Algorithm for Liapunov stability analysis

Development of algorithm provides automatic computation of quadratic estimate of domain of stability for stable equilibrium states of nonlinear systems of ordinary differential equations

Pulse-to-pulse variability of bright accreting pulsars

In addition to coherent pulsation, many accreting neutron stars exhibit flaring activity and strong aperiodic variability on time scales similar to or shorter than their pulsation period. Such a behavior shows that the accretion flow in the vicinity of the accretor must be highly non-stationary. Although from the theoretical point of view the problem of non-stationary accretion has been addressed by many authors, observational study of this phenomenon is often problematic as it requires very high statistics of X-ray data and a specific analysis technique. In our research we used high-resolution data taken with RXTE and INTEGRAL on a sample of bright transient and persistent pulsars, to perform an in-depth study of their variability on time scales comparable to the pulsation period - "pulse-to-pulse variability". The high-quality data allowed us to collect individual pulses of different amplitude and reveal differences in their spectra (such an analysis we refer to as "pulse-to-pulse spectroscopy"). The described approach allowed us for the first time to study luminosity-dependence of pulsars' X-ray spectra in observations where the averaged (over many pulse cycles) luminosity of the source remained constant and discuss them in the frame of the current physical models of the accretion flow close to the neutron star surface.Comment: 6 pages, 5 figures, accepted for publication in Proceedings of Science, 8th INTEGRAL Workshop, The Restless Gamma-ray Universe, 27-30 September 2010, Dublin, Irelan

Is SGR 1900+14 a Magnetar?

We present RXTE observations of the soft gamma--ray repeater SGR 1900+14 taken September 4-18, 1996, nearly 2 years before the 1998 active period of the source. The pulsar period (P) of 5.1558199 +/- 0.0000029 s and period derivative (Pdot) of (6.0 +/- 1.0) X 10^-11 s/s measured during the 2-week observation are consistent with the mean Pdot of (6.126 +/- 0.006) X 10^-11 s/s over the time up to the commencement of the active period. This Pdot is less than half that of (12.77 +/- 0.01) X 10^-11 s/s observed during and after the active period. If magnetic dipole radiation were the primary cause of the pulsar spindown, the implied pulsar magnetic field would exceed the critical field of 4.4 X 10^13 G by more than an order of magnitude, and such field estimates for this and other SGRs have been offered as evidence that the SGRs are magnetars, in which the neutron star magnetic energy exceeds the rotational energy. The observed doubling of Pdot, however, would suggest that the pulsar magnetic field energy increased by more than 100% as the source entered an active phase, which seems very hard to reconcile with models in which the SGR bursts are powered by the release of magnetic energy. Because of this, we suggest that the spindown of SGR pulsars is not driven by magnetic dipole radiation, but by some other process, most likely a relativistic wind. The Pdot, therefore, does not provide a measure of the pulsar magnetic field strength, nor evidence for a magnetar.Comment: 14 pages, aasms4 latex, figures 1 & 2 changed, accepted by ApJ letter

Parameterization of the set of positive- definite matrices and an algorithm for its generation

Numerical analysis on set elements for positive definite symmetric matrices by parameterizatio

Magnetic Field Limits on SGRs

We measure the period and spin-down rate for SGR 1900+14 during the quiescient period two years before the recent interval of renewed burst activity. We find that the spin-down rate doubled during the burst activity which is inconsistent with both mangetic dipole driven spin down and a magnetic field energy source for the bursts. We also show that SGRs 1900+14 and 1806-20 have braking indices of $\sim$1 which indicate that the spin-down is due to wind torques and not magnetic dipole radiation. We further show that a combination of dipole radiation, and wind luminosity, coupled with estimated ages and present spin parameters, imply that the magnetic fields of SGRs 1900+14 and 1806-20 are less than the critical field of 4$\times10^{13}$ G and that the efficiency for conversion of wind luminosity to x-ray luminosity is <2%.Comment: 5 pages, 2 figures submitted to 5th Huntsville GRB Symposium proceeding

Further development of an algorithm for the nonlinear stability analysis of the orbiting astronomical observatory paired-tracker control system Final report

Algorithm development for estimating domain of attraction of OAO paired-tracker equilibrium state with Liapunov function

Renewable Energy Resources Impact on Clean Electrical Power by developing the North-West England Hydro Resource Model.

This paper describes the development of a sequential decision support system to promote hydroelectric power in North-West England. The system, composed of integrated models, addresses barriers to the installation of hydroelectric power schemes. Information is linked through an economic assessment which identifies different turbine options, assesses their suitability for location and demand; and combines the different types of information in a way that supports decision making. The system is structured into five components: the hydrological resource is modelled using Low Flows 2000, the turbine options are identified from hydrological, environmental and demand requirements; and the consequences of different solutions will be fed into other components so that the environmental impacts and public acceptability can be assessed and valued. A preliminary case study is presented on an old gunpowder works to illustrate how the resource model may be employed. Historical architectural structures, power uptake and educational instruction of hydro power technology are considered

Thermonuclear burst physics with RXTE

Recently we have made measurements of thermonuclear burst energetics and recurrence times which are unprecedented in their precision, largely thanks to the sensitivity of the Rossi X-ray Timing Explorer. In the "Clocked Burster", GS 1826-24, hydrogen burns during the burst via the rapid-proton (rp) process, which has received particular attention in recent years through theoretical and modelling studies. The burst energies and the measured variation of alpha (the ratio of persistent to burst flux) with accretion rate strongly suggests solar metallicity in the neutron star atmosphere, although this is not consistent with the corresponding variation of the recurrence time. Possible explanations include extra heating between the bursts, or a change in the fraction of the neutron star over which accretion takes place. I also present results from 4U 1746-37, which exhibits regular burst trains which are interrupted by "out of phase" bursts.Comment: 4 pages, 2 figures, AIP conference proceedings format. To appear in the proceedings of the "X-ray Timing 2003: Rossi and Beyond" meeting held in Cambridge, MA, November, 200