48,369 research outputs found
Properties of solutions of stochastic differential equations driven by the G-Brownian motion
In this paper, we study the differentiability of solutions of stochastic
differential equations driven by the -Brownian motion with respect to the
initial data and the parameter. In addition, the stability of solutions of
stochastic differential equations driven by the -Brownian motion is
obtained
Chaotic cold accretion onto black holes
Using 3D AMR simulations, linking the 50 kpc to the sub-pc scales over the
course of 40 Myr, we systematically relax the classic Bondi assumptions in a
typical galaxy hosting a SMBH. In the realistic scenario, where the hot gas is
cooling, while heated and stirred on large scales, the accretion rate is
boosted up to two orders of magnitude compared with the Bondi prediction. The
cause is the nonlinear growth of thermal instabilities, leading to the
condensation of cold clouds and filaments when t_cool/t_ff < 10. Subsonic
turbulence of just over 100 km/s (M > 0.2) induces the formation of thermal
instabilities, even in the absence of heating, while in the transonic regime
turbulent dissipation inhibits their growth (t_turb/t_cool < 1). When heating
restores global thermodynamic balance, the formation of the multiphase medium
is violent, and the mode of accretion is fully cold and chaotic. The recurrent
collisions and tidal forces between clouds, filaments and the central clumpy
torus promote angular momentum cancellation, hence boosting accretion. On
sub-pc scales the clouds are channelled to the very centre via a funnel. A good
approximation to the accretion rate is the cooling rate, which can be used as
subgrid model, physically reproducing the boost factor of 100 required by
cosmological simulations, while accounting for fluctuations. Chaotic cold
accretion may be common in many systems, such as hot galactic halos, groups,
and clusters, generating high-velocity clouds and strong variations of the AGN
luminosity and jet orientation. In this mode, the black hole can quickly react
to the state of the entire host galaxy, leading to efficient self-regulated AGN
feedback and the symbiotic Magorrian relation. During phases of overheating,
the hot mode becomes the single channel of accretion (with a different cuspy
temperature profile), though strongly suppressed by turbulence.Comment: Accepted by MNRAS: added comments and references. Your feedback is
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On the threshold-width of graphs
The GG-width of a class of graphs GG is defined as follows. A graph G has
GG-width k if there are k independent sets N1,...,Nk in G such that G can be
embedded into a graph H in GG such that for every edge e in H which is not an
edge in G, there exists an i such that both endpoints of e are in Ni. For the
class TH of threshold graphs we show that TH-width is NP-complete and we
present fixed-parameter algorithms. We also show that for each k, graphs of
TH-width at most k are characterized by a finite collection of forbidden
induced subgraphs
Multiple G-It\^{o} integral in the G-expectation space
In this paper, motivated by mathematic finance we introduce the multiple
G-It\^{o} integral in the G-expectation space, then investigate how to
calculate. We get the the relationship between Hermite polynomials and multiple
G-It\^{o} integrals which is a natural extension of the classical result
obtained by It\^{o} in 1951.Comment: 9 page
Dark Energy: Vacuum Fluctuations, the Effective Phantom Phase, and Holography
We aim at the construction of dark energy models without exotic matter but
with a phantom-like equation of state (an effective phantom phase). The first
model we consider is decaying vacuum cosmology where the fluctuations of the
vacuum are taken into account. In this case, the phantom cosmology (with an
effective, observational being less than -1) emerges even for the case
of a real dark energy with a physical equation of state parameter
larger than -1. The second proposal is a generalized holographic model, which
is produced by the presence of an infrared cutoff. It also leads to an
effective phantom phase, which is not a transient one as in the first model.
However, we show that quantum effects are able to prevent its evolution towards
a Big Rip singularity.Comment: 13 pages, 2 figures, revtex4, version to appear in Physical Review
Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators
The aim of the present paper is to study the regularity properties of the
solution of a backward stochastic differential equation with a monotone
generator in infinite dimension. We show some applications to the nonlinear
Kolmogorov equation and to stochastic optimal control
An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation
The classical law of the iterated logarithm (LIL for short)as fundamental
limit theorems in probability theory play an important role in the development
of probability theory and its applications. Strassen (1964) extended LIL to
large classes of functional random variables, it is well known as the
invariance principle for LIL which provide an extremely powerful tool in
probability and statistical inference. But recently many phenomena show that
the linearity of probability is a limit for applications, for example in
finance, statistics. As while a nonlinear expectation--- G-expectation has
attracted extensive attentions of mathematicians and economists, more and more
people began to study the nature of the G-expectation space. A natural question
is: Can the classical invariance principle for LIL be generalized under
G-expectation space? This paper gives a positive answer. We present the
invariance principle of G-Brownian motion for the law of the iterated logarithm
under G-expectation
The Tychonoff uniqueness theorem for the G-heat equation
In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat
equation
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