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

Linear stability and the nonmodal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the uniform shear flow with constant viscosity, and (b) the nonuniform shear flow with 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 nonuniform shear counterpart; for a given Re, the dominant instability (over all streamwise wave numbers, α) of each mean flow belongs to different modes for a range of supersonic M. 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 nonmodal transient growth analysis, it is shown that the maximum temporal amplification of perturbation energy, Gmax, and the corresponding time scale are significantly larger for the uniform shear case compared to those for its nonuniform counterpart. For α=0, the linear stability operator can be partitioned into L∼L̅ +Re2 Lp, and the Re-dependent operator Lp 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∕Re)∼Re2. In contrast, the dominance of Lp is responsible for the invalidity of this scaling law in nonuniform shear flow. An inviscid reduced model, based on Ellingsen-Palm-type solution, has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and nonmodal instability, it is shown that the viscosity stratification of the underlying mean flow would lead to a delayed transition in compressible Couette flow.

The standard molar Gibbs energy of formation of YbPt3 and LuPt3 intermetallics

The standard molar Gibbs energies of formation of YbPt3 and LuPt3 intermetallic compounds have been measured in the temperature range 880 K to 1100 K using the solid-state cells:View the MathML source and View the MathML source The trifluoride of Yb is not stable in equilibrium with Yb or YbPt3. The results can be expressed by the equations: View the MathML source View the MathML source The standard molar Gibbs energy of formation of LuPt3 is −41.1 kJ · mol−1 more negative than that for YbPt3 at 1000 K. Ytterbium is divalent in the pure metal and trivalent in the intermetallic YbPt3. The energy required for the promotion of divalent Yb to the trivalent state is responsible for the less negative ΔfGmo of YbPt3. The enthalpies of formation of the two intermetallics are in reasonable agreement with Miedema's model. Because of the extraordinary stability of these compounds it is possible to reduce oxides of Yb and Lu with hydrogen in the presence of platinum at View the MathML source. The equilibrium chemical potential of oxygen corresponding to the reduction of Yb2O3 and Lu2O3 by hydrogen in the presence of platinum is presented in the form of an Ellingham diagram.

Potentiometric determination of the stability of BaCu2O2

The thermodynamic stability of the compound BaCu2O2 was determined using a solid-state galvanic cell: View the MathML source as a function of temperature in the range 970–1170 K. Single crystal BaF2 was used as the solid electrolyte. The partial pressure of oxygen in the argon gas flowing over the electrodes was 1.27 Pa. The reversible e.m.f. of the cell can be expressed by View the MathML source. The Gibbs free energy of formation of barium cuprite from component oxides according to the reaction View the MathML source is View the MathML source.

Phase-plane techniques for the solution of transient-stability problems

The paper presents a graphical-numerical method for determining the transient stability limits of a two-machine system under the usual assumptions of constant input, no damping and constant voltage behind transient reactance. The method presented is based on the phase-plane criterion,1, 2 in contrast to the usual step-by-step and equal-area methods. For the transient stability limit of a two-machine system, under the assumptions stated, the sum of the kinetic energy and the potential energy, at the instant of fault clearing, should just be equal to the maximum value of the potential energy which the machines can accommodate with the fault cleared. The assumption of constant voltage behind transient reactance is then discarded in favour of the more accurate assumption of constant field flux linkages. Finally, the method is extended to include the effect of field decrement and damping. A number of examples corresponding to each case are worked out, and the results obtained by the proposed method are compared with those obtained by the usual methods.

Stability of developing film flow down an inclined surface

Film flows on inclined surfaces are often assumed to be of constant thickness, which ensures that the velocity profile is half-Poiseuille. It is shown here that by shallow water theory, only flows in a portion of Reynolds number-Froude number (Re-Fr) plane can asymptotically attain constant film thickness. In another portion on the plane, the constant thickness solution appears as an unstable fixed point, while in other regions the film thickness seems to asymptote to a positive slope. Our simulations of the Navier-Stokes equations confirm the predictions of shallow water theory at higher Froude numbers, but disagree with them at lower Froude numbers. We show that different regimes of film flow show completely different stability behaviour from that predicted earlier. Supercritical decelerating flows are shown to be always unstable, whereas accelerating flows become unstable below a certain Reynolds number for a given Froude number. Subcritical flows on the other hand are shown to be unstable above a certain Reynolds number. In some range of parameters, two solutions for the base flowexist, and the attached profile is found to be more stable. All flows except those with separation become more stable as they proceed downstream. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4758299]

Formation energies and the stability of the oxides of K

The most common valencies associated with K and O atoms are 1+ and 2-. As a result, one expects K2O to be the oxide of potassium which is the most stable with respect to its constituents. Calculating the formation energy within electronic structure calculations using hybrid functionals, one finds that K2O2 has the largest formation energy, implying the largest stability of this oxide of potassium with respect to its constituents. This is traced to the presence of oxygen dimers in the K2O2 structure which interact strongly resulting in a larger formation energy compared to the more ionic K2O.

A New Voltage Stability Index based on the Tangent Vector of the Power Flow Jacobian

This paper presents a new voltage stability index based on the tangent vector of the power flow jacobian. This index is capable of providing the relative vulnerability information of the system buses from the point of view of voltage collapse. In an effort to compare this index with a similar index, the popular voltage stability index L is studied and it is shown through system studies that the L index is not a very consistent indicator of the voltage collapse point of the system but is only a reasonable indicator of the vulnerability of the system buses to voltage collapse. We also show that the new index can be used in the voltage stability analysis of radial systems which is not possible with the L index. This is a significant result of this investigation since there is a lot of contemporary interest in distributed generation and microgrids which are by and large radial in nature. Simulation results considering several test systems are provided to validate the results and the computational needs of the proposed scheme is assessed in comparison with other schemes

Stability of the flow in a soft tube deformed due to an applied pressure gradient

A linear stability analysis is carried out for the flow through a tube with a soft wall in order to resolve the discrepancy of a factor of 10 for the transition Reynolds number between theoretical predictions in a cylindrical tube and the experiments of Verma and Kumaran J. Fluid Mech. 705, 322 (2012)]. Here the effect of tube deformation (due to the applied pressure difference) on the mean velocity profile and pressure gradient is incorporated in the stability analysis. The tube geometry and dimensions are reconstructed from experimental images, where it is found that there is an expansion and then a contraction of the tube in the streamwise direction. The mean velocity profiles at different downstream locations and the pressure gradient, determined using computational fluid dynamics, are found to be substantially modified by the tube deformation. The velocity profiles are then used in a linear stability analysis, where the growth rates of perturbations are calculated for the flow through a tube with the wall modeled as a neo-Hookean elastic solid. The linear stability analysis is carried out for the mean velocity profiles at different downstream locations using the parallel flow approximation. The analysis indicates that the flow first becomes unstable in the downstream converging section of the tube where the flow profile is more pluglike when compared to the parabolic flow in a cylindrical tube. The flow is stable in the upstream diverging section where the deformation is maximum. The prediction for the transition Reynolds number is in good agreement with experiments, indicating that the downstream tube convergence and the consequent modification in the mean velocity profile and pressure gradient could reduce the transition Reynolds number by an order of magnitude.

AdS (in)stability: Lessons from the scalar field

We argued in arXiv: 1408.0624 that the quartic scalar field in AdS has features that could be instructive for answering the gravitational stability question of AdS. Indeed, the conserved charges identified there have recently been observed in the full gravity theory as well. In this paper, we continue our investigation of the scalar field in AdS and provide evidence that in the Two-Time Formalism (TTF), even for initial conditions that are far from quasi-periodicity, the energy in the higher modes at late times is exponentially suppressed in the mode number. Based on this and some related observations, we argue that there is no thermalization in the scalar TTF model within time-scales that go as similar to 1/epsilon(2), where epsilon measures the initial amplitude (with only low-lying modes excited). It is tempting to speculate that the result holds also for AdS collapse. (C) 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license.

Rapid synthesis of hybrids and hollow PdO nanostructures by controlled in situ dissolution of a ZnO nanorod template: insights into the formation mechanism and thermal stability

Hollow nanomaterials have attracted a lot of interest by virtue of their wide range of applications that arise primarily due to their unique architecture. A common strategy to synthesize hollow nanomaterials is by nucleation of the shell material over a preformed core and subsequent dissolution of the core in the second step. Herein an ultrafast, microwave route has been demonstrated, to synthesize PdO nanotubes in a single step using ZnO as a sacrificial template. The mechanism of the nanotube formation has been investigated in detail using control experiments. By tuning the starting ratio of PdCl2 : ZnO, hollow to hybrid PdO nanostructures could be obtained using the same method. Conversion of the PdO to Pd nanotubes has been shown by simple NaBH4 treatment. The thermal stability of the PdO nanotubes has been studied. The insights presented here are general and applicable for the synthesis of hybrids/hollow structures in other systems as well.

Precipitation In Small Systems--II. Mean Field Equations More Effective Than Population Balance

Part I (Manjunath et al., 1994, Chem. Engng Sci. 49, 1451-1463) of this paper showed that the random particle numbers and size distributions in precipitation processes in very small drops obtained by stochastic simulation techniques deviate substantially from the predictions of conventional population balance. The foregoing problem is considered in this paper in terms of a mean field approximation obtained by applying a first-order closure to an unclosed set of mean field equations presented in Part I. The mean field approximation consists of two mutually coupled partial differential equations featuring (i) the probability distribution for residual supersaturation and (ii) the mean number density of particles for each size and supersaturation from which all average properties and fluctuations can be calculated. The mean field equations have been solved by finite difference methods for (i) crystallization and (ii) precipitation of a metal hydroxide both occurring in a single drop of specified initial supersaturation. The results for the average number of particles, average residual supersaturation, the average size distribution, and fluctuations about the average values have been compared with those obtained by stochastic simulation techniques and by population balance. This comparison shows that the mean field predictions are substantially superior to those of population balance as judged by the close proximity of results from the former to those from stochastic simulations. The agreement is excellent for broad initial supersaturations at short times but deteriorates progressively at larger times. For steep initial supersaturation distributions, predictions of the mean field theory are not satisfactory thus calling for higher-order approximations. The merit of the mean field approximation over stochastic simulation lies in its potential to reduce expensive computation times involved in simulation. More effective computational techniques could not only enhance this advantage of the mean field approximation but also make it possible to use higher-order approximations eliminating the constraints under which the stochastic dynamics of the process can be predicted accurately.

Studies on the target conditioning for deposition of $LiCoO_{2}$ films

Deposition of good quality thin films of Lithium Cobalt Oxide (LiCoO2), by sputtering is preceded by target conditioning, which dictates the surface composition, morphology and electrochemical performance of the deposited film. Sputtering from a Virgin target surface, results in films with excess of the more reactive elements. The concentration of these reactive elements in the films decreases until the system reaches a steady state after sufficient sputtering from the target. This paper discusses the deposition kinetics in terms of target conditioning of LiCoO2. The composition, morphology and texturing of deposited film during various hours of sputtering were analyzed using X-ray photoelectron Spectroscopy (XPS) and Field Emission Scanning electron microscopy (FESEM). The compositional stability is not observed in the films formed during the initial hours or Sputtering from the fresh target, which becomes stable after several hours of sputtering. The Li and Co concentration in the Films deposited subsequently is found to be varying and possible causes are discussed. After the compositional stability is reached, electrochemical analysis of LiCoO2 thin films was performed, which shows a discharge capacity of 129 mu Ah/cm(2).

Importance of the amino terminus in maintenance of oligomeric structure of sheep liver cytosolic serine hydroxymethyltransferase

The Role Of The Amino And Carboxyl-Terminal Regions Of Cytosolic Serine Hydroxymethyltransferase (SHMT) In Subunit Assembly And Catalysis Was Studied Using Sis Amino-Terminal (Lacking The First 6, 14, 30, 49, 58, And 75 Residues) And Two Carboxyl-Terminal (Lacking The Last 49 And 185 Residues) Deletion Mutants. These Mutants Were Constructed From A Full Length Cdna Clone Using Restriction Enzyme/PCR-Based Methods And Overexpressed In Escherichia Coli. The Overexpressed Proteins, Des-(A1-K6) SHMT And Des-(A1-W14)-SHMT Were Present In The Soluble Fraction And They Were Purified To Homogeneity. The Deletion Clones, For Des-(A1-V30)-SHMT And Des-(A1-L49)-SHMT Were Expressed At Very Low Levels, Whereas Des-(A1-R58)-SHMT, Des-/A1-G75)-SHMT, Des-(Q435-F483)-SHMT And Des-(L299-F483)-SHMT Mutant Proteins Were Not Soluble And Formed Inclusion Bodies. Des-(A1-K6)-SHMT And Des-(A1-W14)-SHMT Catalyzed Both The Tetrahydrofolate-Dependent And Tetrahydrofolate-Independent Reactions, Generating Characteristic Spectral Intermediates With Glycine And Tetrahydrofolate. The Two Mutants Had Similar Kinetic Parameters To That Of The Recombinant SHMT (Rshmt). However, At 55 Degrees C, The Des-(A1-W14)-SHMT Lost Almost All The Activity Within 5 Min, While At The Same Temperature Rshmt And Des-(A1-K6)-SHMT Retained 85% And 70% Activity, Respectively. Thermal Denaturation Studies Showed That Des-(A1-W14)-SHMT Had A Lower Apparent Melting Temperature (52 Degrees C) Compared To Rshmt (56 Degrees C) And Des-(A1-K6)-SHMT (55 Degrees C), Suggesting That N-Terminal Deletion Had Resulted In A Decrease In The Thermal Stability Of The Enzyme. Further Urea Induced Inactivation Of The Enzymes Revealed That 50% Inactivation Occurred At A Lower Urea Concentration (1.2+/-0.1 M) In The Case Of Des-(A1-W14)-SHMT Compared To Rshmt (1.8+/-0.1 M) And Des-(A1 -K6)-SHMT (1.7+/-0.1 M). The Apoenzyme Of Des-/A1-K6)-SHMT Was Present Predominantly In The Dimer Form, Whereas The Apoenzymes Of Rshmt And Des-(A1-K6)-SHMT Were A Mixture Of Tetramers (Approximate To 75% And Approximate To 65%, Respectively) And Dimers. While, Rshmt And Des-(A1-K6)-SHMT Apoenzymes Could Be Reconstituted Upon The Addition Of Pyridoxal-5'-Phosphate To 96% And 94% Enzyme Activity, Respectively Des-(A1-W14)-SHMT Apoenzyme Could Be Reconstituted Only Upto 22%. The Percentage Activity Refined Correlated With The Appearance Of Visible CD At 425 Nm And With The Amount Of Enzyme Present In The Tetrameric Form Upon Reconstitution As Monitored By Gel Filtration. These Results Demonstrate That, In Addition To The Cofactor, The N-Terminal Arm Plays An Important Role In Stabilizing The Tetrameric Structure Of SHMT.

Effect of a magnetic field on the flow and blood oxygenation in channels of variable cross-section

The effect of a magnetic field on the flow and oxygenation of an incompressible Newtonian conducting fluid in channels with irregular boundaries has been investigated. The geometric parameter δ, which is a ratio of the mean half width of the channel d to the characteristic length λ along the channel over which the significant changes in the flow quantities occur, has been used for perturbing the governing equations. Closed form solutions of the various order equations are presented for the stream function. The equations for oxygen partial pressure remain nonlinear even after perturbation, therefore a numerical solution is presented. The expressions for shear stress at a wall and pressure distributions are derived. Here the separation in the flow occurs at a higher Reynolds number than the corresponding non-magnetic case. It is found that the magnetic field has an effect on local oxygen concentration but has a little effect on the saturation length.

Competing A-site and B-site driven ferroelectric instabilities in the (1-x)PbTiO3-(x)BiAlO3 system

The system (1-x)PbTiO3-(x)BiAlO3 has been investigated with regard to its solid solubility, crystal structure, microstructure, and ferroelectric transition. The unit cell volume and the tetragonality exhibit anomalous behavior near x=0.10. The Curie point (T-C) of PbTiO3 was however found to be nearly unchanged. The study seems to suggest that the decrease in the stability of the ferroelectric state due to dilution of the Ti-sublattice by smaller sized Al+3 ions is compensated by the increase in the ferroelectric stability by the Bi+3 ions.