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- aerosol size distribution (2)
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Institut
- Interdisziplinäres Zentrum für Dynamik komplexer Systeme (120) (entfernen)
The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection
(1999)
The ill-posed problem of aerosol distribution determination from a small number of backscatter and extinction lidar measurements was solved successfully via a hybrid method by a variable dimension of projection with B-Splines. Numerical simulation results with noisy data at different measurement situations show that it is possible to derive a reconstruction of the aerosol distribution only with 4 measurements.
The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection
(1999)
Laser beam melt ablation - a contact-free machining process - offers several advantages compared to conventional processing mechanisms: there exists no tool wear and even extremely hard or brittle materials can be processed. During ablation the workpiece is molten by a CO2-laser beam, this melt is then driven out by the impulse of a process gas. The idea behind laser ablation is rather simple, but it has a major limitation in practical applications: with increasing ablation rates surface quality of the workpiece processed declines rapidly. At high ablation rates, depending on the process parameters different periodic-like structures can be observed on the ablated surface. These structures show a dependence on the line energy, which has been identified as a fundamental control parameter. In dependence on this parameter several regimes with different behaviours of the process have been separated. These regimes are distinguishable as well in the surfaces obtained as in the signals gained by the measurement of the process emissions. Further aim is to identify the different modes of the system and reach a deeper understanding of the dynamics of the molten material in order to understand the formation of these surface structures. With this it should be possible to influence the system in the direction of avoiding structure formation even at high ablation rates. Relying on the results on-line monitoring and control of the process should be studied.
We investigate numerically the appearance of heteroclinic behavior in a three-dimensional, buoyancy-driven fluid layer with stress-free top and bottom boundaries, a square horizontal periodicity with a small aspect ratio, and rotation at low to moderate rates about a vertical axis. The Prandtl number is 6.8. If the rotation is not too slow, the skewed-varicose instability leads from stationary rolls to a stationary mixed-mode solution, which in turn loses stability to a heteroclinic cycle formed by unstable roll states and connections between them. The unstable eigenvectors of these roll states are also of the skewed-varicose or mixed-mode type and in some parameter regions skewed-varicose like shearing oscillations as well as square patterns are involved in the cycle. Always present weak noise leads to irregular horizontal translations of the convection pattern and makes the dynamics chaotic, which is verified by calculating Lyapunov exponents. In the nonrotating case, the primary rolls lose, depending on the aspect ratio, stability to traveling waves or a stationary square pattern. We also study the symmetries of the solutions at the intermittent fixed points in the heteroclinic cycle.
We numerically investigate nonlinear asymmetric square patterns in a horizontal convection layer with up-down reflection symmetry. As a novel feature we find the patterns to appear via the skewed varicose instability of rolls. The time-independent nonlinear state is generated by two unstable checkerboard (symmetric square) patterns and their nonlinear interaction. As the bouyancy forces increase, the interacting modes give rise to bifurcations leading to a periodic alternation between a nonequilateral hexagonal pattern and the square pattern or to different kinds of standing oscillations.
In single photon emission computed tomography (SPECT) one is interested in reconstructing the activity distribution f of some radiopharmaceutical. The data gathered suffer from attenuation due to the tissue density µ. Each imaged slice incorporates noisy sample values of the nonlinear attenuated Radon transform (formular at this place in the original abstract) Traditional theory for SPECT reconstruction treats µ as a known parameter. In practical applications, however, µ is not known, but either crudely estimated, determined in costly additional measurements or plainly neglected. We demonstrate that an approximation of both f and µ from SPECT data alone is feasible, leading to quantitatively more accurate SPECT images. The result is based on nonlinear Tikhonov regularization techniques for parameter estimation problems in differential equations combined with Gauss-Newton-CG minimization.
Projection methods based on wavelet functions combine optimal convergence rates with algorithmic efficiency. The proofs in this paper utilize the approximation properties of wavelets and results from the general theory of regularization methods. Moreover, adaptive strategies can be incorporated still leading to optimal convergence rates for the resulting algorithms. The so-called wavelet-vaguelette decompositions enable the realization of especially fast algorithms for certain operators.
The structure of time series and letter sequences is investigated using the concepts of entropy and complexity. First conditional entropy and transinformation are introduced and several generalizations are discussed. Further several measures of complexity are introduced and discussed. The capability of these concepts to describe the structure of time series and letter sequences generated by nonlinear maps, data series from meteorology, astrophysics, cardiology, cognitive psychology and finance is investigated. The relation between the complexity and the predictability of informational strings is discussed. The relation between local order and the predictability of time series is investigated.
We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.