3,719 research outputs found
Deterministic polarization chaos from a laser diode
Fifty years after the invention of the laser diode and fourty years after the
report of the butterfly effect - i.e. the unpredictability of deterministic
chaos, it is said that a laser diode behaves like a damped nonlinear
oscillator. Hence no chaos can be generated unless with additional forcing or
parameter modulation. Here we report the first counter-example of a
free-running laser diode generating chaos. The underlying physics is a
nonlinear coupling between two elliptically polarized modes in a
vertical-cavity surface-emitting laser. We identify chaos in experimental
time-series and show theoretically the bifurcations leading to single- and
double-scroll attractors with characteristics similar to Lorenz chaos. The
reported polarization chaos resembles at first sight a noise-driven mode
hopping but shows opposite statistical properties. Our findings open up new
research areas that combine the high speed performances of microcavity lasers
with controllable and integrated sources of optical chaos.Comment: 13 pages, 5 figure
Modelling and control of chaotic processes through their Bifurcation Diagrams generated with the help of Recurrent Neural Network models: Part 1—simulation studies
Many real-world processes tend to be chaotic and also do not lead to satisfactory analytical modelling. It has been shown here that for such chaotic processes represented through short chaotic noisy time-series, a multi-input and multi-output recurrent neural networks model can be built which is capable of capturing the process trends and predicting the future values from any given starting condition. It is further shown that this capability can be achieved by the Recurrent Neural Network model when it is trained to very low value of mean squared error. Such a model can then be used for constructing the Bifurcation Diagram of the process leading to determination of desirable operating conditions. Further, this multi-input and multi-output model makes the process accessible for control using open-loop/closed-loop approaches or bifurcation control etc. All these studies have been carried out using a low dimensional discrete chaotic system of Hénon Map as a representative of some real-world processes
Time-dependent Turbulence in Stars
Three-dimensional (3D) hydrodynamic simulations of shell oxygen burning
(Meakin and Arnett 2007) exhibit bursty, recurrent fluctuations in turbulent
kinetic energy. These are shown to be due to a global instability in the
convective region, which has been suppressed in calculations of stellar
evolution which use mixing-length theory (MLT). Quantitatively similar behavior
occurs in the model of a convective roll (cell) of Lorenz (1963), which is
known to have a strange attractor that gives rise to random fluctuations in
time.An extension of the Lorenz model, which includes Kolmogorov damping and
nuclear burning, is shown to exhibit bursty, recurrent fluctuations like those
seen in the 3D simulations. A simple model of a convective layer (composed of
multiple Lorenz cells) gives luminosity fluctuations which are suggestive of
irregular variables (red giants and supergiants, Schwarzschild 1975).
Apparent inconsistencies between Arnett, Meakin, and Young (2009) and
Nordlund, Stein, and Asplund (2009) on the nature of convective driving have
been resolved, and are discussed.Comment: 8 pages, 2 figures, IAU Symposium 271 "Astrophysical Dynamics: From
Galaxies to Stars", Nice, FR, 201
Comparative evaluation of approaches in T.4.1-4.3 and working definition of adaptive module
The goal of this deliverable is two-fold: (1) to present and compare different approaches towards learning and encoding movements us- ing dynamical systems that have been developed by the AMARSi partners (in the past during the first 6 months of the project), and (2) to analyze their suitability to be used as adaptive modules, i.e. as building blocks for the complete architecture that will be devel- oped in the project. The document presents a total of eight approaches, in two groups: modules for discrete movements (i.e. with a clear goal where the movement stops) and for rhythmic movements (i.e. which exhibit periodicity). The basic formulation of each approach is presented together with some illustrative simulation results. Key character- istics such as the type of dynamical behavior, learning algorithm, generalization properties, stability analysis are then discussed for each approach. We then make a comparative analysis of the different approaches by comparing these characteristics and discussing their suitability for the AMARSi project
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