Flow in a slowly-tapering channel with oscillating walls

The flow of a fluid in a channel with walls inclined at an angle to each other is investigated at arbitrary Reynolds number. The flow is driven by an oscillatory motion of the wall incorporating a time-periodic displacement perpendicular to the channel centreline. The gap between the walls varies linearly with distance along the channel and is a prescribed periodic function of time. An approximate solution is constructed assuming that the angle of inclination of the walls is small. At leading order the flow corresponds to that in a channel with parallel, vertically oscillating walls examined by Hall and Papageorgiou \cite{HP}. A careful study of the governing partial differential system for the first order approximation controlling the tapering flow due to the wall inclination is conducted. It is found that as the Reynolds number is increased from zero the tapering flow loses symmetry and undergoes exponential growth in time. The loss of symmetry occurs at a lower Reynolds number than the symmetry-breaking for the parallel-wall flow. A window of asymmetric, time-periodic solutions is found at higher Reynolds number, and these are reached via a quasiperiodic transient from a given set of initial conditions. Beyond this window stability is again lost to exponentially growing solutions as the Reynolds number is increased

Energetic impact of size-selected metal cluster ions on graphite

We have investigated the impact of size-selected metal cluster ions (Agn-) on a covalently bonded substrate (graphite) over the energy range 15–1500 eV by a combination of scanning tunneling microscopy and molecular dynamics simulations. The key result is that the fate of the cluster (penetration into the surface versus diffusion and aggregation on the surface), at intermediate energies, depends on the lateral localization of the cluster kinetic energy at specific surface sites and thus, for small clusters, on the orientation of the cluster and the target substrate site

Kernel density classification and boosting: an L2 sub analysis

Kernel density estimation is a commonly used approach to classification. However, most of the theoretical results for kernel methods apply to estimation per se and not necessarily to classification. In this paper we show that when estimating the difference between two densities, the optimal smoothing parameters are increasing functions of the sample size of the complementary group, and we provide a small simluation study which examines the relative performance of kernel density methods when the final goal is classification. A relative newcomer to the classification portfolio is “boosting”, and this paper proposes an algorithm for boosting kernel density classifiers. We note that boosting is closely linked to a previously proposed method of bias reduction in kernel density estimation and indicate how it will enjoy similar properties for classification. We show that boosting kernel classifiers reduces the bias whilst only slightly increasing the variance, with an overall reduction in error. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research

Vertical and interhemispheric links in the stratosphere-mesosphere as revealed by the day-to-day variability of Aura-MLS temperature data

The coupling processes in the middle atmosphere have been a subject of intense research activity because of their effects on atmospheric circulation, structure, variability, and the distribution of chemical constituents. In this study, the day-to-day variability of Aura-MLS (Microwave Limb Sounder) temperature data are used to reveal the vertical and interhemispheric coupling processes in the stratosphere-mesosphere during four Northern Hemisphere winters (2004/2005–2007/2008). The UKMO (United Kingdom Meteorological Office) assimilated data and mesospheric winds from MF (medium frequency) radars are also applied to help highlight the coupling processes. In this study, a clear vertical link can be seen between the stratosphere and mesosphere during winter months. The coolings and reversals of northward meridional winds in the polar winter mesosphere are often observed in relation to warming events (Sudden Stratospheric Warming, SSW for short) and the associated changes in zonal winds in the polar winter stratosphere. An upper-mesospheric cooling usually precedes the beginning of the warming in the stratosphere by 1–2 days. Inter-hemispheric coupling has been identified initially by a correlation analysis using the year-to-year monthly zonal mean temperature. Then the correlation analyses are performed based upon the daily zonal mean temperature. From the original time sequences, significant positive (negative) correlations are generally found between zonal mean temperatures at the Antarctic summer mesopause and in the Arctic winter stratosphere (mesosphere) during northern mid-winters, although these correlations are dominated by the low frequency variability (i.e. the seasonal trend). Using the short-term oscillations (less than 15 days), the statistical result, by looking for the largest magnitude of correlation within a range of time-lags (0 to 10 days; positive lags mean that the Antarctic summer mesopause is lagging), indicates that the temporal variability of zonal mean temperature at the Antarctic summer mesopause is also positively (negatively) correlated with the polar winter stratosphere (mesosphere) during three (2004/2005, 2005/2006, and 2007/2008) out of the four winters. The highest value of the correlation coefficient is over 0.7 in the winter-stratosphere for the three winters. The remaining winter (2006/2007) has more complex correlations structures; correspondingly the polar vortex was distinguished this winter. The time-lags obtained for 2004/2005 and 2006/2007 are distinct from 2005/2006 and 2007/2008 where a 6-day lag dominates for the coupling between the winter stratosphere and the summer mesopause. The correlations are also provided using temperatures in northern longitudinal sectors in a comparison with the Antarctic-mesopause zonal mean temperature. For northern mid-high latitudes (~50–70° N), temperatures in Scandinavia-Eastern Europe and in the Pacific-Western Canada longitudinal sectors often have opposite signs of correlations with zonal mean temperatures near the Antarctic summer mesopause during northern mid-winters. The statistical results are shown to be associated with the Northern Hemisphere's polar vortex characteristics

On Convergence Properties of Shannon Entropy

Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential entropies. A general result for the desired differential entropy convergence is provided, taking into account both compactly and uncompactly supported densities. Convergence of differential entropy is also characterized in terms of the Kullback-Liebler discriminant for densities with fairly general supports, and it is shown that convergence in variation of probability measures guarantees such convergence under an appropriate boundedness condition on the densities involved. Results for the discrete setting are also provided, allowing for infinitely supported probability measures, by taking advantage of the equivalence between weak convergence and convergence in variation in this setting.Comment: Submitted to IEEE Transactions on Information Theor

Measurement of the Forward Cross Section of p(n,d)y at 190 MeV

This work was supported by the National Science Foundation Grant NSF PHY 81-14339 and by Indiana Universit

Studies of Proton-Induced Neutral Pion Production Near Threshold

This work was supported by the National Science Foundation Grant NSF PHY 81-14339 and by Indiana Universit

Proton Radiative Capture by Deuterium at Medium Energies

This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440

Proton Radiative Capture by Deuterium at Medium Energies

This work was supported by the National Science Foundation Grant NSF PHY 81-14339 and by Indiana Universit