Stability of the viscous flow of a fluid through a flexible tube

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (rho VR/eta), the ratio of the viscosities of the wall and fluid eta(r) = (eta(s)/eta), the ratio of radii H and the dimensionless velocity Gamma = (rho V-2/G)(1/2). Here rho is the density of the fluid, G is the coefficient of elasticity of the wall and V is the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter epsilon = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate s((0)), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctuations due to the Reynolds stress. There is an O(epsilon(1/2)) correction to the growth rate, s((1)), due to the presence of a wall layer of thickness epsilon(1/2)R where the viscous stresses are O(epsilon(1/2)) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Gamma and wavenumber k where s((1)) = 0. At these points, the wall layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(epsilon) correction to the growth rate s((2)) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s((2)) increases proportional to (H-1)(-2) for (H-1) much less than 1 (thickness of wall much less than the tube radius), and decreases proportional to H-4 for H much greater than 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube

Unwinding of heterologous DNA by RecA protein during the search for homologous sequences

The search for homologous sequences promoted by RecA protein in vitro involves a presynaptic filament and naked duplex DNA, the multiple contacts of which produce nucleoprotein networks or coaggregates. The single-stranded DNA within the presynaptic filaments, however, is extended to an axial spacing 1.5 times that of B-form DNA. To investigate this paradoxical difference between the spacing of bases in the RecA presynaptic filament versus the target duplex DNA, we explored the effect of heterologous contacts on the conformation of DNA, and vice versa. In the presence of wheat germ topoisomerase I, RecA presynaptic filaments induced a rapid, limited reduction in the linking number of heterologous circular duplex DNA. This limited unwinding of heterologous duplex DNA, termed heterologous unwinding, was detected within 30 seconds and reached a steady state within a few minutes. Presynaptic filaments that were formed in the presence of ATP?S and separated from free RecA protein by gel filtration also generated a ladder of topoisomers upon incubation with relaxed duplex DNA and topoisomerase. The inhibition of heterologous contacts by 60 mImage -NaCl or 5 mImage -ADP resulted in a corresponding decrease in heterologous unwinding. In reciprocal fashion, the stability or number of heterologous contacts with presynaptic filaments was inversely related to the linking number of circular duplex DNA. These observations show that heterologous contacts with the presynaptic filament cause a limited unwinding of the duplex DNA, and conversely that the ability of the DNA to unwind stabilizes transient heterologous contacts.

Uniform algebras generated by holomorphic and close-to-harmonic functions

The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc (D) over bar generated by z and h, where h is a nowhere-holomorphic harmonic function on D that is continuous up to partial derivative D, equals C((D) over bar). The abstract tools used by Axler and Shields make harmonicity of h an essential condition for their result. We use the concepts of plurisubharmonicity and polynomial convexity to show that, in fact, the same conclusion is reached if h is replaced by h + R, where R is a non-harmonic perturbation whose Laplacian is ``small'' in a certain sense.

Optimization studies on limestone beneficiation

Limestone rejects from Bagalkot mines have been beneficiated by froth flotation with a view to reducing the magnesia content. In order to ascertain the effect of the main parameters such as sodium oleate concentration, sodium silicate concentration and pH on the MgO content, statistically designed experiments have been performed. The results indicate that under the optimum conditions arrived at limestone rejects could be beneficiated to produce a concentrate with magnesia. content meeting the specifications for cement manufacture.

Transient absorption studies on 3,6-dibromo polyvinylcarbazole and its model compounds

3,6-Dibromo-N-ethylcarbazole (DBNEC) and its polymeric analogue poly-3,6-dibromovinylcarbazole (PDBVCz) were studied by transient absorption spectroscopy. The transient absorption spectrum of the 3,6-dibromo-N-ethylcarbazole radical cation and decay rate constants of radical cations of 3,6-dibromo-N-ethylcarbazole and its polymeric analogue are presented. In the case of unsubstituted carbazole, the ratio of the yield of radical cation of monomer to polymer is 2.0, whereas in the case of PDBVCz, under the same experimental conditions, the yield of the radical cation is an order of magnitude less in comparison with the monomer model compound DBNEC. This drastic difference in yield has been correlated to the difference in the conformational structure of the polymer as evidenced by nuclear magnetic resonance spectroscopy. (C) 1997 Elsevier Science S.A.

Enhancing lifetime of wireless sensor networks using multiple data sinks

In this paper, we address the fundamental question concerning the limits on the network lifetime in sensor networks when multiple base stations (BSs) are deployed as data sinks. Specifically, we derive upper bounds on the network lifetime when multiple BSs arc employed, and obtain optimum locations of the base stations that maximise these lifetime bounds. For the case of two BSs, we jointly optimise the BS locations by maximising the lifetime bound using genetic algorithm. Joint optimisation for more number of BSs becomes prohibitively complex. Further, we propose a suboptimal approach for higher number of BSs, Individually Optimum method, where we optimise the next BS location using optimum location of previous BSs. Individually Optimum method has advantage of being attractive for solving the problem with more number of BSs at the cost of little compromised accuracy. We show that accuracy degradation is quite small for the case of three BSs.

Isolation and characterization of proteolytic enzymes from the latex of Synadenium grantii Hook, 'f'

Two fractions showing proteolytic enzymes have been obtained from the latex of Synadenium grantii Hook, 'f', using gel-filtration and anion-exchange chromatographic techniques. Both these proteases have the same molecular mass of 76+/-2 kDa each. They exhibit maximal activity at pH 7.0 and at a temperature of 60 degreesC. They display stability over a pH range from 5-10 and are also highly thermostable. Irreversible inhibition by PMSF indicates that they are serine proteases. In addition, histidine residues also appear to play an important role in catalysis as evidenced by inhibition with DEPC. They also exhibit similarity with respect to pH and temperature optima, kinetic properties and thermal stability. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

MOCVD of aluminium oxide films using aluminiurn beta-diketonates as precursors

Deposition of Al2O3 coatings by CVD is of importance because they are often used as abrading material in cemented carbide cutting tools. The conventionally used CVD process for Al2O3 involves the corrosive reactant AlCl3. In this paper, we report on the thermal characterisation of the metalorganic precursors namely aluminium tristetramethyl-heptanedionate [Al(thd)(3)] and aluminium tris-acetylacetonate [Al(acac)(3)] and their application to the CVD of Al2O3 films. Crystalline Al2O3 films were deposited by MOCVD at low temperatures by the pyrolysis of Al(thd)(3) and Al(acac)(3). The films were deposited on a TiN-coated tungsten carbide (TiN/WC) and Si(100) substrates in the temperature range 500-1100degreesC. The as-deposited films were characterised by x-ray diffraction, optical microscopy, scanning and transmission electron microscopy, Auger electron spectroscopy. The observed crystallinity of films grown at low temperatures, their microstructure, and composition may be interpreted in terms of a growth process that involves the melting of the metalorganic precursor on the hot growth surface.

Mossbauer study of La1-xCaxMn1-y (57)FeyO(3) with x = 0, 0.25; y=0.01

Temperature dependent Mossbauer measurements are done on the samples of La1- xCaxMn1-y (FeyO3)-Fe-57 with x=0 and 0.25, and y=0.01. With decreasing temperature, the specimen with x=0.25 shows a paramagnetic to ferromagnetic transition around 175 K. In the specimen x=0.0, the temperature dependence of both the center shift (delta) and the recoilless fraction (f) can be fitted very well with the Debye theory with a theta(D)=320+/-50 K. But for the specimens with x=0.25, f and delta show distinct deviations from the Debye behavior in the temperature range in which the resistivity shows a sharp decrease. Dips observed in both the f and delta around the transition temperature suggest that the Jahn-Teller distortion observed in these systems is dynamic in nature.

The influence of oxygen impurities on the formation of AlN-Al composites by infiltration of molten Al-Mg

The influence of residual oxygen in nitrogen on the formation of AlN-Al matrix by reactive infiltration has been investigated. Increasing the oxygen content from 10 ppm upwards decreased the nitride content in the matrix from 64 to 6%, Based on the analysis of the availability of oxygen at the Al-melt/gas interface, three distinct scenarios have been proposed (i) at lowest values, oxygen does not interfere with either infiltration or nitridation reaction; (ii) at intermediate values, nitridation is suppressed, however infiltration continues; and (iii) at a critical upper value, the melt passivates without any infiltration. This phenomenon offers control of the AlN/Al ratio in the matrix and the possibility of creation of microstructural gradierits by the appropriate choice of gas mixtures. (C) 2002 Elsevier Science B.V. All rights reserved.

Characterization of lithium borate–bismuth tungstate glasses and glass-ceramics by impedance spectroscopy

Transparent glasses in the system (1−x)Li2B4O7–xBi2WO6 (0≤x≤0.35) were prepared via melt quenching technique. Differential thermal analysis was employed to characterize the as-quenched glasses. Glass-ceramics with high optical transparency were obtained by controlled heat-treatment of the glasses at 720 K for 6 h. The amorphous nature of the as-quenched glass and crystallinity of glass-ceramics were confirmed by X-ray powder diffraction studies. High resolution transmission electron microscopy (HRTEM) shows the presence of nearly spherical nanocrystallites of Bi2WO6 in Li2B4O7 glass matrix. Capacitance and dielectric loss measurements were carried out as a function of temperature (300–870 K) in the frequency range 100 Hz–40 MHz. Impedance spectroscopy employed to rationalize the electrical behavior of glasses and glass-ceramics suggest the coexistence of electronic and ionic conduction in these materials. The thermal activation energies for the electronic conduction and ionic conduction were also estimated based on the Arrhenius plots.

Almost quarter-pinched Kähler metrics and Chern numbers

Given n is an element of Z(+) and epsilon > 0, we prove that there exists delta = delta(epsilon, n) > 0 such that the following holds: If (M(n),g) is a compact Kahler n-manifold whose sectional curvatures K satisfy -1 -delta <= K <= -1/4 and c(I)(M), c(J)(M) are any two Chern numbers of M, then |c(I)(M)/c(J)(M) - c(I)(0)/c(J)(0)| < epsilon, where c(I)(0), c(J)(0) are the corresponding characteristic numbers of a complex hyperbolic space form. It follows that the Mostow-Siu surfaces and the threefolds of Deraux do not admit Kahler metrics with pinching close to 1/4.

278. Studies on ass's milk: Composition

The total solids of samples of ass's milk ranged from 7·80 to 9·10, the solids-not-fat from 7·14 to 8·50, and the fat from 0·54 to 0·71%. The nitrogen distribution in ass's milk is: casein 39·5, albumin 35·0, globulin 2·7 and non-protein nitrogen 22·8% of the total nitrogen. Ass's milk contains: casein 0·70, albumin 0·62 and globulin 0·07%. The total protein content is 1·39%. Ass's milk is therefore characterized by a low casein, a low globulin and a high albumin content. The non-protein nitrogen consists of amino nitrogen 8·1, urea nitrogen 24·3 and uric acid 0·7 mg./100 ml. of milk. The urea content is twice that present in cow's milk. The mean chloride and lactose contents of the milk samples are 0·037 and 6·1% respectively. The average calcium and phosphorus content of ass's milk are 0·081 and 0·059% respectively. Half the calcium is ionic, and half is in colloidal form. The phosphorus distribution is: total acid soluble 84·0, acid soluble organic 38·5, easily hydrolysable ester 27·4, inorganic 46·0, and colloidal inorganic 23·0 % of the total phosphorus. The ratio of CaO: P2O5 is 1:1. 46 % of the total phosphorus is in ester form; this is high when compared with only 12 % in cow's milk; most of the phosphoric ester forms soluble barium salts, which is a distinguishing feature of ass's milk. The total sulphur content is 15·8 mg./100 ml. The fat has a penetrating odour and is coloured orange-yellow. It has an iodine value of about 86, which is much higher than that for human milk fat. The Reichert (9·5) and Kirschner values (5·7) are low. In general, the composition of ass's milk resembles that of human rather than of cow's milk.

Stability of the flow of a fluid through a flexible tube at high Reynolds number

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (ρVR / η), the ratio of the viscosities of the wall and fluid ηr = (ηs/η), the ratio of radii H and the dimensionless velocity Γ = (ρV2/G)1/2. Here ρ is the density of the fluid, G is the coefficient of elasticity of the wall and Vis the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter ε = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate do), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctruations due to the Reynolds strees. There is an O(ε1/2) correction to the growth rate, s(1), due to the presence of a wall layer of thickness ε1/2R where the viscous stresses are O(ε1/2) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Γ and wavenumber k where s(l) = 0. At these points, the wail layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(ε) correction to the growth rate s(2) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s(2) increases [is proportional to] (H − 1)−2 for (H − 1) [double less-than sign] 1 (thickness of wall much less than the tube radius), and decreases [is proportional to] (H−4 for H [dbl greater-than sign] 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube.