#### Filter Results:

- Full text PDF available (11)

#### Publication Year

2000

2016

- This year (0)
- Last 5 years (8)
- Last 10 years (11)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

The problem of front propagation in a stirred medium is addressed in the case of cellular flows in three different regimes: slow reaction, fast reaction and geometrical optics limit. It is well known that a consequence of stirring is the enhancement of front speed with respect to the nonstirred case. By means of numerical simulations and theoretical… (More)

An efficient approach to the calculation of the e-entropy is proposed. The method is based on the idea of looking at the information content of a string of data, by analyzing the signal only at the instants when the fluctuations are larger than a certain threshold e, i.e., by looking at the exit-time statistics. The practical and theoretical advantages of… (More)

- Karsten Ahnert, Markus Abel
- Computer Physics Communications
- 2007

In the context of the analysis of measured data, one is often faced with the task to differentiate data numerically. Typically, this occurs when measured data are concerned or data are evaluated numerically during the evolution of partial or ordinary differential equations. Usually, one does not take care for accuracy of the resulting estimates of… (More)

- Markus Abel, Karsten Ahnert, Juergen Kurths, Simon Mandelj
- Physical review. E, Statistical, nonlinear, and…
- 2005

We present a nonparametric way to retrieve an additive system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long-term predictions. We apply our method to a modified chaotic Chua oscillator in order to demonstrate its potential.

- Markus Quade, Markus Abel, Kamran Shafi, Robert K. Niven, Bernd R. Noack
- Physical review. E
- 2016

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or simplified models need to be found. We focus on symbolic regression methods as a part of machine learning. These… (More)

- Markus Abel
- I. J. Bifurcation and Chaos
- 2004

This article describes how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by means of backfitting or more general algorithms, like the alternating conditional expectation value one. The method is illustrated by numerically generated… (More)

- Markus Abel, Karsten Ahnert, S. Bergweiler
- Physical review letters
- 2009

Sound generation and interaction are highly complex, nonlinear, and self-organized. Nearly 150 years ago Rayleigh raised the following problem: two nearby organ pipes of different fundamental frequencies sound together almost inaudibly with identical pitch. This effect is now understood qualitatively by modern synchronization theory M. Abel et al. [J.… (More)

In this article, we present investigations on several techniques for numerical differentiation of data. Local techniques are confronted with global approaches and the differences are discussed in detail. Two basic quantities are used for characterization of results: The variance of the difference of the true derivative and its estimate, and the smoothness… (More)

- Marcel Kappel, Markus Abel, Reimund Gerhard
- The Review of scientific instruments
- 2011

Piezoelectric polymers are known for their flexibility in applications, mainly due to their bending ability, robustness, and variable sensor geometry. It is an optimal material for minimal-invasive investigations in vibrational systems, e.g., for wood, where acoustical impedance matches particularly well. Many applications may be imagined, e.g., monitoring… (More)

- Arthur V. Straube, Markus Abel, Arkady Pikovsky
- Physical review letters
- 2004

We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for… (More)