2,009 research outputs found
Geometrical aspects and connections of the energy-temperature fluctuation relation
Recently, we have derived a generalization of the known canonical fluctuation
relation between heat capacity and
energy fluctuations, which can account for the existence of macrostates with
negative heat capacities . 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
A Survey on Alliances and Related Parameters in Graphs
In this paper, we show that several graph parameters are known in different areas under completely different names.More specifically, our observations connect signed domination, monopolies, -domination, -independence,positive influence domination,and a parameter associated to fast information propagationin networks to parameters related to various notions of global -alliances in graphs.We also propose a new framework, called (global) -alliances, not only in order to characterizevarious known variants of alliance and domination parameters, but also to suggest a unifying framework for the study of alliances and domination.Finally, we also give a survey on the mentioned graph parameters, indicating how results transfer due to our observations
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
A 2MASS All-Sky View of the Sagittarius Dwarf Galaxy: IV. Modeling the Sagittarius Tidal Tails
M giants recovered from the Two Micron All-Sky Survey (2MASS) have recently
been used to map the position and velocity distributions of tidal debris from
the Sagittarius (Sgr) dwarf spheroidal galaxy entirely around the Galaxy. We
compare this data set to both test particle orbits and N-body simulations of
satellite destruction run within a variety of rigid Milky Way potentials and
find that the mass of the Milky Way within 50 kpc of its center should be
3.8-5.6 x 10^11 Msun in order for any Sgr orbit to simultaneously fit the
velocity gradient in the Sgr trailing debris and the apocenter of the Sgr
leading debris. Orbital pole precession of young debris and leading debris
velocities in regions corresponding to older debris provide contradictory
evidence in favor of oblate/prolate Galactic halo potentials respectively,
leading us to conclude that the orbit of Sgr has evolved over the past few Gyr.
Based upon the velocity dispersion and width along the trailing tidal stream
we estimate the current bound mass of Sgr to be M_Sgr = 2 - 5 x 10^8 Msun
independant of the form of the Galactic potential; this corresponds to a range
of mass to light ratios (M/L)_Sgr = 14 - 36 (M/L)_Sun for the Sgr core. Models
with masses in this range best fit the apocenter of leading Sgr tidal debris
when they orbit with a radial period of roughly 0.85 Gyr and have periGalactica
and apoGalactica of about 15 kpc and 60 kpc respectively. These distances will
scale with the assumed distance to the Sgr dwarf and the assumed depth of the
Galactic potential. The density distribution of debris along the orbit in these
models is consistent with the M giant observations, and debris at all orbital
phases where M giants are obviously present is younger (i.e. was lost more
recently from the satellite) than the typical age of a Sgr M giant star.Comment: 42 pages, 13 figures; Accepted for publication by ApJ (October 08,
2004; originally submitted May 10, 2004). Fixed typos and added references.
PDF file with high resolution figures may be downloaded from
http://www.astro.caltech.edu/~drlaw/Papers/Sgr_paper4.pd
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 , we construct a set of
codimension in the space of initial data giving rise to solutions that
blow-up according to the given profile.Comment: 38 page
Thermodynamic fluctuation relation for temperature and energy
The present work extends the well-known thermodynamic relation 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 can account for thermodynamic states
with a negative heat capacity ; at the same time, it represents a
thermodynamic fluctuation relation that imposes some restrictions on the
determination of the microcanonical caloric curve . 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
Tracing Galaxy Formation with Stellar Halos I: Methods
If the favored hierarchical cosmological model is correct, then the Milky Way
system should have accreted ~100-200 luminous satellite galaxies in the past
\~12 Gyr. We model this process using a hybrid semi-analytic plus N-body
approach which distinguishes explicitly between the evolution of light and dark
matter in accreted satellites. This distinction is essential to our ability to
produce a realistic stellar halo, with mass and density profile much like that
of our own Galaxy, and a surviving satellite population that matches the
observed number counts and structural parameter distributions of the satellite
galaxies of the Milky Way. Our model stellar halos have density profiles which
typically drop off with radius faster than those of the dark matter. They are
assembled from the inside out, with the majority of mass (~80%) coming from the
\~15 most massive accretion events. The satellites that contribute to the
stellar halo have median accretion times of ~9 Gyr in the past, while surviving
satellite systems have median accretion times of ~5 Gyr in the past. This
implies that stars associated with the inner halo should be quite different
chemically from stars in surviving satellites and also from stars in the outer
halo or those liberated in recent disruption events. We briefly discuss the
expected spatial structure and phase space structure for halos formed in this
manner. Searches for this type of structure offer a direct test of whether
cosmology is indeed hierarchical on small scales.Comment: 22 pages, 16 figures, submitted to Ap
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