A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

A sufficient criterion for Kelvin–Helmholtz instability in the magnetopause boundary‐layer region

The Kelvin–Helmholtz instability has been investigated for the magnetopause boundary‐layer region by the linearized method. The plasma in magnetosheath and magnetopause is assumed to be semi‐infinitely extended homogeneous, nondissipative, and incompressible. It is observed that, if one relation of two plasma speeds on the two sides of the magnetopause, wave number, and boundary‐layer thickness exceeds a certain threshold, the instability sets in. This new analytically sufficient criterion for excitation of instability in the three‐layer plasma flow generalizes the corresponding Chandrasekhar’s instability criterion for two‐layer plasma flow. The known results have been recovered and modified, the new results have been discovered. It is proved that the velocity threshold for the onset of instability is low when the magnitude of the magnetosheath and boundary‐layer region magnetic field and the angle between them are small. Also the threshold depends on the direction of plasma flow. The following results are observed numerically. The growth of the instability is sensitive to the magnetic field direction in the magnetosheath. A slight variation in the magnetic field direction in the second region can substantially change the relative velocity threshold for instability. When the ratio of the density of the second and third layer (magnetosphere) increases or that of the first and third layer decreases, the threshold decreases. Apart from this a necessary criterion for instability is obtained for a particular case.

Magnetorotational instability driven dynamos at low magnetic Prandtl numbers

Numerical simulations of the magnetorotational instability (MRI) with zero initial net flux in a non-stratified isothermal cubic domain are used to demonstrate the importance of magnetic boundary conditions. In fully periodic systems the level of turbulence generated by the MRI strongly decreases as the magnetic Prandtl number (Pm), which is the ratio of kinematic viscosity and magnetic diffusion, is decreased. No MRI or dynamo action below Pm=1 is found, agreeing with earlier investigations. Using vertical field conditions, which allow magnetic helicity fluxes out of the system, the MRI is found to be excited in the range 0.1

Microstructural features of flow instability in α-titanium cylinders under high strain rate compression at 25°C to 400°C

Cylindrical specimens of commercial pure titanium have been compressed at strain rates in the range of 0.1 to 100 s-1 and temperatures in the range of 25-degrees-C to 400-degrees-C. At strain rates of 10 and 100 s-1, the specimens exhibited adiabatic shear bands. At lower strain rates, the material deformed in an inhomogeneous fashion. These material-related instabilities are examined in the light of the ''phenomenological model'' and the ''dynamic materials mode.'' It is found that the regime of adiabatic shear band formation is predicted by the phenomenological model, while the dynamic materials model is able to predict the inhomogeneous deformation zone. The criterion based on power partitioning is competent to predict the variations within the inhomogeneous deformation zone.

Parametric instability of stochastic columns

Columns which have stochastically distributed Young's modulus and mass density and are subjected to deterministic periodic axial loadings are considered. The general case of a column supported on a Winkler elastic foundation of random stiffness and also on discrete elastic supports which are also random is considered. Material property fluctuations are modeled as independent one-dimensional univariate homogeneous real random fields in space. In addition to autocorrelation functions or their equivalent power spectral density functions, the input random fields are characterized by scale of fluctuations or variance functions for their second order properties. The foundation stiffness coefficient and the stiffnesses of discrete elastic supports are treated to constitute independent random variables. The system equations of boundary frequencies are obtained using Bolotin's method for deterministic systems. Stochastic FEM is used to obtain the discrete system with random as well as periodic coefficients. Statistical properties of boundary frequencies are derived in terms of input parameter statistics. A complete covariance structure is obtained. The equations developed are illustrated using a numerical example employing a practical correlation structure.

Dependence of the large-scale vortex instability on latitude, stratification and domain size

In an earlier study, we reported on the excitation of large-scale vortices in Cartesian hydrodynamical convection models subject to rapid enough rotation. In that study, the conditions for the onset of the instability were investigated in terms of the Reynolds (Re) and Coriolis (Co) numbers in models located at the stellar North pole. In this study, we extend our investigation to varying domain sizes, increasing stratification, and place the box at different latitudes. The effect of the increasing box size is to increase the sizes of the generated structures, so that the principal vortex always fills roughly half of the computational domain. The instability becomes stronger in the sense that the temperature anomaly and change in the radial velocity are observed to be enhanced. The model with the smallest box size is found to be stable against the instability, suggesting that a sufficient scale separation between the convective eddies and the scale of the domain is required for the instability to work. The instability can be seen upto the colatitude of 30 degrees, above which value the flow becomes dominated by other types of mean flows. The instability can also be seen in a model with larger stratification. Unlike the weakly stratified cases, the temperature anomaly caused by the vortex structures is seen to depend on depth.

Snapthrough instability of a stochastic a von Mises truss

A von Mises truss with stochastically varying material properties is investigated for snapthrough instability. The variability of the snap-through load is calculated analytically as a function of the material property variability represented as a stochastic process. The bounds are established which are independent of the knowledge of the complete description of correlation structure which is seldom possible using the experimental data. Two processes are considered to represent the material property variability and the results are presented graphically. Ein von Mises Fachwerk mit stochastisch verteilten Materialeigenschaften wird bezüglich der Durchschlagsinstabilität untersucht. Die Spannbreite der Durchschlagslast wird analytisch als Funktion der Spannbreite der Materialeigenschaften berechnet, die stochastisch verteilt angenommen werden. Eine explizite Gesamtbeschreibung der Struktur ist bei Benutzung experimenteller Daten selten möglich. Deshalb werden Grenzen für die Durchschlagskraft entwickelt, die von der Kenntnis dieser Gesamtbeschreibung unabhängig sind. Zwei Grenzfälle werden betrachtet, um die Spannbreite der Materialeigenschaften darzustellen. Die Ergebnisse werden grafisch dargestellt.

Instability and dewetting of ultrathin solid viscoelastic films on homogeneous and heterogeneous substrates

Instability and dewetting engendered by the van der Waals force in soft thin (<100 nm) linear viscoelastic solid (e. g., elastomeric gel) films on uniform and patterned surfaces are explored. Linear stability analysis shows that, although the elasticity of the film controls the onset of instability and the corresponding critical wavelength, the dominant length-scale remains invariant with the elastic modulus of the film. The unstable modes are found to be long-wave, for which a nonlinear long-wave analysis and simulations are performed to uncover the dynamics and morphology of dewetting. The stored elastic energy slows down the temporal growth of instability significantly. The simulations also show that a thermodynamically stable film with zero-frequency elasticity can be made unstable in the presence of physico-chemical defects on the substrate and can follow an entirely different pathway with far fewer holes as compared to the viscous films. Further, the elastic restoring force can retard the growth of a depression adjacent to the hole-rim and thus suppress the formation of satellite holes bordering the primary holes. These findings are in contrast to the dewetting of viscoelastic liquid films where nonzero frequency elasticity accelerates the film rupture and promotes the secondary instabilities. Thus, the zero-frequency elasticity can play a major role in imposing a better-defined long-range order to the dewetted structures by arresting the secondary instabilities. (C) 2011 American Institute of Physics. doi: 10.1063/1.3554748]

Proposed role of w chromosome inactivation and the absence of dosage compensation in avian sex determination

Three features of avian sex chromosomes - female heterogamety (ZZ male, ZW female), the apparently inactive state of the W chromosome, and dose-dependent expression of Z-linked genes - are examined in regard to their possible relation to sex determination. It is proposed that the W chromosome is facultatively heterochromatic and that the Z and W chromosomes carry one or more homologous sex-determination genes. The absence of dosage compensation in ZZ embryos, and W inactivation in ZW embryos, would then bring about a 2n(ZZ)-n(ZW) inequality in the effective copy number of such genes. The absence of dosage compensation of Z-linked genes in ZZ embryos is viewed as a means by which two copies of Z-W homologous sex determination genes are kept active to meet the requirements of testis determination. W inactivation may promote ovarian development by reducing the effective copy number of these genes from 2n to n. If there is a W-specific gene for femaleness, spread of heterochromatization to this gene in cells forming the right gonadal primordium may explain the latter's normally undifferentiated state; reversal of heterochromatization may similarly explain the development of the right gonad into a testis following left ovariectomy.

Synergistic interaction between particular X-chromosome deletions andSex-lethal causes female lethality inDrosophila melanogaster

We studied the effect on female viability of trans-heterozygous combinations of X-chromosome deficiencies and Sxt-(fl), a null allele of Sex-lethal. Twentyfive deficiencies, which together covered 80% of the X chromosome, were tested. Seven of these trans-heterozygous combinations caused significant levels of female lethality. Two of the seven interacting deficiencies include the previously known sex determination genes sans fille and sisterless-a. Four of the remaining uncover X-chromosomal regions that were not hitherto known to contain sex determination genes. These newly identified regions are defined by deficiencies Df(1)RA2 (7D10; 8A4-5), Df(1)KA14 (7F1-2; 8C6), Df(1)C52 (8E; 9C-D) and Df(1)N19 (17A1; 18A2). These four deficiencies were characterized further to determine whether it was the maternal or zygotic dosage that was primarily responsible for the observed lethality of female embryos, daughterless and extra macrochaetae, two known regulators of Sxl, influence the interaction of these deficiencies with Sxl.

Dynamic analysis of voltage instability in AC-DC systems

This paper presents the analysis and study of voltage collapse at any converter bus in A C-DC systems considering the dynamics of DC system. The problem of voltage instability is acute when HVDC links are connected to weak AC systems, the strength determined by short circuit ratio (SCR) at the converter bus. The converter control strategies are important in determining voltage instability. Small signal analysis is used to identify critical modes and evaluate the effect of AC system strength and control parameters. A sample two-terminal DC system is studied and the results compared with those obtained from static analysis. Also, the results obtained from small signal analysis are validated with nonlinear simulation.

Small Ubiquitin-related Modifier Ligase Activity of Mms21 Is Required for Maintenance of Chromosome Integrity during the Unperturbed Mitotic Cell Division Cycle in Saccharomyces cerevisiae

The SUMO ligase activity of Mms21/Nse2, a conserved member of the Smc5/6 complex, is required for resisting extrinsically induced genotoxic stress. We report that the Mms21 SUMO ligase activity is also required during the unchallenged mitotic cell cycle in Saccharomyces cerevisiae. SUMO ligase-defective cells were slow growing and spontaneously incurred DNA damage. These cells required caffeine-sensitive Mec1 kinase-dependent checkpoint signaling for survival even in the absence of extrinsically induced genotoxic stress. SUMO ligase-defective cells were sensitive to replication stress and displayed synthetic growth defects with DNA damage checkpoint-defective mutants such as mec1, rad9, and rad24. MMS21 SUMO ligase and mediator of replication checkpoint 1 gene (MRC1) were epistatic with respect to hydroxyurea-induced replication stress or methyl methanesulfonate-induced DNA damage sensitivity. Subjecting Mms21 SUMO ligase-deficient cells to transient replication stress resulted in enhancement of cell cycle progression defects such as mitotic delay and accumulation of hyperploid cells. Consistent with the spontaneous activation of the DNA damage checkpoint pathway observed in the Mms21-mediated sumoylation-deficient cells, enhanced frequency of chromosome breakage and loss was detected in these mutant cells. A mutation in the conserved cysteine 221 that is engaged in coordination of the zinc ion in Loop 2 of the Mms21 SPL-RING E3 ligase catalytic domain resulted in strong replication stress sensitivity and also conferred slow growth and Mec1 dependence to unchallenged mitotically dividing cells. Our findings establish Mms21-mediated sumoylation as a determinant of cell cycle progression and maintenance of chromosome integrity during the unperturbed mitotic cell division cycle in budding yeast.

Optimization of cold and warm workability in 304 stainless steel using instability maps

The deformation characteristics of stainless steel type AISI 3O4 under compression in the temperature range 20 degrees C to 600 degrees C and strain-rate range 0.001 to 100 s(-1) have been studied with a view to characterizing the flow instabilities occurring in the microstructure. At strain rates less than 5 s(-1), 304 stainless steel exhibits flow localization, whereas dynamic strain aging occurs at intermediate temperatures and below 0.5 s(-1). At room temperatures and strain rates less than 10 s(-1), martensite formation is observed. To avoid the preceding microstructural instabilities, cold and warm working should be carried out at strain rates greater than 5 s(-1). The continuum criterion, developed on the basis of the principles of maximum rate of entropy production and separability of the dissipation function, predicts accurately all the preceding instability features.