Trace formulas for stochastic evolution operators: Smooth conjugation method

The trace formula for the evolution operator associated with nonlinear stochastic flows with weak additive noise is cast in the path integral formalism. We integrate over the neighborhood of a given saddlepoint exactly by means of a smooth conjugacy, a locally analytic nonlinear change of field variables. The perturbative corrections are transfered to the corresponding Jacobian, which we expand in terms of the conjugating function, rather than the action used in defining the path integral. The new perturbative expansion which follows by a recursive evaluation of derivatives appears more compact than the standard Feynman diagram perturbation theory. The result is a stochastic analog of the Gutzwiller trace formula with the ``hbar'' corrections computed an order higher than what has so far been attainable in stochastic and quantum-mechanical applications.Comment: 16 pages, 1 figure, New techniques and results for a problem we considered in chao-dyn/980703

The Case for Dynamic Models of Learners' Ontologies in Physics

In a series of well-known papers, Chi and Slotta (Chi, 1992; Chi & Slotta, 1993; Chi, Slotta & de Leeuw, 1994; Slotta, Chi & Joram, 1995; Chi, 2005; Slotta & Chi, 2006) have contended that a reason for students' difficulties in learning physics is that they think about concepts as things rather than as processes, and that there is a significant barrier between these two ontological categories. We contest this view, arguing that expert and novice reasoning often and productively traverses ontological categories. We cite examples from everyday, classroom, and professional contexts to illustrate this. We agree with Chi and Slotta that instruction should attend to learners' ontologies; but we find these ontologies are better understood as dynamic and context-dependent, rather than as static constraints. To promote one ontological description in physics instruction, as suggested by Slotta and Chi, could undermine novices' access to productive cognitive resources they bring to their studies and inhibit their transition to the dynamic ontological flexibility required of experts.Comment: The Journal of the Learning Sciences (In Press

Mid-Infrared Diagnostics of LINERs

We report results from the first mid-infrared spectroscopic study of a comprehensive sample of 33 LINERs, observed with the Spitzer Space Telescope. We compare the properties of two different LINER populations: infrared-faint LINERs, with LINER emission arising mostly in compact nuclear regions, and infrared-luminous LINERs, which often show spatially extended (non-AGN) LINER emission. We show that these two populations can be easily distinguished by their mid-infrared spectra in three different ways: (i) their mid-IR spectral energy distributions (SEDs), (ii) the emission features of polycyclic aromatic hydrocarbons (PAHs), and (iii) various combinations of IR fine-structure line ratios. IR-luminous LINERs show mid-IR SEDs typical of starburst galaxies, while the mid-IR SEDs of IR-faint LINERs are much bluer. PAH flux ratios are significantly different in the two groups. Fine structure emission lines from highly excited gas, such as [O IV], are detected in both populations, suggesting the presence of an additional AGN also in a large fraction of IR-bright LINERs, which contributes little to the combined mid-IR light. The two LINER groups occupy different regions of mid-infrared emission-line excitation diagrams. The positions of the various LINER types in our diagnostic diagrams provide important clues regarding the power source of each LINER type. Most of these mid-infrared diagnostics can be applied at low spectral resolution, making AGN- and starburst-excited LINERs distinguishable also at high redshifts.Comment: 11 pages, including 2 eps figures, accepted for publication in ApJ

Phase transition curves for mesoscopic superconducting samples

We compute the phase transition curves for mesoscopic superconductors. Special emphasis is given to the limiting shape of the curve when the magnetic flux is large. We derive an asymptotic formula for the ground state of the Schr\"odinger equation in the presence of large applied flux. The expansion is shown to be sensitive to the smoothness of the domain. The theoretical results are compared to recent experiments.Comment: 8 pages, 1 figur

Deriving a multivariate CO-to-H2_2 conversion function using the [CII]/CO(1-0) ratio and its application to molecular gas scaling relations

We present Herschel PACS observations of the [CII] 158 micron emission line in a sample of 24 intermediate mass (9<logM$_\ast$/M$_\odot$<10) and low metallicity (0.4< Z/Z$_\odot$<1.0) galaxies from the xCOLD GASS survey. Combining them with IRAM CO(1-0) measurements, we establish scaling relations between integrated and molecular region [CII]/CO(1-0) luminosity ratios as a function of integrated galaxy properties. A Bayesian analysis reveals that only two parameters, metallicity and offset from the star formation main sequence, $\Delta$MS, are needed to quantify variations in the luminosity ratio; metallicity describes the total dust content available to shield CO from UV radiation, while $\Delta$MS describes the strength of this radiation field. We connect the [CII]/CO luminosity ratio to the CO-to-H$_2$ conversion factor and find a multivariate conversion function $\alpha_{CO}$, which can be used up to z~2.5. This function depends primarily on metallicity, with a second order dependence on $\Delta$MS. We apply this to the full xCOLD GASS and PHIBSS1 surveys and investigate molecular gas scaling relations. We find a flattening of the relation between gas mass fraction and stellar mass at logM$_\ast$/M$_\odot$<10. While the molecular gas depletion time varies with sSFR, it is mostly independent of mass, indicating that the low L$_{CO}$/SFR ratios long observed in low mass galaxies are entirely due to photodissociation of CO, and not to an enhanced star formation efficiency.Comment: Submitted to MNRAS, this version after referee comments. 21 page

Gravitational Ionization: A Chaotic Net in the Kepler System

The long term nonlinear dynamics of a Keplerian binary system under the combined influences of gravitational radiation damping and external tidal perturbations is analyzed. Gravitational radiation reaction leads the binary system towards eventual collapse, while the external periodic perturbations could lead to the ionization of the system via Arnold diffusion. When these two opposing tendencies nearly balance each other, interesting chaotic behavior occurs that is briefly studied in this paper. It is possible to show that periodic orbits can exist in this system for sufficiently small damping. Moreover, we employ the method of averaging to investigate the phenomenon of capture into resonance.Comment: REVTEX Style, Submitte

The photometric properties of a vast stellar substructure in the outskirts of M33

We have surveyed $\sim40$sq.degrees surrounding M33 with CFHT MegaCam in the g and i filters, as part of the Pan-Andromeda Archaeological Survey. Our observations are deep enough to resolve the top 4mags of the red giant branch population in this galaxy. We have previously shown that the disk of M33 is surrounded by a large, irregular, low-surface brightness substructure. Here, we quantify the stellar populations and structure of this feature using the PAndAS data. We show that the stellar populations of this feature are consistent with an old population with $<[Fe/H]>\sim-1.6$dex and an interquartile range in metallicity of $\sim0.5$dex. We construct a surface brightness map of M33 that traces this feature to $\mu_V\simeq33$mags\,arcsec$^{-2}$. At these low surface brightness levels, the structure extends to projected radii of $\sim40$kpc from the center of M33 in both the north-west and south-east quadrants of the galaxy. Overall, the structure has an "S-shaped" appearance that broadly aligns with the orientation of the HI disk warp. We calculate a lower limit to the integrated luminosity of the structure of $-12.7\pm0.5$mags, comparable to a bright dwarf galaxy such as Fornax or AndII and slightly less than $1\$ of the total luminosity of M33. Further, we show that there is tentative evidence for a distortion in the distribution of young stars near the edge of the HI disk that occurs at similar azimuth to the warp in HI. The data also hint at a low-level, extended stellar component at larger radius that may be a M33 halo component. We revisit studies of M33 and its stellar populations in light of these new results, and we discuss possible formation scenarios for the vast stellar structure. Our favored model is that of the tidal disruption of M33 in its orbit around M31.Comment: Accepted for publication in ApJ. 17 figures. ApJ preprint forma

The impacts of environmental warming on Odonata: a review

Climate change brings with it unprecedented rates of increase in environmental temperature, which will have major consequences for the earth's flora and fauna. The Odonata represent a taxon that has many strong links to this abiotic factor due to its tropical evolutionary history and adaptations to temperate climates. Temperature is known to affect odonate physiology including life-history traits such as developmental rate, phenology and seasonal regulation as well as immune function and the production of pigment for thermoregulation. A range of behaviours are likely to be affected which will, in turn, influence other parts of the aquatic ecosystem, primarily through trophic interactions. Temperature may influence changes in geographical distributions, through a shifting of species' fundamental niches, changes in the distribution of suitable habitat and variation in the dispersal ability of species. Finally, such a rapid change in the environment results in a strong selective pressure towards adaptation to cope and the inevitable loss of some populations and, potentially, species. Where data are lacking for odonates, studies on other invertebrate groups will be considered. Finally, directions for research are suggested, particularly laboratory studies that investigate underlying causes of climate-driven macroecological patterns

A search for broad infrared recombination lines in NGC 1068

We report infrared spectroscopy of the prototypical Seyfert 2 galaxy NGC 1068, aiming at detection of broad components of hydrogen recombination lines that originate in the obscured broad-line region. Using the Short Wavelength Spectrometer on board the Infrared Space Observatory, we have observed for the first time the regions of Brackett beta 2.626um and Pfund alpha 7.460um, and present improved data for Brackett alpha 4.052um. No significant broad components are detected, implying an equivalent visual extinction to the broad-line region of at least 50 magnitudes and an obscuring column density of at least 10^23 cm^-2. While consistent with a highly obscured broad-line region, as required by the classical unified scenario, these limits are not yet significant enough to discriminate strongly between different torus models or to constrain properties of the gas causing the very large X-ray obscuration. We discuss the systematic limitations of infrared broad-line region searches and suggest that Brackett alpha may often be the most favorable transition for future searches.Comment: aastex (V4), 4 eps figures. Accepted by Ap