Wick's Theorem for non-symmetric normal ordered products and contractions

We consider arbitrary splits of field operators into two parts, and use the corresponding definition of normal ordering introduced by Evans and Steer. In this case the normal ordered products and contractions have none of the special symmetry properties assumed in existing proofs of Wick's theorem. Despite this, we prove that Wick's theorem still holds in its usual form as long as the contraction is a c-number. Wick's theorem is thus shown to be much more general than existing derivations suggest, and we discuss possible simplifying applications of this result.Comment: 17 page

An Approximation Scheme for Reflected Stochastic Differential Equations

In this paper we consider the Stratonovich reflected stochastic differential equation $dX_t=\sigma(X_t)\circ dW_t+b(X_t)dt+dL_t$ in a bounded domain \O which satisfies conditions, introduced by Lions and Sznitman, which are specified below. Letting $W^N_t$ be the $N$-dyadic piecewise linear interpolation of $W_t$ what we show is that one can solve the reflected ordinary differential equation $\dot X^N_t=\sigma(X^N_t)\dot W^N_t+b(X^N_t)+\dot L^N_t$ and that the distribution of the pair $(X^N_t,L^N_t)$ converges weakly to that of $(X_t,L_t)$. Hence, what we prove is a distributional version for reflected diffusions of the famous result of Wong and Zakai. Perhaps the most valuable contribution made by our procedure derives from the representation of $\dot X^N_t$ in terms of a projection of $\dot W_t^N$. In particular, we apply our result in hand to derive some geometric properties of coupled reflected Brownian motion in certain domains, especially those properties which have been used in recent work on the "hot spots" conjecture for special domain.Comment: 26 pages, 4 figure

Resonant Orbits in Triaxial Galaxies

Box orbits in triaxial potentials are generically thin, that is, they lie close in phase space to a resonant orbit satisfying a relation of the form l\omega_1 +m\omega_2+n\omega_3=0 between the three fundamental frequencies. Resonant orbits are confined to a membrane; they play roughly the same role, in three dimensions, that closed orbits play in two. Stable resonant orbits avoid the center of the potential; orbits that are thick enough to pass near the center are typically stochastic. Very near the center, where the gravitational potential is dominated by the black hole, resonant orbits continue to exist, including at least one family whose elongation is parallel to the long axes of the triaxial figure.Comment: 20 Latex pages, 11 Postscript figures. Submitted to The Astronomical Journa

Re-examination of the possible tidal stream in front of the LMC

It has recently been suggested that the stars in a vertical extension of the red clump feature seen in LMC color-magnitude diagrams could belong to a tidal stream of material located in front of that galaxy. If this claim is correct, this foreground concentration of stars could contribute significantly to the rate of gravitational microlensing events observed in the LMC microlensing experiments. Here we present radial velocity measurements of stars in this so-called ``vertical red clump'' (VRC) population. The observed stellar sample, it transpires, has typical LMC kinematics. It is shown that it is improbable that an intervening tidal stream should have the same distribution of radial velocities as the LMC, which is consistent with an earlier study that showed that the VRC feature is more likely a young stellar population in the main body of that galaxy. However, the kinematic data do not discriminate against the possibility that the VRC is an LMC halo population.Comment: 10 pages, 3 figures, 1 table. Accepted for publication in ApJ

The Nature of the Compact/Symmetric Near-IR Continuum Source in 4C 40.36

Using NICMOS on HST, we have imaged the emission-line nebulae and the line-free continuum in 4C 40.36, a ultra-steep spectrum FR II radio galaxy at z=2.269. The line-free continuum was found to be extremely compact and symmetric while the emission-line nebulae seen in H-alpha+[N II] show very clumpy structures spreading almost linearly over 16 kpc. However, this linear structure is clearly misaligned from the radio axis. The SED of the line-free continuum is very flat, suggesting that if the continuum emission is produced by a single source, it is likely to be a young bursting stellar population or scattered AGN light. However, because of the lack of a line-free optical image with a comparable spatial resolution, we cannot exclude the possibility that the observed SED is a composite of a young blue population and an old red population.Comment: 4 pages, 2 figures; to appear in the proceedings of "The Hy-Redshift Universe: Galaxy Formation and Evolution at High Redshift", eds. A.J.Bunker and W. J. M. van Breuge

Biological and physical oceanographic observations pertaining to the trawl fishery in a region of persistent coastal upwelling

An upwelling episode in the Point Sal region of the central California coast is examined by using data obtained by a data buoy. The episodes was interrupted by the abrupt abatement of the strong wind which promotes coastal upwelling. The mean hourly upwelling index is calculated to be higher than the 20 year mean monthly value. During 3 days of light wind commercial bottom trawl operations were possible. Shipboard estimates of chlorophyll content in surface waters during trawling show the high concentrations that are indicative of a rich biomass of phytoplankton, a result of the upwelling episode. Satellite imagery shows the extent of the upwelling water to be of the order of 100 km offshore; the result of many upwelling episodes. Shipboard echo sounder data show the presence of various delmersal species and of zooplakton; the latter graze on the phytoplankton in the upper euphotic layers. The fish catch data are recorded according to species for 2 days of trawling, and the catch per trawl hour is recorded

The tidal stripping of satellites

We present an improved analytic calculation for the tidal radius of satellites and test our results against N-body simulations. The tidal radius in general depends upon four factors: the potential of the host galaxy, the potential of the satellite, the orbit of the satellite and {\it the orbit of the star within the satellite}. We demonstrate that this last point is critical and suggest using {\it three tidal radii} to cover the range of orbits of stars within the satellite. In this way we show explicitly that prograde star orbits will be more easily stripped than radial orbits; while radial orbits are more easily stripped than retrograde ones. This result has previously been established by several authors numerically, but can now be understood analytically. For point mass, power-law (which includes the isothermal sphere), and a restricted class of split power law potentials our solution is fully analytic. For more general potentials, we provide an equation which may be rapidly solved numerically. Over short times (\simlt 1-2 Gyrs $\sim 1$ satellite orbit), we find excellent agreement between our analytic and numerical models. Over longer times, star orbits within the satellite are transformed by the tidal field of the host galaxy. In a Hubble time, this causes a convergence of the three limiting tidal radii towards the prograde stripping radius. Beyond the prograde stripping radius, the velocity dispersion will be tangentially anisotropic.Comment: 10 pages, 5 figures. Final version accepted for publication in MNRAS. Some new fully analytic tidal radii have been added for power law density profiles (including the isothermal sphere) and some split power law