5,275 research outputs found
Scaling law of Wolff cluster surface energy
We study the scaling properties of the clusters grown by the Wolff algorithm
on seven different Sierpinski-type fractals of Hausdorff dimension in the framework of the Ising model. The mean absolute value of the surface
energy of Wolff cluster follows a power law with respect to the lattice size.
Moreover, we investigate the probability density distribution of the surface
energy of Wolff cluster and are able to establish a new scaling relation. It
enables us to introduce a new exponent associated to the surface energy of
Wolff cluster. Finally, this new exponent is linked to a dynamical exponent via
an inequality.Comment: 12 pages, 3 figures. To appear in PR
Explicit Space-Time Codes Achieving The Diversity-Multiplexing Gain Tradeoff
A recent result of Zheng and Tse states that over a quasi-static channel,
there exists a fundamental tradeoff, referred to as the diversity-multiplexing
gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity
gain that can be simultaneously achieved by a space-time (ST) block code. This
tradeoff is precisely known in the case of i.i.d. Rayleigh-fading, for T>=
n_t+n_r-1 where T is the number of time slots over which coding takes place and
n_t,n_r are the number of transmit and receive antennas respectively. For T <
n_t+n_r-1, only upper and lower bounds on the D-MG tradeoff are available.
In this paper, we present a complete solution to the problem of explicitly
constructing D-MG optimal ST codes, i.e., codes that achieve the D-MG tradeoff
for any number of receive antennas. We do this by showing that for the square
minimum-delay case when T=n_t=n, cyclic-division-algebra (CDA) based ST codes
having the non-vanishing determinant property are D-MG optimal. While
constructions of such codes were previously known for restricted values of n,
we provide here a construction for such codes that is valid for all n.
For the rectangular, T > n_t case, we present two general techniques for
building D-MG-optimal rectangular ST codes from their square counterparts. A
byproduct of our results establishes that the D-MG tradeoff for all T>= n_t is
the same as that previously known to hold for T >= n_t + n_r -1.Comment: Revised submission to IEEE Transactions on Information Theor
The Origin of C IV Absorption Systems at Redshifts z<1---Discovery of Extended C IV Envelopes Around Galaxies
(Abridged) We report the discovery of extended CIV gaseous envelopes around
galaxies of a wide range of luminosity and morphological type. First, we show
that CIV absorption systems are strongly clustered around galaxies on velocity
scales of v < 250 km/s and impact parameter scales of rho < 100 h^{-1} kpc but
not on larger velocity or impact parameter scales. Next, adopting measurements
of galaxy properties presented in previous papers, we examine how properties of
the CIV absorption systems depend on properties of the galaxies. On the basis
of 14 galaxy and absorber pairs and 36 galaxies that do not produce
corresponding CIV absorption lines to within sensitive upper limits, we find
that: (1) Galaxies of a range of morphological type and luminosity appear to
possess extended CIV gaseous envelopes of radius R ~ 100 h^{-1} kpc, with
abrupt boundaries between the CIV absorbing and non-absorbing regions. (2) The
extent of CIV-absorbing gas around galaxies scales with galaxy B-band
luminosity as R \propto L_B^{0.5 +/- 0.1} but does not depend strongly on
galaxy surface brightness, redshift, or morphological type. And (3) the
covering factor of CIV clouds within ~ 100 h^{-1} kpc of galaxies is nearly
unity, but there is a large scatter in the mean number of clouds encountered
along the line of sight. The most significant implication of the study is that
galaxies of a wide range of luminosity and morphological type are surrounded by
chemically enriched gas that extends for at least ~ 100 h^{-1} kpc. We consider
various scenarios that may have produced metals at large galactic distance and
conclude that accreting satellites are most likely to be responsible for
chemically enriched gas at large galactic distances to regular looking
galaxies.Comment: 19 pages, 3 figures, to appear in ApJ, July 20 200
Near-IR studies of recurrent nova V745 Scorpii during its 2014 outburst
The recurrent nova (RN) V745 Scorpii underwent its third known outburst on
2014 February 6. Infrared monitoring of the eruption on an almost daily basis,
starting from 1.3d after discovery, shows the emergence of a powerful blast
wave generated by the high velocity nova ejecta exceeding 4000 kms
plowing into its surrounding environment. The temperature of the shocked gas is
raised to a high value exceeding 10K immediately after outburst
commencement. The energetics of the outburst clearly surpass those of similar
symbiotic systems like RS Oph and V407 Cyg which have giant secondaries. The
shock does not show a free-expansion stage but rather shows a decelerative
Sedov-Taylor phase from the beginning. Such strong shockfronts are known to be
sites for ray generation. V745 Sco is the latest nova, apart from five
other known novae, to show ray emission. It may be an important
testbed to resolve the crucial question whether all novae are generically
ray emitters by virtue of having a circumbinary reservoir of material
that is shocked by the ejecta rather than ray generation being
restricted to only symbiotic systems with a shocked red giant (RG) wind. The
lack of a free-expansion stage favors V745 Sco to have a density enhancement
around the white dwarf (WD), above that contributed by a RG wind. Our analysis
also suggests that the WD in V745 Sco is very massive and a potential
progenitor for a future SN Ia explosion.Comment: To appear in ApJ (Letters
Critical Behavior of the Ferromagnetic Ising Model on a Sierpinski Carpet: Monte Carlo Renormalization Group Study
We perform a Monte Carlo Renormalization Group analysis of the critical
behavior of the ferromagnetic Ising model on a Sierpi\'nski fractal with
Hausdorff dimension . This method is shown to be relevant to
the calculation of the critical temperature and the magnetic
eigen-exponent on such structures. On the other hand, scaling corrections
hinder the calculation of the temperature eigen-exponent . At last, the
results are shown to be consistent with a finite size scaling analysis.Comment: 16 pages, 7 figure
Critical behavior of the 3-state Potts model on Sierpinski carpet
We study the critical behavior of the 3-state Potts model, where the spins
are located at the centers of the occupied squares of the deterministic
Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo
simulations, for a Hausdorff dimension . The phase
transition is shown to be a second order one. The maxima of the susceptibility
of the order parameter follow a power law in a very reliable way, which enables
us to calculate the ratio of the exponents . We find that the
scaling corrections affect the behavior of most of the thermodynamical
quantities. However, the sequence of intersection points extracted from the
Binder's cumulant provides bounds for the critical temperature. We are able to
give the bounds for the exponent as well as for the ratio of the
exponents , which are compatible with the results calculated from
the hyperscaling relation.Comment: 13 pages, 4 figure
Coherent-State Approach to Two-dimensional Electron Magnetism
We study in this paper the possible occurrence of orbital magnetim for
two-dimensional electrons confined by a harmonic potential in various regimes
of temperature and magnetic field. Standard coherent state families are used
for calculating symbols of various involved observables like thermodynamical
potential, magnetic moment, or spatialdistribution of current. Their
expressions are given in a closed form and the resulting Berezin-Lieb
inequalities provide a straightforward way to study magnetism in various limit
regimes. In particular, we predict a paramagnetic behaviour in the
thermodynamical limit as well as in the quasiclassical limit under a weak
field. Eventually, we obtain an exact expression for the magnetic moment which
yields a full description of the phase diagram of the magnetization.Comment: 21 pages, 6 figures, submitted to PR
Abundance Profiles and Kinematics of Damped Lyman-alpha Absorbing Galaxies at z < 0.65
We present a spectroscopic study of six damped Lya absorption (DLA) systems
at z<0.65, based on moderate-to-high resolution spectra of the galaxies
responsible for the absorbers. Combining known metallicity measurements of the
absorbers with known optical properties of the absorbing galaxies, we confirm
that the low metal content of the DLA population can arise naturally as a
combination of gas cross-section selection and metallicity gradients commonly
observed in local disk galaxies. We also study the Tully-Fisher relation of the
DLA-selected galaxies and find little detectable evidence for evolution in the
disk population between z=0 and z~0.5. Additional results of our analysis are
as follows. (1) The DLA galaxies exhibit a range of spectral properties, from
post-starburst, to normal disks, and to starburst systems, supporting the idea
that DLA galaxies are drawn from the typical field population. (2) Large
rotating HI disks of radius 30 h^{-1} kpc and of dynamic mass M_dyn > 10^{11}
h^{-1} M_sun appear to be common at intermediate redshifts. (3) Using an
ensemble of six galaxy-DLA pairs, we derive an abundance profile that is
characterized by a radial gradient of -0.041 +/- 0.012 dex per kiloparsec (or
equivalently a scale length of 10.6 h^{-1} kpc) from galactic center to 30
h^{-1} kpc radius. (4) Adopting known N(HI) profiles of nearby galaxies and the
best-fit radial gradient, we further derive an N(HI)-weighted mean metallicity
_weighted = -0.50 +/- 0.07 for the DLA population over 100 random lines of
sight, consistent with _weighted = -0.64 (-0.86, +0.40) observed for z~1 DLA
systems from Prochaska et al. Our analysis demonstrates that the low metal
content of DLA systems does not rule out the possibility that the DLA
population trace the field galaxy population.Comment: 57 pages, 17 figures, to appear in the ApJ 20 February 2005 issue; a
pdf version of the paper with full-resolution figures is available at
http://falcon.mit.edu/~hchen/public/tmp/dlachem.pd
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