8,348 research outputs found
Viscosity methods giving uniqueness for martingale problems
Let be a complete, separable metric space and be an operator on
. We give an abstract definition of viscosity sub/supersolution of the
resolvent equation and show that, if the comparison principle
holds, then the martingale problem for has a unique solution. Our proofs
work also under two alternative definitions of viscosity sub/supersolution
which might be useful, in particular, in infinite dimensional spaces, for
instance to study measure-valued processes.
We prove the analogous result for stochastic processes that must satisfy
boundary conditions, modeled as solutions of constrained martingale problems.
In the case of reflecting diffusions in , our assumptions
allow to be nonsmooth and the direction of reflection to be degenerate.
Two examples are presented: A diffusion with degenerate oblique direction of
reflection and a class of jump diffusion processes with infinite variation jump
component and possibly degenerate diffusion matrix
Models of granular ratchets
We study a general model of granular Brownian ratchet consisting of an
asymmetric object moving on a line and surrounded by a two-dimensional granular
gas, which in turn is coupled to an external random driving force. We discuss
the two resulting Boltzmann equations describing the gas and the object in the
dilute limit and obtain a closed system for the first few moments of the system
velocity distributions. Predictions for the net ratchet drift, the variance of
its velocity fluctuations and the transition rates in the Markovian limit, are
compared to numerical simulations and a fair agreement is observed.Comment: 15 pages, 4 figures, to be published on Journal of Statistical
Mechanics: Theory and Experiment
Jets and outflows in Radio Galaxies: implications for AGN feedback
One of the main debated astrophysical problems is the role of the AGN
feedback in galaxy formation. It is known that massive black holes have a
profound effect on the formation and evolution of galaxies, but how black holes
and galaxies communicate is still an unsolved problem. For Radio Galaxies,
feedback studies have mainly focused on jet/cavity systems in the most massive
and X-ray luminous galaxy clusters. The recent high-resolution detection of
warm absorbers in some Broad Line Radio Galaxies allow us to investigate the
interplay between the nuclear engine and the surrounding medium from a
different perspective. We report on the detection of warm absorbers in two
Broad Line Radio Galaxies, 3C 382 and 3C 390.3, and discuss the physical and
energetic properties of the absorbing gas. Finally, we attempt a comparison
between radio-loud and radio-quiet outflows.Comment: To be published in the proceedings of High Energy Phenomena in
Relativistic Outflows III (HEPRO III, IJMPCS). 4 pages, 2 figure
Protein accumulation in the endoplasmic reticulum as a non-equilibrium phase transition
Several neurological disorders are associated with the aggregation of
aberrant proteins, often localized in intracellular organelles such as the
endoplasmic reticulum. Here we study protein aggregation kinetics by mean-field
reactions and three dimensional Monte carlo simulations of diffusion-limited
aggregation of linear polymers in a confined space, representing the
endoplasmic reticulum. By tuning the rates of protein production and
degradation, we show that the system undergoes a non-equilibrium phase
transition from a physiological phase with little or no polymer accumulation to
a pathological phase characterized by persistent polymerization. A combination
of external factors accumulating during the lifetime of a patient can thus
slightly modify the phase transition control parameters, tipping the balance
from a long symptomless lag phase to an accelerated pathological development.
The model can be successfully used to interpret experimental data on
amyloid-\b{eta} clearance from the central nervous system
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