Hans Lustfeld

Statistical properties of the noisy on - off intermittency

The dependence of the escape time on the deviation from the critical point is investigated for the noisy on - off intermittency. The power-law scaling behaviour is destroyed by the noise in a wide region above the critical point. In the general case the width of the region decreases logarithmically with the decrease in the noise amplitude. Below the critical point the noise induced escape time is sensitive to the statistical properties of the chaotic driving signal. Universal exponential dependence holds only for the Gaussian approximation.

Reconstruction of Electric Currents in a Fuel Cell by Magnetic Field Measurements

In this paper the tomographic problem arising in the diagnostics of a fuel cell is discussed. This is concerned with how well the electric current density j (r) be reconstructed by measuring its external magnetic field. We show that (i) exploiting the fact that the current density has to comply with Maxwells equations it can, in fact, be reconstructed at least up to a certain resolution, (ii) the functional connection between the resolution of the current density and the relative precision of the measurement devices can be obtained, and (iii) a procedure can be applied to determine the optimum measuring positions, essentially decreasing the number of measuring points and thus the time scale of measurable dynamical perturbations-without a loss of fine resolution. We present explicit results for (i)-(iii) by applying our formulas to a realistic case of an experimental direct methanol fuel cell.

The correlation functions near intermittency in a one-dimensional Piecewise parabolic map

Piecewise parabolic maps constitute a family of maps in the fully developed chaotic state and depending on a parameter that can be smoothly tuned to a weakly intermittent situation. Approximate analytic expressions are derived for the corresponding correlation functions. These expressions produce power-law decay at intermittency and a crossover from power-law decay to exponential decay below intermittency. It is shown that the scaling functions and the exponent of the power law depend on the kind of the correlations.

New approach to the correlation spectrum near intermittency: A quantum mechanical analogy

The correlation spectrum of fully developed one-dimensional mappings is studied near and at a weakly intermittent situation. Using a suitable infinitematrix representation, the eigenvalue equation of the Frobenius-Perron operator is approximately reduced to the radial Schrödinger equation of the hydrogen atom. Corrections are calculated by quantum mechanical perturbation theory. Analytical expressions for the spectral properties and correlation functions are derived and checked numerically. Compared to our previous work, the accuracy of the present results is significantly higher owing to the controlled and systematic approximation scheme

Uniqueness of magnetotomography for fuel cells and fuel cell stacks

The criterion for the applicability of any tomographic method is its ability to construct the desired inner structure of a system from external measurements, i.e. to solve the inverse problem. Magnetotomography applied to fuel cells and fuel cell stacks aims at determining the inner current densities from measurements of the external magnetic field. This is an interesting idea since in those systems the inner electric current densities are large, several hundred mA per cm2and therefore relatively high external magnetic fields can be expected. Still the question remains how uniquely the inverse problem can be solved. Here we present a proof that by exploiting Maxwells equations extensively the inverse problem of magnetotomography becomes unique under rather mild assumptions and we show that these assumptions are fulfilled in fuel cells and fuel cell stacks. Moreover, our proof holds true for any other device fulfilling the assumptions listed here. Admittedly, our proof has one caveat: it does not contain an estimate of the precision requirements the measurements need to fulfil for enabling reconstruction of the inner current densities from external magnetic fields.

Simulating 2d Flows with Viscous Vortex Dynamics

Approximate solutions of the two-dimensional Navier–Stokes equation can be constructed as a superposition of viscous Lamb vortices. Requiring minimum deviation from the Navier–Stokes equation, one gets a set of ordinary differential equations for the positions, strength and width of the vortices. We calculate the deviation of the solution from the Navier–Stokes equation in the square norm. The time dependence of this error is determined and discussed.

Chaotic motion on Hamiltonian tori

KAM tori are well known to be that (finite!) part of phase space in which the motion of a weakly perturbed classical Hamiltonian system remains integrable. Moreover, they are barriers in the phase space of systems with two degrees of freedom. The authors show that certain Hamiltonian systems contain invariant non-regular tori with compressible flow. Using as an example an electron moving in electromagnetic fields which are periodic in space they demonstrate: (i) that strange attractors (and repellers) of well known autonomous or (quasi-)periodically time-driven systems may occur on such strange tori; (ii) that one may find barriers consisting of non-regular Hamiltonian tori in systems with any number of degrees of freedom (the flow on such barriers is non-chaotic, though); and (iii) that certain KAM tori transform into non-regular tori-rather than breaking up-when the perturbation becomes strong.