Geometrical aspects and connections of the energy-temperature fluctuation relation

Recently, we have derived a generalization of the known canonical fluctuation relation $k_{B}C=\beta^{2}$ between heat capacity $C$ and energy fluctuations, which can account for the existence of macrostates with negative heat capacities $C<0$. In this work, we presented a panoramic overview of direct implications and connections of this fluctuation theorem with other developments of statistical mechanics, such as the extension of canonical Monte Carlo methods, the geometric formulations of fluctuation theory and the relevance of a geometric extension of the Gibbs canonical ensemble that has been recently proposed in the literature.Comment: Version accepted for publication in J. Phys. A: Math and The

Asymmetric supernova remnants generated by Galactic, massive runaway stars

After the death of a runaway massive star, its supernova shock wave interacts with the bow shocks produced by its defunct progenitor, and may lose energy, momentum, and its spherical symmetry before expanding into the local interstellar medium (ISM). We investigate whether the initial mass and space velocity of these progenitors can be associated with asymmetric supernova remnants. We run hydrodynamical models of supernovae exploding in the pre-shaped medium of moving Galactic core-collapse progenitors. We find that bow shocks that accumulate more than about 1.5 Mo generate asymmetric remnants. The shock wave first collides with these bow shocks 160-750 yr after the supernova, and the collision lasts until 830-4900 yr. The shock wave is then located 1.35-5 pc from the center of the explosion, and it expands freely into the ISM, whereas in the opposite direction it is channelled into the region of undisturbed wind material. This applies to an initially 20 Mo progenitor moving with velocity 20 km/s and to our initially 40 Mo progenitor. These remnants generate mixing of ISM gas, stellar wind and supernova ejecta that is particularly important upstream from the center of the explosion. Their lightcurves are dominated by emission from optically-thin cooling and by X-ray emission of the shocked ISM gas. We find that these remnants are likely to be observed in the [OIII] lambda 5007 spectral line emission or in the soft energy-band of X-rays. Finally, we discuss our results in the context of observed Galactic supernova remnants such as 3C391 and the Cygnus Loop.Comment: 21 pages, 16 figure

Constraining the History of the Sagittarius Dwarf Galaxy Using Observations of its Tidal Debris

We present a comparison of semi-analytic models of the phase-space structure of tidal debris with observations of stars associated with the Sagittarius dwarf galaxy (Sgr). We find that many features in the data can be explained by these models. The properties of stars 10-15 degrees away from the center of Sgr --- in particular, the orientation of material perpendicular to Sgr's orbit (c.f. Alard 1996) and the kink in the velocity gradient (Ibata et al 1997) --- are consistent with those expected for unbound material stripped during the most recent pericentric passage ~50 Myrs ago. The break in the slope of the surface density seen by Mateo, Olszewski & Morrison (1998) at ~ b=-35 can be understood as marking the end of this material. However, the detections beyond this point are unlikely to represent debris in a trailing streamer, torn from Sgr during the immediately preceding passage ~0.7 Gyrs ago, but are more plausibly explained by a leading streamer of material that was lost more that 1 Gyr ago and has wrapped all the way around the Galaxy. The observations reported in Majewski et al (1999) also support this hypothesis. We determine debris models with these properties on orbits that are consistent with the currently known positions and velocities of Sgr in Galactic potentials with halo components that have circular velocities v_circ=140-200 km/s. The best match to the data is obtained in models where Sgr currently has a mass of ~10^9 M_sun and has orbited the Galaxy for at least the last 1 Gyr, during which time it has reduced its mass by a factor of 2-3, or luminosity by an amount equivalent to ~10% of the total luminosity of the Galactic halo. These numbers suggest that Sgr is rapidly disrupting and unlikely to survive beyond a few more pericentric passages.Comment: 19 pages, 5 figures, accepted to Astronomical Journa

Thermodynamic fluctuation relation for temperature and energy

The present work extends the well-known thermodynamic relation $C=\beta ^{2}< \delta {E^{2}}>$ for the canonical ensemble. We start from the general situation of the thermodynamic equilibrium between a large but finite system of interest and a generalized thermostat, which we define in the course of the paper. The resulting identity $=1+< \delta {E^{2}}> \partial ^{2}S(E) /\partial {E^{2}}$ can account for thermodynamic states with a negative heat capacity $C<0$; at the same time, it represents a thermodynamic fluctuation relation that imposes some restrictions on the determination of the microcanonical caloric curve $\beta (E) =\partial S(E) /\partial E$. Finally, we comment briefly on the implications of the present result for the development of new Monte Carlo methods and an apparent analogy with quantum mechanics.Comment: Version accepted for publication in J. Phys. A: Math and The

Angular momentum I ground state probabilities of boson systems interacting by random interactions

In this paper we report our systematic calculations of angular momentum $I$ ground state probabilities ($P(I)$) of boson systems with spin $l$ in the presence of random two-body interactions. It is found that the P(0) dominance is usually not true for a system with an odd number of bosons, while it is valid for an even number of bosons, which indicates that the P(0) dominance is partly connected to the even number of identical particles. It is also noticed that the $P(I_{max})$'s of bosons with spin $l$ do not follow the 1/N ($N=l+1$, referring to the number of independent two-body matrix elements) relation. The properties of the $P(I)$'s obtained in boson systems with spin $l$ are discussed.Comment: 8 pages and 3 figure

N-transfer through aspen litter and feather moss layers after fertilization with ammonium nitrate and urea

When fertilizer is broadcast in boreal forest stands, the applied nutrients must pass through a thick layer of either feather moss or leaf litter which covers the forest floor. In a growth chamber experiment we tested the transfer of N through living feather moss or aspen litter when fertilized with urea ((NH2)2CO) or NH4NO3 at a rate of 100 kg ha−1 and under different watering regimes. When these organic substrates were frequently watered to excess they allowed the highest transfer of nutrients through, although 72% of the applied fertilizer was captured in the substrates. In a field experiment we also fertilized moss and aspen litter with urea ((NH2)2CO) or NH4NO3 at a more operationally relevant rate of 330 kg ha−1. We captured the NO3− or NH4+ by ion exchange resin at the substrate–mineral soil interface. In contrast to the growth chamber experiment, this fertilizer rate killed the moss and there was no detectable increase in nutrient levels in the aspen litter or feather moss layers. Instead, the urea was more likely transferred into the mineral soil; mineral soil of the urea treatment had 1.6 times as much extractable N compared to the NH4NO3 treatment. This difference between the growth chamber and field studies was attributed to observed fertilizer- damage to the living moss and possibly damage to the litter microflora due to the higher rate of fertilization in the field. In addition, the early and substantial rainfall after fertilization in the field experiment produced conditions for rapid leaching of N through the organic layers into the mineral soil. In the field, only 8% of the urea-N that was applied was captured by the ion exchange resin, while 34% was captured in for the NH4NO3 fertilization. Thus, the conditions for rapid leaching in the field moved much of the N in the form of urea through the organic layers and into the mineral soil before it was hydrolyzed

Large conductance voltage- and Ca2+-gated potassium (BK) channel beta4 subunit influences sensitivity and tolerance to alcohol by altering its response to kinases

Tolerance is a well described component of alcohol abuse and addiction. The large conductance voltage- and Ca(2+)-gated potassium channel (BK) has been very useful for studying molecular tolerance. The influence of association with the beta4 subunit can be observed at the level of individual channels, action potentials in brain slices, and finally, drinking behavior in the mouse. Previously, we showed that 50 mm alcohol increases both alpha and alphabeta4 BK channel open probability, but only alpha BK develops acute tolerance to this effect. Currently, we explore the possibility that the influence of the beta4 subunit on tolerance may result from a striking effect of beta4 on kinase modulation of the BK channel. We examine the influence of the beta4 subunit on PKA, CaMKII, and phosphatase modulation of channel activity, and on molecular tolerance to alcohol. We record from human BK channels heterologously expressed in HEK 293 cells composed of its core subunit, alpha alone (Insertless), or co-expressed with the beta4 BK auxiliary subunit, as well as, acutely dissociated nucleus accumbens neurons using the cell-attached patch clamp configuration. Our results indicate that BK channels are strongly modulated by activation of specific kinases (PKA and CaMKII) and phosphatases. The presence of the beta4 subunit greatly influences this modulation, allowing a variety of outcomes for BK channel activity in response to acute alcohol

Universality in Blow-Up for Nonlinear Heat Equations

We consider the classical problem of the blowing-up of solutions of the nonlinear heat equation. We show that there exist infinitely many profiles around the blow-up point, and for each integer $k$, we construct a set of codimension $2k$ in the space of initial data giving rise to solutions that blow-up according to the given profile.Comment: 38 page