Biomedical subjects

Dieter Armbruster

Publications and source records attributed to Dieter Armbruster.

4 recordsLinked to original sources

PubMed2003

Localized solutions in parametrically driven pattern formation.

The Mathieu partial differential equation (PDE) is analyzed as a prototypical model for pattern formation due to parametric resonance. After averaging and scaling, it is shown to be a perturbed nonlinear Schrödinger equation (NLS). Adiabatic perturbation theory for solitons is applied to determine which solitons of the NLS survive the perturbation due to damping and parametric forcing. Numerical simulations compare the perturbation results to the dynamics of the Mathieu PDE. Stable and weakly unstable soliton solutions are identified. They are shown to be closely related to oscillons found in parametrically driven sand experiments.

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PubMed2001

Parametrically forced pattern formation.

Pattern formation in a nonlinear damped Mathieu-type partial differential equation defined on one space variable is analyzed. A bifurcation analysis of an averaged equation is performed and compared to full numerical simulations. Parametric resonance leads to periodically varying patterns whose spatial structure is determined by amplitude and detuning of the periodic forcing. At onset, patterns appear subcritically and attractor crowding is observed for large detuning. The evolution of patterns under the increase of the forcing amplitude is studied. It is found that spatially homogeneous and temporally periodic solutions occur for all detuning at a certain amplitude of the forcing. Although the system is dissipative, spatial solitons are found representing domain walls creating a phase jump of the solutions. Qualitative comparisons with experiments in vertically vibrating granular media are made. (c) 2001 American Institute of Physics.

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PubMed1999

Noise and O(1) amplitude effects on heteroclinic cycles.

The dynamics of structurally stable heteroclinic cycles connecting fixed points with one-dimensional unstable manifolds under the influence of noise is analyzed. Fokker-Planck equations for the evolution of the probability distribution of trajectories near heteroclinic cycles are solved. The influence of the magnitude of the stable and unstable eigenvalues at the fixed points and of the amplitude of the added noise on the location and shape of the probability distribution is determined. As a consequence, the jumping of solution trajectories in and out of invariant subspaces of the deterministic system can be explained. (c) 1999 American Institute of Physics.

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PubMed1994

kltool: A tool to analyze spatiotemporal complexity.

We announce the availability of a software package, called kltool, that can extract phase space information from complex spatiotemporal data via the Karhunen-Loeve analysis. Data generated by the periodic, quasiperiodic or chaotic evolution of a small number of spatially coherent structures can be processed. A key feature of kltool is that it allows the user to interact easily with the data processing and its graphical display. We illustrate the use of kltool on numerical data from the Kuramoto-Sivashinsky equation and laboratory data from a flame experiment.

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