117 research outputs found
Two hard spheres in a pore: Exact Statistical Mechanics for different shaped cavities
The Partition function of two Hard Spheres in a Hard Wall Pore is studied
appealing to a graph representation. The exact evaluation of the canonical
partition function, and the one-body distribution function, in three different
shaped pores are achieved. The analyzed simple geometries are the cuboidal,
cylindrical and ellipsoidal cavities. Results have been compared with two
previously studied geometries, the spherical pore and the spherical pore with a
hard core. The search of common features in the analytic structure of the
partition functions in terms of their length parameters and their volumes,
surface area, edges length and curvatures is addressed too. A general framework
for the exact thermodynamic analysis of systems with few and many particles in
terms of a set of thermodynamic measures is discussed. We found that an exact
thermodynamic description is feasible based in the adoption of an adequate set
of measures and the search of the free energy dependence on the adopted measure
set. A relation similar to the Laplace equation for the fluid-vapor interface
is obtained which express the equilibrium between magnitudes that in extended
systems are intensive variables. This exact description is applied to study the
thermodynamic behavior of the two Hard Spheres in a Hard Wall Pore for the
analyzed different geometries. We obtain analytically the external work, the
pressure on the wall, the pressure in the homogeneous zone, the wall-fluid
surface tension, the line tension and other similar properties
On the twin paradox in static spacetimes: I. Schwarzschild metric
Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider
the twin paradox in static spacetimes. According to a well known theorem in
Lorentzian geometry the longest timelike worldline between two given points is
the unique geodesic line without points conjugate to the initial point on the
segment joining the two points. We calculate the proper times for static twins,
for twins moving on a circular orbit (if it is a geodesic) around a centre of
symmetry and for twins travelling on outgoing and ingoing radial timelike
geodesics. We show that the twins on the radial geodesic worldlines are always
the oldest ones and we explicitly find the conjugate points (if they exist)
outside the relevant segments. As it is of its own mathematical interest, we
find general Jacobi vector fields on the geodesic lines under consideration. In
the first part of the work we investigate Schwarzschild geometry.Comment: 18 pages, paper accepted for publication in Gen. Rel. Gra
Metric gravity theories and cosmology:II. Stability of a ground state in f(R) theories
A fundamental criterion of viability of any gravity theory is existence of a
stable ground-state solution being either Minkowski, dS or AdS space. Stability
of the ground state is independent of which frame is physical. In general, a
given theory has multiple ground states and splits into independent physical
sectors. All metric gravity theories with the Lagrangian being a function of
Ricci tensor are dynamically equivalent to Einstein gravity with a source and
this allows us to study the stability problem using methods developed in GR. We
apply these methods to f(R) theories. As is shown in 13 cases of Lagrangians
the stability criterion works simply and effectively whenever the curvature of
the ground state is determined. An infinite number of gravity theories have a
stable ground state and further viability criteria are necessary.Comment: A modified and expanded version of a second part of the paper which
previously appeared as gr-qc/0702097v1. The first, modified part is now
published as gr-qc/0702097v2 and as a separate paper in Class. Qu. Grav. The
present paper matches the published versio
Virial series for inhomogeneous fluids applied to the Lennard-Jones wall-fluid surface tension at planar and curved walls
We formulate a straightforward scheme of statistical mechanics for
inhomogeneous systems that includes the virial series in powers of the activity
for the grand free energy and density distributions. There, cluster integrals
formulated for inhomogeneous systems play a main role. We center on second
order terms that were analyzed in the case of hard-wall confinement, focusing
in planar, spherical and cylindrical walls. Further analysis was devoted to the
Lennard-Jones system and its generalization the 2k-k potential. For this
interaction potentials the second cluster integral was evaluated analytically.
We obtained the fluid-substrate surface tension at second order for the planar,
spherical and cylindrical confinement. Spherical and cylindrical cases were
analyzed using a series expansion in the radius including higher order terms.
We detected a dependence of the surface tension for the
standard Lennard-Jones system confined by spherical and cylindrical walls, no
matter if particles are inside or outside of the hard-walls. The analysis was
extended to bending and Gaussian curvatures, where exact expressions were also
obtained.Comment: 15 pages, 6 figure
Inflation in Multidimensional Quantum Cosmology
We extend to multidimensional cosmology Vilenkin's prescription of tunnelling
from nothing for the quantum origin of the observable Universe. Our model
consists of a -dimensional spacetime of topology , with a scalar field (``chaotic inflaton'') for the
matter component. Einstein gravity and Casimir compactification are assumed.
The resulting minisuperspace is 3--dimensional. Patchwise we find an
approximate analytic solution of the Wheeler--DeWitt equation through which we
discuss the tunnelling picture and the probability of nucleation of the
classical Universe with compactifying extra dimensions. Our conclusion is that
the most likely initial conditions, although they do not lead to the
compactification of the internal space, still yield (power-law) inflation for
the outer space. The scenario is physically acceptable because the inner space
growth is limited to in 100 e-foldings of inflation, starting
from the Planck scale.Comment: RevTeX, 30 pages, 4 figures available via fax on request to
[email protected], submitted to Phys. Rev.
Graviton Spectra in String Cosmology
We propose to uncover the signature of a stringy era in the primordial
Universe by searching for a prominent peak in the relic graviton spectrum. This
feature, which in our specific model terminates an increase and
initiates an decrease, is induced during the so far overlooked
bounce of the scale factor between the collapsing deflationary era (or pre-Big
Bang) and the expanding inflationary era (or post-Big Bang). We evaluate both
analytically and numerically the frequency and the intensity of the peak and we
show that they may likely fall in the realm of the new generation of
interferometric detectors. The existence of a peak is at variance with
ordinarily monotonic (either increasing or decreasing) graviton spectra of
canonical cosmologies; its detection would therefore offer strong support to
string cosmology.Comment: 14 pages, RevTex source and 6 figures.p
The catalog of short periods stars from the ''Pi of the Sky'' data
Based on the data from the ''Pi of the Sky'' project we made a catalog of the
variable stars with periods from 0.1 to 10 days. We used data collected during
a period of two years (2004 and 2005) and classified 725 variable stars. Most
of the stars in our catalog are eclipsing binaries - 464 (about 64%), while the
number of pulsating stars is 125 (about 17%). Our classification is based on
the shape of the light curve, as in the GCVS catalog. However, some stars in
our catalog were classified as of different type than in the GCVS catalog. We
have found periods for 15 stars present in the GCVS catalog with previously
unknown period.Comment: New Astronomy in prin
Absolute properties of BG Ind - a bright F3 system just leaving the Main Sequence
We present photometric and spectroscopic analysis of the bright detached
eclipsing binary BG Ind. The masses of the components are found to be 1.428 +-
0.008 and 1.293 +- 0.008 Msun and the radii to be 2.290+-0.017 and 1.680+-0.038
Rsun for primary and secondary stars, respectively. Spectra- and
isochrone-fitting coupled with color indices calibration yield
[Fe/H]=-0.2+-0.1. At an age of 2.65+-0.20 Gyr BG Ind is well advanced in the
main-sequence evolutionary phase - in fact, its primary is at TAMS or just
beyond it. Together with three similar systems (BK Peg, BW Aqr and GX Gem) it
offers an interesting opportunity to test the theoretical description of
overshooting in the critical mass range 1.2-1.5 Msun.Comment: 8 pages, 5 figures, corrected bugs in author lis
Oscillatory behavior of closed isotropic models in second order gravity theory
Homogeneous and isotropic models are studied in the Jordan frame of the
second order gravity theory. The late time evolution of the models is analysed
with the methods of the dynamical systems. The normal form of the dynamical
system has periodic solutions for a large set of initial conditions. This
implies that an initially expanding closed isotropic universe may exhibit
oscillatory behaviour.Comment: 16 pages, 3 figures. With some minor improvements. To appear in
General Relativity and Gravitatio
On the issue of gravitons
We investigate the problem of whether one can anticipate any features of the
graviton without a detailed knowledge of a full quantum gravity. Assuming that
in linearized gravity the graviton is in a sense similar to the photon, we
derive a curious large number coincidence between the number of gravitons
emitted by a solar planet during its orbital period and the number of its
nucleons. In Einstein's GR the analogy between the graviton and the photon is
ill founded. A generic relationship between quanta of a quantum field and plane
waves of the corresponding classical field is broken in the case of GR. The
graviton cannot be classically approximated by a generic pp wave nor by the
exact plane wave. Most important, the ADM energy is a zero frequency
characteristic of any asymptotically flat spacetime and this means that any
general relationship between energy and frequency is a priori impossible. In
particular the formula does not hold. The graviton must have
features different from those of the photon and these cannot be predicted from
classical general relativity.Comment: 14 pages. One phrase adde
- …