Third post-Newtonian angular momentum flux and the secular evolution of orbital elements for inspiralling compact binaries in quasi-elliptical orbits

The angular-momentum flux from an inspiralling binary system of compact objects moving in quasi-elliptical orbits is computed at the third post-Newtonian (3PN) order using the multipolar post-Minkowskian wave generation formalism. The 3PN angular-momentum flux involves the instantaneous, tail, and tail-of-tails contributions as for the 3PN energy flux, and in addition a contribution due to nonlinear memory. We average the angular-momentum flux over the binary's orbit using the 3PN quasi-Keplerian representation of elliptical orbits. The averaged angular-momentum flux provides the final input needed for gravitational-wave phasing of binaries moving in quasi-elliptical orbits. We obtain the evolution of orbital elements under 3PN gravitational radiation reaction in the quasi-elliptic case. For small eccentricities, we give simpler limiting expressions relevant for phasing up to order e(2). This work is important for the construction of templates for quasi-eccentric binaries, and for the comparison of post-Newtonian results with the numerical relativity simulations of the plunge and merger of eccentric binaries.

Robust flight stability and control for micro air vehicles.

This chapter presents the real time validation of fixed order robust 112 controller designed for the lateral stabilisation of a micro air vehicle named Sarika2. Digital signal processor (DSP) based onboard computer named flight instrumentation controller (FIC) is designed to operate under automatic or manual mode. FIC gathers data from multitude of sensors and is capable of closed loop control to enable autonomous flight. Fixed order lateral H-2 controller designed with the features such as incorporation of level I flying qualities, gust alleviation and noise rejection is coded on to the FIC. Challenging real time hardware in loop simulation (HILS) is done with dSPACE1104 RTI/RTW. Responses obtained from the HILS are compared with those obtained from the offline simulation. Finally, flight trials are conducted to demonstrate the satisfactory performance of the closed loop system. The generic design methodology developed is applicable to all classes of Mini and Micro air vehicles.

Stability of scheduled multi-access communication over quasi-static flat fading channels with random coding and independent decoding

The stability of scheduled multiaccess communication with random coding and independent decoding of messages is investigated. The number of messages that may be scheduled for simultaneous transmission is limited to a given maximum value, and the channels from transmitters to receiver are quasistatic, flat, and have independent fades. Requests for message transmissions are assumed to arrive according to an i.i.d. arrival process. Then, we show the following: (1) in the limit of large message alphabet size, the stability region has an interference limited information-theoretic capacity interpretation, (2) state-independent scheduling policies achieve this asymptotic stability region, and (3) in the asymptotic limit corresponding to immediate access, the stability region for non-idling scheduling policies is shown to be identical irrespective of received signal powers.

Detection of a periodic structure hidden in random background: the role of signal amplitude in the matched filter detection method

The matched filter method for detecting a periodic structure on a surface hidden behind randomness is known to detect up to (r(0)/Lambda) gt;= 0.11, where r(0) is the coherence length of light on scattering from the rough part and 3 is the wavelength of the periodic part of the surface-the above limit being much lower than what is allowed by conventional detection methods. The primary goal of this technique is the detection and characterization of the periodic structure hidden behind randomness without the use of any complicated experimental or computational procedures. This paper examines this detection procedure for various values of the amplitude a of the periodic part beginning from a = 0 to small finite values of a. We thus address the importance of the following quantities: `(a)lambda) `, which scales the amplitude of the periodic part with the wavelength of light, and (r(0))Lambda),in determining the detectability of the intensity peaks.

Novel composite coded pattern for small angle measurement using imaging method -art.no.62891D

A novel approach for measurement of small rotation angles using imaging method is proposed and demonstrated. A plane mirror placed on a precision rotating table is used for imaging the newly designed composite coded pattern. The imaged patterns are captured with the help of a CCD camera. The angular rotation of the plane mirror is determined from a pair of the images of the pattern, captured once before and once after affecting the tilt of the mirror. Both simulation and experimental results suggest that the proposed approach not only retains the advantages of the original imaging method but also contributes significantly to the enhancement of its measuring range (+/- 4.13 degrees with accuracy of the order of 1 arcsec).

Trishanku, a novel regulator of cell-type stability and morphogenesis in Dictyostelium discoideum

We have identified a novel gene, trishanku (triA), by random insertional mutagenesis of Dictyostelium discoideum. TriA is a Broad complex Tramtrack bric-a-brac domain-containing protein that is expressed strongly during the late G2 phase of cell cycle and in presumptive spore (prespore (psp)) cells. Disrupting triA destabilizes cell fate and reduces aggregate size; the fruiting body has a thick stalk, a lowered spore: stalk ratio, a sub-terminal spore mass and small, rounded spores. These changes revert when the wild-type triA gene is re-expressed under a constitutive or a psp-specific promoter. By using short- and long-lived reporter proteins, we show that in triA(-) slugs the prestalk (pst)/psp proportion is normal, but that there is inappropriate transdifferentiation between the two cell types. During culmination, regardless of their current fate, all cells with a history of pst gene expression contribute to the stalk, which could account for the altered cell-type proportion in the mutant.

On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.

Bounded-input/bounded-output stability of linear multidimensional time- varying systems

The present study of the stability of systems governed by a linear multidimensional time-varying equation, which are encountered in spacecraft dynamics, economics, demographics, and biological systems, gives attention the lemma dealing with L(inf) stability of an integral equation that results from the differential equation of the system under consideration. Using the proof of this lemma, the main result on L(inf) stability is derived according; a corollary of the theorem deals with constant coefficient systems perturbed by small periodic terms. (O.C.)

sRNAscanner: A Computational Tool for Intergenic Small RNA Detection in Bacterial Genomes

Background:Bacterial non-coding small RNAs (sRNAs) have attracted considerable attention due to their ubiquitous nature and contribution to numerous cellular processes including survival, adaptation and pathogenesis. Existing computational approaches for identifying bacterial sRNAs demonstrate varying levels of success and there remains considerable room for improvement. Methodology/Principal Findings: Here we have proposed a transcriptional signal-based computational method to identify intergenic sRNA transcriptional units (TUs) in completely sequenced bacterial genomes. Our sRNAscanner tool uses position weight matrices derived from experimentally defined E. coli K-12 MG1655 sRNA promoter and rho-independent terminator signals to identify intergenic sRNA TUs through sliding window based genome scans. Analysis of genomes representative of twelve species suggested that sRNAscanner demonstrated equivalent sensitivity to sRNAPredict2, the best performing bioinformatics tool available presently. However, each algorithm yielded substantial numbers of known and uncharacterized hits that were unique to one or the other tool only. sRNAscanner identified 118 novel putative intergenic sRNA genes in Salmonella enterica Typhimurium LT2, none of which were flagged by sRNAPredict2. Candidate sRNA locations were compared with available deep sequencing libraries derived from Hfq-co-immunoprecipitated RNA purified from a second Typhimurium strain (Sittka et al. (2008) PLoS Genetics 4: e1000163). Sixteen potential novel sRNAs computationally predicted and detected in deep sequencing libraries were selected for experimental validation by Northern analysis using total RNA isolated from bacteria grown under eleven different growth conditions. RNA bands of expected sizes were detected in Northern blots for six of the examined candidates. Furthermore, the 5'-ends of these six Northern-supported sRNA candidates were successfully mapped using 5'-RACE analysis. Conclusions/Significance: We have developed, computationally examined and experimentally validated the sRNAscanner algorithm. Data derived from this study has successfully identified six novel S. Typhimurium sRNA genes. In addition, the computational specificity analysis we have undertaken suggests that similar to 40% of sRNAscanner hits with high cumulative sum of scores represent genuine, undiscovered sRNA genes. Collectively, these data strongly support the utility of sRNAscanner and offer a glimpse of its potential to reveal large numbers of sRNA genes that have to date defied identification. sRNAscanner is available from: http://bicmku.in:8081/sRNAscanner or http://cluster.physics.iisc.ernet.in/sRNAscanner/.

Trends in the stability of ternary oxides: Systems M-Pb-O (M = Ca, Sr, Ba)

Recent experimental investigations of phase equilibria and thermodynamic properties of the systems M-Pb-O, where M = Ca, Sr or Ba, indicate a regular increase in thermodynamic stability of ternary oxides, MPbO3 and M2PbO4, with increasing basicity of the oxide of the alkaline-earth metal. Number of stable interoxide compounds at 1100 K in the systems M-Pb-O (M = Mg, Ca, Sr, Ba) increases in unit increments from Mg to Ba. In this paper, experimentally determined standard Gibbs energies of formation of M2PbO4 (M = Ca, Sr, Ba) and MPbO3 (M = Sr, Ba) from their component binary monoxides and oxygen gas are combined with an estimated value for CaPbO3 to delineate systematic trends in thermodynamic stability of the ternary oxides. The trends are interpreted using concepts of tolerance factor and acid-base interactions. All the ternary oxides in these systems contain lead in the tetravalent state. The small Pb4+ ions polarize the surrounding oxygen ions and cause the formation of oxyanions which are acidic in character. Hence, the higher oxidation state of lead is stabilized in the presence of basic oxides of alkaline-earth group. A schematic subsolidus temperature-composition phase diagram is presented for the system BaO-PbO-O-2 to illustrate the change in oxidation states in binary and ternary oxides with temperature.

Microstructure evolution and hardness variation during annealing of equal channel angular pressed ultra-fine grained nickel subjected to 12 passes

The microstructure, thermal stability and hardness of ultra-fine grained (UFG) Ni produced by 12 passes of equal channel angular pressing (ECAP) through the route Bc were studied. Comparing the microstructure and hardness of the as-ECAPed samples with the published data on UFG Ni obtained after 8 passes of ECAP through the route Bc reveals a smaller average grain size (230 nm in the present case compared with 270 nm in 8-pass Ni), significantly lower dislocation density (1.08 x 10(14) m(-2) compared with 9 x 10(14) m(-2) in 8-pass Ni) and lower hardness (2 GPa compared with 2.45 GPa for 8-pass Ni). Study of the thermal stability of the 12-pass UFG Ni revealed that recovery is dominant in the temperature range 150-250A degrees C and recrystallisation occurred at temperatures > 250 A degrees C. The UFG microstructure is relatively stable up to about 400 A degrees C. Due to the lower dislocation density and consequently a lower stored energy, the recrystallisation of 12-pass ECAP Ni occurred at a higher temperature (similar to 250 A degrees C) compared with the 8-pass Ni (similar to 200 A degrees C). In the 12-pass Nickel, hardness variation shows that its dependence on grain size is inversely linear rather than the common grain size(-0.5) dependence.

Parallel computing concepts and methods for floquet analysis of helicopter trim and stability

Floquet analysis is widely used for small-order systems (say, order M < 100) to find trim results of control inputs and periodic responses, and stability results of damping levels and frequencies, Presently, however, it is practical neither for design applications nor for comprehensive analysis models that lead to large systems (M > 100); the run time on a sequential computer is simply prohibitive, Accordingly, a massively parallel Floquet analysis is developed with emphasis on large systems, and it is implemented on two SIMD or single-instruction, multiple-data computers with 4096 and 8192 processors, The focus of this development is a parallel shooting method with damped Newton iteration to generate trim results; the Floquet transition matrix (FTM) comes out as a byproduct, The eigenvalues and eigenvectors of the FTM are computed by a parallel QR method, and thereby stability results are generated, For illustration, flap and flap-lag stability of isolated rotors are treated by the parallel analysis and by a corresponding sequential analysis with the conventional shooting and QR methods; linear quasisteady airfoil aerodynamics and a finite-state three-dimensional wake model are used, Computational reliability is quantified by the condition numbers of the Jacobian matrices in Newton iteration, the condition numbers of the eigenvalues and the residual errors of the eigenpairs, and reliability figures are comparable in both the parallel and sequential analyses, Compared to the sequential analysis, the parallel analysis reduces the run time of large systems dramatically, and the reduction increases with increasing system order; this finding offers considerable promise for design and comprehensive-analysis applications.

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

Stability of non-parabolic flow in a flexible tube

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such 'non-parabolic' flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

Examining the effects of species richness on community stability: an assembly model approach

We build dynamic models of community assembly by starting with one species in our model ecosystem and adding colonists. We find that the number of species present first increases, then fluctuates about some level. We ask: how large are these fluctuations and how can we characterize them statistically? As in Robert May's work, communities with weaker interspecific interactions permit a greater number of species to coexist on average. We find that as this average increases, however, the relative variation in the number of species and return times to mean community levels decreases. In addition, the relative frequency of large extinction events to small extinction events decreases as mean community size increases. While the model reproduces several of May's results, it also provides theoretical support for Charles Elton's idea that diverse communities such as those found in the tropics should be less variable than depauperate communities such as those found in arctic or agricultural settings.