Block Implicit One-Step Methods

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAB-07-67-C-0199Office of Naval Research / ONR N00014-67-A-0305-001

An Implicit Fourth Order Difference Method for Viscous Flows

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAB-07-67-C-0199Office of Naval Research / ONR N00014-67-A-0305-001

Implementation of Finite Difference Schemes of Solving Fluid Dynamic Problems on ILLIAC IV

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryOffice of Naval Research / ONR-N00014-67-A-0305-001

Study of a zirconium getter for purification of xenon gas

Oxygen, nitrogen and methane purification efficiencies for a common zirconium getter are measured in 1050 Torr of xenon gas. Starting with impurity concentrations near 10^{-6} g/g, the outlet impurity level is found to be less than 120*10^{-12} g/g for O2 and less than 950*10^{-12} g/g for N2. For methane we find residual contamination of the purified gas at concentrations varying over three orders of magnitude, depending on the purifier temperature and the gas flow rate. A slight reduction in the purifier's methane efficiency is observed after 13 mg of this impurity has been absorbed, which we attribute to partial exhaustion of the purifier's capacity for this species. We also find that the purifier's ability to absorb N2 and methane can be extinguished long before any decrease in O2 performance is observed, and slower flow rates should be employed for xenon purification due to the cooling effect that the heavy gas has on the getter.Comment: 14 pages, 5 figure

Exact Occupation Time Distribution in a Non-Markovian Sequence and Its Relation to Spin Glass Models

We compute exactly the distribution of the occupation time in a discrete {\em non-Markovian} toy sequence which appears in various physical contexts such as the diffusion processes and Ising spin glass chains. The non-Markovian property makes the results nontrivial even for this toy sequence. The distribution is shown to have non-Gaussian tails characterized by a nontrivial large deviation function which is computed explicitly. An exact mapping of this sequence to an Ising spin glass chain via a gauge transformation raises an interesting new question for a generic finite sized spin glass model: at a given temperature, what is the distribution (over disorder) of the thermally averaged number of spins that are aligned to their local fields? We show that this distribution remains nontrivial even at infinite temperature and can be computed explicitly in few cases such as in the Sherrington-Kirkpatrick model with Gaussian disorder.Comment: 10 pages Revtex (two-column), 1 eps figure (included

On distributions of functionals of anomalous diffusion paths

Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger equation in imaginary time. In recent years there is a growing interest in particular functionals of non-Brownian motion, or anomalous diffusion, but no equation existed for their PDF. Here, we derive a fractional generalization of the Feynman-Kac equation for functionals of anomalous paths based on sub-diffusive continuous-time random walk. We also derive a backward equation and a generalization to Levy flights. Solutions are presented for a wide number of applications including the occupation time in half space and in an interval, the first passage time, the maximal displacement, and the hitting probability. We briefly discuss other fractional Schrodinger equations that recently appeared in the literature.Comment: 25 pages, 4 figure

Sensitivity of the surface orographic gravity wave drag to vertical wind shear over Antarctica

The effects of vertical wind shear on orographic gravity wave drag derived previously from inviscid linear theory are evaluated using reanalysis data. Emphasis is placed on the relative importance of uniform and directional shear (associated with first and second vertical derivatives of the wind velocity), which are theoretically predicted, respectively, to reduce and enhance the surface drag. Two levels at which the wind derivatives are estimated are considered for evaluating the shear corrections to the drag: a height just above the parametrized boundary layer height in the ECMWF model (BLH), and a height of order the standard deviation of the subgrid-scale orography elevation (SDH), adopted by previous authors. A climatology of the Richardson number (Ri) computed for the decade 2006-2015 suggests that the Antarctic region has a high incidence of low Ri values, implying high shear conditions. Shear estimated at the BLH has a relatively modest impact on the drag, whereas shear estimated at the SDH has a stronger impact. Predicted drag enhancement is more widespread than drag reduction because terms involving second wind derivatives dominate the drag correction for a larger fraction of the time than terms involving first derivatives. A comparison of climatologies of the drag corrections for horizontally elliptical mountains (which represent anisotropic subgrid-scale orography in parametrizations) and axisymmetric mountains always results in drag enhancement over Antarctica, with a maximum during the JJA season, showing qualitative robustness to both calculation height and orography anisotropy. However, this enhancement is smaller when using elliptical instead of axisymmetric orography. This is because the shear vector is predominantly oriented along mountain ridges rather than across them when the orography is anisotropic

Charge ordering and antiferromagnetic exchange in layered molecular crystals of the theta type

We consider the electronic properties of layered molecular crystals of the type theta-D$_2$A, where A is an anion and D is a donor molecule such as BEDT-TTF [where BEDT-TTF is bis-(ethylenedithia-tetrathiafulvalene)] which is arranged in the theta type pattern within the layers. We argue that the simplest strongly correlated electron model that can describe the rich phase diagram of these materials is the extended Hubbard model on the square lattice at a quarter filling. In the limit where the Coulomb repulsion on a single site is large, the nearest-neighbour Coulomb repulsion, V, plays a crucial role. When V is much larger than the intermolecular hopping integral t the ground state is an insulator with charge ordering. In this phase antiferromagnetism arises due to a novel fourth-order superexchange process around a plaquette on the square lattice. We argue that the charge ordered phase is destroyed below a critical non-zero value V, of the order of t. Slave boson theory is used to explicitly demonstrate this for the SU(N) generalisation of the model, in the large N limit. We also discuss the relevance of the model to the all-organic family beta''-(BEDT-TTF)$_2$SF$_5$YSO$_3$ where Y = CH$_2$CF$_2$, CH$_2$, CHF.Comment: 15 pages, 6 eps figure

Extreme Ultra-Violet Spectroscopy of the Lower Solar Atmosphere During Solar Flares

The extreme ultraviolet portion of the solar spectrum contains a wealth of diagnostic tools for probing the lower solar atmosphere in response to an injection of energy, particularly during the impulsive phase of solar flares. These include temperature and density sensitive line ratios, Doppler shifted emission lines and nonthermal broadening, abundance measurements, differential emission measure profiles, and continuum temperatures and energetics, among others. In this paper I shall review some of the advances made in recent years using these techniques, focusing primarily on studies that have utilized data from Hinode/EIS and SDO/EVE, while also providing some historical background and a summary of future spectroscopic instrumentation.Comment: 34 pages, 8 figures. Submitted to Solar Physics as part of the Topical Issue on Solar and Stellar Flare

Interlayer hopping properties of electrons in layered metals

A formalism is proposed to study the electron tunneling between extended states, based on the spin-boson Hamiltonian previously used in two-level systems. It is applied to analyze the out--of--plane tunneling in layered metals considering different models. By studying the effects of in--plane interactions on the interlayer tunneling of electrons near the Fermi level, we establish the relation between departure from Fermi liquid behavior driven by electron correlations inside the layer and the out of plane coherence. Response functions, directly comparable with experimental data are obtained