Convective instability and transient growth in flow over a backward-facing step

Transient energy growths of two- and three-dimensional optimal linear perturbations to two-dimensional flow in a rectangular backward-facing-step geometry with expansion ratio two are presented. Reynolds numbers based on the step height and peak inflow speed are considered in the range 0–500, which is below the value for the onset of three-dimensional asymptotic instability. As is well known, the flow has a strong local convective instability, and the maximum linear transient energy growth values computed here are of order 80×103 at Re = 500. The critical Reynolds number below which there is no growth over any time interval is determined to be Re = 57.7 in the two-dimensional case. The centroidal location of the energy distribution for maximum transient growth is typically downstream of all the stagnation/reattachment points of the steady base flow. Sub-optimal transient modes are also computed and discussed. A direct study of weakly nonlinear effects demonstrates that nonlinearity is stablizing at Re = 500. The optimal three-dimensional disturbances have spanwise wavelength of order ten step heights. Though they have slightly larger growths than two-dimensional cases, they are broadly similar in character. When the inflow of the full nonlinear system is perturbed with white noise, narrowband random velocity perturbations are observed in the downstream channel at locations corresponding to maximum linear transient growth. The centre frequency of this response matches that computed from the streamwise wavelength and mean advection speed of the predicted optimal disturbance. Linkage between the response of the driven flow and the optimal disturbance is further demonstrated by a partition of response energy into velocity components

Convective instability and transient growth in steady and pulsatile stenotic flows

We show that suitable initial disturbances to steady or long-period pulsatile flows in a straight tube with an axisymmetric 75%-occlusion stenosis can produce very large transient energy growths. The global optimal disturbances to an initially axisymmetric state found by linear analyses are three-dimensional wave packets that produce localized sinuous convective instability in extended shear layers. In pulsatile flow, initial conditions that trigger the largest disturbances are either initiated at, or advect to, the separating shear layer at the stenosis in phase with peak systolic flow. Movies are available with the online version of the paper

Two-Photon Total Annihilation of Molecular Positronium

The rate for complete two-photon annihilation of molecular positronium Ps$_{2}$ is reported. This decay channel involves a four-body collision among the fermions forming Ps$_{2}$, and two photons of 1.022 MeV, each, as the final state. The quantum electrodynamics result for the rate of this process is found to be $\Gamma_{Ps_{2} \rightarrow \gamma\gamma}$ = 9.0 $\times 10^{-12}$ s$^{-1}$. This decay channel completes the most comprehensive decay chart for Ps$_{2}$ up to date.Comment: 4 pages, 2figures and 1 tabl

The Role of CI(-) Channel-inhibition in the Brain on the Phonotactic Selectivity of Female Crickets

The goal of this project was to determine if picrotoxin influences phonotactic selectivity of female crickets when nanoinjected into the supraesophageal ganglion. Adult females of Acheta domesticus were pre-tested for phonotaxis on a treadmill to a range of calling songs with different syllable periods. Following dissection to expose the brain, 9.2 nL of either saline (control group) or 10-5 M picrotoxin (experimental group) was nanoinjected into the supraesophageal ganglion. Post-tests following saline injection (10 min later) were similar to the pre-tests. Picrotoxin-treated females became more phonotactically selective displaying a preference for calling songs with the shorter syllable periods

High-stakes Testing and Special Populations

This opinion paper critically examines the use of high-stakes testing on special populations. Without appropriate accommodations, standardized exams are not valid for some students with special needs. Unfortunately, many classroom teachers who must initiate testing accommodations lack knowledge of appropriate accommodations and regularly fail to provide the necessary testing accommodations. The deficit understanding of testing accommodations makes comparisons between classrooms, schools, and districts invalid since some scores loose validity. Solutions specific to standardized testing and students with special needs are offered and a more encompassing solution to the problems incurred from these tests when used for high-stakes is suggested

Five Approaches to Literacy in Correctional Education

This article introduces literacy from a few “big picture” perspectives, and then reviews five paradigms that have shaped the teaching and learning of literacy in residential confinement institutions for juveniles and adults. The paradigms are specific to correctional education, but they will be familiar to all alternative teachers and advocates of literacy instruction

Optimal suppression of flow perturbations using boundary control

Boundary perturbations are considered as flow control forcing and their distributions are optimised to suppress transient energy growth induced by the most energetic disturbances in the domain. For a given control cost (square integration of the control forcing), the optimal control calculated from the proposed optimisation algorithm is proved to be unique. For small values of control cost, a sensitivity solution is obtained and its distribution indicates the sensitivity of perturbation energy on boundary control. For larger control cost, the distribution of the optimal control approaches the stablest mode of a direct-adjoint operator and tends to be grid-to-grid oscillatory. A controllability analysis is further conducted to identify the uncontrollable component of perturbations in the domain. This work underpins the recently thriving linear feed-back flow control investigations, most of which use empirically distributed control actuators, in terms of choosing the location and magnitude of the control forcing and evaluating the maximum control effect. Two case studies are conducted to demonstrate the proposed algorithm; in a stenotic flow, the optimised wall boundary control is observed to suppress over 95% of the transient energy growth induced by the global optimal initial perturbation; in the Batchelor vortex flow, the optimal inflow control can effectively suppress the spiral vortex breakdown induced by the development of initial perturbations

Influence of localised smooth steps on the instability of a boundary layer

We consider a smooth, spanwise-uniform forward facing step de ned by the Gauss error function of height 4-30% and four times the width of the local boundary layer thickness δ_99. The boundary layer flow over a smooth forward-facing stepped plate is studied with particular emphasis on stabilisation and destabilisation of the two-dimensional Tollmien- Schlichting (TS) waves and subsequently on three-dimensional disturbances at transition. The interaction between TS waves at a range of frequencies and a base flow over a single or two forward facing smooth steps is conducted by linear analysis. The results indicate that for a TS wave with a frequency F 2 [140; 160] (F=! =U21 106 where ! and U1 denote the perturbation angle frequency and freestream velocity magnitude, respectively), the amplitude of the TS wave is attenuated in the unstable regime of the neutral stability curve corresponding to a at plate boundary layer. Furthermore, it is observed that two smooth forward facing steps lead to a more acute reduction of the amplitude of the TS wave. When the height of a step is increased to more than 20% of the local boundary layer thickness for a xed width parameter, the TS wave is amplified and thereby a destabilisation e ect is introduced. Therefore, stabilisation or destabilisation effect of a smooth step is typically dependent on its shape parameters. To validate the results of the linear stability analysis, where a TS wave is damped by the forward facing smooth steps direct numerical simulation (DNS) is performed. The results of the DNS correlate favorably with the linear analysis and show that for the investigated frequency of the TS wave, the K-type transition process is altered whereas the onset of the H-type transition is delayed. The results of the DNS suggest that for the perturbation with the non-dimensional frequency parameter F = 150 and in the absence of other external perturbations, two forward facing smooth steps of height 5% and 12% of the boundary layer thickness delayed H-type transition scenario and completely suppresses it for the Ktype transition. By considering Gaussian white noise with both xed and random phase shift, it is demonstrated by DNS that transition is postponed in time and space by two forward facing smooth steps

Assessment in Music Education: Relationships between Classroom Practice and Professional Publication Topics

The purpose of this study was to investigate the relationship between actual current assessment practices of elementary music teachers and the assessment topics as published in the literature aimed at those teachers. Specifically, this study sought to: 1) identify the current assessment techniques utilized by elementary music teachers; 2) identify the types of assessment techniques included in the current music teacher literature, and 3) identify any relationships between the assessment techniques that are most frequently utilized by teachers and those that are most frequently included in teacher-focused music education publications. The researchers first examined data collected from the 100 elementary general music educators from the Northwestern United States who participated in a survey designed to identify the assessment practices of elementary general music teachers. The researchers next reviewed ten years (1999 – 2009) of the national publications Teaching Music and Music Educators Journal searching for articles that addressed the topic of classroom music assessment. Finally, the researchers ranked both the classroom and literature assessment techniques by frequency of use and frequency of inclusion in the literature and then examined the results in order to identify possible relationships. The researchers found that there is a possible disconnect between the assessment strategies reported as used by the classroom music educators participating in this study and the major professional publications in the music education field