From Baking a Cake to Solving the Schrodinger Equation

The primary emphasis of this study has been to explain how modifying a cake recipe by changing either the dimensions of the cake or the amount of cake batter alters the baking time. Restricting our consideration to the genoise, one of the basic cakes of classic French cuisine, we have obtained a semi-empirical formula for its baking time as a function of oven temperature, initial temperature of the cake batter, and dimensions of the unbaked cake. The formula, which is based on the Diffusion equation, has three adjustable parameters whose values are estimated from data obtained by baking genoises in cylindrical pans of various diameters. The resulting formula for the baking time exhibits the scaling behavior typical of diffusion processes, i.e. the baking time is proportional to the (characteristic length scale)^2 of the cake. It also takes account of evaporation of moisture at the top surface of the cake, which appears to be a dominant factor affecting the baking time of a cake. In solving this problem we have obtained solutions of the Diffusion equation which are interpreted naturally and straightforwardly in the context of heat transfer; however, when interpreted in the context of the Schrodinger equation, they are somewhat peculiar. The solutions describe a system whose mass assumes different values in two different regions of space. Furthermore, the solutions exhibit characteristics similar to the evanescent modes associated with light waves propagating in a wave guide. When we consider the Schrodinger equation as a non-relativistic limit of the Klein-Gordon equation so that it includes a mass term, these are no longer solutions.Comment: 23 pages, 10 Postscript figure

Exoplanets or Dynamic Atmospheres? The Radial Velocity and Line Shape Variations of 51 Pegasi and Tau Bootis

Because of our relatively low spectral resolution, we compare our observations with Gray's line bisector data by fitting observed line profiles to an expansion in terms of orthogonal (Hermite) functions. To obtain an accurate comparison, we model the emergent line profiles from rotating and pulsating stars, taking the instrumental point spread function into account. We describe this modeling process in detail. We find no evidence for line profile or strength variations at the radial velocity period in either 51 Peg or in Tau Boo. For 51 Peg, our upper limit for line shape variations with 4.23-day periodicity is small enough to exclude with 10 sigma confidence the bisector curvature signal reported by Gray & Hatzes; the bisector span and relative line depth signals reported by Gray (1997) are also not seen, but in this case with marginal (2 sigma) confidence. We cannot, however, exclude pulsations as the source of 51 Peg's radial velocity variation, because our models imply that line shape variations associated with pulsations should be much smaller than those computed by Gray & Hatzes; these smaller signals are below the detection limits both for Gray & Hatzes' data and for our own. Tau Boo's large radial velocity amplitude and v*sin(i) make it easier to test for pulsations in this star. Again we find no evidence for periodic line-shape changes, at a level that rules out pulsations as the source of the radial velocity variability. We conclude that the planet hypothesis remains the most likely explanation for the existing data.Comment: 44 pages, 19 figures, plain TeX, accepted to ApJS (companion to letter astro-ph/9712279

Clostridial Neurotoxins and Substrate Proteolysis in Intact Neurons BOTULINUM NEUROTOXIN C ACTS ON SYNAPTOSOMAL-ASSOCIATED PROTEIN OF 25 kDa

Clostridial neurotoxins are zinc endopeptidases that block neurotransmission and have been shown to cleave, in vitro, specific proteins involved in synaptic vesicle docking and/or fusion. We have used immunohistochemistry and immunoblotting to demonstrate alterations in toxin substrates in intact neurons under conditions of toxin-induced blockade of neurotransmitter release. Vesicle-associated membrane protein, which co-localizes with synaptophysin, is not detectable in tetanus toxin-blocked cultures. Syntaxin, also concentrated in synaptic sites, is cleaved by botulinum neurotoxin C. Similarly, the carboxyl terminus of the synaptosomal-associated protein of 25 kDa (SNAP-25) is not detectable in botulinum neurotoxin A-treated cultures. Unexpectedly, tetanus toxin exposure causes an increase in SNAP-25 immunofluorescence, reflecting increased accessibility of antibodies to antigenic sites rather than increased expression of the protein. Furthermore, botulinum neurotoxin C causes a marked loss of the carboxyl terminus of SNAP-25 when the toxin is added to living cultures, whereas it has no action on SNAP-25 in in vitro preparations. This study is the first to demonstrate in functioning neurons that the physiologic response to these toxins is correlated with the proteolysis of their respective substrates. Furthermore, the data demonstrate that botulinum neurotoxin C, in addition to cleaving syntaxin, exerts a secondary effect on SNAP-25

THE THERMAL STATE OF KS 1731−260 AFTER 14.5 YEARS IN QUIESCENCE

Crustal cooling of accretion-heated neutron stars provides insight into the stellar interior of neutron stars. The neutron star X-ray transient, KS~1731$-$260, was in outburst for 12.5 years before returning to quiescence in 2001. We have monitored the cooling of this source since then through {\it Chandra} and {\it XMM-Newton} observations. Here, we present a 150 ks {\it Chandra} observation of KS~1731$-$260 taken in August 2015, about 14.5 years into quiescence, and 6 years after the previous observation. We find that the neutron star surface temperature is consistent with the previous observation, suggesting that crustal cooling has likely stopped and the crust has reached thermal equilibrium with the core. Using a theoretical crust thermal evolution code, we fit the observed cooling curves and constrain the core temperature (T$_c = 9.35\pm0.25\times10^7$ K), composition (Q$_{imp} = 4.4^{+2.2}_{-0.5}$) and level of extra shallow heating required (Q$_{sh} = 1.36\pm0.18$ MeV/nucleon). We find that the presence of a low thermal conductivity layer, as expected from nuclear pasta, is not required to fit the cooling curve well, but cannot be excluded either.Comment: 7 pages, 6 figures, 1 table, accepted to Ap

Astrophysical False Positives Encountered in Wide-Field Transit Searches

Wide-field photometric transit surveys for Jupiter-sized planets are inundated by astrophysical false positives, namely systems that contain an eclipsing binary and mimic the desired photometric signature. We discuss several examples of such false alarms. These systems were initially identified as candidates by the PSST instrument at Lowell Observatory. For three of the examples, we present follow-up spectroscopy that demonstrates that these systems consist of (1) an M-dwarf in eclipse in front of a larger star, (2) two main-sequence stars presenting grazing-incidence eclipses, and (3) the blend of an eclipsing binary with the light of a third, brighter star. For an additional candidate, we present multi-color follow-up photometry during a subsequent time of eclipse, which reveals that this candidate consists of a blend of an eclipsing binary and a physically unassociated star. We discuss a couple indicators from publicly-available catalogs that can be used to identify which candidates are likely giant stars, a large source of the contaminants in such surveys.Comment: 10 pages, 9 figures, to appear in AIP Conf Proc: The Search for Other Worlds, eds. S. S. Holt & D. Demin

Prompt Quark Production by exploding Sphalerons

Following recent works on production and subsequent explosive decay of QCD sphaleron-like clusters, we discuss the mechanism of quark pair production in this process. We first show how the gauge field explosive solution of Luscher and Schechter can be achieved by non-central conformal mapping from the O(4)-symmetric solution. Our main result is a new solution to the Dirac equation in real time in this configuration, obtained by the same inversion of the fermion O(4) zero mode. It explicitly shows how the quark acceleration occurs, starting from the spherically O(3) symmetric zero energy chiral quark state to the final spectrum of non-zero energies. The sphaleron-like clusters with any Chern-Simons number always produce ${\rm N_F} {\bar {\bf L}}{\bf R}$ quarks, and the antisphaleron-like clusters the chirality opposite. The result are relevant for hadron-hadron and nucleus-nucleus collisions at large $\sqrt{s}$, wherein such clusters can be produced

Incidence and In-Hospital Mortality of Acute Kidney Injury (AKI) and Dialysis Requiring AKI (AKI-D) After Cardiac Catheterization in the National Inpatient Sample

Background: Acute kidney injury (AKI) and dialysis‐requiring AKI (AKI‐D) are common, serious complications of cardiac procedures. Methods and Results: We evaluated 3 633 762 (17 765 214 weighted population) cardiac catheterization or percutaneous coronary intervention (PCI) hospital discharges from the nationally representative National Inpatient Sample to determine annual population incidence rates for AKI and AKI‐D in the United States from 2001 to 2011. Odds ratios for both conditions and associated in‐hospital mortality were calculated for each year in the study period using multiple logistic regression. The number of cardiac catheterization or PCI cases resulting in AKI rose almost 3‐fold from 2001 to 2011. The adjusted odds of AKI and AKI‐D per year among cardiac catheterization and PCI patients were 1.11 (95% CI: 1.10–1.12) and 1.01 (95% CI: 0.99–1.02), respectively. Most importantly, in‐hospital mortality significantly decreased from 2001 to 2011 for AKI (19.6–9.2%) and AKI‐D (28.3–19.9%), whereas odds of associated in‐hospital mortality were 0.50 (95% CI: 0.45–0.56) and 0.70 (95% CI: 0.55–0.93) in 2011 versus 2001, respectively. The population‐attributable risk of mortality for AKI and AKI‐D was 25.8% and 3.8% in 2001 and 41.1% and 6.5% in 2011, respectively. Males and females had similar patterns of AKI increase, although males outpaced females. Conclusions: The Incidence of AKI among cardiac catheterization and PCI patients has increased sharply in the United States, and this should be addressed by implementing prevention strategies. However, mortality has significantly declined, suggesting that efforts to manage AKI and AKI‐D after cardiac catheterization and PCI have reduced mortality