Quantum Correlations in Two-Particle Anderson Localization

We predict the quantum correlations between non-interacting particles evolving simultaneously in a disordered medium. While the particle density follows the single-particle dynamics and exhibits Anderson localization, the two-particle correlation develops unique features that depend on the quantum statistics of the particles and their initial separation. On short time scales, the localization of one particle becomes dependent on whether the other particle is localized or not. On long time scales, the localized particles show oscillatory correlations within the localization length. These effects can be observed in Anderson localization of non-classical light and ultra-cold atoms.Comment: 4 pages, 4 figures, comments welcom

Bloch oscillations of Path-Entangled Photons

We show that when photons in N-particle path entangled |N,0> + |0,N> state undergo Bloch oscillations, they exhibit a periodic transition between spatially bunched and antibunched states. The transition occurs even when the photons are well separated in space. We study the scaling of the bunching-antibunching period, and show it is proportional to 1/N.Comment: An error in figure 1b of the original manuscript was corrected, and the period $\lambda_B$ was redefine

Simulation of Hydrogen Generation from Methane Partial Oxidation in a Plasma Fuel Reformer

A model for the chemistry in a plasma fuel reformer or plasmatron has been developed. The plasma fuel reformer is set up to produce syngas (hydrogen and carbon monoxide gas mixture) from partial oxidation of hydrocarbons. The behavior of methane as fuel has been investigated to characterize and simulate the plasmatron performance. The goal of this work has been improved understanding of the physical/chemical processes within the reactor. The simulation tool used was CHEMKIN 3.7, using the GRI methane combustion mechanism. The Partially Stirred Reactor application (PASR) simulates random mixing by a frequency mixing parameter, which is directly dependant of the system fluid dynamic properties. The fuel reformer was designed as a reactor where combustion is initiated by an electric discharge due to ohmic heating of the arc region. From discharge observations, energy estimations and model simulations, it was found that the electric arc initiates combustion by locally raising the temperature and then propagating the reaction by heat and mass transfer/mixing to the surroundings. Simulation results demonstrated that there is an optimum characteristic mixing time for each residence time, depending on the initial temperature reached at the arc. It was also found that for given power input into the system, the more spread the energy is, or the more mass is heated to a moderate temperature, the better the calculated performance

Thermal collapse of a granular gas under gravity

Free cooling of a gas of inelastically colliding hard spheres represents a central paradigm of kinetic theory of granular gases. At zero gravity the temperature of a freely cooling homogeneous granular gas follows a power law in time. How does gravity, which brings inhomogeneity, affect the cooling? We combine molecular dynamics simulations, a numerical solution of hydrodynamic equations and an analytic theory to show that a granular gas cooling under gravity undergoes thermal collapse: it cools down to zero temperature and condenses on the bottom of the container in a finite time.Comment: 4 pages, 12 eps figures, to appear in PR

Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas

We employ Navier-Stokes granular hydrodynamics to investigate the long-time behavior of clustering instability in a freely cooling dilute granular gas in two dimensions. We find that, in circular containers, the homogeneous cooling state (HCS) of the gas loses its stability via a sub-critical pitchfork bifurcation. There are no time-independent solutions for the gas density in the supercritical region, and we present analytical and numerical evidence that the gas develops thermal collapse unarrested by heat diffusion. To get more insight, we switch to a simpler geometry of a narrow-sector-shaped container. Here the HCS loses its stability via a transcritical bifurcation. For some initial conditions a time-independent inhomogeneous density profile sets in, qualitatively similar to that previously found in a narrow-channel geometry. For other initial conditions, however, the dilute gas develops thermal collapse unarrested by heat diffusion. We determine the dynamic scalings of the flow close to collapse analytically and verify them in hydrodynamic simulations. The results of this work imply that, in dimension higher than one, Navier-Stokes hydrodynamics of a dilute granular gas is prone to finite-time density blowups. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.Comment: 18 pages, 19 figure