Dirac Quantization of the Pais-Uhlenbeck Fourth Order Oscillator

As a model, the Pais-Uhlenbeck fourth order oscillator with equation of motion $d^4q/dt^4+(\omega_1^2+\omega_2^2)d^2q/dt^2 +\omega_1^2\omega_2^2 q=0$ is a quantum-mechanical prototype of a field theory containing both second and fourth order derivative terms. With its dynamical degrees of freedom obeying constraints due to the presence of higher order time derivatives, the model cannot be quantized canonically. We thus quantize it using the method of Dirac constraints to construct the correct quantum-mechanical Hamiltonian for the system, and find that the Hamiltonian diagonalizes in the positive and negative norm states that are characteristic of higher derivative field theories. However, we also find that the oscillator commutation relations become singular in the $\omega_1 \to \omega_2$ limit, a limit which corresponds to a prototype of a pure fourth order theory. Thus the particle content of the $\omega_1 =\omega_2$ theory cannot be inferred from that of the $\omega_1 \neq \omega_2$ theory; and in fact in the $\omega_1 \to \omega_2$ limit we find that all of the $\omega_1 \neq \omega_2$ negative norm states move off shell, with the spectrum of asymptotic in and out states of the equal frequency theory being found to be completely devoid of states with either negative energy or negative norm. As a byproduct of our work we find a Pais-Uhlenbeck analog of the zero energy theorem of Boulware, Horowitz and Strominger, and show how in the equal frequency Pais-Uhlenbeck theory the theorem can be transformed into a positive energy theorem instead.Comment: RevTeX4, 20 pages. Final version, to appear in Phys. Rev.

Non-Universality and Evolution of the Sivers Function

We examine the large-x QCD evolution of the twist-three gluonic-pole strength defining an effective T-odd Sivers function, where evolution of the T-even transverse-spin DIS structure function g2 is multiplicative. The result corresponds to a colour-factor modified spin-averaged twist-two evolution.Comment: Presented at the ECT* Workshop on Recent Advances in Perturbative QCD and Hadronic Physics (20-25 July 2009} - final version (minor modifications

Keck Measurement of the XTE J2123-058 Radial Velocity Curve

We measured the radial velocity curve of the companion of the neutron star X-ray transient XTE J2123-058. Its semi-amplitude (K_2) of 298.5 +/- 6.9 km/s is the highest value that has been measured for any neutron star LMXB. The high value for K_2 is, in part, due to the high binary inclination of the system but may also indicate a high neutron star mass. The mass function (f_2) of 0.684 +/- 0.047 solar masses, along with our constraints on the companion's spectral type (K5V-K9V) and previous constraints on the inclination, gives a likely range of neutron star masses from 1.2 to 1.8 solar masses. We also derive a source distance of 8.5 +/- 2.5 kpc, indicating that XTE J2123-058 is unusually far, 5.0 +/- 1.5 kpc, from the Galactic plane. Our measurement of the systemic radial velocity is -94.5 +/- 5.5 km/s, which is significantly different from what would be observed if this object corotates with the disk of the Galaxy.Comment: 4 pages, accepted by ApJ Letters after minor revision

Cosmogenesis and Collapse

Some possible benefits of dynamical collapse for a quantum theory of cosmogenesis are discussed. These are a possible long wait before creation begins, creation of energy and space, and choice of a particular universe out of a superposition.Comment: For a festschrift in Foundations of Physics in honor of Daniel Greenberger and Helmut Rauch in Foundations of Physics. This updates the previous version by adding an appendix (Appendix B) which contains the exact solution of a partial differential equation of importance in the pape

Confined compression of collagen hydrogels

Reconstituted collagen hydrogels are often used for in vitro studies of cell-matrix interaction and as scaffolds for tissue engineering. Understanding the mechanical and transport behaviours of collagen hydrogels is therefore extremely important, albeit difficult due to their very high water content (typically > 99.5%). In the present study the mechanical behaviour of collagen hydrogels in confined compression was investigated using biphasic theory (J. Biomech. Eng. 102 (1980) 73), to ascertain whether the technique is sufficiently sensitive to determine differences in the characteristics of hydrogels of between 0.2% and 0.4% collagen. Peak stress, equilibrium stress, aggregate modulus and hydraulic permeability of the hydrogels exhibited sensitivity to collagen content, demonstrating that the technique is clearly able to discriminate between hydrogels with small differences in collagen content and may also be sensitive to factors that affect matrix remodelling. The results also offer additional insight into the deformation-dependent permeability of collagen hydrogels. This study suggests that confined compression, together with biphasic theory, is a suitable technique for assessing the mechanical properties of collagen hydrogels

Modelling the dynamics of turbulent floods

Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre manifold theory to derive dynamical models for the evolution of the water depth and of vertically averaged flow velocity and turbulent parameters. This new model for the shallow water dynamics of turbulent flow: resolves the vertical structure of the flow and the turbulence; includes interaction between turbulence and long waves; and gives a rational alternative to classical models for turbulent environmental flows

Adjusting for bias introduced by instrumental variable estimation in the Cox Proportional Hazards Model

Instrumental variable (IV) methods are widely used for estimating average treatment effects in the presence of unmeasured confounders. However, the capability of existing IV procedures, and most notably the two-stage residual inclusion (2SRI) procedure recommended for use in nonlinear contexts, to account for unmeasured confounders in the Cox proportional hazard model is unclear. We show that instrumenting an endogenous treatment induces an unmeasured covariate, referred to as an individual frailty in survival analysis parlance, which if not accounted for leads to bias. We propose a new procedure that augments 2SRI with an individual frailty and prove that it is consistent under certain conditions. The finite sample-size behavior is studied across a broad set of conditions via Monte Carlo simulations. Finally, the proposed methodology is used to estimate the average effect of carotid endarterectomy versus carotid artery stenting on the mortality of patients suffering from carotid artery disease. Results suggest that the 2SRI-frailty estimator generally reduces the bias of both point and interval estimators compared to traditional 2SRI.Comment: 27 pages, 8 figures, 4 table

The Low Quiescent X-Ray Luminosity of the Neutron Star Transient XTE J2123-058

We report on the first X-ray observations of the neutron star soft X-ray transient (SXT) XTE J2123-058 in quiescence, made by Chandra and BeppoSAX, as well as contemporaneous optical observations. In 2002, the Chandra spectrum of XTE J2123-058 is consistent with a power-law model, or the combination of a blackbody plus a power-law, but it is not well-described by a pure blackbody. Using the interstellar column density, the power-law fit gives photon index of 3.1 (+0.7,-0.6) and indicates a 0.3-8 keV unabsorbed luminosity of 9(+4,-3)E31 (d/8.5 kpc)^2 ergs/s (90% confidence errors). Fits with models consisting of thermal plus power-law components indicate that the upper limit on the temperature of a 1.4 solar mass, 10 km radius neutron star with a hydrogen atmosphere is kT_eff < 66 eV, and the upper limit on the bolometric luminosity is L_infinity < 1.4E32 ergs/s, assuming d = 8.5 kpc. Of the neutron star SXTs that exhibit short (< 1 year) outbursts, including Aql X-1, 4U 1608-522, Cen X-4, and SAX J1810.8-2609, the lowest temperatures and luminosities are found for XTE J2123-058 and SAX J1810.8-2609. From the BeppoSAX observation of XTE J2123-058 in 2000, we obtained an upper limit on the 1-10 keV unabsorbed luminosity of 9E32 ergs/s. Although this upper limit allows that the X-ray luminosity may have decreased between 2000 and 2002, that possibility is not supported by our contemporaneous R-band observations, which indicate that the optical flux increased significantly. Motivated by the theory of deep crustal heating by Brown and co-workers, we characterize the outburst histories of the five SXTs. The low quiescent luminosity for XTE J2123-058 is consistent with the theory of deep crustal heating without requiring enhanced neutron star cooling if the outburst recurrence time is >~ 70 years.Comment: 8 pages, accepted by Ap