Author
W. Eberl
Bio: W. Eberl is an academic researcher from Technische Universität München. The author has contributed to research in topics: Separable partial differential equation & Exponential integrator. The author has an hindex of 1, co-authored 1 publications receiving 4 citations.
Papers
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TL;DR: The stroboscopic map of nonlinear dynamical systems can be described by means of a series expansion with only few non-trivial coefficients, provided that the frequency of the stroboscope coincides with the basic frequency of an oscillator.
Abstract: The stroboscopic map of some nonlinear dynamical systems can be described by means of a series expansion with only few non-trivial coefficients, provided that the frequency of the stroboscope coincides with the basic frequency of the oscillator. An analytic representation of such a ‘simple’ map can be obtained by the following two methods: (i) analytical integration of the ordinary differential equation, or (ii) numerical integration on a discrete grid scheme and subsequent approximation by an appropriate series of functions.
4 citations
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TL;DR: In this article, Shah and Ramachandran considered weak space charge effects in an rf trap and obtained an analytic expression for the time varying distribution function of the 1D plasma, which was shown to be a Maxwellian up to the lowest order in nonlinearity.
Abstract: Exact solutions for one-dimensional (1D) plasma dynamics in an rf trap are known when space charge effects are neglected [K. Shah and H. S. Ramachandran, Phys. Plasmas 15, 062303 (2008)]. In this work, weak space charge effects in an rf trap are considered. An analytic expression for the time varying distribution function of the 1D plasma is obtained. It is shown that the plasma is a Maxwellian up to the lowest order in nonlinearity and that the spatially constant temperature periodically oscillates in time at the same rate as the rf frequency. It was shown by Krapchev [Phys. Rev. Lett. 42, 497 (1979)] that the time averaged distribution function is double humped with respect to velocity beyond a certain threshold in space. The time average of the complete time varying distribution function is obtained and some of the predictions of Krapchev are recovered, while also finding discrepancies. The relationship between stroboscopic orbits and the time averaged ponderomotive orbit are obtained for such traps.
16 citations
TL;DR: The interpolated Poincare map is proposed in this article based on numerical integration in one period or less and spline interpolation, which is illustrated via a study of mixing of fluids in a co-rotating discontinuous cavity flow.
Abstract: The interpolated Poincare map is proposed based on numerical integration in one period or less and spline interpolation. Efficiency and applicability of this method is illustrated via a study of mixing of fluids in a co-rotating discontinuous cavity flow.
5 citations
TL;DR: In this article, an iterative, rigorous algebraic method for the calculation of the coefficients of a Taylor expansion of a stroboscopic map from ODEs with not necessarily small nonlinearities is presented.
1 citations
TL;DR: In this paper, a method for nonlinear system identification, based on the technique of interpolated mapping, is formulated, where the input to the procedure is a map, taking initial conditions on a regular grid to their images after a fixed time step.