100,582 research outputs found
The Fluctuation Theorem as a Gibbs Property
Common ground to recent studies exploiting relations between dynamical
systems and non-equilibrium statistical mechanics is, so we argue, the standard
Gibbs formalism applied on the level of space-time histories. The assumptions
(chaoticity principle) underlying the Gallavotti-Cohen fluctuation theorem make
it possible, using symbolic dynamics, to employ the theory of one-dimensional
lattice spin systems. The Kurchan and Lebowitz-Spohn analysis of this
fluctuation theorem for stochastic dynamics can be restated on the level of the
space-time measure which is a Gibbs measure for an interaction determined by
the transition probabilities. In this note we understand the fluctuation
theorem as a Gibbs property as it follows from the very definition of Gibbs
state. We give a local version of the fluctuation theorem in the Gibbsian
context and we derive from this a version also for some class of spatially
extended stochastic dynamics
Addressing Complexity in Laboratory Experiments: The Scaling of Dilute Multiphase Flows in Magmatic Systems.
The kinematic and dynamic scaling of dilute multiphase mixtures in magmatic systems is the only guarantee for the geological verisimilitude of laboratory experiments. We present scaling relations that can provide a more complete framework to scale dilute magmatic systems because they explicitly take into account the complexity caused by the feedback between particles (crystal, bubble, or pyroclast) and the continuous phase (liquid or gas). We consider three canonical igneous systems: magma chambers, volcanic plumes, and pyroclastic surges, and we provide estimates of the proposed scaling relations for published experiments on those systems. Dilute magmatic mixtures can display a range of distinct dynamical regimes that we characterize with a combination of average (Eulerian) properties and instantaneous (Lagrangian) variables. The Eulerian properties of the mixtures yield the Reynolds number (Re), which indicates the level of unsteadiness in the continuous phase. The Lagrangian acceleration of particles is a function of the viscous drag and gravity forces, and from these two forces are derived the Stokes number (ST) and the stability number (ÎŁT), two dimensionless numbers that describe the dynamic behavior of the particles within the mixture. The compilation of 17 experimental studies relevant for pyroclastic surges and volcanic plumes indicates that there is a need for experiments above the mixing transition (Re>104), and for scaling ST and ÎŁT. Among the particle dynamic regimes present in surges and plumes, some deserve special attention, such as the role of mesoscale structures on transport and sedimentary processes, or the consequences of the transition to turbulence on particle gathering and dispersal. The compilation of 7 experimental studies relevant to magma bodies indicates that in the laminar regime, crystals mostly follow the motion of the melt, and thus the physical state of the system can be approximated as single phase. In the transition to turbulence, magmas can feature spatially heterogeneous distributions of laminar regions and important velocity gradients. This heterogeneity has a strong potential for crystals sorting. In conclusion, the Re-ST-ÎŁT framework demonstrates that, despite numerous experimental studies on processes relevant to magmatic systems, some and perhaps most, geologically important parameter ranges still need to be addressed at the laboratory scale
Simulation and Bisimulation over Multiple Time Scales in a Behavioral Setting
This paper introduces a new behavioral system model with distinct external
and internal signals possibly evolving on different time scales. This allows to
capture abstraction processes or signal aggregation in the context of control
and verification of large scale systems. For this new system model different
notions of simulation and bisimulation are derived, ensuring that they are,
respectively, preorders and equivalence relations for the system class under
consideration. These relations can capture a wide selection of similarity
notions available in the literature. This paper therefore provides a suitable
framework for their comparisonComment: Submitted to 22nd Mediterranean Conference on Control and Automatio
Role of unstable periodic orbits in phase transitions of coupled map lattices
The thermodynamic formalism for dynamical systems with many degrees of
freedom is extended to deal with time averages and fluctuations of some
macroscopic quantity along typical orbits, and applied to coupled map lattices
exhibiting phase transitions. Thereby, it turns out that a seed of phase
transition is embedded as an anomalous distribution of unstable periodic
orbits, which appears as a so-called q-phase transition in the spatio-temporal
configuration space. This intimate relation between phase transitions and
q-phase transitions leads to one natural way of defining transitions and their
order in extended chaotic systems. Furthermore, a basis is obtained on which we
can treat locally introduced control parameters as macroscopic ``temperature''
in some cases involved with phase transitions.Comment: 13 pages, 9 figures; further explanation and 2 figures are added
(minor revision
Abstractions of Stochastic Hybrid Systems
In this paper we define a stochastic bisimulation concept for a very general class of stochastic hybrid systems, which subsumes most classes of stochastic hybrid systems. The definition of this bisimulation builds on the concept of zigzag morphism defined for strong Markov processes.
The main result is that this stochastic bisimulation is indeed an equivalence relation. The secondary result is that this bisimulation relation for the stochastic hybrid system models used in this paper implies the same
kind of bisimulation for their continuous parts and respectively for their jumping structures
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