Statistics of Chaotic Resonances in an Optical Microcavity

Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs. chaotic), and is often instrumental to identify classical-to-quantum correspondence. Here, we study, both theoretically and experimentally, the statistics of chaotic resonances in an optical microcavity with a mixed phase space of both regular and chaotic dynamics. Information on the number of chaotic modes is extracted by counting regular modes, which couple to the former via dynamical tunneling. The experimental data are in agreement with a known semiclassical prediction for the dependence of the number of chaotic resonances on the number of open channels, while they deviate significantly from a purely random-matrix-theory-based treatment, in general. We ascribe this result to the ballistic decay of the rays, which occurs within Ehrenfest time, and importantly, within the timescale of transient chaos. The present approach may provide a general tool for the statistical analysis of chaotic resonances in open systems.Comment: 5 pages, 5 figures, and a supplemental informatio

Turbulent Formation of Interstellar Structures and the Connection Between Simulations and Observations

I review recent results derived from numerical simulations of the turbulent interstellar medium (ISM), in particular concerning the nature and formation of turbulent clouds, methods for comparing the structure in simulations and observations, and the effects of projection of three-dimensional structures onto two dimensions. Clouds formed as turbulent density fluctuations are probably not confined by thermal pressure, but rather their morphology may be determined by the large-scale velocity field. Also, they may have shorter lifetimes than normally believed, as the large-scale turbulent modes have larger associated velocities than the clouds' internal velocity dispersions. Structural characterization algorithms have started to distinguish the best fitting simulations to a particular observation, and have opened several new questions, such as the nature of the observed line width-size relation and of the relation between the structures seen in channel maps and the true spatial distribution of the density and velocity fields. The velocity field apparently dominates the morphology seen in intensity channel maps, at least in cases when the density field exhibits power spectra steep enough. Furthermore, the selection of scattered fluid parcels along the line of sight (LOS) by their LOS-velocity inherent to the construction of spectroscopic data may introduce spurious small-scale structure in high spectral resolution channel maps.Comment: 15 pages, no figures. To appear in the Proceedings of "The Chaotic Universe", Roma/Pescara, Italy, 1-5 Feb. 1999, eds. V. Gurzadyan and L. Bertone. Uses included .cls fil

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Forecasting wind speeds at tall tower heights within Missouri

Forecasting of wind speeds is necessary for the planning and operations of the wind power generating plants. This research investigates the short term forecasting of wind speeds at tall tower heights for stations within Missouri: Columbia, Neosho and Blanchard. The first objective was to characterize the chaotic nature of this parameter using mono and multi fractal analysis using the Rescale Range Analysis (R/S Analysis) and the Multifractal Detrended Fluctuation Analysis respectively (MF-DFA). It was determined that the system was fractal and there were no trends indicative of increasing fractality and complexity with increasing height. The second objective was the qualitative and quantitative chaotic characterization of the wind speeds using phase-space portraits and the Largest Lyapunov Exponent (LLE) respectively. The methods confirm the results of the fractal analyses. A simple non-linear prediction algorithm, Empirical Dynamical Modeling (EDM) was then used to forecast the wind speeds using a moving window. It was determined that the EDM was comparable to persistence. It beats this benchmark model in the very short term range of one time step or 10 minutes. The third objective was to cluster the data using Self-Organizing Maps (SOMs), having identified the optimum number of clusters as 4 using the Elbow and Silhouette Methods, among others. Three continuous intervals belonging to a particular cluster, which represented approximately 50 percent and over of the input vectors or rows from the data frame were identified. These intervals were then used as inputs into a Long Short-Term Memory Network (LSTM) with variables, pressure and wind speeds, as well as a lagged series LSTM with embedding dimension, d, and time delay (tau). These were compared to the Moving window Auto Regressive Integrated Moving Average (ARIMA) and to persistence. It was determined that the lagged series LSTM improved on the LSTM with wind speed and pressure series inputs, and all models beat persistence. The lagged LSTM beats the Moving ARIMA for at least 2 of the forecasting times of 60 and 120 minutes for all intervals.Includes bibliographical references

On application of dynamical system methods in biomedical engineering

The spectrum of various methods and tools used for solving bioengineering problems is sufficiently wide. Dynamical systems (including the symbolic ones) in many cases become a base for design and implementation of methods of investigation and computer modeling complex processes. Whereas for solving direct problems we have many well-developed methods, results for inverse problems are much more modest. We discuss two methods for such tasks: Takens’ method for reconstruction attractor by a time series, and the based on ideas of symbolic dynamics method for digital image analysis using stationary flow on graph and weighted entropy. The results of numerical experiments are given