Inverse-power potential

We consider a general inverse power potential function of the form... 

Agrawal, R. Kofke, D. A., Solid-fluid coexistence for inverse-power potentials, Phys. Rev. Lett. 1995, 74, 122-125... 

The cation-anion pair potential for a symmetrical salt may be written as the sum of the core repulsion and the coulomb interaction. For example, if the core repulsion is an inverse power potential, then ... 

To determine the differential cross section dcr(E, T) for the transfer of energy between T and T + dT from the ion to the target atom and from one target atom to another. dcr(E, T) is, for example, approximated by Equation 9 for an inverse power potential. 

The Sigmund theory, strictly speaking, is only valid for amorphous, monatomic targets and scattering using an inverse power potential. Moreover, it should be most accurate for mediiun mass ions in the keV range and relatively more inaccurate in... 

GATHER is faster than computing all but the simplest inverse power potentials. By comparison a square root takes 14 machine cycles/element and the entire pairwise sum takes an average of 98 machine cycles/pair. Note that temporaries are set up for the scaling factors of the potential, as well as the addresses for the start of the tables. These temporaries are changed only rarely and so do not affect the timing. They would be unnecessary if there were only one type of particle. 

E. I. Dashevskaya, 1. Litvin, A.I.Maergoiz, E.E.Nikitin, and J. Troe, Low-temperature behavior of capture rate eonstants for inverse power potentials, J. Chem. Phys. 118, 7313 (2003)... 

R. Agrawal and D. A. Kofke (1995) Solid-Fluid Coexistence for Inverse-Power Potentials. Phys. Rev. Lett. 74, p. 122... 

DFT has been much less successful for the soft repulsive sphere models. The definitive study of DFT for such potentials is that of Laird and Kroll [186] who considered both the inverse power potentials and the Yukawa potential. They showed that none of the theories existing at that time could describe the fluid to bcc transitions correctly. As yet, there is no satisfactory explanation for the failure of the DFTs considered by Laird and Kroll for soft potentials. However, it appears that some progress with such systems can be made within the context of Rosenfeld s fundamental measures functionals [130]. 

Other types of interatomic potential functions may be modified in a similar way. For example, the general inverse power potential may be modified to... 

On the low-temperature limit of the capture rate constants for inverse power potentials, J.C/jew.P/jy i. 118, 7313-7321. 

W. G. Hoover, S. G. Gray, and K. W. Johnson, Thermodynamic properties of the fluid and solid phases for inverse power potentials, J. Chem. Phys. 55, 1128-1136 (1971). 

Further efficiency can be achieved by using the simplified molecular potentials, for example, the inverse power potential and simple R-T cross sections. 

In addition to the electrical interactions, particles interact, at short-range by a repulsive interaction generally taken to be a hard sphere potential. In ER (MR) fluids where the short range repulsions extend over distances much shorter than the size of the particles this is a reasonable approximation. However, in dynamical simulations a discontinuous potential is not convenient and the hard sphere potential is generally replaced by a continuous exponential or inverse power potential with parameters chosen to closely mimic a hard sphere potential. As shown in [173] too soft a potential may lead to im-realistic aggregation of the particles. Potentials of a similar functional form have been used for the wall-particle interaction. 

Figure 10 Comparison of short-range Lennard-Jones and inverse-power potential for K+ and CC in aqueous solution.

In the case of hard spheres only the face centred cubic (FCC) structure is stable. However when the interparticle repulsion is sufficiently soft both FCC and body-centred cubic (BCC) structures have a stability range that depends on temperature and density. For the case of inverse power potentials... 

The majority of the liquid-solid simulation studies have involved simple, single-component systems in which the particles interact either with a Lennard-Jones potential (discussed in Section 4.2) or via a pairwise additive, purely repulsive inverse power potential ... 

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