Exact analysis of Burgers equation on semiline with flux condition at the origin

The initial boundary value problem for the Burgers equation in the domain x greater-or-equal, slanted 0, t > 0 with flux boundary condition at x = 0 has been solved exactly. The behaviour of the solution as t tends to infinity is studied and the “asymptotic profile at infinity” is obtained. In addition, the uniqueness of the solution of the initial boundary value problem is proved and its inviscid limit as var epsilon → 0 is obtained.

Universal behaviour in erosive burning of solid propellants

This paper considers the extensive data and correlations on the erosive burning of solid propellants. A relatively simple nondimensional relationship between the ratio of the actual to nonerosive burn rate (eta) and a quantity g, which is the product of g(0)-the ratio of free stream mass flux to the mass flux from the surface for nonerosive condition-and Re-0(m), where Re-0 is the Reynolds number based on the nonerosive mass flux of the propellant and port diameter, is shown to correlate most data within the accuracies of the experiments with m = -0.125. This shows the above relationship to account for the effects of pressure, aluminum, even up to a proportion of 17%, burn rate catalysts, and motor size. It is concluded that the suggested correlation between eta and g may be adopted universally for most practical propellants. (C) 1997 by The Combustion Institute.

Structural, Electrical and Magnetic Behaviour of FeTe0.5Se0.5 Superconductor

We report the synthesis as well as structural and physical properties of the bulk polycrystalline FeTe and FeTe0.5Se0.5 compounds. These samples are synthesised by the solid state-reaction method via vacuum encapsulation. Both studied compounds are crystallized in a tetragonal phase with space group P4/nmm. The parent FeTe compound shows an anomaly in resistivity measurement at around 78 K, which is due to the structural change along with a magnetic phase transition. The superconductivity in the FeTe0.5Se0.5 sample at 13 K is confirmed by the resistivity measurements. DC magnetisation along with an isothermal (M-H) loop shows that FeTe0.5Se0.5 possesses bulk superconductivity. The upper critical field is estimated through resistivity rho (T,H) measurements using Gingzburg-Landau (GL) theory and is above 50 T with 50 % resistivity drop criterion. The origin of the resistive transition broadening under magnetic field is investigated by thermally activated flux flow. The magnetic field dependence of the activation energy of the flux motion is discussed.

Behaviour of turbulent Prandtl/Schmidt number in compressible mixing layer

The behaviour of turbulent Prandtl/Schmidt number is explored through the model-free simulation results. It has been observed that compressibility affects the Reynolds scalar flux vectors. Reduced peak values are also observed for compressible convective Mach number mixing layer as compared with the incompressible convective Mach number counterpart, indicating a reduction in the mixing of enthalpy and species. Pr-t and Sc-t variations also indicate a reduction in mixing. It is observed that unlike the incompressible case, it is difficult to assign a constant value to these numbers due to their continuous variation in space. Modelling of Pr-t and Sc-t would be necessary to cater for this continuous spatial variation. However, the turbulent Lewis number is evaluated to be near unity for the compressible case, making it necessary to model only one of the Pr-t and Sc-t..

An analysis of MONTBLEX data on heat and momentum flux at Jodhpur

Parameterization of sensible heat and momentum fluxes as inferred from an analysis of tower observations archived during MONTBLEX-90 at Jodhpur is proposed, both in terms of standard exchange coefficients C-H and C-D respectively and also according to free convection scaling. Both coefficients increase rapidly at low winds (the latter more strongly) and with increasing instability. All the sensible heat flux data at Jodhpur (wind speed at 10m <(U)over bar (10)>, < 8ms(-1)) also obey free convection scaling, with the flux proportional to the '4/3' power of an appropriate temperature difference such as that between 1 and 30 m. Furthermore, for <(U)over bar (10)> < 4 ms(-1) the momentum flux displays a linear dependence on wind speed.

Solute induced liquid crystalline behaviour of a quaternary ammonium salt and its application to structure determination

A new liquid crystalline phase, induced by the addition of small amounts of a non-mesogenic solute (such as dimethyl sulphoxide or methyl iodide) to a quaternary ammonium salt, N-methyl-N,N,N-trioctadecylammonium iodide (MTAI), has been detected by NMR and optical microscopic studies. In some cases, there is a coexistence of nematic and smectic phases. Information on the ordering of the phases in the magnetic field of the spectrometer has been derived from NMR spectra of a dissolved molecule, C-13-enriched methyl iodide. The low order parameter of the pure thermotropic nematic phase of the salt provides first-order spectra of the dissolved oriented molecules. Analyses of spectra of cis,cis-mucononitrile exemplifies the utility of the MTAI nematic phase in the determination of structural parameters of the solute.

Swelling behaviour of soil-bentonite mixtures

Studies on the swelling behaviour of mixtures of bentonite clay and nonswelling coarser fractions of different sizes and shapes reveal that observed swelling occurs only after the voids of the nonswelling particles are filled up with swollen clay particles. The magnitude of the swell within the voids, called intervoid swelling is large when the size and percentage of the nonswelling coarser fraction is large. The observable swell, after intervoid swelling, is called primary swelling and follows a rectangular hyperbolic relationship with time. The total swell per gram of the clay decreases with an increase in the size of the nonswelling fraction and with a decrease in the percentage of swelling clay. Time-swell relationships show that swelling continues to occur for a long time after the primary swelling, and this is called secondary swelling.

Nonlinear Enzyme Kinetics Can Lead to High Metabolic Flux Control Coefficients: Implications for the Evolution of Dominance

In a classic study, Kacser & Burns (1981, Genetics 97, 639-666) demonstrated that given certain plausible assumptions, the flux in a metabolic pathway was more or less indifferent to the activity of any of the enzymes in the pathway taken singly. It was inferred from this that the observed dominance of most wild-type alleles with respect to loss-of-function mutations did not require an adaptive, meaning selectionist, explanation. Cornish-Bowden (1987, J. theor. Biol. 125, 333-338) showed that the Kacser-Burns inference was not valid when substrate concentrations were large relative to the relevant Michaelis constants. We find that in a randomly constructed functional pathway, even when substrate levels are small, one can expect high values of control coefficients for metabolic flux in the presence of significant nonlinearities as exemplified by enzymes with Hill coefficients ranging from two to six, or by the existence of oscillatory loops. Under these conditions the flux can be quite sensitive to changes in enzyme activity as might be caused by inactivating one of the two alleles in a diploid. Therefore, the phenomenon of dominance cannot be a trivial ''default'' consequence of physiology but must be intimately linked to the manner in which metabolic networks have been moulded by natural selection.

Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions

We present a generalization of the finite volume evolution Galerkin scheme [M. Lukacova-Medvid'ova,J. Saibertov'a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533-562; M. Luacova-Medvid'ova, K.W. Morton, G. Warnecke, Finite volume evolution Galerkin (FVEG) methods for hyperbolic problems, SIAM J. Sci. Comput. (2004) 26 1-30] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex systems. The finite volume evolution Galerkin (FVEG) method is a predictor-corrector method combining the finite volume corrector step with the evolutionary predictor step. In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator. The latter is constructed using the theory of bicharacteristics under the assumption of spatially dependent wave speeds. To approximate heterogeneous medium a staggered grid approach is used. Several numerical experiments for wave propagation with continuous as well as discontinuous wave speeds confirm the robustness and reliability of the new FVEG scheme.

High temperature time-dependent low cycle fatigue behaviour of a type 316L(N) stainless steel

Total strain controlled low cycle fatigue tests on 316L(N) stainless steel have been conducted in air at various strain rates in the temperature range of 773-873 K to identify the operative time-dependent mechanisms and to understand their influence on the cyclic deformation and fracture behaviour of the alloy. The cyclic stress response at all the testing conditions was marked by an initial hardening followed by stress saturation. A negative strain rate stress response is observed under specific testing conditions which is attributed to dynamic strain ageing (DSA). Transmission electron microscopy studies reveal that there is an increase in the dislocation density and enhanced slip planarity in the DSA regime. Fatigue life is found to decrease with a decrease in strain rate. The degradation in fatigue resistance is attributed to the detrimental effects associated with DSA and oxidation. Quantitative measurement of secondary cracks indicate that both transgranular and intergranular cracking are accelerated predominantly under conditions conducive to DSA.

Influence of lanthanum doping on the dielectric, ferroelectric and relaxor behaviour of barium bismuth titanate ceramics

Barium lanthanum bismuth titanate (Ba1−(3/2)xLaxBi4Ti4O15, x = 0–0.4) ceramics were fabricated using the powders synthesized via the solid-state reaction route. X-ray powder diffraction analysis confirmed the above compositions to be monophasic and belonged to the m = 4 member of the Aurivillius family of oxides. The effect of the partial presence of La3+ on Ba2+ sites on the microstructure, dielectric and relaxor behaviour of BaBi4Ti4O15 (BBT) ceramics was investigated. For the compositions pertaining to x ≤ 0.1, the dielectric constant at both room temperature and in the vicinity of the temperature of the dielectric maximum (Tm) of the parent phase (BBT) increased significantly with an increase in x while Tm remained almost constant. Tm shifted towards lower temperatures accompanied by a decrease in the magnitude of the dielectric maximum (εm) with an increase in the lanthanum content (0.1 < x ≤ 0.4). The dielectric relaxation was modelled using the Vogel–Fulcher relation and a decrease in the activation energy for frequency dispersion with increasing x was observed. The frequency dispersion of Tm was found to decrease with an increase in lanthanum doping, and for compositions corresponding to x ≥ 0.3, Tm was frequency independent. Well-developed P(polarization)–E(electric field) hysteresis loops were observed at 150 °C for all the samples and the remanent polarization (2Pr) was improved from 6.3 µC cm−2 for pure BBT to 13.4 µC cm−2 for Ba0.7La0.2Bi4Ti4O15 ceramics. Dc conductivities and associated activation energies were evaluated using impedance spectroscopy.

Resolidification behaviour of laser surface-melted metals and alloys

The solidification behaviour is described of two pure metals (Bi and Ni) and two eutectic alloys (A1-Ge and AI-Cu) under nonequilibrium conditions, in particular the microsecond pulsed laser surface melting. The resolidification behaviour of bismuth shows that epitaxial regrowth is the dominant mechanism. For mixed grain size, regrowth of larger grains dominates the microstructure and can result in the development of texture. In the case of nickel, epitaxial growth has been noted. For lower energy pulse-melted pool, grain refinement takes place, indicating nucleation of fresh nickel grains. The A1-Ge eutectic alloy indicates the nucleation and columnar growth of a metastable monoclinic phase from the melt-substrate interface at a high power density laser irradiation. An equiaxed microstructure containing the same monoclinic phase is obtained at a lower power density laser irradiation. It is shown that the requirement of solution partition acts as a barrier to eutectic regrowth from the substrate. The laser-melted pool of A1-Cu eutectic alloy includes columnar growth of c~-A1 and 0-A12Cu phase followed by the dendritic growth of A12Cu phase with ct-Al forming at the interdendritic space. In addition, a banded microstructure was observed in the resolidified laser-melted pool.

Pressure transitions and electron transport behaviour of crystalline Se-Te alloys

Pressure transitions of Se-Te alloys have been studied over the entire range of compositions. Conductivities have also been measured as a function of temperature and alloy composition. Transition pressures, activation barriers and isothermal conductivities exhibit distinct changes of slope in their variation as a function of composition at about 8 at % of Te. Transition pressures change slope at not, vert, similar 35% Te also. An attempt has been made to explain these observations on the basis of the size effect of Te which, in turn, affects the electron energy dispersions in the band structure.

Using lead sulphate instead of lead oxide in flux growth of yttrium iron garnet(YIG) crystals

Crystal growth of YIG from fluxes containing lead sulphate in place of lead oxide in the usual lead oxide-lead fluoride-boron oxide flux system has been tried. Lead sulphate decomposes during crystal growth giving lead oxide and sulphur trioxide. Due to the influence of sulphur trioxide in the system the yield of crystals almost doubles. There is no change either in the morphology of the crystals or their lattice parameter. It is possible that solubility of YIG is different in the new flux and the changed solubility causes the increase in yield of crystals.

Influence of heat treatment on the strength and fracture behaviour of Fe-12Cr-6Al ferritic stainless steel

The changes in the tensile properties and fracture mode brought about by heat treatment of Fe-12Cr-6Al ferritic stainless steel have been studied. A favourable combination of high strength and good ductility is obtained by heating the material at 1370 K for 2 h followed by a water quench. The high-temperature treatment results in carbide dissolution as well as an increase in the grain size. The mechanism of strengthening has been evaluated from the apparent activation energy (28 kJ mol–1) and is identified to be the unpinning of dislocations from the atmosphere of carbon atoms. As the heat-treatment temperature is increased, the fracture behaviour changes from ductile to brittle mode and this is related to the changes in grain size and friction stress.