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Chaos transition despite linear stability
Physical Review E, 1994We present a linearly stable model in two complex dimensions that can be triggered by an initial perturbation or external noise to exhibit chaotic dynamics although all linear perturbations are damped. The transition to chaos is caused by an interplay between transient linear growth and nonlinear, energy conserving mixing.
, Gebhardt, , Grossmann
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1994
Laminar-to-turbulent transition can occur through several mechanisms, such as in linear instability, bypass transition, Gortler instability, and cross-flow instability. For more discussion of this issue see Bushnell et al. (1988), Gortler (1965), Dagenhart et al. (1989, 1990), and Saric and Benmalek (1991).
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Laminar-to-turbulent transition can occur through several mechanisms, such as in linear instability, bypass transition, Gortler instability, and cross-flow instability. For more discussion of this issue see Bushnell et al. (1988), Gortler (1965), Dagenhart et al. (1989, 1990), and Saric and Benmalek (1991).
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Stability of Linear Positive Systems
Ukrainian Mathematical Journal, 2001The author considers the linear system \[ \dot H+MH=G(t),\quad t\geq 0,\tag{1} \] where \(M:\mathcal{E} \mapsto \mathcal{E}\) is a bounded operator in a Banach space \(\mathcal{E}\), which has the structure of a partially ordered space with respect to a fixed cone \(\mathcal{K}\subset\mathcal{E}\).
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2013
This chapter describes a linear stability analysis (that is, solving for the critical Rayleigh number Ra and mode) that allows readers to check their linear codes against the analytic solution. For this linear analysis, each Fourier mode n can be considered a separate and independent problem.
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This chapter describes a linear stability analysis (that is, solving for the critical Rayleigh number Ra and mode) that allows readers to check their linear codes against the analytic solution. For this linear analysis, each Fourier mode n can be considered a separate and independent problem.
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Uniform Stability and Stabilization of Linear Thermoelastic Systems
Journal of Dynamical and Control Systems, 2000The object of the paper is to study mathematical models of elastic, heat conductive media. For such linear thermoelastic systems, uniform stability and stabilization methods are investigated. An explicit stabilizing feedback for such system is developed and proposed. The exponential stability for this stabilizer is proved using Lyapunov functions.
Benabdallah, A., Soufyane, A.
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2017
To date, only one study presented a linear stability analysis of pattern formation in buoyancy-thermocapillary convection which correctly predicts the formation of a stationary pattern at Bo D = O(1). This study by Priede and Gerbeth [18] is, however, based on a one-layer model where phase change is neglected and the free surface is considered ...
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To date, only one study presented a linear stability analysis of pattern formation in buoyancy-thermocapillary convection which correctly predicts the formation of a stationary pattern at Bo D = O(1). This study by Priede and Gerbeth [18] is, however, based on a one-layer model where phase change is neglected and the free surface is considered ...
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STABILIZATION OF LINEAR DISTRIBUTED SYSTEMS
IFAC Proceedings Volumes, 1983Abstract The problem of shifting a finite set of eigenvalues to predetermined points on the complex plane in infinite dimensional systems is considered. Basing on that a stabilization method is given for systems in which the unstable subspace of the state space is finite dimensional.
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Stability in linear elasticity
International Journal of Solids and Structures, 1968Abstract Conditions are established ensuring the continuous dependence on the initial data of the equilibrium solution and certain other classes of solution to the elastodynamic initial boundary value problem. The method of proof depends upon logarithmic convexity arguments and is notable for the absence of any definiteness condition on the ...
Knops, R. J., Payne, L. E.
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Linear Morphological Stability
2010In Chapter 8 the foundational subject of interface capillarity was developed to explain why curved crystal-melt boundaries exhibit modified thermodynamic properties compared to their planar counterparts, especially regarding their equilibrium temperature and solubility.
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Stability: Basic Concepts and Linear Stability
2021Basic stability concepts and methods for characterizing the stability of linear time invariant dynamical systems are presented, including phase plane analysis, bounded input bounded output stability and Routh’s Stability Criterion.
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