Entrainment of short-wavelength free-stream vortical disturbances in compressible and incompressible boundary layers

The fundamental difference between continuous modes of the Orr–Sommerfeld/Squire equations and the entrainment of free-stream vortical disturbances (FSVD) into the boundary layer has been investigated in a recent paper (Dong &amp; Wu, J. Fluid Mech., vol. 732, 2013, pp. 616–659). It was shown there that the non-parallel-flow effect plays a leading-order role in the entrainment, and neglecting it at the outset, as is done in the continuous-mode formulation, leads to non-physical features of ‘Fourier entanglement’ and abnormal anisotropy. The analysis, which was for incompressible boundary layers and for FSVD with a characteristic wavelength of the order of the local boundary-layer thickness, is extended in this paper to compressible boundary layers and FSVD with even shorter wavelengths, which are comparable with the width of the so-called edge layer. Non-parallelism remains a leading-order effect in the present scaling, which turns out to be more general in that the equations and solutions in the previous paper are recovered in the appropriate limit. Appropriate asymptotic solutions in the main and edge layers are obtained to characterize the entrainment. It is found that when the Prandtl number \mathit{Pr}<1, free-stream vortical disturbances of relatively low frequency generate very strong temperature fluctuations within the edge layer, leading to formation of thermal streaks. A composite solution, uniformly valid across the entire boundary layer, is constructed, and it can be used in receptivity studies and as inlet conditions for direct numerical simulations of bypass transition. For compressible boundary layers, continuous spectra of the disturbance equations linearized about a parallel base flow exhibit entanglement between vortical and entropy modes, namely, a vortical mode necessarily induces an entropy disturbance in the free stream and vice versa, and this amounts to a further non-physical behaviour. High Reynolds number asymptotic analysis yields the relations between the amplitudes of entangled modes.</jats:p

A New Approach for Computing the Bandwidth Statistics of Avalanche Photodiodes

A new approach for characterizing the avalanche-buildup-time-limited bandwidth of avalanche photodiodes (APDs) is introduced which relies on the direct knowledge of the statistics of the random response time. The random response time is the actual duration of the APD’s finite buildup-limited random impulse response function. A theory is developed characterizing the probability distribution function (PDF) of the random response time. Recurrence equations are derived and numerically solved to yield the PDF of the random response time. The PDF is then used to compute the mean and the standard deviation of the bandwidth. The dependence of the mean and the standard deviation of the bandwidth on the APD mean gain and the ionization coefficient ratio is investigated. Exact asymptotics of the tail of the PDF of the response time are also developed to aid the computation efficiency. The technique can be readily applied to multiplication models which incorporate dead space and can be extended to cases for which the carrier ionization coefficient is position dependent

Z-graded weak modules and regularity

It is proved that if any Z-graded weak module for vertex operator algebra V is completely reducible, then V is rational and C_2-cofinite. That is, V is regular. This gives a natural characterization of regular vertex operator algebras.Comment: 9 page

Neutron star magnetospheres: the binary pulsar, Crab and magnetars

A number of disparate observational and theoretical pieces of evidence indicate that, contrary to the conventional wisdom, neutron stars' closed field lines are populated by dense, hot plasma and may be responsible for producing some radio and high energy emission. This conclusion is based on eclipse modeling of the binary pulsar system PSR J0737-3039A/B (Lyutikov & Thompson 2005), a quantitative theory of Crab giant pulses (Lyutikov 2007) and a number of theoretical works related to production of non-thermal spectra in magnetars through resonant scattering. In magnetars, dense pair plasma is produced by twisting magnetic field lines and associated electric fields required to lift the particles from the surface. In long period pulsars, hot particles on closed field lines can be efficiently trapped by magnetic mirroring, so that relatively low supply rate, e.g. due to a drift from open field lines, may result in high density. In short period pulsars, magnetic mirroring does not work; large densities may still be expected at the magnetic equator near the Y-point.Comment: Proceedings, Huangshan meeting "Astrophysics of Compact Objects

Learning distance to subspace for the nearest subspace methods in high-dimensional data classification

The nearest subspace methods (NSM) are a category of classification methods widely applied to classify high-dimensional data. In this paper, we propose to improve the classification performance of NSM through learning tailored distance metrics from samples to class subspaces. The learned distance metric is termed as ‘learned distance to subspace’ (LD2S). Using LD2S in the classification rule of NSM can make the samples closer to their correct class subspaces while farther away from their wrong class subspaces. In this way, the classification task becomes easier and the classification performance of NSM can be improved. The superior classification performance of using LD2S for NSM is demonstrated on three real-world high-dimensional spectral datasets

Dynamic and Leakage Power-Composition Profile Driven Co-Synthesis for Energy and Cost Reduction

Recent research has shown that combining dynamic voltage scaling (DVS) and adaptive body bias (ABB) techniques achieve the highest reduction in embedded systems energy dissipation [1]. In this paper we show that it is possible to produce comparable energy saving to that obtained using combined DVS and ABB techniques but with reduced hardware cost achieved by employing processing elements (PEs) with separate DVS or ABB capability. A co-synthesis methodology which is aware of tasks’ power-composition profile (the ratio of the dynamic power to the leakage power) is presented. The methodology selects voltage scaling capabilities (DVS, ABB, or combined DVS and ABB) for the PEs, maps, schedules, and voltage scales applications given as task graphs with timing constraints, aiming to dynamic and leakage energy reduction at low hardware cost. We conduct detailed experiments, including a real-life example, to demonstrate the effectiveness of our methodology. We demonstrate that it is possible to produce designs that contain PEs with only DVS or ABB technique but have energy dissipation that are only 4.4% higher when compared with the same designs that employ PEs with combined DVS and ABB capabilities