Non-linear couette flow with heat transfer using the B-G-K model

In recent years a large number of investigators have devoted their efforts to the study of flow and heat transfer in rarefied gases, using the BGK [1] model or the Boltzmann kinetic equation. The velocity moment method which is based on an expansion of the distribution function as a series of orthogonal polynomials in velocity space, has been applied to the linearized problem of shear flow and heat transfer by Mott-Smith [2] and Wang Chang and Uhlenbeck [3]. Gross, Jackson and Ziering [4] have improved greatly upon this technique by expressing the distribution function in terms of half-range functions and it is this feature which leads to the rapid convergence of the method. The full-range moments method [4] has been modified by Bhatnagar [5] and then applied to plane Couette flow using the B-G-K model. Bhatnagar and Srivastava [6] have also studied the heat transfer in plane Couette flow using the linearized B-G-K equation. On the other hand, the half-range moments method has been applied by Gross and Ziering [7] to heat transfer between parallel plates using Boltzmann equation for hard sphere molecules and by Ziering [83 to shear and heat flow using Maxwell molecular model. Along different lines, a moment method has been applied by Lees and Liu [9] to heat transfer in Couette flow using Maxwell's transfer equation rather than the Boltzmann equation for distribution function. An iteration method has been developed by Willis [10] to apply it to non-linear heat transfer problems using the B-G-K model, with the zeroth iteration being taken as the solution of the collisionless kinetic equation. Krook [11] has also used the moment method to formulate the equivalent continuum equations and has pointed out that if the effects of molecular collisions are described by the B-G-K model, exact numerical solutions of many rarefied gas-dynamic problems can be obtained. Recently, these numerical solutions have been obtained by Anderson [12] for the non-linear heat transfer in Couette flow,

The nature of non-equilibrium solidification of undercooled Agsingle bondCu alloys in contact with primary copper dendrites

Liquids of silver-copper alloys with near eutectic compositions embedded in a copper matrix were undercooled. The structural and microstructural investigations of these alloys solidified from undercooled temperature indicated the absence of both the eutectic reaction and diffusionless transformation below the equal free energy curve (T0). Instead the liquid maintained local equilibrium with the copper dendrites continuously until it intersected the extended solidus of the silver rich solid solution.

Analysis of an internally mountable accelerometer balance system for use with non-isotropic models in shock tunnels

Knowledge of drag force is an important design parameter in aerodynamics. Measurement of aerodynamic forces at hypersonic speed is a challenge and usually ground test facilities like shock tunnels are used to carry out such tests. Accelerometer based force balances are commonly employed for measuring aerodynamic drag around bodies in hypersonic shock tunnels. In this study, we present an analysis of the effect of model material on the performance of an accelerometer balance used for measurement of drag in impulse facilities. From the experimental studies performed on models constructed out of Bakelite HYLEM and Aluminum, it is clear that the rigid body assumption does not hold good during the short testing duration available in shock tunnels. This is notwithstanding the fact that the rubber bush used for supporting the model allows unconstrained motion of the model during the short testing time available in the shock tunnel. The vibrations induced in the model on impact loading in the shock tunnel are damped out in metallic model, resulting in a smooth acceleration signal, while the signal become noisy and non-linear when we use non-isotropic materials like Bakelite HYLEM. This also implies that careful analysis and proper data reduction methodologies are necessary for measuring aerodynamic drag for non-metallic models in shock tunnels. The results from the drag measurements carried out using a 60 degrees half angle blunt cone is given in the present analysis.

Constitutive modeling of shape memory alloy wire with non-local rate kinetics

A constitutive modeling approach for shape memory alloy (SMA) wire by taking into account the microstructural phase inhomogeneity and the associated solid-solid phase transformation kinetics is reported in this paper. The approach is applicable to general thermomechanical loading. Characterization of various scales in the non-local rate sensitive kinetics is the main focus of this paper. Design of SMA materials and actuators not only involve an optimal exploitation of the hysteresis loops during loading-unloading, but also accounts for fatigue and training cycle identifications. For a successful design of SMA integrated actuator systems, it is essential to include the microstructural inhomogeneity effects and the loading rate dependence of the martensitic evolution, since these factors play predominant role in fatigue. In the proposed formulation, the evolution of new phase is assumed according to Weibull distribution. Fourier transformation and finite difference methods are applied to arrive at the analytical form of two important scaling parameters. The ratio of these scaling parameters is of the order of 10(6) for stress-free temperature-induced transformation and 10(4) for stress-induced transformation. These scaling parameters are used in order to study the effect of microstructural variation on the thermo-mechanical force and interface driving force. It is observed that the interface driving force is significant during the evolution. Increase in the slopes of the transformation start and end regions in the stress-strain hysteresis loop is observed for mechanical loading with higher rates.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

Topochemical dimerization of non-parallel double bonds: 7-methoxycoumarin

X-ray crystal structure analysis of 7-methoxycoumarin reveals that the reactive double bonds are rotated by about 65° with respect to each other, the centre-to-centre distance between the double bonds being 3.83 Å. In spite of this unfavourable arrangement, photodimerization occurs in the crystalline state yielding the syn-head-tail dimer as the only product. Lattice energy calculations on ground-state molecules in crystals throw light on the mechanism of the reaction.

Nucleation parameters for polymer crystallization from non-isothermal thermal analysis

Differential scanning calorimetry (DSC) has been used to obtain kinetic and nucleation parameters for polymer crystallization under a non-isothermal mode of operation. The available isothermal nucleation growth-rate equation has been modified for non-isothermal kinetic analysis. The values of the nucleation constant (K g ) and surface free energies (sgr, sgr e ) have been obtained for i-polybutene-1, i-polypropylene, poly(L-lactic acid), and polyoxymethylene and are compared with those obtained from isothermal kinetic analysis; a good agreement in both is seen.

Sequences that adopt non-B-DNA conformation in form V DNA as probed by enzymic methylation

pBR322 form V DNA is a highly torsionally strained molecule with a linking number of zero. We have used sequence- specific DNA methylases as probes for B-DNA in this molecule, exploiting the inability of methylases to methylate single-stranded DNA and Z-DNA, both of which are known to occur in form V DNA. Some sequences in form V DNA were shown to be totally in the B-form, others were totally in an altered, unmethylatable conformation, while still other sites appeared to exist partly in altered and partly in normal B-conformation. Some potential Z-forming sequences (alternating pyrimidine/purine) of less than seven base-pairs were not in the Z conformation in form V DNA, whereas others did adopt an altered structure, indicating a modulating influence of flanking sequences. Furthermore, regions of imperfect alternating pyrimidine/purine structure were sometimes capable of adopting an altered structure. In addition, some regions of altered structure had no apparent Z-forming sequences, nor were they in polypurine stretches, which have also been proposed to form left-handed DNA. These non-B-DNA conformations may represent novel left-handed helical structures or sequences that become single stranded under torsional strain. Long regions of either altered (unmethylatable) DNA or B-DNA were not always observed. In fact, one region showed three transitions between B-like DNA and altered structure within 26 base-pairs.

Self-tuning control of a class of multivariable non-linear systems

Self-tuning is applied to the minimum variance control of non-linear multivariable systems which can be characterized by a ' multivariable Hammerstein model '. It is also shown that such systems are not amenable to self-tuning control if control costing is to be included in the performance criterion.

Non-equilibrium trapping in Al---In system

The comparative trapping efficiency of indium in aluminium solid solution during vapour deposition and rapid solidification at room temperature was evaluated by studying the nature of the decomposition of the metastable solid solution. A spinodal decomposition was observed in the case of rapid solidification while vapour deposited foils decompose by a nucleation and growth type of process. From this we conclude that rapid solidification effects a more efficient non-equilibrium trapping of indium in aluminium solid solution compared to vapour deposition at room temperature.

Non-ohmic conduction and electrical switching under pressure of the charge transfer complexo-tolidine-iodine

The current voltage characteristics ofo-tolidine-iodine, with stoichiometry 1:1 grown from benzene, have been studied under high pressures upto 6 GPa atT=300 K andT=77 K. The characteristics show a pronounced deviation from ohmicity beyond a certain current for all pressures studied. At room temperature, beyond a threshold field the system switches from a low conductingOFF state to a high conductingON state with σON/σOFF ∼ 103. TheOFF state can be restored by the application of an a.c. pulse of low frequency. The temperature dependence of the two states studied indicates that theOFF state is semiconducting while theON state, beyond a certain applied pressure is metallic. The characteristics atT=77 K do not show any switching.

Korteweg-De Vries Equation for Non-Linear Ion-Acoustic Waves in a Plasma with Negative Ions

The theoretical analysis, based on the perturbation technique, of ion-acoustic waves in the vicinity of a Korteweg-de Vries (K-dV) equation derived in a plasma with some negative ions has been made. The investigation shows that the negative ions in plasma with isothermal electrons introduced a critical concentration at which the ion-acoustic wave plays an important role of wave-breaking and forming a precursor while the plasma with non-isothermal electrons has no such singular behaviour of the wave. These two distinct features of ion waves lead to an overall different approach of present study of ion-waves. A distinct feature of non-uniform transition from the nonisothermal case to isothermal case has been shown. Few particular plasma models have been chosen to show the characteristics behaviour of the ion-waves existing in different cases

Characterization of the restriction enzyme-like endonuclease encoded by the Entamoeba histolytica non-long terminal repeat retrotransposon EhLINE1

The genome of the human pathogen Entamoeba histolytica, a primitive protist, contains non-long terminal repeat retrotransposable elements called EhLINEs. These encode reverse transcriptase and endonuclease required for retrotransposition. The endonuclease shows sequence similarity with bacterial restriction endonucleases. Here we report the salient enzymatic features of one such endonuclease. The kinetics of an EhLINE1-encoded endonuclease catalyzed reaction, determined under steady-state and single-turnover conditions, revealed a significant burst phase followed by a slower steady-state phase, indicating that release of product could be the slower step in this reaction. For circular supercoiled DNA the K-m was 2.6 x 10-8 m and the k(cat) was 1.6 x 10-2 sec-1. For linear E. histolytica DNA substrate the K-m and k(cat) values were 1.3 x 10-8 m and 2.2 x 10-4 sec-1 respectively. Single-turnover reaction kinetics suggested a noncooperative mode of hydrolysis. The enzyme behaved as a monomer. While Mg2+ was required for activity, 60% activity was seen with Mn2+ and none with other divalent metal ions. Substitution of PDX12-14D (a metal-binding motif) with PAX(12-14)D caused local conformational change in the protein tertiary structure, which could contribute to reduced enzyme activity in the mutated protein. The protein underwent conformational change upon the addition of DNA, which is consistent with the known behavior of restriction endonucleases. The similarities with bacterial restriction endonucleases suggest that the EhLINE1-encoded endonuclease was possibly acquired from bacteria through horizontal gene transfer. The loss of strict sequence specificity for nicking may have been subsequently selected to facilitate spread of the retrotransposon to intergenic regions of the E. histolytica genome.

On the Structure of Contractible Edges in k-connected Partial k-trees

Contraction of an edge e merges its end points into a new single vertex, and each neighbor of one of the end points of e is a neighbor of the new vertex. An edge in a k-connected graph is contractible if its contraction does not result in a graph with lesser connectivity; otherwise the edge is called non-contractible. In this paper, we present results on the structure of contractible edges in k-trees and k-connected partial k-trees. Firstly, we show that an edge e in a k-tree is contractible if and only if e belongs to exactly one (k + 1) clique. We use this characterization to show that the graph formed by contractible edges is a 2-connected graph. We also show that there are at least |V(G)| + k - 2 contractible edges in a k-tree. Secondly, we show that if an edge e in a partial k-tree is contractible then e is contractible in any k-tree which contains the partial k-tree as an edge subgraph. We also construct a class of contraction critical 2k-connected partial 2k-trees.

Ion pairs in non-redundant protein structures

Ion pairs contribute to several functions including the activity of catalytic triads, fusion of viral membranes, stability in thermophilic proteins and solvent-protein interactions. Furthermore, they have the ability to affect the stability of protein structures and are also a part of the forces that act to hold monomers together. This paper deals with the possible ion pair combinations and networks in 25% and 90% non-redundant protein chains. Different types of ion pairs present in various secondary structural elements are analysed. The ion pairs existing between different subunits of multisubunit protein structures are also computed and the results of various analyses are presented in detail. The protein structures used in the analysis are solved using X-ray crystallography, whose resolution is better than or equal to 1.5 angstrom and R-factor better than or equal to 20%. This study can, therefore, be useful for analyses of many protein functions. It also provides insights into the better understanding of the architecture of protein structure.