Biomedical subjects

J W Dufty

Publications and source records attributed to J W Dufty.

5 recordsLinked to original sources

PubMed2004

Temperature-dependent quantum pair potentials and their application to dense partially ionized hydrogen plasmas.

Extending our previous work [J. Phys. A 36, 5957 (2003)]], we present a detailed discussion of accuracy and practical applications of finite-temperature pseudopotentials for two-component Coulomb systems. Different pseudopotentials are discussed: (i) the diagonal Kelbg potential, (ii) the off-diagonal Kelbg potential, (iii) the improved diagonal Kelbg potential, (iv) an effective potential obtained with the Feynman-Kleinert variational principle, and (v) the "exact" quantum pair potential derived from the two-particle density matrix. For the improved diagonal Kelbg potential, a simple temperature-dependent fit is derived which accurately reproduces the "exact" pair potential in the whole temperature range. The derived pseudopotentials are then used in path integral Monte Carlo and molecular-dynamics (MD) simulations to obtain thermodynamical properties of strongly coupled hydrogen. It is demonstrated that classical MD simulations with spin-dependent interaction potentials for the electrons allow for an accurate description of the internal energy of hydrogen in the difficult regime of partial ionization down to the temperatures of about 60 000 K. Finally, we point out an interesting relationship between the quantum potentials and the effective potentials used in density-functional theory.

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PubMed2001

Nonequilibrium phase transition for a heavy particle in a granular fluid.

It is shown that the homogeneous cooling state (HCS) for a heavy impurity particle in a granular fluid supports two distinct phases. The order parameter straight phi;(s) is the mean square velocity of the impurity particle relative to that of a fluid particle, and the control parameter xi* is the fluid cooling rate relative to the impurity collision rate. For xi*<1 there is a "normal" phase for which straight phi;(s) scales as the fluid/impurity mass ratio, just as for a system with elastic collisions. For xi*>1 an "ordered" phase occurs in which straight phi;(s) is finite even for vanishingly small mass ratio, representing an extreme violation of energy equipartition. The phenomenon can be described in terms of a Landau-like free energy for a second order phase transition. The dynamics leading to the HCS is studied in detail using an asymptotic analysis of the Enskog-Lorentz kinetic equation near each phase and the critical domain. Critical slowing is observed with a divergent relaxation time at the critical point. The stationary velocity distributions are determined in each case, showing a crossover from Maxwellian in the normal phase to an exponential quartic function of the velocity that is sharply peaked about the nonzero straight phi;(s) for the ordered phase. It is shown that the diffusion coefficient in the normal phase diverges at the critical point and remains so in the ordered phase. This is interpreted as a transition from diffusive to ballistic dynamics between the normal and ordered phases.

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PubMed2001

Critical behavior of a heavy particle in a granular fluid.

A second order phase transition is observed for the homogeneous cooling state of a heavy impurity particle in a granular fluid. The order parameter straight phi is the ratio of impurity mean square velocity to that of the fluid, with a conjugate field h proportional to the mass ratio. A parameter beta, measuring the fluid cooling rate relative to the impurity-fluid collision rate, is the analog of the inverse temperature. For beta<1 the fluid is "normal" with straight phi = 0 at h = 0, as in the case of elastic collisions. For beta>1 an "ordered" state with straight phi not equal0 occurs at h = 0, representing an extreme breakdown of equipartition. Critical slowing and qualitative changes in the velocity distribution function near the transition are noted.

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PubMed1999

Dense fluid transport for inelastic hard spheres.

The revised Enskog theory for inelastic hard spheres is considered as a model for rapid flow granular media at finite densities. A normal solution is obtained via the Chapman-Enskog method for states near the local homogeneous cooling state. The analysis is performed to first order in the spatial gradients, allowing identification of the Navier-Stokes order transport coefficients associated with the heat and momentum fluxes. In addition, the cooling rate is calculated to first order in the gradients and expressed in terms of the transport coefficients. The transport coefficients are determined from linear integral equations analogous to those for elastic collisions. The solubility conditions for these equations are confirmed and the transport coefficients are calculated as explicit functions of the density and restitution coefficient using a Sonine polynomial expansion. The results are not limited to small dissipation. Finally, the analysis is repeated using a simpler kinetic model. Excellent agreement is obtained with the results from the revised Enskog equation.

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PubMed1999

Brownian motion in a granular gas.

The dynamics of a heavy particle in a gas of much lighter particles is studied via the Boltzmann-Lorentz equation with inelastic collisions among all particles. A formal expansion in the ratio of gas to tagged particle mass transforms the Boltzmann-Lorentz equation into a Fokker Planck equation. The predictions of the latter are tested here using direct Monte Carlo simulation of the Boltzmann-Lorentz equation. Excellent agreement is obtained for the approach to a homogeneous cooling state, the temperature of that state, approach to diffusion, and the dependence of the diffusion constant on dissipation parameters. Some results from molecular-dynamics simulations are also presented and shown to agree with the theoretical predictions.

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