Biomedical subjects

Jan Nagler

Publications and source records attributed to Jan Nagler.

5 recordsLinked to original sources

PubMed2005

Directed and undirected multiurn models in a one-dimensional ring.

The flea model by Ehrenfest describes the jumps of a fixed number of fleas between two dogs. In each time step a randomly selected flea jumps on the other dog. We study directed and undirected multiurn models in a one-dimensional ring. The introduced models represent generalizations of three recently proposed multiurn models which themselves are generalizations of Ehrenfest's model. The models are solved analytically. For the directed case we find oscillations of the average number of balls or fleas in a certain urn before the system reaches its equilibrium state. The discussed models may serve as basic models of dynamics of granular media in connected periodic compartment systems.

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PubMed2005

1/f(alpha) spectra in elementary cellular automata and fractal signals.

We systematically compute the power spectra of the one-dimensional elementary cellular automata introduced by Wolfram. On the one hand our analysis reveals that one automaton displays 1/f spectra though considered as trivial, and on the other hand that various automata classified as chaotic or complex display no 1/f spectra. We model the results generalizing the recently investigated Sierpinski signal to a class of fractal signals that are tailored to produce 1/f(alpha) spectra. From the widespread occurrence of (elementary) cellular automata patterns in chemistry, physics, and computer sciences, there are various candidates to show spectra similar to our results.

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PubMed2005

Crash test for the restricted three-body problem.

The restricted three-body problem serves to investigate the chaotic behavior of a small body under the gravitational influence of two heavy primary bodies. We analyze numerically the phase space mixing of bounded motion, escape, and crash in this simple model of (chaotic) celestial mechanics. The presented extensive numerical analysis reveals a high degree of complexity. We extend the recently presented findings for the Copenhagen case of equal main masses to the general case of different primary body masses. Collisions of the small body onto the primaries are comparatively frequent, and their probability displays a scale-free dependence on the size of the primaries as shown for the Copenhagen case. Interpreting the crash as leaking in phase space the results are related to both chaotic scattering and the theory of leaking Hamiltonian systems.

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PubMed2004

Sierpinski signal generates 1/f alpha spectra.

We investigate the row sum of the binary pattern generated by the Sierpinski automaton: Interpreted as a time series we calculate the power spectrum of this Sierpinski signal analytically and obtain a unique rugged fine structure with underlying power law decay with an exponent of approximately 1.15. Despite the simplicity of the model, it can serve as a model for 1/f(alpha) spectra in a certain class of experimental and natural systems such as catalytic reactions and mollusc patterns.

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PubMed2004

Crash test for the Copenhagen problem.

The Copenhagen problem is a simple model in celestial mechanics. It serves to investigate the behavior of a small body under the gravitational influence of two equally heavy primary bodies. We present a partition of orbits into classes of various kinds of regular motion, chaotic motion, escape and crash. Collisions of the small body onto one of the primaries turn out to be unexpectedly frequent, and their probability displays a scale-free dependence on the size of the primaries. The analysis reveals a high degree of complexity so that long term prediction may become a formidable task. Moreover, we link the results to chaotic scattering theory and the theory of leaking Hamiltonian systems.

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