A Thermodynamically-Consistent Non-Ideal Stochastic Hard-Sphere Fluid

A grid-free variant of the Direct Simulation Monte Carlo (DSMC) method is proposed, named the Isotropic DSMC (I-DSMC) method, that is suitable for simulating dense fluid flows at molecular scales. The I-DSMC algorithm eliminates all grid artifacts from the traditional DSMC algorithm; it is Galilean invariant and microscopically isotropic. The stochastic collision rules in I-DSMC are modified to yield a non-ideal structure factor that gives consistent compressibility, as first proposed in [Phys. Rev. Lett. 101:075902 (2008)]. The resulting Stochastic Hard Sphere Dynamics (SHSD) fluid is empirically shown to be thermodynamically identical to a deterministic Hamiltonian system of penetrable spheres interacting with a linear core pair potential, well-described by the hypernetted chain (HNC) approximation. We apply a stochastic Enskog kinetic theory for the SHSD fluid to obtain estimates for the transport coefficients that are in excellent agreement with particle simulations over a wide range of densities and collision rates. The fluctuating hydrodynamic behavior of the SHSD fluid is verified by comparing its dynamic structure factor against theory based on the Landau-Lifshitz Navier-Stokes equations. We also study the Brownian motion of a nano-particle suspended in an SHSD fluid and find a long-time power-law tail in its velocity autocorrelation function consistent with hydrodynamic theory and molecular dynamics calculations.Comment: 30 pages, revision adding some clarifications and a new figure. See also arXiv:0803.035

Diffusive Transport Enhanced by Thermal Velocity Fluctuations

We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. The enhancement of the diffusive transport depends on the system size L and grows as \ln(L/L_0) in quasi two-dimensional systems, while in three dimensions it scales as L_0^{-1}-L^{-1}, where L_0 is a reference length. The predictions of a simple fluctuating hydrodynamics theory are compared to results from particle simulations and a finite-volume solver and excellent agreement is observed. Our results conclusively demonstrate that the nonlinear advective terms need to be retained in the equations of fluctuating hydrodynamics when modeling transport in small-scale finite systems.Comment: To appear in Phys. Rev. Lett., 201

Intermittent fluctuations in the Alcator C-Mod scrape-off layer for ohmic and high confinement mode plasmas

Plasma fluctuations in the scrape-off layer of the Alcator C-Mod tokamak in ohmic and high confinement modes have been analyzed using gas puff imaging data. In all cases investigated, the time series of emission from a single spatially-resolved view into the gas puff are dominated by large-amplitude bursts, attributed to blob-like filament structures moving radially outwards and poloidally. There is a remarkable similarity of the fluctuation statistics in ohmic plasmas and in edge localized mode-free and enhanced D-alpha high confinement mode plasmas. Conditionally averaged wave forms have a two-sided exponential shape with comparable temporal scales and asymmetry, while the burst amplitudes and the waiting times between them are exponentially distributed. The probability density functions and the frequency power spectral densities are self-similar for all these confinement modes. These results are strong evidence in support of a stochastic model describing the plasma fluctuations in the scrape-off layer as a super-position of uncorrelated exponential pulses. Predictions of this model are in excellent agreement with experimental measurements in both ohmic and high confinement mode plasmas. The stochastic model thus provides a valuable tool for predicting fluctuation-induced plasma-wall interactions in magnetically confined fusion plasmas.Comment: 17 pages, 10 figure

The Rayleigh-Brillouin Spectrum in Special Relativistic Hydrodynamics

In this paper we calculate the Rayleigh-Brillouin spectrum for a relativistic simple fluid according to three different versions available for a relativistic approach to non-equilibrium thermodynamics. An outcome of these calculations is that Eckart's version predicts that such spectrum does not exist. This provides an argument to question its validity. The remaining two results, which differ one from another, do provide a finite form for such spectrum. This raises the rather intriguing question as to which of the two theories is a better candidate to be taken as a possible version of relativistic non-equilibrium thermodynamics. The answer will clearly require deeper examination of this problem.Comment: 13 pages, no figures. Accepted for publication in Phys. Rev.

New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential

New exact analytical bound-state solutions of the D-dimensional Klein-Gordon equation for a large set of couplings and potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional generalized Morse potential. The eigenfunctions are expressed in terms of generalized Laguerre polynomials, and the eigenenergies are expressed in terms of solutions of irrational equations at the worst. Several analytical results found in the literature, including the so-called Klein-Gordon oscillator, are obtained as particular cases of this unified approac