeneous, composed of solvent entrapped in the void space, support material, and active catalyst, for example a metal. If the particles involved are considerably smaller than the penetration depth of the IR radiation, the radiation probes an effective medium. Still, in such a situation the formalism outlined above can be applied. The challenge is associated with the determination of the effective optical constants of the composite layer. Effective medium theories have been developed, such as Maxwell-Garnett 61, Bruggeman 62, and other effective medium theories 63, which predict the optical constants of a composite layer. Such theories were applied to metal-particle thin films on IREs to predict enhanced IR absorption within such films. The results were in qualitative agreement with experiment 30. However, quantitative results of these theories depend not only on the bulk optical constants of the materials (which in most cases are known precisely), but also critically on the size and shape (aspect ratio) of the metal particles and the distance between them. Accurate information of this kind is seldom available for powder catalysts. 

A. Horner. Self-diffusion in metallic glasses Approximation of the effective medium and molecular simulation. PhD thesis, Stuttgart University, 1993. In German. 

There is a general shrinking of the band, compared to the numerical simulations. This is clearest at higher concentrations and stems from a similar defect of the HCPA effective medium. 

Two other approaches have been taken to modelling the conductivity of composites, effective medium theories (Landauer, 1978) and computer simulation. In the effective medium approach the properties of the composite are determined by a combination of the properties of the two components. Treating a composite containing spherical inclusions as a series combination of slabs of the component materials leads to the Maxwell-Wagner relations, see Section 3.6.1. Treating the composite as a mixture of spherical particles with a broad size distribution in order to minimise voids leads to the equation ... 

The purpose of our work was to examine whether the compressed hot cluster provides an effective medium for reactions with high barriers. In the simplest case of cluster impact experiments, the reactants are embedded inside a rare gas cluster, and this cold droplet is incident on an inert surface at various velocities. Two classes of reactions were examined in detail using standard molecular dynamics simulations the dissociation of halogen molecules and four-center reactions. ... 

Facilitating the insight into the complex inter-linked phenomena of chemical reactions and turbulent flow field behaviour as well as for the investigation of parametric effects, the simulation program AIOLOS is used as an effective tool for the investigation of the combustion processes in small and medium scale wood combustion systems. 

A legitimate question concerns the limitations of a model where the membrane is treated as an effective medium. To explore this issue, a series of simulations were done where each lipid molecule in the bilayer was represented by a dumbbell, and the effect of curvature on the transport of a structureless polymer was explored [241]. Interestingly, when the membrane is highly curved, there is almost irreversible transport from the outside to the inside of the spherical vesicle. This arises from entropic effects. Basically, because the interior leaflet is of lower density, after penetrating into the membrane, the polymer prefers to remain in this region. In... 

A fundamental requirement on all of the computational studies on metal surface dynamics is fhe need fo perform simulafions with realistic potentials and in a feasible amounf of fime. To this end, the temperature-accelerated dynamics method [14,74,75] has arisen as a possible approach for reaching the latter limit. With the exception of quanfum simulations, most classical simulations are based on semiempirical potentials derived either from the embedded atom method or effective medium theory [76-78]. However a recent potential energy surface for hydrogen on Cu(l 10) based on density functional theory calculations produced qualitatively different results from those of the embedded atom method including predictions of differenf preferred binding sites [79]. 

The SEIRA spectra can be simulated by using effective medium theories and the Fresnel equations [8-11, 17, 19, 24). Such simulations predict that (i) the SEIRA effect is not limited to coinage metals and can also occur on most transition metals, (ii) the enhancement factor is primarily a function of the size, shape, and proximity between the metal particles, and (iii) the band shapes of the enhanced absorption depend on the morphology of the metal film. These predictions have been well confirmed by experiments. 

Effective medium theory was originally introduced in the early 1980s to describe chemisorption of gas atoms on metal surfaces. It has since been developed as a relatively efficient method for describing bonding in solids, particularly metals, and therefore has found considerable use in materials model-ing. It also forms the quantum mechanical basis for the more empirical and widely used embedded-atom method discussed below. Specific implementations of effective medium theory for materials simulation have been developed by Norskov, Jacobsen, and co-workers and by DePristo and co-workers. ... 

Fig. 9 Theoretical simulated spectra of CO adsorbed on the nanostructured Pt thin films with variation in/using the Bruggeman EMT. The values of d g used in the simulation when/equals 0.47 and 0.53 were 36 and 142nm, respectively. [Reprinted with permission from by Z.-F. Su, S.-G. Sun, C.-X. Wu and Z.-P. Cai, Study of anomalous infrared properties of nanomaterials through effective medium theory , J. Chem. Phys., 2008, 129, 044707. Copyright 2008, American Institute of Physics.]...

Z. Sun, E.J. Garboczi and S.P. Shah Modeling the Elastic Properties of Concrete Composites Experiment, Differential Effective Medium Theory, and Numerical Simulation, Cement and Concrete Composites Vol. 29, No. 1 (2007), p. 22-38. 

Figure 4.1.9. Simulated impedance and modulus spectra for a two-phase microstructure, based on the effective medium model. Values of the input parameters are given in Table 4.1.1. (a, b) Spectra for a matrix of phase 1 containing 25% by volume of spheres of phase 2. Resolution is achieved in the modulus spectrum (b) but not the impedance spectrum (a), (c, d) Spectra for a spherical grain of phase 2 surrounded by a grain boundary shell of phase 1. The ratio of shell thickness to sphere radius is 10" Resolution is achieved in the impedance spectrum (c) but not the modulus spectrum (d).

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