Unsteady convective diffusion in a rotating parallel plate channel

The paper presents an exact analysis of the dispersion of a passive contaminant in a viscous fluid flowing in a parallel plate channel driven by a uniform pressure gradient. The channel rotates about an axis perpendicular to its walls with a uniform angular velocity resulting in a secondary flow. Using a generalized dispersion model which is valid for all time, we evaluate the longitudinal dispersion coefficientsK _i (i=1, 2, ...) as functions of time. It is shown thatK ₁=0 andK ₃,K ₄, ... decay rapidly in comparison withK ₂. ButK ₂ decreases with increasing (the dimensionless rotation parameter) for values of upto approximately =2.2. ThereafterK ₂ increases with further increase in and its value gets saturated for large values of (say, 500) and does not change any further with increase in . A physical explanation of this anomalous behaviour ofK ₂ is given.

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Instationäre konvektive Diffusion in einem rotierenden Parallelplattenkanal

Zusammenfassung In dieser Untersuchung wird eine exakte Analyse der Ausbreitung eines passiven Kontaminierungsstoffes in einer zähen Flüssigkeit gegeben, die, befördert durch einen gleichförmigen Druckgradienten, in einem Parallelplattenkanal strömt. Der Kanal rotiert mit gleichförmiger Winkelgeschwindigkeit um eine zu seinen Wänden senkrechte Achse, wodurch sich eine Sekundärströmung ausbildet. Unter Verwendung eines generalisierten, für alle Zeiten gültigen Dispersionsmodells werden die longitudinalen DispersionskoeffizientenK _i (i=1, 2, ...) als Funktionen der Zeit ermittelt. Es wird gezeigt, daßK ₁=0 gilt und dieK ₃,K ₄, ... gegenüberK ₂ schnell abnehmen.K ₂ nimmt ab, wenn , der dimensionslose Rotationsparameter, bis etwa zum Wert 2,2 ansteigt. Danach wächstK ₂ mit bis auf einem Endwert an, der etwa ab =500 erreicht wird. Dieses anomale Verhalten vonK ₂ findet eine physikalische Erklärung.

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List of symbols C solute concentration - D molecular diffusivity - K _i longitudinal dispersion coefficients - 2L depth of the channel - P ₀ dimensionless pressure gradient along main flow - Pe Péclet number - q velocity vector - Q _x,Q _y mass flux along the main flow and the secondary flow directions - dimensionless average velocity along the main flow direction - (x, y, z) Cartesian co-ordinates Greek symbols dimensionless rotation parameter - the inclination of side walls withx-axis - kinematic viscosity - fluid density - dimensionless time - angular velocity of the channel - dimensionless distance along the main flow direction - dimensionless distance along the vertical direction - dimensionless solute concentration - integral of the dispersion coefficientK ₂() over a time interval     

An alignment-free method to find similarity among protein sequences via the general form of Chou’s pseudo amino acid composition

In this paper, we propose a method to create the 60-dimensional feature vector for protein sequences via the general form of pseudo amino acid composition. The construction of the feature vector is based on the contents of amino acids, total distance of each amino acid from the first amino acid in the protein sequence and the distribution of 20 amino acids. The obtained cosine distance metric (also called the similarity matrix) is used to construct the phylogenetic tree by the neighbour joining method. In order to show the applicability of our approach, we tested it on three proteins: 1) ND5 protein sequences from nine species, 2) ND6 protein sequences from eight species, and 3) 50 coronavirus spike proteins. The results are in agreement with known history and the output from the multiple sequence alignment program ClustalW, which is widely used. We have also compared our phylogenetic results with six other recently proposed alignment-free methods. These comparisons show that our proposed method gives a more consistent biological relationship than the others. In addition, the time complexity is linear and space required is less as compared with other alignment-free methods that use graphical representation. It should be noted that the multiple sequence alignment method has exponential time complexity.     

Effect of Electron Beam Irradiation on the Kinetics of Non-isothermal Crystallization of Nylon 66

The non-isothermal crystallization kinetics was studied by differential scanning calorimetric analysis on nylon 66 and e-beam irradiated nylon 66 at different cooling rates. The Modified Avrami equation, the Ozawa equation and the Combined Avrami-Ozawa equation were applied to study the kinetics of non-isothermal crystallization of nylon 66. The crystallization behavior of pristine nylon 66 polymer was compared with that of e-beam irradiated nylon 66 and observed that the kinetics of non-isothermal crystallization of nylon66 was affected largely upon e-beam irradiation. E-beam irradiation not only decreased the crystallization temperature of nylon 66, but influenced the mechanism of nucleation and crystal growth and reduced the overall crystallization rate of nylon 66 also. The crystallization activation energy calculated by the Kissinger method for irradiated nylon 66 was lower than that of pristine nylon 66.     

Effect of tackifier and crosslinkers on electron beam curable polyurethane pressure sensitive adhesive

Polyurethane based pressure sensitive adhesive using monofunctional urethane acrylate and difunctional urethane acrylate has been made using electron beam irradiation. The effect of varying electron beam doses on the adhesion properties viz., peel adhesion, shear adhesion and initial tack has been studied. Effect of tackifier and crosslinkers viz., polymeric methylene diphenyl diisocynate, carbodiimide modified methylene diphenyl diisocynate and triallyl cynurate on adhesion properties as well as on moisture vapor transmission rate and gel content of the polyurethane based pressure sensitive adhesive has also been studied. It was found that with increasing dose, tackifier and crosslinkers concentration, all the adhesion properties viz., peel adhesion, shear adhesion strength and initial tack were increased upto a certain dose, concentration of tackifier and crosslinkers, reached a plateau and then levelled off with further increasing the dose, tackifier and crosslinkers concentration. Similarly, moisture vapor transmission rate was decreased and the gel content increased with increasing dose of electron beam.     

Effect of semi-empirical parameters on the simple random-phase approximation calculations of conjugated hydrocarbons

Singlet-singlet transition energies, oscillator strengths, triplet energy levels, and the ground state correlation energy of a number of conjugated hydrocarbons have been calculated by the simple random-phase approximation (RPA ) within the framework of the Pariser-Parr-Pople (PPP ) model. The effect of semi-empirical parameters in such calculations has been examined in detail. A set of parameters has been deduced from these parametric studies which is found to yield results for the singlet spectra of the molecules in excellent agreement with experiment. It is, however, not possible to treat the triplet states using these same parameters, since they produce triplet instabilities in all the molecules. The triplet instability problem associated with semi-empirical RPA calculations has been discussed in detail.     

Chromatographic purification and properties of soluble single-walled carbon nanotubes.

We report an improved chromatographic purification of soluble single-walled carbon nanotubes (s-SWNTs) using gel permeation chromatography. Three fractions are separated by gel permeation chromatography, and the first fraction contains 74% of the s-SWNTs as detected by atomic force microscopy and UV and near-infrared spectroscopy.     

Learning theory: stability is sufficient for generalization and necessary and sufficient for consistency of empirical risk minimization

Solutions of learning problems by Empirical Risk Minimization (ERM) – and almost-ERM when the minimizer does not exist – need to be consistent, so that they may be predictive. They also need to be well-posed in the sense of being stable, so that they might be used robustly. We propose a statistical form of stability, defined as leave-one-out (LOO) stability. We prove that for bounded loss classes LOO stability is (a) sufficient for generalization, that is convergence in probability of the empirical error to the expected error, for any algorithm satisfying it and, (b) necessary and sufficient for consistency of ERM. Thus LOO stability is a weak form of stability that represents a sufficient condition for generalization for symmetric learning algorithms while subsuming the classical conditions for consistency of ERM. In particular, we conclude that a certain form of well-posedness and consistency are equivalent for ERM. Dedicated to Charles A. Micchelli on his 60th birthday Mathematics subject classifications (2000) 68T05, 68T10, 68Q32, 62M20. Tomaso Poggio: Corresponding author.     

A perturbation solution of non-linear vibration of rectangular orthotropic plates

Classical perturbation theory is applied to the non-linear dynamic response of orthotropic plates. Expressions are derived for the ratio of non-linear to linear frequency, membrane stress, and the ratio of the maximum total stress to the maximum bending stress. Where possible the analysis is compared to other available numerical solutions, and excellent agreement is shown.