Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier-Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e(vertical bar k vertical bar/kd) at high wavenumbers vertical bar k vertical bar. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e-(C(k/kd) ln(vertical bar k vertical bar/kd)) for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C-* = 1/ ln 2. The same behavior with a universal constant C-* is conjectured for the Navier-Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier-Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.

Nonlinear secondary whirl of an overhung rotor

Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here, we study an idealized asymmetric nonlinear overhung rotor model of Crandall and Brosens, spinning close to its gravity critical speed.Nonlinearities arise from finite displacements, and the rotor's staticlateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow modulations of whirl amplitudes are studied using the method of multiple scales. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike the typical resonant oscillations. Nevertheless,the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three-dimensional space oftwo modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line,a parabola and an ellipse.

Determination of skin friction in strong pressure-gradient equilibrium and near-equilibrium turbulent boundary layers

The conventional Clauser-chart method for determination of local skin friction in zero or weak pressure-gradient turbulent boundary layer flows fails entirely in strong pressure-gradient situations. This failure occurs due to the large departure of the mean velocity profile from the universal logarithmic law upon which the conventional Clauser-chart method is based. It is possible to extend this method,even for strong pressure-gradient situations involving equilibrium or near-equilibrium turbulent boundary layers by making use of the so-called non-universal logarithmic laws. These non-universal log laws depend on the local strength of the pressure gradient and may be regarded as perturbations of the universal log law.The present paper shows that the modified Clauser-chart method, so developed, yields quit satisfactory results in terms of estimation of local skin friction in strongly accelerated or retarded equilibrium and near-equilibrium turbulent boundary layers that are not very close to relaminarization or separation.

Search for chaos in neutron star systems: Is Cyg X-3 a black hole?

The accretion disk around a compact object is a nonlinear general relativistic system involving magnetohydrodynamics. Naturally, the question arises whether such a system is chaotic (deterministic) or stochastic (random) which might be related to the associated transport properties whose origin is still not confirmed. Earlier, the black hole system GRS 1915+105 was shown to be low-dimensional chaos in certain temporal classes. However, so far such nonlinear phenomena have not been studied fairly well for neutron stars which are unique for their magnetosphere and kHz quasi-periodic oscillation (QPO). On the other hand, it was argued that the QPO is a result of nonlinear magnetohydrodynamic effects in accretion disks. If a neutron star exhibits chaotic signature, then what is the chaotic/correlation dimension? We analyze RXTE/PCA data of neutron stars Sco X-1 and Cyg X-2, along with the black hole Cyg X-1 and the unknown source Cyg X-3, and show that while Sco X-1 and Cyg X-2 are low dimensional chaotic systems, Cyg X-1 and Cyg X-3 are stochastic sources. Based on our analysis, we argue that Cyg X-3 may be a black hole.

PIM2 Induced COX-2 and MMP-9 Expression in Macrophages Requires PI3K and Notch1 Signaling

Activation of inflammatory immune responses during granuloma formation by the host upon infection of mycobacteria is one of the crucial steps that is often associated with tissue remodeling and breakdown of the extracellular matrix. In these complex processes, cyclooxygenase-2 (COX-2) plays a major role in chronic inflammation and matrix metalloproteinase-9 (MMP-9) significantly in tissue remodeling. In this study, we investigated the molecular mechanisms underlying Phosphatidyl-myo-inositol dimannosides (PIM2), an integral component of the mycobacterial envelope, triggered COX-2 and MMP-9 expression in macrophages. PIM2 triggers the activation of Phosphoinositide-3 Kinase (PI3K) and Notch1 signaling leading to COX-2 and MMP-9 expression in a Toll-like receptor 2 (TLR2)-MyD88 dependent manner. Notch1 signaling perturbations data demonstrate the involvement of the cross-talk with members of PI3K and Mitogen activated protein kinase pathway. Enforced expression of the cleaved Notch1 in macrophages induces the expression of COX-2 and MMP-9. PIM2 triggered significant p65 nuclear factor-kappa B (NF-kappa B) nuclear translocation that was dependent on activation of PI3K or Notch1 signaling. Furthermore, COX-2 and MMP-9 expression requires Notch1 mediated recruitment of uppressor of Hairless (CSL) and NF-kappa B to respective promoters. Inhibition of PIM2 induced COX-2 resulted in marked reduction in MMP-9 expression clearly implicating the role of COX-2 dependent signaling events in driving the MMP-9 expression. Taken together, these data implicate PI3K and Notch1 signaling as obligatory early proximal signaling events during PIM2 induced COX-2 and MMP-9 expression in macrophages.

The evolution of loop structures in flux rings within the solar convection zone

Choudhuri and Gilman (1987) considered certain implications of the hypothesis that the magnetic flux within the Sun is generated at the bottom of the convection zone and then rises through it. Taking flux rings symmetric around the rotation axis and using reasonable values of different parameters, they found that the Coriolis force deflects these flux rings into trajectories parallel to the rotation axis so that they emerge at rather high latitudes. This paper looks into the question of whether the action of the Coriolis force is subdued when the initial configuration of the flux ring has non-axisymmetries in the form of loop structures. The results depend dramatically on whether the flux ring with the loops lies completely within the convection zone or whether the lower parts of it are embedded in the stable layers underneath the convection zone. In the first case, the Coriolis force supresses the non-axisymmetric perturbations so that the flux ring tends to remain symmetric and the trajectories are very similar to those of Choudhuri and Gilman (1987). In the second case, however, the lower parts of the flux ring may remain anchored underneath the bottom of the convection zone, but the upper parts of the loops still tend to move parallel to the rotation axis and emerge at high latitudes. Thus the problem of the magnetic flux not being able to come out at the sunspot latitudes still persists after the non-axisymmetries in the flux rings are taken into account.

Nitric Oxide Is Involved in Mycobacterium bovis Bacillus Calmette-Guerin-Activated Jagged1 and Notch1 Signaling.

Pathogenic mycobacteria have evolved unique strategies to survive within the hostile environment of macrophages. Modulation of key signaling cascades by NO, generated by the host during infection, assumes critical importance in overall cell-fate decisions. We show that NO is a critical factor in Mycobacterium bovis bacillus Calmette-Guérin-mediated Notch1 activation, as the generation of activated Notch1 or expression of Notch1 target genes matrix metalloproteinase-9 (MMP-9) or Hes1 was abrogated in macrophages derived from inducible NO synthase (iNOS) knockout (iNOS(-/-)), but not from wild-type, mice. Interestingly, expression of the Notch1 ligand Jagged1 was compromised in M. bovis bacillus Calmette-Guérin-stimulated iNOS(-/-) macrophages, and loss of Jagged1 expression or Notch1 signaling could be rescued by NO donors. Signaling perturbations or genetic approaches implicated that robust expression of MMP-9 or Hes1 required synergy and cross talk between TLR2 and canonical Notch1-PI3K cascade. Further, CSL/RBP-Jk contributed to TLR2-mediated expression of MMP-9 or Hes1. Correlative evidence shows that, in a murine model for CNS tuberculosis, this mechanism operates in vivo only in brains derived from WT but not from iNOS(-/-) mice. Importantly, we demonstrate the activation of Notch1 signaling in vivo in granulomatous lesions in the brains of Mycobacterium tuberculosis-infected human patients with tuberculous meningitis. Current investigation identifies NO as a pathological link that modulates direct cooperation of TLR2 with Notch1-PI3K signaling or Jagged1 to regulate specific components of TLR2 responses. These findings provide new insights into mechanisms by which Notch1, TLR2, and NO signals are integrated in a cross talk that modulates a defined set of effector functions in macrophages.

A Compact Defected Ground Microstrip Device with Photonic Bandgap Effects

Filters and other devices using photonic bandgap (PBG) theory are typically implemented in microstrip lines by etching periodic holes on the ground plane of the microstrip. The period of such several holes corresponds to nearly half the guided wavelength of the transmission line. In this paper we study the effects of miniaturization of the PBG device by meandering the microstrip line about one single hole in the ground plane. A comparison of the S-parameters and dispersion behavior of the modified geometry and a conventional PBG device with a straight microstrip line shows that these devices have similar behaviors.

Apparent shortening of the Csp(3)-Csp(3) bond analysed via a variable-temperature X-ray diffraction study in racemic 1,1 '-binaphthalene-2,2 '-diyl diethyl bis(carbonate)

Crystal structure determination at room temperature [292 (2) K] of racemic 1,1'-binaphthalene-2,2'-diyl diethyl bis(carbonate), C26H22O6, showed that one of the terminal carbon-carbon bond lengths is very short [Csp(3)-Csp(3) = 1.327 (6) angstrom]. The reason for such a short bond length has been analysed by collecting data sets on the same crystal at 393, 150 and 90 K. The values of the corrected bond lengths clearly suggest that the shortening is mainly due to positional disorder at two sites, with minor perturbations arising as a result of thermal vibrations. The positional disorder has been resolved in the analysis of the 90 K data following the changes in the unit-cell parameters for the data sets at 150 and 90 K, which appear to be an artifact of a near centre of symmetry relationship between the two independent molecules in the space group P (1) over bar at these temperatures. Indeed, the unit cell at low temperature (150 and 90 K) is a supercell of the room-temperature unit cell.

Asymptotic analysis for the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell: The beam mode

Using asymptotics, the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell vibrating in the beam mode (viz. circumferential wave order n = 1) are studied. Initially, the uncoupled wavenumbers of the acoustic fluid and the cylindrical shell structure are discussed. Simple closed form expressions for the structural wavenumbers (longitudinal, torsional and bending) are derived using asymptotic methods for low- and high-frequencies. It is found that at low frequencies the cylinder in the beam mode behaves like a Timoshenko beam. Next, the coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic fluid, with an added fluid-loading term involving a parameter mu due to the coupling. An asymptotic expansion involving mu is substituted in this equation. Analytical expressions are derived for the coupled wavenumbers (as modifications to the uncoupled wavenumbers) separately for low- and high-frequency ranges and further, within each frequency range, for large and small values of mu. Only the flexural wavenumber, the first rigid duct acoustic cut-on wavenumber and the first pressure-release acoustic cut-on wavenumber are considered. The general trend found is that for small mu, the coupled wavenumbers are close to the in vacuo structural wavenumber and the wavenumbers of the rigid-acoustic duct. With increasing mu, the perturbations increase, until the coupled wavenumbers are better identified as perturbations to the pressure-release wavenumbers. The systematic derivation for the separate cases of small and large mu gives more insight into the physics and helps to continuously track the wavenumber solutions as the fluid-loading parameter is varied from small to large values. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. This method of asymptotics is simple to implement using a symbolic computation package (like Maple). (C) 2008 Elsevier Ltd. All rights reserved.

Crystallite size effects in stacking faulted nickel hydroxide and its electrochemical behaviour

P-Nickel hydroxide comprises a long range periodic arrangement of atoms with a stacking sequence of AC AC AC-having an ideal composition Ni(OH)(2). Variation in the preparative conditions can lead to the changes in the stacking sequence (AC AC BA CB AC AC or AC AC AB AC AC) This type of variation in stacking sequence can result in the formation of stacking fault in nickel hydroxide. The stability of the stacking fault depends on the free energy content of the sample. Stacking faults in nickel hydroxide is essential for better electrochemical activity. Also there are reports correlating particle size to the better electrochemical activity. Here we present the effect of crystallite size on the stacking faulted nickel hydroxide samples. The electrochemical performance of stacking faulted nickel hydroxide with small crystallite size exchanges 0.8e/Ni, while the samples with larger crystallite size exchange 0.4e/Ni. Hence a right combination of crystallite size and stacking fault content has to be controlled for good electrochemical activity of nickel hydroxide. (C) 2008 Elsevier B.V. All rights reserved.

Vave propagation and bandgaps in a parametrically modulated composite laminate

Wave propagation and its frequency bandgaps in a parametrically modulated composite laminate are reported in this paper. The modulated properties under considerations are due to periodic microstructure, for example honeycomb core sandwich composite, which can be parameterized and homogenized in a suitable scale. Wave equations are derived by assuming a third-order shear deformation theory. Homogenization of the wave equations is carried out in the scale of wavelength. In-plane wave and flexural-shear wave dispersions are obtained for a range of values of a stiffness modulation coefficient (alpha). A clear pattern of stop-bands is observed for alpha >= 4. To validate the band-gap phenomena, we take recourse to time domain response obtained from finite element simulation. As predicted by the proposed analytical technique, a distinct correlation between the chosen frequency band and the simulated wave arrival time and amplitude reduction is found. This promises practical applications of the proposed analytical technique to designing parametrically modulated composite laminate for wave suppression. (C) 2009 Elsevier B.V. All rights reserved.