Transverse Contraction Criteria for Existence, Stability, and Robustness of a Limit Cycle

This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI), thus allowing convex optimization tools such as sum-of-squares programming to be used to search for certificates of the existence of a stable limit cycle. Many desirable properties of contracting dynamics are extended to this context, including preservation of contraction under a broad class of interconnections. In addition, by introducing the concepts of differential dissipativity and transverse differential dissipativity, contraction and transverse contraction can be established for large scale systems via LMI conditions on component subsystems.Comment: 6 pages, 1 figure. Conference submissio

Output-Feedback Control of Nonlinear Systems using Control Contraction Metrics and Convex Optimization

Control contraction metrics (CCMs) are a new approach to nonlinear control design based on contraction theory. The resulting design problems are expressed as pointwise linear matrix inequalities and are and well-suited to solution via convex optimization. In this paper, we extend the theory on CCMs by showing that a pair of "dual" observer and controller problems can be solved using pointwise linear matrix inequalities, and that when a solution exists a separation principle holds. That is, a stabilizing output-feedback controller can be found. The procedure is demonstrated using a benchmark problem of nonlinear control: the Moore-Greitzer jet engine compressor model.Comment: Conference submissio

Bounds on Compactness for LMXB Neutron Stars from X-ray Burst Oscillations

We have modelled X-ray burst oscillations observed with the Rossi X-ray Timing Explorer (RXTE) from two low mass X-ray binaries (LMXB): 4U 1636-53 with a frequency of 580 Hz, and 4U 1728-34 at a frequency of 363 Hz. We have computed least squares fits to the oscillations observed during the rising phase of bursts using a model which includes emission from either a single circular hot spot or a pair of circular antipodal hot spots on the surface of a neutron star. We model the spreading of the thermonuclear hot spots by assuming that the hot spot angular size grows linearly with time. We calculate the flux as a function of rotational phase from the hot spots and take into account photon deflection in the relativistic gravitational field of the neutron star assuming the exterior spacetime is the Schwarzschild metric. We find acceptable fits with our model and we use these to place constraints on the compactness of the neutron stars in these sources. For 4U 1636-53, in which detection of a 290 Hz sub-harmonic supports the two spot model, we find that the compactness (i.e., mass/radius ratio) is constrained to be M/R < 0.163 at 90% confidence (G = c = 1). This requires a relatively stiff equation of state (EOS) for the stellar interior. For example, if the neutron star has a mass of 1.4 Msun then its radius must be > 12.8 km. Fits using a single hot spot model are not as highly constraining. We discuss the implications of our findings for recent efforts to calculate the EOS of dense nucleon matter and the structure of neutron stars.Comment: 27 pages, 6 figures, AASTeX. Revised and expanded version. Resubmitted to Astrophysical Journa

Characterization study of polycrystalline tin oxide surfaces before and after reduction in CO

Polycrystalline tin oxide surfaces have been examined before and after reduction in 40 Torr of CO at 100 and 175 C using Auger electron spectroscopy (AES), electron spectroscopy for chemical analysis (ESCA), ion scattering spectroscopy (ISS) and electron stimulated desorption (ESD). The changes in the surface composition and chemical states of the surface species generally are subtle for the reductive conditions used. However, significant changes do occur with regard to the amounts and the chemical forms of the hydrogen-containing species remaining after both the 100 and 175 C reductions

X-ray Bursts from the Accreting Millisecond Pulsar XTE J1814-338

Since the discovery of the accreting millisecond pulsar XTE J1814-338 a total of 27 thermonuclear bursts have been observed from the source with the Proportional Counter Array (PCA) onboard the Rossi X-ray Timing Explorer (RXTE). Spectroscopy of the bursts, as well as the presence of continuous burst oscillations, suggests that all but one of the bursts are sub-Eddington. The remaining burst has the largest peak bolometric flux of 2.64 x E^-8 erg/sec/cm^2, as well as a gap in the burst oscillations, similar to that seen in Eddington limited bursts from other sources. Assuming this burst was Eddington limited we obtain a source distance of about 8 kpc. All the bursts show coherent oscillations at the 314.4 Hz spin frequency. The burst oscillations are strongly frequency and phase locked to the persistent pulsations. Only two bursts show evidence for frequency drift in the first few seconds following burst onset. In both cases the initial drift corresponds to a spin down of a few tenths of a Hz. The large oscillation amplitude during the bursts confirms that the burst flux is modulated at the spin frequency. We detect, for the first time, a significant first harmonic component in burst oscillations. The ratio of countrate in the first harmonic to that in the fundamental can be > 0.25 and is, on average, less than that of the persistent pulsations. If the pulsations result from a single bright region on the surface, the harmonic strength suggests the burst emission is beamed, perhaps due to a stronger magnetic field than in non-pulsing LMXBs. Alternatively, the harmonic content could result from a geometry with two bright regions.Comment: AASTeX, 15 pages, 4 figures. Accepted for publication in the Astrophysical Journal Letter

A streamwise-constant model of turbulent pipe flow

A streamwise-constant model is presented to investigate the basic mechanisms responsible for the change in mean flow occuring during pipe flow transition. Using a single forced momentum balance equation, we show that the shape of the velocity profile is robust to changes in the forcing profile and that both linear non-normal and nonlinear effects are required to capture the change in mean flow associated with transition to turbulence. The particularly simple form of the model allows for the study of the momentum transfer directly by inspection of the equations. The distribution of the high- and low-speed streaks over the cross-section of the pipe produced by our model is remarkably similar to one observed in the velocity field near the trailing edge of the puff structures present in pipe flow transition. Under stochastic forcing, the model exhibits a quasi-periodic self-sustaining cycle characterized by the creation and subsequent decay of "streamwise-constant puffs", so-called due to the good agreement between the temporal evolution of their velocity field and the projection of the velocity field associated with three-dimensional puffs in a frame of reference moving at the bulk velocity. We establish that the flow dynamics are relatively insensitive to the regeneration mechanisms invoked to produce near-wall streamwise vortices and that using small, unstructured background disturbances to regenerate the streamwise vortices is sufficient to capture the formation of the high- and low-speed streaks and their segregation leading to the blunting of the velocity profile characteristic of turbulent pipe flow

Rapidity particle spectra in sudden hadronization of QGP

We show that the remaining internal longitudinal flow of colliding quarks in nuclei offers a natural explanation for the diversity of rapidity spectral shapes observed in Pb--Pb 158AGeV nuclear collisions. Thus QGP sudden hadronization reaction picture is a suitable approach to explain the rapidity spectra of hadrons produced.Comment: 3 pages including 2 figure