Quantum Transport through Hierarchical Structures

The transport of quantum electrons through hierarchical lattices is of interest because such lattices have some properties of both regular lattices and random systems. We calculate the electron transmission as a function of energy in the tight binding approximation for two related Hanoi networks. HN3 is a Hanoi network with every site having three bonds. HN5 has additional bonds added to HN3 to make the average number of bonds per site equal to five. We present a renormalization group approach to solve the matrix equation involved in this quantum transport calculation. We observe band gaps in HN3, while no such band gaps are observed in linear networks or in HN5.Comment: 15 pages, RevTex, 10 figures, for related work, see http://www.physics.emory.edu/faculty/boettcher

Anomalous Defects and Their Quantized Transverse Conductivities

Using a description of defects in solids in terms of three-dimensional gravity, we study the propagation of electrons in the background of disclinations and screw dislocations. We study the situations where there are bound states that are effectively localized on the defect and hence can be described in terms of an effective 1+1 dimensional field theory for the low energy excitations. In the case of screw dislocations, we find that these excitations are chiral and can be described by an effective field theory of chiral fermions. Fermions of both chirality occur even for a given direction of the magnetic field. The ``net'' chirality of the system however is not always the same for a given direction of the magnetic field, but changes from one sign of the chirality through zero to the other sign as the Fermi momentum or the magnitude of the magnetic flux is varied. On coupling to an external electromagnetic field, the latter becomes anomalous, and predicts novel conduction properties for these materials.Comment: New material added. ReVTeX , 31 pgs., 4 figs.(uses epsf

Far Field Deposition Of Scoured Regolith Resulting From Lunar Landings

As a lunar lander approaches a dusty surface, the plume from the descent engine impinges on the ground, entraining loose regolith into a high velocity dust spray. Without the inhibition of a background atmosphere, the entrained regolith can travel many kilometers from the landing site. In this work, we simulate the flow field from the throat of the descent engine nozzle to where the dust grains impact the surface many kilometers away. The near field is either continuum or marginally rarefied and is simulated via a loosely coupled hybrid DSMC - Navier Stokes (DPLR) solver. Regions of two-phase and polydisperse granular flows are solved via DSMC. The far field deposition is obtained by using a staged calculation, where the first stages are in the near field where the flow is quasi-steady and the outer stages are unsteady. A realistic landing trajectory is approximated by a set of discrete hovering altitudes which range from 20m to 3m. The dust and gas motions are fully coupled using an interaction model that conserves mass, momentum, and energy statistically and inelastic collisions between dust particles are also accounted for. Simulations of a 4 engine configuration are also examined, and the erosion rates as well as near field particle fluxes are discussed.Astronom

Transition to the ultimate regime in two-dimensional Rayleigh-B\'enard convection

The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue in thermal convection, since the seminal work by Kraichnan [Phys. Fluids 5, 1374 (1962)]. Yet, when this transition takes place and how the local flow induces it is not fully understood. Here, by performing two-dimensional simulations of Rayleigh-B\'enard turbulence covering six decades in Rayleigh number Ra up to $10^{14}$ for Prandtl number Pr $=1$, for the first time in numerical simulations we find the transition to the ultimate regime, namely at $\textrm{Ra}^*=10^{13}$. We reveal how the emission of thermal plumes enhances the global heat transport, leading to a steeper increase of the Nusselt number than the classical Malkus scaling $\textrm{Nu} \sim \textrm{Ra}^{1/3}$ [Proc. R. Soc. London A 225, 196 (1954)]. Beyond the transition, the mean velocity profiles are logarithmic throughout, indicating turbulent boundary layers. In contrast, the temperature profiles are only locally logarithmic, namely within the regions where plumes are emitted, and where the local Nusselt number has an effective scaling $\textrm{Nu} \sim \textrm{Ra}^{0.38}$, corresponding to the effective scaling in the ultimate regime.Comment: 6 pages, 4figure

Model based methodology development for energy recovery in ash heat exchange systems

Flash tank evaporation combined with a condensing heat exchanger can be used when heat exchange is required between two streams and where at least one of these streams is difficult to handle (in terms of solid particles content, viscosity, pH, consistency etc.). To increase the efficiency of heat exchange, a cascade of these units in series can be used. Heat transfer relationships in such a cascade are very complex due to their interconnectivity, thus the impact of any changes proposed is difficult to predict. In this report, a mathematical model of a single unit ash tank evaporator combined with a condensing heat exchanger unit is proposed. This model is then developed for a chain of the units. The purpose of this model is to allow an accurate evaluation of the effect and result of an alteration to the system. The resulting model is applied to the RUSAL Aughinish Alumina digester area

Evaluation of a multimode fiber optic low coherence interferometer for path length resolved Doppler measurements of diffuse light \ud

The performance of a graded index multimode fiber optic low coherence Mach-Zehnder interferometer with phase modulation is analyzed. Investigated aspects were its ability to measure path length distributions and to perform path length resolved Doppler measurements of multiple scattered photons in a turbid suspension of particles undergoing Brownian and translational motion. The path length resolution of this instrument is compared with a system using single mode fibers for illumination and detection. The optical path lengths are determined from the zero order moment of the phase modulation peak in the power spectrum. The weighted first moment, which is equal to the average Doppler shift, shows a linear response for different mean flow velocities within the physiological rang

Variance Reduction For A Discrete Velocity Gas

We extend a variance reduction technique developed by Baker and Hadjiconstantinou [1] to a discrete velocity gas. In our previous work, the collision integral was evaluated by importance sampling of collision partners [2]. Significant computational effort may be wasted by evaluating the collision integral in regions where the flow is in equilibrium. In the current approach, substantial computational savings are obtained by only solving for the deviations from equilibrium. In the near continuum regime, the deviations from equilibrium are small and low noise evaluation of the collision integral can be achieved with very coarse statistical sampling. Spatially homogenous relaxation of the Bobylev-Krook-Wu distribution [3,4], was used as a test case to verify that the method predicts the correct evolution of a highly non-equilibrium distribution to equilibrium. When variance reduction is not used, the noise causes the entropy to undershoot, but the method with variance reduction matches the analytic curve for the same number of collisions. We then extend the work to travelling shock waves and compare the accuracy and computational savings of the variance reduction method to DSMC over Mach numbers ranging from 1.2 to 10.Aerospace Engineering and Engineering Mechanic