Global ETD Search
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Showing 1 to 10 of 10 for “"Spatiotemporal Chaos"”.
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Spatiotemporal chaos in the nonlinear three wave interaction
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 1992
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Gaining New Insights into Spatiotemporal Chaos with Numerics
… of systems driven far-from-equilibrium is spatiotemporal chaos where the dynamics are aperiodic in both time and space. We explored this numerically for three systems: the Lorenz-96 model, the Swift-Hohenberg equation, and Rayleigh-Bénard convection. The Lorenz-96 model is a continuous in …
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Dynamical systems approach to one-dimensional spatiotemporal chaos -- A cyclist's view
… systems approach to the study of weak turbulence(spatiotemporal chaos) based on the periodic orbit theory, emphasizing the role of recurrent patterns and coherent structures. After a brief review of the periodic orbit theory and its application to low-dimensional dynamics, we discuss its possible …
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Exact coherent structures in spatiotemporal chaos: From qualitative description to quantitative predictions
The term spatiotemporal chaos refers to physical phenomena that exhibit irregular oscillations in both space and time. Examples of such phenomena range from cardiac dynamics to fluid turbulence, where the motion is described by nonlinear partial differential equations. It is well known from the …
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Solitons, spatiotemporal chaos and synchronization in arrays of damped driven nonlinear oscillators
… sequence of transitions to temporal chaos and the degeneration into spatiotemporal chaos for larger driving strengths. Next, we explore the effect of introducing weak disorder in the simplest form, a single impurity, into the chain. We describe how a long impurity can induce a pinned …
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Spatiotemporal Chaos in Large Systems Driven Far-From-Equilibrium: Connecting Theory with Experiment
There are still many open questions regarding spatiotemporal chaos although many well developed theories exist for chaos in time. Rayleigh-B'enard convection is a paradigmatic example of spatiotemporal chaos that is also experimentally accessible. Discoveries uncovered using numerics can often be …
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Solitons,spatiotemporal choas and synchronization in arrays of damped driven nonlinear oscillators
… and study the effect of disorder on the spatiotemporal chaos. The chain we consider consists of torsionally coupled, damped, parametrically driven pendulums. We show that the amplitudes of the pendulums satisfy a system of equations in slow time, the "nonlinear Schrodinger (NLS) …
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Neural networks for the prediction of chaos and turbulence
Chaos is a deterministic, yet unpredictable, phenomenon that appears in multiple engineering applications. Predicting chaotic dynamics is challenging because infinitesimal perturbations to the system’s initial conditions grow exponentially in time. To further add complexity to the phenomenon, …
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Active Transport in Chaotic Rayleigh-Bénard Convection
… time-dependent flow field characterized by a spatiotemporally chaotic state of Rayleigh-Be?nard convection. A nonlinear Fischer-Kolmogorov-Petrovskii-Piskunov reaction is selected to study the transport within these flows. A highly efficient, parallel spectral element approach is employed to …
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The Complex Spatiotemporal Dynamics of a Shallow Fluid Layer
The nonlinear and chaotic dynamics of a shallow fluid layer are investigated numerically using large-scale parallel numerical simulations. Two particular situations are studied in detail. First, a fluid layer is placed between rigid boundaries and heated from below to yield the chaotic dynamics of …