Chaos in dissipativen Systemen

Leven, R.; Koch, B. P.; Pompe, Bernd

doi:10.1007/978-3-322-84175-9

Cited by 42 publications

(19 citation statements)

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“…The dynamic simulations reach a cyclic steady state (CSS) after a certain number of cycles, which can vary significantly depending on the external devices and the operating parameters. A stopping criterion based on a Poincaré map [25] is used to identify the CSS in each simulation. Typically, around 15 complete cycles are required.…”

Section: Mathematical Model and Optimizationmentioning

confidence: 99%

Integrated Simulated Moving Bed Processes for Production of Single Enantiomers

2011

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Based on the assumption of true moving bed processes it was demonstrated that integration of a racemization reaction into a continuous chromatographic process can improve the production of single enantiomers. In view of possible practical implementations, the analysis is extended to more realistic simulated moving bed (SMB) processes. Superstructures of SMB-based systems are defined that reflect the three general concepts of flow sheet, partial, and total process integration. Process candidates are generated by simultaneously optimizing process structure and operating conditions. Optimal process setups are determined under idealized conditions as a function of the purity requirement. The best performance is achieved by fully integrated processes. These are compared under more realistic conditions to units with side reactors. The results indicate that a simple fully integrated SMB system with three zones is a particularly promising new process option. The new concept is investigated in detail to identify relevant practical aspects.

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Section: Mathematical Model and Optimizationmentioning

confidence: 99%

Integrated Simulated Moving Bed Processes for Production of Single Enantiomers

2011

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“…Each dimension is connected with one Lyapunov exponent that indicates the stretching, invariance or shrinking of the assigned attractor direction by values greater than, equal to or smaller than zero (see e.g. Leven, Koch and Pompe, 1989). The reconstruction of the phase space from a chaotic time series by the embedding technique (e.g.…”

Section: Chaotic Behaviourmentioning

confidence: 99%

Series resonance circuit with ferroelectric capacitor

et al. 1993

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A series resonance circuit under sinuousoidal driving is investigated experimentally. The inductance consists of an air coil. The capacitance is made up of a ferroelectric material that introduces its nonlinear dielectric properties into the circuit. The dynamical system linear coil -nonlinear capacaitor shows an interesting behaviour. The phase portrait differs in general from the ellipse of the harmonic oscillator. For appropriate external conditions period doubling sequences, chaos and therein enclosed periodic windows might occur. Starting from a cubic nonlinearity of the dielectric properties a Duffing equation is proposed as a model for periodic behaviour of the series resonance circuit. Simulations of experimentally recorded phase portraits yield good agreement between experiment and model.

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“…Information is lost, or conversely, more information is required to specify the system with the original precision; the entropy has increased. The rate of information change is called Kolmogorov Entropy [1][2][3][11][12][13][14]. It is defined as:…”

Section: Kolmogorov Entropymentioning

confidence: 99%