Biomedical subjects

T Tel

Publications and source records attributed to T Tel.

5 recordsLinked to original sources

PubMed2000

Multifractal structure of chaotically advected chemical fields

The structure of the concentration field of a decaying substance produced by chemical sources and advected by a smooth incompressible two-dimensional flow is investigated. We focus our attention on the nonuniformities of the Holder exponent of the resulting filamental chemical field. They appear most evidently in the case of open flows where irregularities of the field exhibit strong spatial intermittency as they are restricted to a fractal manifold. Nonuniformities of the Holder exponent of the chemical field in closed flows appears as a consequence of the nonuniform stretching of the fluid elements. We study how this affects the scaling exponents of the structure functions, displaying anomalous scaling, and relate the scaling exponents to the distribution of local Lyapunov exponents of the advection dynamics. Theoretical predictions are compared with numerical experiments.

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PubMed2000

Topological scaling and gap filling at crisis

Scaling laws associated with an interior crisis of chaotic dynamical systems are studied. We argue that open gaps of the chaotic set become densely filled at the crisis due to the sudden appearance of unstable periodic orbits with extremely long periods. We formulate a scaling theory for the associated growth of the topological entropy.

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PubMed2000

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. An 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.

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PubMed2000

Fluctuation theorems for entropy production in open systems

We derive a fluctuation theorem to describe entropy fluctuations in steady states of systems with density gradients due to open boundaries. The fluctuations are related to the growth rate of the phase-space density, instead of the phase-space contraction rate. Explicit derivations are presented for a multibaker map, but the arguments are rather general, and should hold for a much wider class of dynamical systems. A comparison with recent results for stochastic systems is also given.

Journal Article↗

PubMed2000

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, in addition to 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 the 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 thermostating algorithm, similar to the one considered in nonequilibrium molecular dynamics.

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