30,775 research outputs found
The size of the largest fluctuations in a market model with Markovian switching
This paper considers the size of the large fluctuations of a stochastic differential equation with Markovian switching. We concentrate on processes which obey the Law of the Iterated Logarithm, or obey upper and lower iterated logarithm growth bounds on their almost sure partial maxima. The results are applied to financial market models which are subject to random regime shifts. We prove that the security exhibits the same long-run growth properties and deviations from the trend rate of growth as conventional geometric Brownian motion, and also that the returns, which are non-Gaussian, still exhibit the same growth rate in their almost sure large deviations as stationary continuous-time Gaussian processes
The Formation of Galactic Disks
We study the population of galactic disks expected in current hierarchical
clustering models for structure formation. A rotationally supported disk with
exponential surface density profile is assumed to form with a mass and angular
momentum which are fixed fractions of those of its surrounding dark halo. We
assume that haloes respond adiabatically to disk formation, and that only
stable disks can correspond to real systems. With these assumptions the
predicted population can match both present-day disks and the damped Lyman
alpha absorbers in QSO spectra. Good agreement is found provided: (i) the
masses of disks are a few percent of those of their haloes; (ii) the specific
angular momenta of disks are similar to those of their haloes; (iii)
present-day disks were assembled recently (at z<1). In particular, the observed
scatter in the size-rotation velocity plane is reproduced, as is the slope and
scatter of the Tully-Fisher relation. The zero-point of the TF relation is
matched for a stellar mass-to-light ratio of 1 to 2 h in the I-band, consistent
with observational values derived from disk dynamics. High redshift disks are
predicted to be small and dense, and could plausibly merge together to form the
observed population of elliptical galaxies. In many (but not all) currently
popular cosmogonies, disks with rotation velocities exceeding 200 km/s can
account for a third or more of the observed damped Lyman alpha systems at
z=2.5. Half of the lines-of-sight to such systems are predicted to intersect
the absorber at r>3kpc/h and about 10% at r>10kpc/h. The cross-section for
absorption is strongly weighted towards disks with large angular momentum and
so large size for their mass. The galaxy population associated with damped
absorbers should thus be biased towards low surface brightness systems.Comment: 47 pages, Latex, aaspp4.sty, 14 figs included, submitted to MNRA
The Structure and Clustering of Lyman Break Galaxies
The number density and clustering properties of Lyman-break galaxies (LBGs)
are consistent with them being the central galaxies of the most massive dark
halos present at z~3. This conclusion holds in all currently popular
hierarchical models for structure formation, and is almost independent of the
global cosmological parameters. We examine whether the sizes, luminosities,
kinematics and star-formation rates of LBGs are also consistent with this
identification. Simple formation models tuned to give good fits to low redshift
galaxies can predict the distribution of these quantities in the LBG
population. The LBGs should be small (with typical half-light radii of 0.6-2
kpc/h), should inhabit haloes of moderately high circular velocity (180-290
km/s) but have low stellar velocity dispersions (70-120 km/s) and should have
substantial star formation rates (15-100 Msun/yr). The numbers here refer to
the predicted median values in the LBG sample of Adelberger et al. (1998); the
first assumes an Omega=1 universe and the second a flat universe with
Omega=0.3. For either cosmology these predictions are consistent with the
current (rather limited) observational data. Following the work of Kennicutt
(1998) we assume stars to form more rapidly in gas of higher surface density.
This predicts that LBG samples should preferentially contain objects with low
angular momentum, and so small size, for their mass. In contrast, samples of
damped Lyman alpha systems (DLSs), should be biased towards objects with large
angular momentum. Bright LBGs and DLSs may therefore form distinct populations,
with very different sizes and star formation rates, LBGs being smaller and more
metal-rich than DLSs of similar mass and redshift.Comment: 27 pages, 9 figures, MNRAS submitte
Energy Spectra of Anti-nucleons in Finite Nuclei
The quantum vacuum in a many-body system of finite nuclei has been
investigated within the relativistic Hartree approach which describes the bound
states of nucleons and anti-nucleons consistently. The contributions of the
Dirac sea to the source terms of the meson-field equations are taken into
account up to the one-nucleon loop and one-meson loop. The tensor couplings for
the - and -meson are included in the model. The overall nucleon
spectra of shell-model states are in agreement with the data. The calculated
anti-nucleon spectra in the vacuum differ about 20 -- 30 MeV with and without
the tensor-coupling effects.Comment: 4 pages, to appear in the Proceedings of MENU 2004 (Beijing, Aug. 29
-- Sept. 4, 2004
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