Admissible fundamental operators(star)

Let F and G be two bounded operators on two Hilbert spaces. Let their numerical radii be no greater than one. This note investigates when there is a Gamma-contraction (S, P) such that F is the fundamental operator of (S, P) and G is the fundamental operator of (S*, P*). Theorem 1 puts a necessary condition on F and G for them to be the fundamental operators of (S, P) and (S*, P*) respectively. Theorem 2 shows that this necessary condition is also sufficient provided we restrict our attention to a certain special case. The general case is investigated in Theorem 3. Some of the results obtained for Gamma-contractions are then applied to tetrablock contractions to figure out when two pairs (F1, F2) and (G(1), G(2)) acting on two Hilbert spaces can be fundamental operators of a tetrablock contraction (A, B, P) and its adjoint (A*, B*, P*) respectively. This is the content of Theorem 3. (C) 2015 Elsevier Inc. All rights reserved.

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.

Third post-Newtonian gravitational waveforms for compact binary systems in general orbits: Instantaneous terms

We compute the instantaneous contributions to the spherical harmonic modes of gravitational waveforms from compact binary systems in general orbits up to the third post-Newtonian (PN) order. We further extend these results for compact binaries in quasielliptical orbits using the 3PN quasi-Keplerian representation of the conserved dynamics of compact binaries in eccentric orbits. Using the multipolar post-Minkowskian formalism, starting from the different mass and current-type multipole moments, we compute the spin-weighted spherical harmonic decomposition of the instantaneous part of the gravitational waveform. These are terms which are functions of the retarded time and do not depend on the history of the binary evolution. Together with the hereditary part, which depends on the binary's dynamical history, these waveforms form the basis for construction of accurate templates for the detection of gravitational wave signals from binaries moving in quasielliptical orbits.

A cis-Regulatory Mutation in Troponin-I of Drosophila Reveals the Importance of Proper Stoichiometry of Structural Proteins During Muscle Assembly

Rapid and high wing-beat frequencies achieved during insect flight are powered by the indirect flight muscles, the largest group of muscles present in the thorax. Any anomaly during the assembly and/or structural impairment of the indirect flight muscles gives rise to a flightless phenotype. Multiple mutagenesis screens in Drosophila melanogaster for defective flight behavior have led to the isolation and characterization of mutations that have been instrumental in the identification of many proteins and residues that are important for muscle assembly, function, and disease. In this article, we present a molecular-genetic characterization of a flightless mutation, flightless-H (fliH), originally designated as heldup-a (hdp-a). We show that fliH is a cis-regulatory mutation of the wings up A (wupA) gene, which codes for the troponin-I protein, one of the troponin complex proteins, involved in regulation of muscle contraction. The mutation leads to reduced levels of troponin-I transcript and protein. In addition to this, there is also coordinated reduction in transcript and protein levels of other structural protein isoforms that are part of the troponin complex. The altered transcript and protein stoichiometry ultimately culminates in unregulated acto-myosin interactions and a hypercontraction muscle phenotype. Our results shed new insights into the importance of maintaining the stoichiometry of structural proteins during muscle assembly for proper function with implications for the identification of mutations and disease phenotypes in other species, including humans.

Role of Areca Nut Induced TGF-beta and Epithelial-Mesenchymal Interaction in the Pathogenesis of Oral Submucous Fibrosis

Areca nut consumption has been implicated in the progression of Oral Submucous fibrosis (OSF); an inflammatory precancerous fibrotic condition. Our previous studies have demonstrated the activation of TGF-beta signaling in epithelial cells by areca nut components and also propose a role for epithelial expressed TGF-beta in the pathogenesis of OSF. Although the importance of epithelial cells in the manifestation of OSF has been proposed, the actual effectors are fibroblast cells. However, the role of areca nut and TGF-beta in the context of fibroblast response has not been elucidated. Therefore, to understand their role in the context of fibroblast response in OSF pathogenesis, human gingival fibroblasts (hGF) were treated with areca nut and/or TGF-beta followed by transcriptome profiling. The gene expression profile obtained was compared with the previously published transcriptome profiles of OSF tissues and areca nut treated epithelial cells. The analysis revealed regulation of 4666 and 1214 genes by areca nut and TGF-beta treatment respectively. The expression of 413 genes in hGF cells was potentiated by areca nut and TGF-beta together. Further, the differentially expressed genes of OSF tissues compared to normal tissues overlapped significantly with areca nut and TGF-beta induced genes in epithelial and hGF cells. Several positively enriched pathways were found to be common between OSF tissues and areca nut + TGF-beta treated hGF cells. In concordance, areca nut along with TGF-beta enhanced fibroblast activation as demonstrated by potentiation of alpha SMA, gamma SMA and collagen gel contraction by hGF cells. Furthermore, TGF-beta secreted by areca nut treated epithelial cells influenced fibroblast activation and other genes implicated in fibrosis. These data establish a role for areca nut influenced epithelial cells in OSF progression by activation of fibroblasts and emphasizes the importance of epithelial-mesenchymal interaction in OSF.

Computational modeling of reactive hot pressing of zirconium carbide

A model of reactive hot pressing of zirconium carbide (ZrCx, 0.5 < x < 1) has been constructed that incorporates four processes that occur in parallel: creep of zirconium (Zr), reaction of Zr and carbon (C), increase in volume fraction of hard phase with progressive reaction that reduces the creep of Zr and, finally, de-densification associated with volume reduction during reaction. The reasonable agreement of the model with experimental results verifies that plastic deformation of Zr is the main factor that is responsible for the low-temperature reactive densification of ZrC and that ZrC may be treated as a rigid inclusion that contributes little to densification. It predicts that densification is impaired by increasing carbon stoichiometry due to the increasing amount of starting hard phase and the greater contraction upon reaction. Additionally, the model predicts that mixtures of Zr and ZrC should show equal or better densification than Zr and C mixtures.

DOES THE CHEMOTHERMAL INSTABILITY HAVE ANY ROLE IN THE FRAGMENTATION OF PRIMORDIAL GAS

The collapse of the primordial gas in the density regime similar to 10(8)-10(10) cm(-3) is controlled by the three-body H-2 formation process, in which the gas can cool faster than free-fall time-a condition proposed as the chemothermal instability. We investigate how the heating and cooling rates are affected during the rapid transformation of atomic to molecular hydrogen. With a detailed study of the heating and cooling balance in a 3D simulation of Pop III collapse, we follow the chemical and thermal evolution of the primordial gas in two dark matter minihalos. The inclusion of sink particles in modified Gadget-2 smoothed particle hydrodynamics code allows us to investigate the long-term evolution of the disk that fragments into several clumps. We find that the sum of all the cooling rates is less than the total heating rate after including the contribution from the compressional heating (pdV). The increasing cooling rate during the rapid increase of the molecular fraction is offset by the unavoidable heating due to gas contraction. We conclude that fragmentation occurs because H-2 cooling, the heating due to H-2 formation and compressional heating together set a density and temperature structure in the disk that favors fragmentation, not the chemothermal instability.

A note on tetrablock contractions

A commuting triple of operators (A, B, P) on a Hilbert space H is called a tetrablock contraction if the closure of the set E = {(a(11),a(22),detA) : A = GRAPHICS] with parallel to A parallel to <1} is a spectral set. In this paper, we construct a functional model and produce a set of complete unitary invariants for a pure tetrablock contraction. In this construction, the fundamental operators, which are the unique solutions of the operator equations A - B* P = DPX1DP and B - A* P = DPX2DP where X-1, X-2 is an element of B(D-P) play a pivotal role. As a result of the functional model, we show that every pure tetrablock isometry (A, B, P) on an abstract Hilbert space H is unitarily equivalent to the tetrablock contraction (MG1*+G2z, MG2*+G1z, M-z) on H-DP*(2). (D), where G(1) and G(2) are the fundamental operators of (A*, B*, P*). We prove a Beurling Lax Halmos type theorem for a triple of operators (MF1*+F2z, MF2*+F1z, M-z), where epsilon is a Hilbert space and F-1, F-2 is an element of B(epsilon). We also deal with a natural example of tetrablock contraction on a functions space to find out its fundamental operators.

Design and Validation of On-chip Planar Mixer Based on Advection and Viscoelastic Effects

Mixing at low Reynolds number is usually due to diffusion and requires longer channel lengths for complete mixing. In order to reduce the mixing lengths, advective flow can be induced by varying the channel geometry. Additionally, in non-newtonian fluids, appropriate modifications to channel geometry can be used to aid the mixing process by capitalizing on their viscoelastic nature. Here we have exploited the advection and viscoelastic effects to implement a planar passive micro-mixer. Microfluidic devices incorporating different blend of mixing geometries were conceived. The optimum design was chosen based on the results of the numerical simulations performed in COMSOL. The chosen design had sudden expansion and contraction along with teeth patterns along the channel walls to improve mixing. Mixing of two different dyes was performed to validate the mixing efficiency. Particle dispersion experiments were also carried out. The results indicated effective mixing. In addition, the same design was also found to be compatible with electrical power free pumping mechanism like suction. The proposed design was then used to carry out on-chip chemical cell lysis with human whole blood samples to establish its use with non-newtonian fluids. Complete lysis of the erythrocytes was observed leaving behind the white blood cells at the outlet.

大偏心率远距离航天器编队飞行设计

为寻求适用于大偏心率远距离航天器编队设计的方法，摒弃了简化航天器相对运动非线性微分方程的传统思路，致力于简化该微分方程的解析解。首先，在同周期假定前提下，由运动学得到了椭圆轨道航天器相对于圆轨道航天器运动的封闭解析解，然后将其展开成傅立叶级数，证明了在特定条件下，单倍频项是最主要的，从而导出了编队飞行设计的新公式。最后以空间圆形编队设计为例，阐明了利用新公式进行编队设计的步骤，并用精确的数值计算验证了设计结果的正确性。与C—W方法和一般轨道参数设计方法相比，推导过程中并未采用小偏心率近距离假定，因此导出的新公式可适用于大偏心率远距离航天器的编队设计。

Characterization of a Laser-Discrete Quenched Steel Substrate/Chromium System by Dissolving Coatings

A laser-discrete quenched steel (LDQS) substrate/as-deposited chromium (top high-contraction (HC) and underlying low-contraction (LC) chromium) system was investigated by dissolving coatings in order to reveal the mechanism that the service life of the coated parts is largely improved using the hybrid technique of laser pre-quenching plus chromium post-depositing. It was found that the surface characteristics of the substrate, LC and HC chromium layer can be simultaneously revealed owing to the dissolution edge effect of chromium coatings. Moreover, the periodical gradient morphologies of the LDQS substrate are clearly shown: the surfaces of laser transformation-hardened regions are rather smooth; a lot of fine micro-holes exist in the transition zones; there are many micro-dimples in the original substrate. Furthermore, the novel method of dissolving coatings with sharp interfaces may be used to reveal the structural features of a substrate/coating system, explore the effect of the substrate on the initial microstructure and morphologies of coatings, and check the quality of the coated-parts.

Influence of surfactant solubility on the deformation and breakup of a bubble or capillary jet in a viscous fluid

In a previous study [M. Hameed, J. Fluid Mech. 594, 307 (2008)] the authors investigated the influence of insoluble surfactant on the evolution of a stretched, inviscid bubble surrounded by a viscous fluid via direct numerical simulation of the Navier-Stokes equations, and showed that the presence of surfactant can cause the bubble to contract and form a quasisteady slender thread connecting parent bubbles, instead of proceeding directly toward pinch-off as occurs for a surfactant-free bubble. Insoluble surfactant significantly retards pinch-off and the thread is stabilized by a balance between internal pressure and reduced capillary pressure due to a high concentration of surfactant that develops during the initial stage of contraction. In the present study we investigate the influence of surfactant solubility on thread formation. The adsorption-desorption kinetics for solubility is in the diffusion controlled regime. A long-wave model for the evolution of a capillary jet is also studied in the Stokes flow limit, and shows dynamics that are similar to those of the evolving bubble. With soluble surfactant, depending on parameter values, a slender thread forms but can pinch-off later due to exchange of surfactant between the interface and exterior bulk flow. © 2009 American Institute of Physics.

Propeller unsteady distortion noise

Turbulence, as naturally occurs in the atmosphere, is known to become highly anisotropic in the presence of the flow induced by a propeller. This turbulent distortion, caused by the streamtube contraction, significantly affects the tonal content of the radiated noise due to turbulence ingestion. We present here an analytic framework in which turbulent distortion may be assessed for any irrotational mean flow which approaches uniform axial flow far upstream. Sound spectra are presented for the case of two rotors in close proximity, for which the distortion is asymmetric. Quantities such as the turbulence spectrum at the rotor face and sound directivity then vary with azimuthal angle φ. © 2010 by Rosalyn A.V. Robison & N. Peake.

Case Study: Influence Of Morphological Changes On Flooding In Jingjiang River

The middle reach of the Yangtze River, customarily called the Jingjiang River, together with its diversion channels and Dongting Lake, form a large complicated drainage system. In the last five decades, significant geomorphological changes have occurred in the drainage system, including the shrinkage of diversion channels, contraction of Dongting Lake, changes in the rating curve at the Luoshan station, and cutoffs of the lower Jingjiang River. These changes are believed to be the cause of the occurrence of abnormal floods in the Jingjiang River. Qualitative analyses suggest that the first three factors aggravate the flood situation in the lower Jingjiang River, while the last factor seems beneficial for flood prevention. To quantitatively evaluate these conclusions, a finite-volume numerical model was constructed. A series of numerical simulations were carried out to test the individual and combined effects of the aforementioned four factors, and these simulations showed that high flood stages in the Jingjiang River clearly are related to the geomorphological changes.

Orthotropy rescaling and implications for fracture in composites

For most practically important plane elasticity problems of orthotropic materials, stresses depend on elastic constants through two nondimensional combinations. A spatial rescaling has been found to reduce the orthotropic problems to equivalent problems in materials with cubic symmetry. The latter, under favorable conditions, may be approximated by isotropic materials. Consequently, solutions for orthotropic materials can be constructed approximately from isotropic material solutions or rigorously from cubic ones. The concept is developed to gain insight into the interplay between anisotropy and finite geometry. The inherent simplicity of the solutions allows a variety of technical problems to be addressed efficiently. Included are stress concentration related cracking, effective contraction of orthotropic material specimens, crack deflection onto easy fracture planes, and surface flaw induced delamination.