Random site model

Jin X, Wang NHL, Tarjus G and Talbot J 1993 Irreversible adsorption on nonuniform surfaoes the random site model J. Phys. Chem. 97 4256-8... 

Finally, we should note that molecules cannot cover a surface completely. As a first approximation, the random site model [37] assumes that they can be represented by impenetrable spheres, adsorbing sequentially on a uniform surface, in locations selected randomly (see Figure 3.5). If the molecule adsorbing on a new trial position overlaps with a previously adsorbed molecule, it does not stick to the surface otherwise, it is adsorbed. An initially fresh surface covers quickly. 

A simple mapping enables tire RSA fonnalism to be applied to binding of a ligand L to receptors R embedded in a surface (tire RSA-random site (RSA-RS) model) [149,... 

The spatial temperature distribution established under steady-state conditions is the result both of thermal conduction in the fluid and in the matrix material and of convective flow. Figure 2. 9.10, top row, shows temperature maps representing this combined effect in a random-site percolation cluster. The convection rolls distorted by the flow obstacles in the model object are represented by the velocity maps in Figure 2.9.10. All experimental data (left column) were recorded with the NMR methods described above, and compare well with the simulated data obtained with the aid of the FLUENT 5.5.1 [40] software package (right-hand column). Details both of the experimental set-up and the numerical simulations can be found in Ref. [8], The spatial resolution is limited by the same restrictions associated with spin... 

Resulting maps of the current density in a random-site percolation cluster both of the experiments and simulations are represented by Figure 2.9.13(b2) and (bl), respectively. The transport patterns compare very well. It is also possible to study hydrodynamic flow patterns in the same model objects. Corresponding velocity maps are shown in Figure 2.9.13(d) and (c2). In spite of the similarity of the... 

When the random-walk model is expanded to take into account the real structures of solids, it becomes apparent that diffusion in crystals is dependent upon point defect populations. To give a simple example, imagine a crystal such as that of a metal in which all of the atom sites are occupied. Inherently, diffusion from one normally occupied site to another would be impossible in such a crystal and a random walk cannot occur at all. However, diffusion can occur if a population of defects such as vacancies exists. In this case, atoms can jump from a normal site into a neighboring vacancy and so gradually move through the crystal. Movement of a diffusing atom into a vacant site corresponds to movement of the vacancy in the other direction (Fig. 5.7). In practice, it is often very convenient, in problems where vacancy diffusion occurs, to ignore atom movement and to focus attention upon the diffusion of the vacancies as if they were real particles. This process is therefore frequently referred to as vacancy diffusion... 

The random-walk model of diffusion needs to be modified if it is to accurately represent the mechanism of the diffusion. One important change regards the number of point defects present. It has already been pointed out that vacancy diffusion in, for example, a metal crystal cannot occur without an existing population of vacancies. Because of this the random-walk jump probability must be modified to take vacancy numbers into account. In this case, the probability that a vacancy is available to a diffusing atom can be approximated by the number of vacant sites present in the crystal, d], expressed as a fraction, that is... 

Random substitutional models are used for phases such as the gas phase or simple metallic liquid and solid solutions where components can mix on any atial position which is available to the phase. For example, in a simple body-centred cubic phase any of the components could occupy any of the atomic sites which define the cubic structure as shown below (Fig. 5.1). 

The transition to a model of random bonds neglects the correlations imposed by construction between passing bonds around an A site, as is shown distinctly in Fig. 4.15, where two lattices satisfying the equivalence (4.83) are compared one lattice with random bond distribution, and one lattice with random site suppressions. Aggregation of bonds is easily discernable in the case of site percolation. However, as a matter of fact, these correlations have no importance in the case of conductivity, so that we may obtain a good approximation when leaving them out.178 It will be shown below that this approximation is questionable for more local properties where the microscopic arrangements of bonds may be crucial. 

In the model of bond percolation on the square lattice, the elements are the bonds formed between the monomers and not the sites, i.e., the elements of the clusters are the connected bonds. The extent of a polymerization reaction corresponds to the fraction of reacted bonds. Mathematically, this is expressed by the probability p for the presence of bonds. These concepts can allow someone to create randomly connected bonds (clusters) assigning different values for the probability p. Accordingly, the size of the clusters of connected bonds increases as the probability p increases. It has been found that above a critical value of pc = 0.5 the various bond configurations that can be formed randomly share a common characteristic a cluster percolates through the lattice. A more realistic case of a percolating cluster can be obtained if the site model of a square lattice is used with probability p = 0.6, Figure 1.5. Notice that the critical value of pc is 0.593 for the 2-dimensional site model. Also, the percolation thresholds vary according to the type of model (site or bond) as well as with the dimensionality of the lattice (2 or 3). 

Guanine is the most easily oxidize DNA base. This means that holes, created at random sites, will move around until encountering a guanine. In order to be stably trapped on guanine, the cation will have to deprotonate. The site of deprotonation has only recently been determined. EPR/ENDOR results predicted a cation deprotonated at the exocyclic amine G(N2-H) while model calculations predicted a cation deprotonated at N1 G(N1-H). ... 

Let us note, however, that it has been proposed recently that the disorder-induced one-dimensional localization could not be effective in particular cases namely, if the sites with random potential can be associated by pairs, or dimers. In that case the random dimer model shows that there should exist an energy spectrum of electrons that can propagate freely [31]. 

Recent models for ion transport in glasses inclnde the weak electrolyte , the random site , and the Anderson and Stnart models. ... 

Typical MC examples include nonintersecting random walks on a lattice or off-lattice necklaces of hard spheres jointed freely, The latter case involves a polymer chain lattice model in which the real chain is substituted by a selfavoiding random walk model on a periodic lattice. The excluded volume effect is taken into account by the condition that no site may be occupied more than once. 

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