Flatness of tracer density profile produced by a point source in turbulence

The average concentration of tracers advected from a point source by a multivariate normal velocity field is shown to deviate from a Gaussian profile. The flatness (kurtosis) is calculated using an asymptotic series expansion valid for velocity fields with short correlation times or weak space dependence. An explicit formula for the excess flatness at first order demonstrates maximum deviation from a Gaussian profile at time t of the order of five times the velocity correlation time, with a t–1 decay to the Gaussian value at large times. Monotonically decaying forms of the velocity time correlation function are shown to yield negative values for the first order excess flatness, but positive values can result when the correlation function has an oscillatory tail

On the spectrum of a stretched spiral vortex

Corrections are found to the k^–5/3 spectrum of Lundgren [Phys. Fluids 25, 2193 (1982)] for a stretched spiral vortex model (a is the stretching strain rate and k the scalar wave number) of turbulent fine scales. These take the form of additional terms arising from the early time evolution, when the stretching of vortex lines is small. For the special case when the spiral takes the form of a rolled-up shear layer, it is shown that the composite spectrum is divergent, thus requiring the introduction of a finite early cutoff time tau1 in the time integral for the nonaxisymmetric contribution. The identity nuomega2 = 2nu[integral]0[infinity]k^2E(k)dk which gives the dissipation is then satisfied self-consistently. Direct numerical calculation of the energy spectrum from the approximate vorticity field for a special choice of spiral structure nevertheless indicates that the one-term k^–5/3-spectrum result is asymptotically valid in the inertial range provided atau1 is O(1) but that the numerically calculated dissipation spectrum appears to lie somewhere between an exp(–B1k2) and an exp(–B2k) form. It is also shown that the stretched, rolled-up shear-layer model predicts asymptotic shell-summed spectra of the energy dissipation and of the square of the vorticity, each asymptotically constant, with no power-law dependence, for k smaller than the Kolmogorov wave number.The corresponding one-dimensional spectra each show –log(k1) behavior for small k1. The extension of the model given by Pullin and Saffman [Phys. Fluids A 5, 126 (1993)] is reformulated by the introduction of a long-time cutoff in the vortex lifetime and an additional requirement that the vortex structures be approximately space filling. This gives a reduction in the number of model free-parameters but introduces a dependence of the calculated Kolmogorov constant and skewness on the ratio of the initial vortex radius to the equivalent Burgers-vortex radius. A scaling for this ratio in terms of the Taylor microscale Reynolds number is proposed in which the stretching strain is assumed to be provided by the large scales with spatial coherence limited to the maximum stretched length of the structures. Postdictions of the fourth-order flatness factor and of higher moments of the longitudinal velocity gradient statistics are compared with numerical simulation

Anticipated and Actual Bequests

This paper uses data on anticipated bequests from two waves of the Health and Retirement Study and the Asset and Health Dynamics of the Oldest Old (AHEAD), and on actual bequests from AHEAD. Actual bequests were measured in exit interviews given by proxy respondents for 774 AHEAD respondents who died between waves 1 and 2. Because the exit interview is representative of the elderly population, the distribution of estate values is quite different from that obtained from estate records, which represent just a wealthy subset of the population. Anticipated bequests were measured by the subjective probability of leaving bequests. Between waves 1 and 2, increases in bequest probabilities were associated with increases in the subjective probability of surviving, increments in household wealth, and widowing while out-of-pocket medical expenses reduced the likelihood of a bequest. By comparing bequest probabilities with baseline wealth we were able to test a main prediction of the life-cycle model, that individuals will dissave at advanced old-age. The AHEAD respondents anticipate substantial dissaving before they die.

Reconciling Synthesis and Decomposition: A Composite Approach to Capability Identification

Stakeholders' expectations and technology constantly evolve during the lengthy development cycles of a large-scale computer based system. Consequently, the traditional approach of baselining requirements results in an unsatisfactory system because it is ill-equipped to accommodate such change. In contrast, systems constructed on the basis of Capabilities are more change-tolerant; Capabilities are functional abstractions that are neither as amorphous as user needs nor as rigid as system requirements. Alternatively, Capabilities are aggregates that capture desired functionality from the users' needs, and are designed to exhibit desirable software engineering characteristics of high cohesion, low coupling and optimum abstraction levels. To formulate these functional abstractions we develop and investigate two algorithms for Capability identification: Synthesis and Decomposition. The synthesis algorithm aggregates detailed rudimentary elements of the system to form Capabilities. In contrast, the decomposition algorithm determines Capabilities by recursively partitioning the overall mission of the system into more detailed entities. Empirical analysis on a small computer based library system reveals that neither approach is sufficient by itself. However, a composite algorithm based on a complementary approach reconciling the two polar perspectives results in a more feasible set of Capabilities. In particular, the composite algorithm formulates Capabilities using the cohesion and coupling measures as defined by the decomposition algorithm and the abstraction level as determined by the synthesis algorithm.Comment: This paper appears in the 14th Annual IEEE International Conference and Workshop on the Engineering of Computer Based Systems (ECBS); 10 pages, 9 figure

Optical coherence tomography with a Fizeau interferometer configuration

We report the investigation of a Fizeau interferometer-based OCT system. A secondary processing interferometer is necessary in this configuration, to compensate the optical path difference formed in the Fizeau interferometer between the end of the fibre and the sample. The Fizeau configuration has the advantage of 'downlead insensitivity', which eliminates polarisation fading. An optical circulator is used in our system to route light efficiently from the source to the sample, and backscattered light from the sample and the fibre end through to the Mach-Zehnder processing interferometer. The choice of a Mach- Zehnder processing interferometer, from which both antiphase outputs are available, facilitates the incorporation of balanced detection, which often results in a large improvement in the Signal-to-Noise ratio (SNR) compared with the use of a single detector. Balanced detection comprises subtraction of the two antiphase interferometer outputs, implying that the signal amplitude is doubled and the noise is well reduced. It has been discerned that the SNR drops when the refractive index variation at a boundary is small. Several OCT images of samples (resin, resin + crystals, fibre composite) are presented

U.S. East Coast Trough Indices at 500 hPa and New England Winter Climate Variability

Using monthly gridded 500-hPa data, two synoptic indices are defined to better understand the principle mechanisms controlling intraseasonal to multiannual winter climate variability in NewEngland (NE). The “trough axis index” (TAI) is created to quantify the mean longitudinal position of the common East Coast pressure trough, and the “trough intensity index” (TII) is calculated to estimate the relative amplitude of this trough at 42.5°N. The TAI and TII are then compared with records for NE regional winter precipitation, temperature, and snowfall with the goal of understanding physical mechanisms linking NE winter climate with regional sea surface temperatures (SST), the North Atlantic Oscillation (NAO), and the Pacific–North American (PNA) teleconnection pattern. The TAI correlates most significantly with winter precipitation at inland sites, such that a western (eastern)trough axis position is associated with greater (lower) average monthly precipitation. Also, significant correlations between the TAI and both NE regional SSTs and the NAO suggest that longitudinal shifting of the trough is one possible mechanism linking the North Atlantic with NE regional winterclimate variability. The NE winter temperature is significantly correlated with the TII, regional SSTs, and the NAO. While the PNA also correlates with the TII, NE winter climate variables are apparently unrelated to the PNA index

A universal scaling law for the evolution of granular gases

Dry, freely evolving granular materials in a dilute gaseous state coalesce into dense clusters only due to dissipative interactions. This clustering transition is important for a number of problems ranging from geophysics to cosmology. Here we show that the evolution of a dilute, freely cooling granular gas is determined in a universal way by the ratio of inertial flow and thermal velocities, that is, the Mach number. Theoretical calculations and direct numerical simulations of the granular Navier--Stokes equations show that irrespective of the coefficient of restitution, density or initial velocity distribution, the density fluctuations follow a universal quadratic dependence on the system's Mach number. We find that the clustering exhibits a scale-free dynamics but the clustered state becomes observable when the Mach number is approximately of $\mathcal{O}(1)$. Our results provide a method to determine the age of a granular gas and predict the macroscopic appearance of clusters