339,518 research outputs found
Exact Simulation of Wishart Multidimensional Stochastic Volatility Model
In this article, we propose an exact simulation method of the Wishart
multidimensional stochastic volatility (WMSV) model, which was recently
introduced by Da Fonseca et al. \cite{DGT08}. Our method is based onanalysis of
the conditional characteristic function of the log-price given volatility
level. In particular, we found an explicit expression for the conditional
characteristic function for the Heston model. We perform numerical experiments
to demonstrate the performance and accuracy of our method. As a result of
numerical experiments, it is shown that our new method is much faster and
reliable than Euler discretization method.Comment: 27 page
Diffusive Shock Acceleration in Test-Particle Regime
We examine the test-particle solution for diffusive shock acceleration, based
on simple models for thermal leakage injection and Alfv'enic drift. The
critical injection rate, \xi_c, above which the cosmic ray (CR) pressure
becomes dynamically significant, depends mainly on the sonic shock Mach number,
M, and preshock gas temperature, T_1. In the hot-phase interstellar medium
(ISM) and intracluster medium, \xi_c < 10^{-3} for shocks with M < 5, while
\xi_c ~ 10^{-4}(T_1/10^6 K)^{1/2} for shocks with M > 10. For T_1=10^6 K, for
example, the test-particle solution would be valid if the injection momentum,
p_{inj} > 3.8 p_{th}. This leads to the postshock CR pressure less than 10% of
the shock ram pressure. If the Alfv'en speed is comparable to the sound speed
in the preshock flow, as in the hot-phase ISM, the power-law slope of CR
spectrum can be significantly softer than the canonical test-particle slope.
Then the CR spectrum at the shock can be approximated by the revised
test-particle power-law with an exponential cutoff at the highest accelerated
momentum, p_{max}(t). An analytic form of the exponential cutoff is also
suggested.Comment: 17 pages, 5 figures, to appear in Ap
Self-Similar Evolution of Cosmic-Ray-Modified Quasi-Parallel Plane Shocks
Using an improved version of the previously introduced CRASH (Cosmic Ray
Acceleration SHock) code, we have calculated the time evolution of cosmic-ray
(CR) modified quasi-parallel plane shocks for Bohm-like diffusion, including
self-consistent models of Alfven wave drift and dissipation, along with thermal
leakage injection of CRs. The new simulations follow evolution of the CR
distribution to much higher energies than our previous study, providing a
better examination of evolutionary and asymptotic behaviors. The postshock CR
pressure becomes constant after quick initial adjustment, since the evolution
of the CR partial pressure expressed in terms of a momentum similarity variable
is self-similar. The shock precursor, which scales as the diffusion length of
the highest energy CRs, subsequently broadens approximately linearly with time,
independent of diffusion model, so long as CRs continue to be accelerated to
ever-higher energies. This means the nonlinear shock structure can be described
approximately in terms of the similarity variable, x/(u_s t), where u_s is the
shock speed once the postshock pressure reaches an approximate time asymptotic
state. As before, the shock Mach number is the key parameter determining the
evolution and the CR acceleration efficiency, although finite Alfven wave drift
and wave energy dissipation in the shock precursor reduce the effective
velocity change experienced by CRs, so reduce acceleration efficiency
noticeably, thus, providing a second important parameter at low and moderate
Mach numbers.Comment: 29 pages, 8 figure
Young wall realization of crystal graphs for U_q(C_n^{(1)})
We give a realization of crystal graphs for basic representations of the
quantum affine algebra U_q(C_n^{(1)}) using combinatorics of Young walls. The
notion of splitting blocks plays a crucial role in the construction of crystal
graphs
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