Internal wave pressure, velocity, and energy flux from density perturbations

Determination of energy transport is crucial for understanding the energy budget and fluid circulation in density varying fluids such as the ocean and the atmosphere. However, it is rarely possible to determine the energy flux field $\mathbf{J} = p \mathbf{u}$, which requires simultaneous measurements of the pressure and velocity perturbation fields, $p$ and $\mathbf{u}$. We present a method for obtaining the instantaneous $\mathbf{J}(x,z,t)$ from density perturbations alone: a Green's function-based calculation yields $p$, and $\mathbf{u}$ is obtained by integrating the continuity equation and the incompressibility condition. We validate our method with results from Navier-Stokes simulations: the Green's function method is applied to the density perturbation field from the simulations, and the result for $\mathbf{J}$ is found to agree typically to within $1\%$ with $\mathbf{J}$ computed directly using $p$ and $\mathbf{u}$ from the Navier-Stokes simulation. We also apply the Green's function method to density perturbation data from laboratory schlieren measurements of internal waves in a stratified fluid, and the result for $\mathbf{J}$ agrees to within $6\%$ with results from Navier-Stokes simulations. Our method for determining the instantaneous velocity, pressure, and energy flux fields applies to any system described by a linear approximation of the density perturbation field, e.g., to small amplitude lee waves and propagating vertical modes. The method can be applied using our Matlab graphical user interface EnergyFlux

Stationary state volume fluctuations in a granular medium

A statistical description of static granular material requires ergodic sampling of the phase space spanned by the different configurations of the particles. We periodically fluidize a column of glass beads and find that the sequence of volume fractions phi of post-fluidized states is history independent and Gaussian distributed about a stationary state. The standard deviation of phi exhibits, as a function of phi, a minimum corresponding to a maximum in the number of statistically independent regions. Measurements of the fluctuations enable us to determine the compactivity X, a temperature-like state variable introduced in the statistical theory of Edwards and Oakeshott [Physica A {\bf 157}, 1080 (1989)].Comment: published with minor change

Bringing Scotland’s wilderness ‘within the reach of the people’: William Eagle Clarke (1853-1938) and representations of place

William Eagle Clarke was on the staff of the Royal Scottish Museum, Edinburgh, (now incorporated into National Museums Scotland) from 1888 to 1921. This poster presents two related aspects of his construct of representations of Scotland’s landscape

Bridging the ARCH model for finance and nonextensive entropy

Engle's ARCH algorithm is a generator of stochastic time series for financial returns (and similar quantities) characterized by a time-dependent variance. It involves a memory parameter $b$ ($b=0$ corresponds to {\it no memory}), and the noise is currently chosen to be Gaussian. We assume here a generalized noise, namely $q_n$-Gaussian, characterized by an index $q_{n} \in {\cal R}$ ($q_{n}=1$ recovers the Gaussian case, and $q_n>1$ corresponds to tailed distributions). We then match the second and fourth momenta of the ARCH return distribution with those associated with the $q$-Gaussian distribution obtained through optimization of the entropy S_{q}=\frac{% 1-\sum_{i} {p_i}^q}{q-1}, basis of nonextensive statistical mechanics. The outcome is an {\it analytic} distribution for the returns, where an unique $q\ge q_n$ corresponds to each pair $(b,q_n)$ ($q=q_n$ if $b=0$). This distribution is compared with numerical results and appears to be remarkably precise. This system constitutes a simple, low-dimensional, dynamical mechanism which accommodates well within the current nonextensive framework.Comment: 4 pages, 5 figures.Figure 4 fixe

Centrifugal acceleration of ions in the polar magnetosphere

The transport of ionospheric ions originating near the dayside cusp into the magnetotail is parametrically studied using a 3-D model of ion trajectories. It is shown that the centrifugal term in the guiding center parallel force equation dominates the parallel motion after about 4 Re geocentric distance. The dependence of the equatorial crossing distance on initial latitude, energy and convection electric field is presented for ions originating on the dayside ionosphere in the noon-midnight plane. It is also found that up to altitudes of about 5 Re, the motion is similar to that of a bead on a rotating rod, for which a simple analytical solution exists

Phase transition in a static granular system

We find that a column of glass beads exhibits a well-defined transition between two phases that differ in their resistance to shear. Pulses of fluidization are used to prepare static states with well-defined particle volume fractions $\phi$ in the range 0.57-0.63. The resistance to shear is determined by slowly inserting a rod into the column of beads. The transition occurs at $\phi=0.60$ for a range of speeds of the rod.Comment: 4 pages, 4 figures. The paper is significantly extended, including new dat

Geometry-induced asymmetric diffusion

Past work has shown that ions can pass through a membrane more readily in one direction than the other. We demonstrate here in a model and an experiment that for a mixture of small and large particles such asymmetric diffusion can arise solely from an asymmetry in the geometry of the pores of the membrane. Our deterministic simulation considers a two-dimensional gas of elastic disks of two sizes diffusing through a membrane, and our laboratory experiment examines the diffusion of glass beads of two sizes through a metal membrane. In both experiment and simulation, the membrane is permeable only to the smaller particles, and the asymmetric pores lead to an asymmetry in the diffusion rates of these particles. The presence of even a small percentage of large particles can clog a membrane, preventing passage of the small particles in one direction while permitting free flow of the small particles in the other direction. The purely geometric kinetic constraints may play a role in common biological contexts such as membrane ion channels.Comment: published with minuscule change

Novel Technique for Ultra-sensitive Determination of Trace Elements in Organic Scintillators

A technique based on neutron activation has been developed for an extremely high sensitivity analysis of trace elements in organic materials. Organic materials are sealed in plastic or high purity quartz and irradiated at the HFIR and MITR. The most volatile materials such as liquid scintillator (LS) are first preconcentrated by clean vacuum evaporation. Activities of interest are separated from side activities by acid digestion and ion exchange. The technique has been applied to study the liquid scintillator used in the KamLAND neutrino experiment. Detection limits of <2.4X10**-15 g 40K/g LS, <5.5X10**-15 g Th/g LS, and <8X10**-15 g U/g LS have been achieved.Comment: 16 pages, 3 figures, accepted for publication in Nuclear Instruments and Methods

Rhombic Patterns: Broken Hexagonal Symmetry

Landau-Ginzburg equations derived to conserve two-dimensional spatial symmetries lead to the prediction that rhombic arrays with characteristic angles slightly differ from 60 degrees should form in many systems. Beyond the bifurcation from the uniform state to patterns, rhombic patterns are linearly stable for a band of angles near the 60 degrees angle of regular hexagons. Experiments conducted on a reaction-diffusion system involving a chlorite-iodide-malonic acid reaction yield rhombic patterns in good accord with the theory.Energy Laboratory of the University of HoustonOffice of Naval ResearchU.S. Department of Energy Office of Basic Energy SciencesRobert A. Welch FoundationCenter for Nonlinear Dynamic