Attachment probability

On the other hand, many of those plates generally considered modern fakes were made by a repousee technique and involved an outer, plain-curved back that was folded over at the rim to form a double-walled hollow plate. Occasionally a separate (cast) piece, usually a raised front leg of the horse, was attached, probably by soldering. These fakes and copies of existing museum plates all have less than 0.6% Au in Ag (in agreement with the fake Sasanian coins, Figure 5) and 14 of the 18 fakes in Figure 6 have less than 94% Ag + Au. 

Separate fractions (nanophases) of near-surface water attached probably by hydrophobic surface segments and hydrophobic pores as well as by polar chemical groups have been revealed in water fullerene and shungite carbon nanoparticles... 

Alldredge A. L. and McGillivary P. (1991) The attachment probabilities of marine snow and their implications for particle coagulation in the ocean. Deep-Sea Res. 38, 431-443. 

Alpha in Deposition The sticking coefficient or attachment probability, a, of particles depositing in porous media is defined as follows ... 

The attachment probability iVatt.iV increases with size of the cluster, because more and more sites per cluster for attachment are offered. The detachment probability. w et.N I in contrast, decreases with increasing N, because the atoms get bound to the cluster more and more strongly. Hence, with increasing N, the transformation rate to lower classes decreases, so that for a sufficiently large value of N, e.g., S, the rate of... 

The detachment-attachment probability ratio det, .jr / att,M, for given sitez of a crystalline cluster is independent of the cluster size characterized by , but depends on the configuration of the site x (cf. Section 2.2). The product n(iV),... 

The attachment probability, w att.Ncrit > e critical cluster depends on... 

From an experimental point of view, however, it seems that little progress has been made since the evaluation of the Volmer-Weber [4.11] equation in 1926. The experimentalist is bound to use eqs. (4.32) and (4.33), disregarding the small uninformative dependence of A on 77 derived from the Zeldovich factor F or the attachment probability Watt.yVcnt More significant progress seems to have been made with the development of the small cluster model based on the atomistic approach of Becker and Doering. 

In these results the effects of surface and solution chemistry on particle deposition are represented by the sticking coefficient or attachment probability (or), defined in this case as the rate at which particles adhere to a grain of aquifer media divided by the rate at which they contact it. In Figure 11, a is assumed as 1 (perfect sticking) and also as 10-3 (one collision in every 1000... 

Figure 11. Distance required to remove 99% of particles from suspension (L ) as a function of suspended particle radius for two chemical conditions (attachment probabilities). Flow rate = O.lm/day, media radius = 0.025 cm, temperature = 25 °C, particle density = 1.05 g/cm3, and aquifer porosity = 0.4. (Reproduced with permission from reference 29. Copyright 1987.)...

The first and most fundamental characteristic of this system is that it is based on a probabilistic data model. This means that we attach probabilities to the following ... 

Discussion of these results is directed at the following question. How do these field results compare with present theories for the kinetics of aggregation and sedimentation in aquatic systems In answering this question, some laboratory determinations of attachment probabilities will be used in modelling simulations of the kinetics and effects of colloid chemical processes in lakes. 

Particle aggregation in Lake Zurich is considered here to have an attachment probability of 0.1 (Table 5). When both coagulation and sedimentation are occurring [i.e., if rx(/, 0.1 and pp — 1.05 gem 3], smaller particles are... 

The interaction in a two-body collision in a dilute suspension has been expanded to provide a useful and quantitative understanding of the aggregation and sedimentation of particulate matter in a lake. In this view, Brownian diffusion, fluid shear, and differential sedimentation provide contact opportunities that can change sedimentation processes in a lake, particularly when solution conditions are such that the particles attach readily as they do in Lake Zurich [high cc(i,j)exp]. Coagulation provides a conceptual framework that connects model predictions with field observations of particle concentrations and size distributions in lake waters and sediment traps, laboratory determinations of attachment probabilities, and measurements of the composition and fluxes of sedimenting materials (Weilenmann et al., 1989). 

Until such theories can be developed, laboratory experiments can be performed to determine chemical effects in aquatic colloid chemical processes for actual situations. This is suggested by the analysis presented in this chapter of the aquifer study by Harvey et al. (1989) and is illustrated for Lake Zurich by the study of Weilenmann et al. (1989). Since mass transport can be described with some success [e.g., p, c),heor and 2(r,y )slhcor], this knowledge can be combined with laboratory determinations of attachment probabilities such as those illustrated in Table 2 for a(p, c)exp and listed in Table 5 for ci(i,j)s exp to describe the kinetics of deposition and aggregation (e.g., Eqs. 5 and 6) in aquatic systems. 

The attachment probability can be influenced by several parameters. For example, one can control the attachment probability and consequently the growth rate via temperature. Crystallization is only possible below the melting point of the system. Exactly at the melting temperature, the probabihty for attaching a molecule to the crystal is so low that the molecule will not stay attached. Thus, the crystal will not grow. Attachment may also be in competition with the displacement of other molecules like solvent molecules, additives or impurities. For example, if an additive is strongly adsorbed onto the crystal surface the crystal will not grow as fast as in cases when these additional molecules are not present. 

The attachment probability involves all three interfaces, SG, SL, and LG. In equilibrium, at constant p and T, the change in Gibbs energy per unit interfacial area, AGa, upon attachment of a particle (S) on a bubble (G) is given by... 

In this case, y represents the interfacial energy, is a function of the activity ( ) for foreign substrates, which is different for different substrates. Z is the attachment probability (sticking coefficient) of molecules of the parent phase to the nucleus. Therefore, Z is related to epitaxy. For crystallization in glass, Z is approx. lO". The viscosity of the parent phase is represented by J. The difference between the chemical potentials of the melt and the crystal is represented by p. It is determined by Eq. 1-13. 

According to the molecular scattering theory, a particle incident to the surface has a certain probability for a certain amount to stay on the surface, and the rest is scattered back into the gas phase, a is an initial attaching probability and is a parameter to be determined through a molecular dynamics simulation based on quantum chemistry. Although in surface chemistry, a thermal accommodation coefficient is also used, in atmospheric chemistry a mass accommodation coefficient is solely used so that here it is simply called an accommodation coefficient. In general a cannot be determined directly by experiments, and the experimentally determined parameter of intake of a gaseous molecule to the particle surface is an uptake coefficient y defined by... 

Viewed in terms of quantum computational principles, lipid selectivity is the interaction of molecules embedded in a many-dimensional (Hilbert) state space. In this view, geometry-dependent orbital surfaces are not 3D manifolds but sets of fluctuating hypersurfaces, each with an attached probability value, existing in linear superposition [33,3], The molecular interactions are thus a massively parallel search for a local energy minimum. These features would appear to fulfill the requirements for a quantum computing system. In terms of Atmar s... 

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