Poisson\u27s Equation

This presentation deals with how to solve Poisson\u27s Equation for a two dimensional plate. The numbers can be represented as heat, charge density, and gravitational force. This is a generalization of Laplace\u27s Equation, which are steady state problems. In this problem, it is broken up into two simpler problems. For the first part, there are two ways of solving it since it is two dimensional. This presentation covers both ways of solving it using separation of variables, orthogonality, and partial differential equations. In addition, it shows how to solve the second part and finalize Poisson\u27s Equation

Entropic equality for worst-case work at any protocol speed

We derive an equality for non-equilibrium statistical mechanics in finite-dimensional quantum systems. The equality concerns the worst-case work output of a time-dependent Hamiltonian protocol in the presence of a Markovian heat bath. It has has the form "worst-case work = penalty - optimum". The equality holds for all rates of changing the Hamiltonian and can be used to derive the optimum by setting the penalty to 0. The optimum term contains the max entropy of the initial state, rather than the von Neumann entropy, thus recovering recent results from single-shot statistical mechanics. Energy coherences can arise during the protocol but are assumed not to be present initially. We apply the equality to an electron box.Comment: 4 page + 14 page appendix; 8 figures; AA

Alpha1 -adrenergic stimulation selectively enhances endothelium-mediated vasodilation in rat cremaster arteries.

We have systematically investigated how vascular smooth muscle α1 -adrenoceptor activation impacts endothelium-mediated vasodilation in isolated, myogenically active, rat cremaster muscle 1A arteries. Cannulated cremaster arteries were pressurized intraluminally to 70 mmHg to induce myogenic tone, and exposed to vasoactive agents via bath superfusion at 34°C. Smooth muscle membrane potential was measured via sharp microelectrode recordings in pressurized, myogenic arteries. The α1 -adrenergic agonist phenylephrine (25-100 nmol/L) produced further constriction of myogenic arteries, but did not alter the vasorelaxant responses to acetylcholine (0.3 μmol/L), SKA-31 (an activator of endothelial Ca2+ -dependent K+ channels) (3 μmol/L) or sodium nitroprusside (10 μmol/L). Exposure to 0.25-1 μmol/L phenylephrine or 1 μmol/L norepinephrine generated more robust constrictions, and also enhanced the vasodilations evoked by acetylcholine and SKA-31, but not by sodium nitroprusside. In contrast, the thromboxane receptor agonist U46619 (250 nmol/L) dampened responses to all three vasodilators. Phenylephrine exposure depolarized myogenic arteries, and mimicking this effect with 4-aminopyridine (1 mmol/L) was sufficient to augment the SKA-31-evoked vasodilation. Inhibition of L-type Ca2+ channels by 1 μmol/L nifedipine decreased myogenic tone, phenylephrine-induced constriction and prevented α1 -adrenergic enhancement of endothelium-evoked vasodilation; these latter deficits were overcome by exposure to 3 and 10 μmol/L phenylephrine. Mechanistically, augmentation of ACh-evoked dilation by phenylephrine was dampened by eNOS inhibition and abolished by blockade of endothelial KCa channels. Collectively, these data suggest that increasing α1 -adrenoceptor activation beyond a threshold level augments endothelium-evoked vasodilation, likely by triggering transcellular signaling between smooth muscle and the endothelium. Physiologically, this negative feedback process may serve as a "brake" to limit the extent of vasoconstriction in the skeletal microcirculation evoked by the elevated sympathetic tone

Characterization the Cool KOIs. II. The M Dwarf KOI-254 and its Hot Jupiter

We report the confirmation and characterization of a transiting gas giant planet orbiting the M dwarf KOI-254 every 2.455239 days, which was originally discovered by the Kepler mission. We use radial velocity measurements, adaptive optics imaging, and near-infrared spectroscopy to confirm the planetary nature of the transit events. KOI-254 b is the first hot Jupiter discovered around an M-type dwarf star. We also present a new model-independent method of using broadband photometry to estimate the mass and metallicity of an M dwarf without relying on a direct distance measurement. Included in this methodology is a new photometric metallicity calibration based on J – K colors. We use this technique to measure the physical properties of KOI-254 and its planet. We measure a planet mass of M_P = 0.505 M_(Jup), radius R_P = 0.96 R_(Jup), and semimajor axis a = 0.030 AU, based on our measured stellar mass M_* = 0.59 M_☉ and radius R_* = 0.55 R_☉. We also find that the host star is metal-rich, which is consistent with the sample of M-type stars known to harbor giant planets

Prenatal Phthalate Exposures and Body Mass Index Among 4- to 7-Year-old Children: A Pooled Analysis

Phthalates are hypothesized to cause obesity, but few studies have assessed whether prenatal phthalate exposures are related to childhood body mass index (BMI)

The GJ 436 System: Directly Determined Astrophysical Parameters of an M-Dwarf and Implications for the Transiting Hot Neptune

The late-type dwarf GJ 436 is known to host a transiting Neptune-mass planet in a 2.6-day orbit. We present results of our interferometric measurements to directly determine the stellar diameter ($R_{\star} = 0.455 \pm 0.018 R_{\odot}$) and effective temperature ($T_{\rm EFF} = 3416 \pm 54$ K). We combine our stellar parameters with literature time-series data, which allows us to calculate physical and orbital system parameters, including GJ 436's stellar mass ($M_{\star} = 0.507^{+ 0.071}_{- 0.062} M_{\odot}$) and density ($\rho_* = 5.37^{+ 0.30}_{- 0.27} \rho_\odot$), planetary radius ($R_{p} = 0.369^{+ 0.015}_{- 0.015} R_{Jupiter}$), planetary mass ($M_{p} = 0.078^{+ 0.007}_{- 0.008} M_{Jupiter}$), implying a mean planetary density of $\rho_{p} = 1.55^{+ 0.12}_{- 0.10} \rho_{Jupiter}$. These values are generally in good agreement with previous literature estimates based on assumed stellar mass and photometric light curve fitting. Finally, we examine the expected phase curves of the hot Neptune GJ 436b, based on various assumptions concerning the efficiency of energy redistribution in the planetary atmosphere, and find that it could be constrained with {\it Spitzer} monitoring observations.Comment: 10 pages, 4 tables, 9 figures; accepted for publication in ApJ; incorporated referee's comments and associated change

Characterizing the Cool KOIs. V. KOI-256: A Mutually Eclipsing Post-common Envelope Binary

We report that Kepler Object of Interest 256 (KOI-256) is a mutually eclipsing post-common envelope binary (ePCEB), consisting of a cool white dwarf (M_★ = 0.592 ± 0.089 M_☉, R_★ = 0.01345 ± 0.00091 R_☉, T_(eff) = 7100 ± 700 K) and an active M3 dwarf (M_★ = 0.51 ± 0.16 M_☉, R_★ = 0.540 ± 0.014 R_☉, T_(eff) = 3450 ± 50 K) with an orbital period of 1.37865 ± 0.00001 days. KOI-256 is listed as hosting a transiting planet-candidate by Borucki et al. and Batalha et al.; here we report that the planet-candidate transit signal is in fact the occultation of a white dwarf as it passes behind the M dwarf. We combine publicly-available long- and short-cadence Kepler light curves with ground-based measurements to robustly determine the system parameters. The occultation events are readily apparent in the Kepler light curve, as is spin-orbit synchronization of the M dwarf, and we detect the transit of the white dwarf in front of the M dwarf halfway between the occultation events. The size of the white dwarf with respect to the Einstein ring during transit (R_(Ein) = 0.00473 ± 0.00055 R ☉) causes the transit depth to be shallower than expected from pure geometry due to gravitational lensing. KOI-256 is an old, long-period ePCEB and serves as a benchmark object for studying the evolution of binary star systems as well as white dwarfs themselves, thanks largely to the availability of near-continuous, ultra-precise Kepler photometry

Characterizing the cool kois. V. koi-256: A mutually eclipsing post-common envelope binary

We report that Kepler Object of Interest 256 (KOI-256) is a mutually eclipsing post-common envelope binary (ePCEB), consisting of a cool white dwarf (M* = 0.592 ± 0.089 M, R = 0.01345 ± 0.00091 R , T eff = 7100 ± 700 K) and an active M3 dwarf (M* = 0.51 ± 0.16 M , R* = 0.540 ± 0.014 R , T eff = 3450 ± 50 K) with an orbital period of 1.37865 ± 0.00001 days. KOI-256 is listed as hosting a transiting planet-candidate by Borucki et al. and Batalha et al.; here we report that the planet-candidate transit signal is in fact the occultation of a white dwarf as it passes behind the M dwarf. We combine publicly-available long- and short-cadence Kepler light curves with ground-based measurements to robustly determine the system parameters. The occultation events are readily apparent in the Kepler light curve, as is spin-orbit synchronization of the M dwarf, and we detect the transit of the white dwarf in front of the M dwarf halfway between the occultation events. The size of the white dwarf with respect to the Einstein ring during transit (R Ein = 0.00473 ± 0.00055 R ) causes the transit depth to be shallower than expected from pure geometry due to gravitational lensing. KOI-256 is an old, long-period ePCEB and serves as a benchmark object for studying the evolution of binary star systems as well as white dwarfs themselves, thanks largely to the availability of near-continuous, ultra-precise Kepler photometry. © 2013. The American Astronomical Society. All rights reserved.

Characterizing the Cool KOIs II. The M Dwarf KOI-254 and its Hot Jupiter

We report the confirmation and characterization of a transiting gas giant planet orbiting the M dwarf KOI-254 every 2.455239 days, which was originally discovered by the Kepler mission. We use radial velocity measurements, adaptive optics imaging and near infrared spectroscopy to confirm the planetary nature of the transit events. KOI-254b is the first hot Jupiter discovered around an M-type dwarf star. We also present a new model-independent method of using broadband photometry to estimate the mass and metallicity of an M dwarf without relying on a direct distance measurement. Included in this methodology is a new photometric metallicity calibration based on J-K colors. We use this technique to measure the physical properties of KOI-254 and its planet. We measure a planet mass of Mp = 0.505 Mjup, radius Rp = 0.96 Rjup and semimajor axis a = 0.03 AU, based on our measured stellar mass Mstar = 0.59 Msun and radius Rstar = 0.55 Rsun. We also find that the host star is metal-rich, which is consistent with the sample of M-type stars known to harbor giant planets.Comment: AJ accepted (in press