17 research outputs found
Non-Equilibrium Statistical Physics of Currents in Queuing Networks
We consider a stable open queuing network as a steady non-equilibrium system
of interacting particles. The network is completely specified by its underlying
graphical structure, type of interaction at each node, and the Markovian
transition rates between nodes. For such systems, we ask the question ``What is
the most likely way for large currents to accumulate over time in a network
?'', where time is large compared to the system correlation time scale. We
identify two interesting regimes. In the first regime, in which the
accumulation of currents over time exceeds the expected value by a small to
moderate amount (moderate large deviation), we find that the large-deviation
distribution of currents is universal (independent of the interaction details),
and there is no long-time and averaged over time accumulation of particles
(condensation) at any nodes. In the second regime, in which the accumulation of
currents over time exceeds the expected value by a large amount (severe large
deviation), we find that the large-deviation current distribution is sensitive
to interaction details, and there is a long-time accumulation of particles
(condensation) at some nodes. The transition between the two regimes can be
described as a dynamical second order phase transition. We illustrate these
ideas using the simple, yet non-trivial, example of a single node with
feedback.Comment: 26 pages, 5 figure
Characteristic Crack Dimensions of Saturated Drying Soils: Theory and Applications
Rosana G. Moreira, Editor-in-Chief; Texas A&M UniversityThis is a Technical Paper from International Commission of Agricultural Engineering (CIGR, Commission Internationale du Genie Rural) E-Journal Volume 4 (2002): V.Y. Chertkov. Characteristic Crack Dimensions of Saturated Drying Soils: Theory and Applications. Vol. IV. December 2002
Linear PDEs and eigenvalue problems corresponding to ergodic stochastic optimization problems on compact manifolds
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