Trajectory analysis for non-Brownian inertial suspensions in simple shear flow

We analyse pair trajectories of equal-sized spherical particles in simple shear flow for small but finite Stokes numbers. The Stokes number, \mbox{\textit{St}} \,{=}\, \dot{\gamma} \tau_p, is a dimensionless measure of particle inertia; here, $\tau_p$ is the inertial relaxation time of an individual particle and $\dot{\gamma}$ is the shear rate. In the limit of weak particle inertia, a regular small-\mbox{\textit{St}} expansion of the particle velocity is used in the equations of motion to obtain trajectory equations to the desired order in \mbox{\textit{St}}. The equations for relative trajectories are then solved, to O(\mbox{\textit{St}}), in the dilute limit, including only pairwise interactions. Particle inertia is found to destroy the fore–aft symmetry of the zero-Stokes trajectories, and finite-\mbox{\textit{St}} open trajectories suffer net transverse displacements in the velocity gradient and vorticity directions. The vorticity displacement remains O(\mbox{\textit{St}}), while the scaling of the gradient displacement increases from O(\mbox{\textit{St}}) for far-field open trajectories, to O(\mbox{\textit{St}}^{{1}/{2}}) for open trajectories with O(\mbox{\textit{St}}^{{1}/{2}}) upstream gradient offsets. The gradient displacement also changes sign, being negative close to the plane of the reference sphere (the shearing plane) on account of dominant lubrication interactions, and then becoming positive at larger off-plane separations. The transverse displacements accompanying successive pair interactions lead to a diffusive behaviour for long times. The shear-induced diffusivity in the vorticity direction is O(\mbox{\textit{St}}^2\phi \dot{\gamma} a^2), while that in the gradient direction scales as O(\mbox{\textit{St}}^2 \ln \mbox{\textit{St}}\,\phi \dot{\gamma} a^2) and O(\mbox{\textit{St}}^2 \phi \ln (1/\phi) \dot{\gamma} a^2) in the limits \phi \,{\ll}\, \mbox{\textit{St}}^{{1}/{3}} and \mbox{\textit{St}}^{{1}/{3}} \,{\ll}\, \phi \,{\ll}\, 1, respectively. Further, the region of zero-Stokes closed trajectories is destroyed, and there exists a new attracting limit cycle whose location in the shearing plane is, at leading order, independent of \mbox{\textit{St}}. The extension of the present analysis to include a generic linear flow, and the implications of the finite-\mbox{\textit{St}} trajectory modifications for coagulating systems are discussed

Aid and Growth: What Does the Cross-Country Evidence Really Show?

We examine the effects of aid on growth--in cross-sectional and panel data--after correcting for the bias that aid typically goes to poorer countries, or to countries after poor performance. Even after thiscorrection, we find little robust evidence of a positive (or negative) relationship between aid inflows into a country and its economic growth. We also find no evidence that aid works better in better policy or geographical environments, or that certain forms of aid work better than others. Our findings, which relate to the past, do not imply that aid cannot be beneficial in the future. But they do suggest that for aid to be effective in the future, the aid apparatus will have to be rethought. Our findings raise the question: what aspects of aid offset what ought to be the indisputable growth enhancing effects of resource transfers? Thus, our findings support efforts under way at national and international levels to understand and improve aid effectiveness.

Aid, Dutch Disease, and Manufacturing Growth

We examine the effects of aid on the growth of manufacturing, using a methodology that exploits the variation within countries and across manufacturing sectors, and corrects for possible reverse causality. We find that aid inflows have systematic adverse effects on a country’s competitiveness, as reflected in the lower relative growth rate of exportable industries. We provide some evidence suggesting that the channel for these effects is the real exchange rate appreciation caused by aid inflows. We conjecture that this may explain, in part, why it is hard to find robust evidence that foreign aid helps countries grow.manufacturing; economic development; dutch disease; cgd; center for global development

Many-Sources Large Deviations for Max-Weight Scheduling

In this paper, a many-sources large deviations principle (LDP) for the transient workload of a multi-queue single-server system is established where the service rates are chosen from a compact, convex and coordinate-convex rate region and where the service discipline is the max-weight policy. Under the assumption that the arrival processes satisfy a many-sources LDP, this is accomplished by employing Garcia's extended contraction principle that is applicable to quasi-continuous mappings. For the simplex rate-region, an LDP for the stationary workload is also established under the additional requirements that the scheduling policy be work-conserving and that the arrival processes satisfy certain mixing conditions. The LDP results can be used to calculate asymptotic buffer overflow probabilities accounting for the multiplexing gain, when the arrival process is an average of \emph{i.i.d.} processes. The rate function for the stationary workload is expressed in term of the rate functions of the finite-horizon workloads when the arrival processes have \emph{i.i.d.} increments.Comment: 44 page

Frequency and time profiles of metric wave isolated Type I solar noise storm bursts at high spectral and temporal resolution

Type I noise storms constitute a sizeable faction of the active-Sun radio emission component. Observations of isolated instances of such bursts, in the swept-frequency-mode at metric wavelengths, have remained sparse, with several unfilled regions in the frequency coverage. Dynamic spectra of the burst radiation, in the 30 - 130 MHz band, obtained from the recently commissioned digital High Resolution Spectrograph (HRS) at the Gauribidanur Radio Observatory, on account of the superior frequency and time resolution, have unravelled in explicit detail the temporal and spectral profiles of isolated bursts. Apart from presenting details on their fundamental emission features, the time and frequency profile symmetry, with reference to custom-specific Gaussian distributions, has been chosen as the nodal criterion to statistically explain the state of the source regions in the vicinity of magnetic reconnections, the latent excitation agent that contributes to plasma wave energetics, and the quenching phenomenon that causes damping of the burst emission.Comment: 9 pages 7 black and white / grey-scale figures (inclusive of 3 composite). MNRAS - accepte