Smoothed-particle

Essmann U, Perera L, Berkowitz M L, Darden T, Lee H and Pedersen L G 1995 A smooth particle mesh Ewald method J. Chem. Phys. 103 8577-93... 

U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen. The smooth particle mesh ewald method. J. Chem. Phys., 103 8577, 1995. Brock A. Luty, Ilario G. Tironi, and Wilfried F. van Gunsteren. Lattice-sum methods for calculating electrostatic interactions in molecular simulations. J. Chem. Phys., 103 3014-3021, 1995. 

Frequently when < 10, Sp and S, are combined for convenience, the sum of which is typically 0.07.5 for smooth particles and can be as high as 0.3.5 for rough-surface particles. This has to be determined from tests. ... 

The leading dimensionless coefficient of 1.8 pertains to smooth particles. For rough particles, 4.0 is recommended. 

In the case of the reciprocal sum, two methods have been implemented, smooth particle mesh Ewald (SPME) [65] and fast Fourier Poisson (FFP) [66], SPME is based on the realization that the complex exponential in the structure factors can be approximated by a well behaved function with continuous derivatives. For example, in the case of Hermite charge distributions, the structure factor can be approximated by... 

For example, Dixon (1979,1981) based most of his suggestions and observations on plastic powders and granules (i.e., relatively smooth particles with narrow size ranges). 

Gas Atomization 50-300 Standard deviation 1.9-2.5 <10-50 at high gas pressures with close-coupled atomizer Solder materials. Precious metals, Cu, Fe, Al, Mg, Co, Ti, Zn, Al-6Cr-3Fe-2Zr alloy. Low-alloy steels. High speed steels. Stainless steels, Specialty alloys, Ni-base superalloys, Alumina, Intermetallics io3-.o5 1-70 Spherical smooth particles. Cleanliness, Rapidly-solidified structures, Acceptable production rates High cost, Low 1 volume, Low energy efficiency (EE), Gas-filled porosity in particles H... 

Rotating Disk Atomization (RSR) -60 Standard deviation 1.4-1.6 Ni-superalloys, Al, Be, Ti, Mo, Cu alloys, Steels, Silicide 105-107 3-18 <0.9 Spherical, clean, smooth particles, Narrow size distribution, High EE Relatively low capacity throughput... 

Welton, W. C. and S. B. Pope (1997). PDF model calculations of compressible turbulent flows using smoothed particle hydrodynamics. Journal of Computational Physics 134,150-168. 

Simulations of this scenario have been performed by Lee (Lee 2001 and references therein) using Newtonian gravity and polytropic equations of state of varying stiffness. Ruffert, Janka and Eberl performed similar simulations but with a detailed microphysics input (nuclear equation of state and neutrino leakage ). In our own simulations of NS-BH mergers we used a relativistic mean field equation of state together with three-dimensional smoothed particle hydrodynamics and a detailed, multiflavour neutrino treatment. 

The most general smooth particle—one without edges or comers—of regular shape is an ellipsoid with semiaxes a > b > c (Fig. 5.5), the surface of which is specified by... 

Next, let us consider the application of Equation (21) to a particle migrating in an electric field. We recall from Chapter 4 that the layer of liquid immediately adjacent to a particle moves with the same velocity as the surface that is, whatever the relative velocity between the particle and the fluid may be some distance from the surface, it is zero at the surface. What is not clear is the actual distance from the surface at which the relative motion sets in between the immobilized layer and the mobile fluid. This boundary is known as the surface of shear. Although the precise location of the surface of shear is not known, it is presumably within a couple of molecular diameters of the actual particle surface for smooth particles. Ideas about adsorption from solution (e.g., Section 7.7) in general and about the Stern layer (Section 11.8) in particular give a molecular interpretation to the stationary layer and lend plausibility to the statement about its thickness. What is most important here is the realization that the surface of shear occurs well within the double layer, probably at a location roughly equivalent to the Stern surface. Rather than identify the Stern surface as the surface of shear, we define the potential at the surface of shear to be the zeta potential f. It is probably fairly close to the... 

Results from several studies on the toxicity of various forms of quartz suggest that such differences in toxicity may stem from the fact that the crystal examined originates from different sources. Thus the differences in behavior between Min-U-Sil 5 and the nano-quartz may also be ascribed to the well known variability of quartz hazard24,25 and not size. It must be considered that the hydrothermal conditions in which the sample was prepared usually provide smooth particles whose surface is equilibrated with moisture, thus much less reactive. 

Fig. 9.9 depicts some of the results from such trials. Despite some scatter in the angle range 95°-105°, it is readily seen that at 9< 95° none of the films ruptures, while at 0> 105° all the films rupture. Experiments with suspensions of solid particles (Teflon, hydrophobed glass beads and ground glass) showed that in the case of smooth particles, the defoaming... 

Fumed silica aggregates are obviously linear and branched particle structures with a mean size of about 100 to 200 nm. By TEM we derive the size of the partially fused primary particles of about 10 run. This very small particle size correlates well with the high surfaces area of fumed silica which usually is larger than 100 m g as determined by nitrogen adsorption at 78 K according to BET [5]. Adsorption techniques and electron microscopy provide very close values of surface areas. This indicates that fumed silica exhibits a smooth particle surface in the range of nanometers, apparently its surface is free of micropores. 

There is a growing number of approaches to treat the essentially infinite reach of charge-charge interactions. To mention just a few of the more traditional numerical ones which are well adapted to the requirements of MD, we have charge group cut-off [63], Ewald [72] summation, smooth particle Ewald [66] summation and particle-particle-particle-mesh (P M) [73]. There are also several variations of hierarchical methods [74] a few examples are the method of Bames and Hut (BH) [75], the fast multipole method (EMM), with [76] and without [77] multipoles, and the cell multipole method [78]. 

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