Publications with Abstracts by Alfred Hübler (2003)

1. * J. Xu, A. Hübler, Enhanced Diffraction Pattern from a Fibonacci Chain, Phys.Rev.B 67, 2242XX (2003)
   Abstract: We study the diffraction patterns of a one-dimensional Fibonnaci chain from quasiperiodic pulse trains. We find a single prominent peak when the dynamics of the incident wave matches the arrangement of the scatterers, that is, when the pulse train and the scatterers are in resonance. The maximum diffraction angle and the resonant pulse train determine the position of the scatterers. These results may provide a methodology for the quality control of Fibonnaci multilayers, and may have further impact when extended to higher dimensions.

   Reprint

2. G. Foster, A. Hübler, Robust and Efficient Interaction with Complex Systems, Proceedings of 2003 IEEE International Conference on Systems, Man & Cybernetics, 2029-2034 (2003).
   Abstract: Low-dimensional chaotic map dynamics has been successfully used to predict the dynamics of high-dimensional systems far from equilibrium. For control, low-dimensional models can be used only if the the control force is very small, otherwise hidden degrees of freedom may become excited. We study the control of chaotic map dynamics with extremely small forcing functions.. We find that the smallest forcing function, which is called a resonant forcing function, echoes the natural dynamics of the system. This means, when the natural dynamics of the system is irregular, the optimal forcing function is irregular too. If the natural dynamics contains a certain periodicity, the optimal forcing function contains that periodicity too. We show that such controls are effective even if the system has hidden degrees of freedom and if the probes of the control system have a low resolution. Further we show that resonant forcing functions of chaotic systems decrease exponentially, where the rate equals the Liapunov exponent of the unperturbed system. We apply resonant forcing functions for efficient control of chaotic systems and for system identification.

   Reprint

3. * D. Smyth, A. Hübler, A Conductivity-Dependent Phase Transition from Closed-Loop to Open-Loop Dendritic Networks, Complexity 9, 56-60 (2003).
   Abstract: Motivated by a principle of minimum dissipation per channel length, we introduce a model for branching, hierarchical networks in an open, dissipative system. Global properties of the resulting structures are observed to scale with a ratio of conductivity in the dendrite material to conductivity in the lattice material. Beyond a critical conductivity ratio, the resulting structures are naturally self-avoiding and possess scale-independent branching ratios. Our findings suggest that the conductivity ratio determines the geometric properties of naturally-arising dendritic structures. We discuss empirical verification in the context of a system of self-organizing agglomerates of metal particles on castor oil.

   Reprint

4. A. Barr and A. Hübler, Adaptation to the Edge of Chaos in a Non-Isothermal Autocatalator, submitted to J. Chem. Phys.
   Abstract: Numerical simulations of a low-pass filtered feedback from a dynamical variable to the system parameter of a non-isothermal autocatalator are examined. Parameter values for which the limiting dynamics is chaotic are found to evolve to nearby values yielding periodic dynamics while parameter values yielding periodic dynamics are uneffected. The system thus exhibits adaptation to the edge of chaos. This suggests that low-pass filters, believed to be quite common in chemical reactions, may be one reason few chaotic reactions have been observed experimentally.

   Preprint