The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

Popular Mixed Matchings

We study the problem of matching applicants to jobs under one-sided preferences: that is, each applicant ranks a non-empty subset of jobs under an order of preference, possibly involving ties. A matching M is said to be rnore popular than T if the applicants that prefer M to T outnumber those that prefer T to M. A matching is said to be popular if there is no matching more popular than it. Equivalently, a matching M is popular if phi(M,T) >= phi(T, M) for all matchings T, where phi(X, Y) is the number of applicants that prefer X to Y. Previously studied solution concepts based oil the popularity criterion are either not guaranteed to exist for every instance (e.g., popular matchings) or are NP-hard to compute (e.g., least unpopular matchings). This paper addresses this issue by considering mixed matchings. A mixed matching is simply a probability distributions over matchings in the input graph. The function phi that compares two matchings generalizes in a natural manner to mixed matchings by taking expectation. A mixed matching P is popular if phi(P,Q) >= phi(Q,P) for all mixed matchings Q. We show that popular mixed matchings always exist. and we design polynomial time algorithms for finding them. Then we study their efficiency and give tight bounds on the price of anarchy and price of stability of the popular matching problem.

The pulse response of non-linear third order systems

The response of a third order non-linear system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form in which the method of variation of parameters is applicable for the solution of the problem. The method is applied to a single axis gyrostabilized platform subjected to an exponentially decaying pulse. The analytical results are compared with digital and analog computer solutions.

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.

CFD analysis of high frequency miniature pulse tube refrigerators for space applications with thermal non-equilibrium model

High frequency, miniature, pulse tube cryocoolers are extensively used in space applications because of their simplicity. Parametric studies of inertance type pulse tube cooler are performed with different length-to-diameter ratios of the pulse tube with the help of the FLUENT (R) package. The local thermal non-equilibrium of the gas and the matrix is taken into account for the modeling of porous zones, in addition to the wall thickness of the components. Dynamic characteristics and the actual mechanism of energy transfer in pulse are examined with the help of the pulse tube wall time constant. The heat interaction between pulse tube wall and the oscillating gas, leading to surface heat pumping, is quantified. The axial heat conduction is found to reduce the performance of the pulse tube refrigerator. The thermal non-equilibrium predicts a higher cold heat exchanger temperature compared to thermal equilibrium. The pressure drop through the porous medium has a strong non-linear effect due to the dominating influence of Forchheimer term over that of the linear Darcy term at high operating frequencies. The phase angle relationships among the pressure, temperature and the mass flow rate in the porous zones are also important in determining the performance of pulse tuberefrigerator.