The Role Of Dispersion In The Generalized Kuramoto Sivashinsky Equation

Author(s):  
C. M. Alfaro ◽  
R. D. Benguria ◽  
M. C. Depassier
Keyword(s):  
2019 ◽  
Vol 61 (3) ◽  
pp. 270-285 ◽  
Author(s):  
RUSSELL A. EDSON ◽  
J. E. BUNDER ◽  
TRENT W. MATTNER ◽  
A. J. ROBERTS

The Kuramoto–Sivashinsky equation is a prototypical chaotic nonlinear partial differential equation (PDE) in which the size of the spatial domain plays the role of a bifurcation parameter. We investigate the changing dynamics of the Kuramoto–Sivashinsky PDE by calculating the Lyapunov spectra over a large range of domain sizes. Our comprehensive computation and analysis of the Lyapunov exponents and the associated Kaplan–Yorke dimension provides new insights into the chaotic dynamics of the Kuramoto–Sivashinsky PDE, and the transition to its one-dimensional turbulence.


2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
V. I. Emel’yanov

It is shown that the bulk defect-deformational (DD) nanostructuring of isotropic solids can be described by a closed three-dimensional (3D) nonlinear DD equation of the Kuramoto-Sivashinsry (KS) type for the nonequilibrium defect concentration, derived here in the framework of the nonlocal elasticity theory (NET). The solution to the linearized DDKS equation describes the threshold appearance of the periodic self-consistent strain modulation accompanied by the simultaneous formation of defect piles at extremes of the strain. The period and growth rate of DD nanostructure are determined. Based on the obtained results, a novel mechanism of nanostructuring of solids under the severe plastic deformation (SPD), stressing the role of defects generation and selforganization, described by the DDKS, is proposed. Theoretical dependencies of nanograin size on temperature and shear strain reproduce well corresponding critical dependencies obtained in experiments on nanostructuring of metals under the SPD, including the effect of saturation of nanofragmentation. The scaling parameter of the NET is estimated and shown to determine the limiting small grain size.


2019 ◽  
Vol 61 ◽  
pp. 270-285
Author(s):  
Russell A. Edson ◽  
Judith E. Bunder ◽  
Trent W. Mattner ◽  
Anthony J. Roberts

The Kuramoto–Sivashinsky equation is a prototypical chaotic nonlinear partial differential equation (PDE) in which the size of the spatial domain plays the role of a bifurcation parameter. We investigate the changing dynamics of the Kuramoto–Sivashinsky PDE by calculating the Lyapunov spectra over a large range of domain sizes. Our comprehensive computation and analysis of the Lyapunov exponents and the associated Kaplan–Yorke dimension provides new insights into the chaotic dynamics of the Kuramoto–Sivashinsky PDE, and the transition to its one-dimensional turbulence. doi:10.1017/S1446181119000105


2006 ◽  
Vol 63 (6) ◽  
pp. 1659-1671 ◽  
Author(s):  
S. Vannitsem

Abstract The dynamics of model error due to parameterization uncertainties are investigated in the context of two spatially distributed systems: the one-dimensional convection system known as the extended Kuramoto–Sivashinsky equation and a quasigeostrophic atmospheric model. In addition to the different phases of error growth already reported for low-order systems, unexpected behaviors associated with the spectral characteristics of the model perturbation sources have been brought out. Notably, the predictability of the system is less affected by model uncertainties acting at small scales than at larger ones. An interpretation in terms of the spectral properties of the Lyapunov vectors is advanced.


JAMA ◽  
1966 ◽  
Vol 195 (12) ◽  
pp. 1005-1009 ◽  
Author(s):  
D. J. Fernbach
Keyword(s):  

JAMA ◽  
1966 ◽  
Vol 195 (3) ◽  
pp. 167-172 ◽  
Author(s):  
T. E. Van Metre

2018 ◽  
Vol 41 ◽  
Author(s):  
Winnifred R. Louis ◽  
Craig McGarty ◽  
Emma F. Thomas ◽  
Catherine E. Amiot ◽  
Fathali M. Moghaddam

AbstractWhitehouse adapts insights from evolutionary anthropology to interpret extreme self-sacrifice through the concept of identity fusion. The model neglects the role of normative systems in shaping behaviors, especially in relation to violent extremism. In peaceful groups, increasing fusion will actually decrease extremism. Groups collectively appraise threats and opportunities, actively debate action options, and rarely choose violence toward self or others.


2018 ◽  
Vol 41 ◽  
Author(s):  
Kevin Arceneaux

AbstractIntuitions guide decision-making, and looking to the evolutionary history of humans illuminates why some behavioral responses are more intuitive than others. Yet a place remains for cognitive processes to second-guess intuitive responses – that is, to be reflective – and individual differences abound in automatic, intuitive processing as well.


2020 ◽  
Vol 43 ◽  
Author(s):  
Stefen Beeler-Duden ◽  
Meltem Yucel ◽  
Amrisha Vaish

Abstract Tomasello offers a compelling account of the emergence of humans’ sense of obligation. We suggest that more needs to be said about the role of affect in the creation of obligations. We also argue that positive emotions such as gratitude evolved to encourage individuals to fulfill cooperative obligations without the negative quality that Tomasello proposes is inherent in obligations.


2020 ◽  
Vol 43 ◽  
Author(s):  
Andrew Whiten

Abstract The authors do the field of cultural evolution a service by exploring the role of non-social cognition in human cumulative technological culture, truly neglected in comparison with socio-cognitive abilities frequently assumed to be the primary drivers. Some specifics of their delineation of the critical factors are problematic, however. I highlight recent chimpanzee–human comparative findings that should help refine such analyses.


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