In the Yukawa potential, A is an inverse range parameter. The value A = 1.8 is appropriate for the inert gases. Each of the above potentials has a hard core. Real molecules are hard but not infinitely so. A slightly softer core is more desirable. The Lennard-Jones potential [Pg.137]

This r dependence is also known as a Yukawa potential. This type of potential has been used to describe the behaviour of latex suspensions at low ionic strength. [Pg.2678]

Figure 11. Two trajectories of the periodic Yukawa-potential Lorentz gas. They start from the same position but have velocities that differ by one part in a million. |

The introduction of the van der Waals potential in combination with a Yukawa potential produces a curve in which the primary minimum is always deeper than the secondary minimum. This must be so because the primary minimum state is that for which the particles have coalesced and the valency of the nth plate Zn has dropped to zero since Z —> 0 as Xmn —> 2a, —> 0 as —> 2a, and the van der Waals force [Pg.33]

Exercise 9.3 (For students of the Fourier transform) Calculate the Fourier transform of the Yukawa potential, e f x, where k > (k Take a limit to show that the Fourier transform of / x is An/ pf. [Pg.298]

This other Lorentz gas is similar to the previous one except that the hard disks are replaced by Yukawa potentials centered here at the vertices of a square lattice. The Hamiltonian of this system is given by [Pg.106]

Here, ur/p r) describes the interaction between nonbonded units and oa is the effective unit size (

For many practically important interaction functions, the Fourier coefficients in Eq. (D.9) have finite analytic forms, for example, the Lennard-Jones potential, the Yukawa potential, the Morse potential, and functions that can be derived from those functions. For a power-law interaction [Pg.355]

For large r, G(f, Fo) must vanish, which requires that A = 0. For small distances, where kf < < 1, it should be identical to the Coulomb potential, which requires that 5=1. Finally, we find that the Green s function of the Schrodinger equation in vacuum is the Yukawa potential. [Pg.348]

When applied to spatially extended dynamical systems, the PoUicott-Ruelle resonances give the dispersion relations of the hydrodynamic and kinetic modes of relaxation toward the equilibrium state. This can be illustrated in models of deterministic diffusion such as the multibaker map, the hard-disk Lorentz gas, or the Yukawa-potential Lorentz gas [1, 23]. These systems are spatially periodic. Their time evolution Frobenius-Perron operator [Pg.100]

The solution detennines c(r) inside the hard core from which g(r) outside this core is obtained via the Omstein-Zemike relation. For hard spheres, the approximation is identical to tire PY approximation. Analytic solutions have been obtained for hard spheres, charged hard spheres, dipolar hard spheres and for particles interacting witli the Yukawa potential. The MS approximation for point charges (charged hard spheres in the limit of zero size) yields the Debye-Fluckel limiting law distribution fiinction. [Pg.480]

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