2,981 research outputs found
Thermodynamic Cross-Effects from Dynamical Systems
We give a thermodynamically consistent description of simultaneous heat and
particle transport, as well as of the associated cross-effects, in the
framework of a chaotic dynamical system, a generalized multibaker map. Besides
the density, a second field with appropriate source terms is included in order
to mimic, after coarse graining, a spatial temperature distribution and its
time evolution. A new expression is derived for the irreversible entropy
production in a steady state, as the average of the growth rate of the relative
density, a unique combination of the two fields.Comment: 4 pages, 2 postscript figure
A MultiBaker Map for Thermodynamic Cross-Effects in Dynamical Systems
A consistent description of simultaneous heat and particle transport,
including cross effects, and the associated entropy balance is given in the
framework of a deterministic dynamical system. This is achieved by a multibaker
map where, besides the phase-space density of the multibaker, a second field
with appropriate source terms is included in order to mimic a spatial
temperature distribution and its time evolution. Conditions are given to ensure
consistency in an appropriately defined continuum limit with the thermodynamic
entropy balance. They leave as the only free parameter of the model the entropy
flux let directly into a surroundings. If it vanishes in the bulk, the
transport properties of the model are described by the thermodynamic transport
equations. Another choice leads to a uniform temperature distribution. It
represents transport problems treated by means of a thermostatting algorithm,
similar to the one considered in non-equilibrium molecular dynamics.Comment: 18 pages, 3 postscript figure
Escape-rate formalism, decay to steady states, and divergences in the entropy-production rate
In summer 1997 we were sitting with Bob Dorfman and a few other friends
interested in chaotic systems and transport theory on a terrace close to
Oktogon in Budapest. While taking our (decaf) coffee after a very nice Italian
meal, we discussed about logarithmic divergences in the entropy production of
systems with absorbing boundary conditions and their consequences for the
escape-rate formalism. It was guessed at that time that the problem could be
resolved by a careful discussion of the physical content of the absorbing
boundary conditions. To our knowledge a thorough analysis of this long-standing
question is still missing. We dedicate it hereby to Bob on occasion of his 65th
birthday.Comment: 16 pages; RevTex 4 with graphicx package; eps-figure
Termination Detection of Local Computations
Contrary to the sequential world, the processes involved in a distributed
system do not necessarily know when a computation is globally finished. This
paper investigates the problem of the detection of the termination of local
computations. We define four types of termination detection: no detection,
detection of the local termination, detection by a distributed observer,
detection of the global termination. We give a complete characterisation
(except in the local termination detection case where a partial one is given)
for each of this termination detection and show that they define a strict
hierarchy. These results emphasise the difference between computability of a
distributed task and termination detection. Furthermore, these
characterisations encompass all standard criteria that are usually formulated :
topological restriction (tree, rings, or triangu- lated networks ...),
topological knowledge (size, diameter ...), and local knowledge to distinguish
nodes (identities, sense of direction). These results are now presented as
corollaries of generalising theorems. As a very special and important case, the
techniques are also applied to the election problem. Though given in the model
of local computations, these results can give qualitative insight for similar
results in other standard models. The necessary conditions involve graphs
covering and quasi-covering; the sufficient conditions (constructive local
computations) are based upon an enumeration algorithm of Mazurkiewicz and a
stable properties detection algorithm of Szymanski, Shi and Prywes
Total algorithms
We define the notion of total algorithms for networks of processes. A total algorithm enforces that a "decision" is taken by a subset of the processes, and that participation of all processes is required to reach this decision. Total algorithms are an important building block in the design of distributed algorithms. For some important network control problems it can be shown that an algorithm solving it is necessarily total, and that any total algorithm can solve the problem. We study some total algorithms for a variety of network topologies. Constructions are shown to derive algorithms for Mutual Exclusion, Election, and Distributed Infirnum Approximation from arbitrary total algorithms. The paper puts many results and paradigms about designing distributed algorithms in a general framework.
This report oulines several other works of the author. Total algorithms, their properties, and some additional examples, as well as traversal algorithms and the time complexity of distributed algorithms are studied in [Tel94, Chap.6]. The construction of algorithms for distributed infirnum approximation is treated in [CBT94, Tel86] and [Tel91, Sec. 4.1]
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