12,590 research outputs found
On vanishing sums of th roots of unity in finite fields
In an earlier work, the authors have determined all possible weights for
which there exists a vanishing sum of th roots
of unity in characteristic 0. In this paper, the same problem is
studied in finite fields of characteristic . For given and , results
are obtained on integers such that all integers are in the
``weight set'' . The main result in this paper guarantees,
under suitable conditions, the existence of solutions of
with all coordinates not equal to zero over a finite field
Modeling the IDV emissions of the BL Lac Objects with a Langevin type stochastic differential equation
In this paper, we introduce a simplified model for explaining the
observations of the optical intraday variability (IDV) of the BL Lac Objects.
We assume that the source of the IDV are the stochastic oscillations of an
accretion disk around a supermassive black hole. The Stochastic Fluctuations on
the vertical direction of the accretion disk are described by using a Langevin
type equation with a damping term and a random, white noise type force.
Furthermore, the preliminary numerical simulation results are presented, which
are based on the numerical analysis of the Langevin stochastic differential
equation.Comment: 4 pages, 4 figures, accepted for publication in J. Astrophys. Ast
Ordering dynamics of the driven lattice gas model
The evolution of a two-dimensional driven lattice-gas model is studied on an
L_x X L_y lattice. Scaling arguments and extensive numerical simulations are
used to show that starting from random initial configuration the model evolves
via two stages: (a) an early stage in which alternating stripes of particles
and vacancies are formed along the direction y of the driving field, and (b) a
stripe coarsening stage, in which the number of stripes is reduced and their
average width increases. The number of stripes formed at the end of the first
stage is shown to be a function of L_x/L_y^\phi, with \phi ~ 0.2. Thus,
depending on this parameter, the resulting state could be either single or
multi striped. In the second, stripe coarsening stage, the coarsening time is
found to be proportional to L_y, becoming infinitely long in the thermodynamic
limit. This implies that the multi striped state is thermodynamically stable.
The results put previous studies of the model in a more general framework
Quasinormal Modes of Dirty Black Holes
Quasinormal mode (QNM) gravitational radiation from black holes is expected
to be observed in a few years. A perturbative formula is derived for the shifts
in both the real and the imaginary part of the QNM frequencies away from those
of an idealized isolated black hole. The formulation provides a tool for
understanding how the astrophysical environment surrounding a black hole, e.g.,
a massive accretion disk, affects the QNM spectrum of gravitational waves. We
show, in a simple model, that the perturbed QNM spectrum can have interesting
features.Comment: 4 pages. Published in PR
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