Nonmodal energy growth and optimal perturbations in compressible plane Couette flow

Nonmodal transient growth studies and estimation of optimal perturbations have been made for the compressible plane Couette flow with three-dimensional disturbances. The maximum amplification of perturbation energy over time, $G_{\max}$, is found to increase with increasing Reynolds number ${\it Re}$, but decreases with increasing Mach number $M$. More specifically, the optimal energy amplification $G_{\rm opt}$ (the supremum of $G_{\max}$ over both the streamwise and spanwise wavenumbers) is maximum in the incompressible limit and decreases monotonically as $M$ increases. The corresponding optimal streamwise wavenumber, $\alpha_{\rm opt}$, is non-zero at M=0, increases with increasing $M$, reaching a maximum for some value of $M$ and then decreases, eventually becoming zero at high Mach numbers. While the pure streamwise vortices are the optimal patterns at high Mach numbers, the modulated streamwise vortices are the optimal patterns for low-to-moderate values of the Mach number. Unlike in incompressible shear flows, the streamwise-independent modes in the present flow do not follow the scaling law $G(t/{\it Re}) \sim {\it Re}^2$, the reasons for which are shown to be tied to the dominance of some terms in the linear stability operator. Based on a detailed nonmodal energy analysis, we show that the transient energy growth occurs due to the transfer of energy from the mean flow to perturbations via an inviscid {\it algebraic} instability. The decrease of transient growth with increasing Mach number is also shown to be tied to the decrease in the energy transferred from the mean flow ($\dot{\mathcal E}_1$) in the same limit

Linear stability, transient energy growth and the role of viscosity stratification in compressible plane Couette flow

Linear stability and the non-modal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the {\it uniform shear} flow with constant viscosity, and (b) the {\it non-uniform shear} flow with {\it stratified} viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers ($M$). For a given $M$, the critical Reynolds number ($Re$) is significantly smaller for the uniform shear flow than its non-uniform shear counterpart. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean-flow to perturbations. It is shown that the energy-transfer from mean-flow occurs close to the moving top-wall for ``mode I'' instability, whereas it occurs in the bulk of the flow domain for ``mode II''. For the non-modal analysis, it is shown that the maximum amplification of perturbation energy, $G_{\max}$, is significantly larger for the uniform shear case compared to its non-uniform counterpart. For $\alpha=0$, the linear stability operator can be partitioned into ${\cal L}\sim \bar{\cal L} + Re^2{\cal L}_p$, and the $Re$-dependent operator ${\cal L}_p$ is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: $G(t/{\it Re}) \sim {\it Re}^2$. A reduced inviscid model has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and non-modal instability, it is shown that the {\it viscosity-stratification} of the underlying mean flow would lead to a delayed transition in compressible Couette flow

Geometrical Aspects Of BRST Cohomology In Augmented Superfield Formalism

In the framework of augmented superfield approach, we provide the geometrical origin and interpretation for the nilpotent (anti-)BRST charges, (anti-)co-BRST charges and a non-nilpotent bosonic charge. Together, these local and conserved charges turn out to be responsible for a clear and cogent definition of the Hodge decomposition theorem in the quantum Hilbert space of states. The above charges owe their origin to the de Rham cohomological operators of differential geometry which are found to be at the heart of some of the key concepts associated with the interacting gauge theories. For our present review, we choose the two $(1 + 1)$-dimensional (2D) quantum electrodynamics (QED) as a prototype field theoretical model to derive all the nilpotent symmetries for all the fields present in this interacting gauge theory in the framework of augmented superfield formulation and show that this theory is a {\it unique} example of an interacting gauge theory which provides a tractable field theoretical model for the Hodge theory.Comment: LaTeX file, 25 pages, Ref. [49] updated, correct page numbers of the Journal are give

Nilpotent Symmetries For Matter Fields In Non-Abelian Gauge Theory: Augmented Superfield Formalism

In the framework of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, the derivation of the (anti-)BRST nilpotent symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem. In our present investigation, the local, covariant, continuous and off-shell nilpotent (anti-)BRST symmetry transformations for the Dirac fields $(\psi, \bar\psi)$ are derived in the framework of the augmented superfield formulation where the four $(3 + 1)$-dimensional (4D) interacting non-Abelian gauge theory is considered on the six $(4 + 2)$-dimensional supermanifold parametrized by the four even spacetime coordinates $x^\mu$ and a couple of odd elements ($\theta$ and $\bar\theta$) of the Grassmann algebra. The requirement of the invariance of the matter (super)currents and the horizontality condition on the (super)manifolds leads to the derivation of the nilpotent symmetries for the matter fields as well as the gauge- and the (anti-)ghost fields of the theory in the general scheme of the augmented superfield formalism.Comment: LaTeX file, 16 pages, printing mistakes in the second paragraph of `Introduction' corrected, a footnote added, these modifications submitted as ``erratum'' to IJMPA in the final for

Nucleotide specificity of the enzymatic and motile activities of dynein, kinesin, and heavy meromyosin.

The substrate specificities of dynein, kinesin, and myosin substrate turnover activity and cytoskeletal filament-driven translocation were examined using 15 ATP analogues. The dyneins were more selective in their substrate utilization than bovine brain kinesin or muscle heavy meromyosin, and even different types of dyneins, such as 14S and 22S dynein from Tetrahymena cilia and the beta-heavy chain-containing particle from the outer-arm dynein of sea urchin flagella, could be distinguished by their substrate specificities. Although bovine brain kinesin and muscle heavy meromyosin both exhibited broad substrate specificities, kinesin-induced microtubule translocation varied over a 50-fold range in speed among the various substrates, whereas heavy meromyosin-induced actin translocation varied only by fourfold. With both kinesin and heavy meromyosin, the relative velocities of filament translocation did not correlate well with the relative filament-activated substrate turnover rates. Furthermore, some ATP analogues that did not support the filament translocation exhibited filament-activated substrate turnover rates. Filament-activated substrate turnover and power production, therefore, appear to become uncoupled with certain substrates. In conclusion, the substrate specificities and coupling to motility are distinct for different types of molecular motor proteins. Such nucleotide "fingerprints" of enzymatic activities of motor proteins may prove useful as a tool for identifying what type of motor is involved in powering a motility-related event that can be reconstituted in vitro

Contacting single bundles of carbon nanotubes with alternating electric fields

Single bundles of carbon nanotubes have been selectively deposited from suspensions onto sub-micron electrodes with alternating electric fields. We explore the resulting contacts using several solvents and delineate the differences between Au and Ag as electrode materials. Alignment of the bundles between electrodes occurs at frequencies above 1 kHz. Control over the number of trapped bundles is achieved by choosing an electrode material which interacts strongly with the chemical functional groups of the carbon nanotubes, with superior contacts being formed with Ag electrodes.Comment: 4 pages, RevTe

Locating the ‘radical’ in 'Shoot the Messenger'

This is the author's accepted manuscript. The final published article is available from the link below, copyright 2013 @ Edinburgh University Press.The 2006 BBC drama Shoot the Messenger is based on the psychological journey of a Black schoolteacher, Joe Pascale, accused of assaulting a Black male pupil. The allegation triggers Joe's mental breakdown which is articulated, through Joe's first-person narration, as a vindictive loathing of Black people. In turn, a range of common stereotypical characterisations and discourses based on a Black culture of hypocrisy, blame and entitlement is presented. The text is therefore laid wide open to a critique of its neo-conservatism and hegemonic narratives of Black Britishness. However, the drama's presentation of Black mental illness suggests that Shoot the Messenger may also be interpreted as a critique of social inequality and the destabilising effects of living with ethnicised social categories. Through an analysis of issues of representation, the article reclaims this controversial text as a radical drama and examines its implications for and within a critical cultural politics of ‘race’ and representation

Dynamics of entropy perturbations in assisted dark energy with mixed kinetic terms

We study dynamics of entropy perturbations in the two-field assisted dark energy model. Based on the scenario of assisted dark energy, in which one scalar field is subdominant compared with the other in the early epoch, we show that the entropy perturbations in this two-field system tend to be constant on large scales in the early epoch and hence survive until the present era for a generic evolution of both fields during the radiation and matter eras. This behaviour of the entropy perturbations is preserved even when the fields are coupled via kinetic interaction. Since, for assisted dark energy, the subdominant field in the early epoch becomes dominant at late time, the entropy perturbations can significantly influence the dynamics of density perturbations in the universe. Assuming correlations between the entropy and curvature perturbations, the entropy perturbations can enhance the integrated Sachs-Wolfe (ISW) effect if the signs of the contributions from entropy perturbations and curvature perturbations are opposite after the matter era, otherwise the ISW contribution is suppressed. For canonical scalar field the effect of entropy perturbations on ISW effect is small because the initial value of the entropy perturbations estimated during inflation cannot be sufficiently large. However, in the case of k-essence, the initial value of the entropy perturbations can be large enough to affect the ISW effect to leave a significant imprint on the CMB power spectrum.Comment: 25 pages, 8 figures, revised version, accepted for publication in JCA

Cohomological Operators and Covariant Quantum Superalgebras

We obtain an interesting realization of the de Rham cohomological operators of differential geometry in terms of the noncommutative q-superoscillators for the supersymmetric quantum group GL_{qp} (1|1). In particular, we show that a unique superalgebra, obeyed by the bilinears of fermionic and bosonic noncommutative q-(super)oscillators of GL_{qp} (1|1), is exactly identical to that obeyed by the de Rham cohomological operators. A set of discrete symmetry transformation for a set of GL_{qp} (1|1) covariant superalgebras turns out to be the analogue of the Hodge duality * operation of differential geometry. A connection with an extended BRST algebra obeyed by the nilpotent (anti-)BRST and (anti-)co-BRST charges, the ghost charge and a bosonic charge (which is equal to the anticommutator of (anti-)BRST and (anti-)co-BRST charges) is also established.Comment: LaTeX file, 21 page