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Bifurcations in rotating spherical shell convection under the influence of differential rotation
(2021)
The bifurcations of thermal convection in a rotating spherical shell heated from the inner sphere and driven by the buoyancy of a central gravity field are studied numerically. This model of spherical Rayleigh-Benard convection describes large-scale convection in planets and in the outer zones of celestial bodies. In this work, the influence of an additionally imposed differential rotation of the inner sphere with respect to the outer one on the heat transfer and, more generally, on the whole bifurcation structure is investigated. In addition to numerical simulations, path-following techniques are applied in order to compute both stable and unstable solution branches. The dynamics and the heat transfer are essentially determined by a global bifurcation, which we have identified as a homoclinic bifurcation that consists of a collision of a stable modulated rotating with an unstable rotating wave.
We apply linear and nonlinear methods to study the properties of surfaces generated by a laser beam melt ablation process. As a result we present a characterization and ordering of the surfaces depending on the adjusted process parameters. Our findings give some insight into the performance of two widely applied multifractal analysis methods-the detrended fluctuation analysis and the wavelet transform modulus maxima method-on short real world data
The problem of the existence of strange nonchaotic attractors (SNA's) in autonomous systems is discussed. It is demonstrated that the recently reported example of a SNA in an autonomous system [V. S. Anishchenko et al., Phys. Rev. E 54, 3231 (1996)] is in fact a chaotic attractor with positive largest Lyapunov exponent.
The quasiperiodically forced logistic map is analyzed at the terminal point of the torus-doubling bifurcation curve, where the dynamical regimes of torus, doubled torus, strange nonchaotic attractor, and chaos meet. Using the renormalization group approach we reveal scaling properties both for the critical attractor and for the parameter plane topography near the critical point.
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.
Aspects of open ocean deep convection variability are explored with a two-box model. In order to place the model in a region of parameter space relevant to the real ocean, it is fitted to observational data from the Labrador Sea. A systematic fit to OWS Bravo data allows us to determine the model parameters and to locate the position of the Labrador Sea on a stability diagram. The model suggests that the Labrador Sea is in a bistable regime where winter convection can be either ?on? or ?off?, with both these possibilities being stable climate states. When shifting the surface buoyancy forcing slightly to warmer or fresher conditions, the only steady solution is one without winter convection. We then introduce short-term variability by adding a noise term to the surface temperature forcing, turning the box model into a stochastic climate model. The surface forcing anomalies generated in this way induce jumps between the two model states. These state transitions occur on the interannual to decadal timescale. Changing the average surface forcing towards more buoyant conditions lowers the frequency of convection. However, convection becomes more frequent with stronger variability in the surface forcing. As part of the natural variability, there is a non-negligible probability for decadal interruptions of convection. The results highlight the role of surface forcing variability for the persistence of convection in the ocean.
Towards a better understanding of laser beam melt ablation using methods of statistical analysis
(2002)
Laser beam melt ablation, as a contact free machining process, offers several advantages compared to conventional processing mechanisms. Although the idea behind it is rather simple, the process has a major limitation: with increasing ablation rate surface quality of the workpiece processed declines rapidly. The structures observed show a clear dependence of the line energy. In dependence of this parameter several regimes of the process have been separated. These are clearly distinguishable as well in the surfaces obtained as in the signals gained by the measurement of the process emissions which is the observed quantity chosen.