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Showing 1 to 11 of 11 for “"Kuramoto-Sivashinsky"”.
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Inherent Instabilities and Discontinuities: The Kuramoto-Sivashinsky Equation and a Suspension Flow as Exemplars
… instability present at small times in the Kuramoto Sivashinsky equation, formulated as a perturbation of the kinematic-wave equation. This instability is invisible to regular matched asymptotic expansions, which, at small times, see no deviation in the leading-order solution from the …
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Application of Uncertainty Inequalities to Bound the Radius of the Attractor for the Kuramoto -Sivashinsky Equation
Made available in DSpace on 2015-09-28T15:19:58Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3250245.pdf: 2544352 bytes, checksum: 11ab9c7e28e1b2b45fc82c5713d9e645 (MD5) Previous issue date: 2006
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Dynamical systems approach to one-dimensional spatiotemporal chaos -- A cyclist's view
… the extensive numerical exploration of the Kuramoto-Sivashinsky system in the chaotic regime: structure of the equilibrium solutions, our search for the shortest periodic orbits, description of the chaotic invariant set in terms of intrinsic coordinates and return maps on the Poincare …
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Exact coherent structures in spatiotemporal chaos: From qualitative description to quantitative predictions
… manifolds. Specifically, we investigate the Kuramoto-Sivashinsky equation, which describes the velocity of a flame front, and the Navier-Stokes equation for an incompressible fluid in a circular pipe. We argue with examples that this approach can lead to a theory of turbulence with predictive …
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Reduced-space Gaussian process regression forecast for nonlinear dynamical systems
… systems including the Lorenz 63, Lorenz 96, the Kuramoto-Sivashinsky, as well as a prototype climate model. We also study the performance of the proposed approach as the intrinsic dimensionality of the system attractor increases in highly turbulent regimes.
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Combining Physics-based Modeling, Machine Learning, and Data Assimilation for Forecasting Large, Complex, Spatiotemporally Chaotic Systems
… of the system's past evolution. Using the Kuramoto-Sivashinsky equation as our test model, we demonstrate that this technique produces more accurate short-term forecasts than either the knowledge-based or the ML component model acting alone and is scalable to large spatial domains. We …
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Nonlinear long-wave interfacial stability of two-layer gas-liquid flow
… analysis in this case, we obtain the modified Kuramoto-Sivashinsky equation with an additional integral term, influencing the speed of propagation but not the shape of the interfacial wave. For the strongly nonlinear case, admissible criteria for Lax shocks, undercompressive shocks and …
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Nonlinear interfacial stability of core-annular film flows in the presence of surfactants
… of surfactarits, the system reduces to the Kuramoto-Sivashinsky equation which has been extensively studied as a paradigm for one-dimensional turbulence in dissipative systems. The surfactant modifies the flow by inducing Marangoni forces along the interface which in turn modify both the …
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Mathematical models of combustion at high pressure
… model is carried out, resulting in a modified Kuramoto-Sivashinsky (K-S) equation, accounting for effects of Soret Diffusion. Linear stability analysis shows that the flame front is unstable with respect to long-waves in a range of Soret diffusion coefficient that corresponds to no and weak …
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Leveraging the Linear Response Theory in Sensitivity Analysis of Chaotic Dynamical Systems and Turbulent Flows
… oscillators) and partial differential equations (Kuramoto-Sivashinsky and 3D Navier-Stokes system).
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Mathematical problems arising in interfacial electrohydrodynamics
… evolution is governed by an extension of the Kuramoto-Sivashinsky (KS) equation. Global existence and uniqueness results are proved, and refined estimates of the radius of the absorbing ball in L^2 are obtained in terms of the parameters of the equations for a generalized class of modified KS …