The Role Of Dispersion In The Generalized Kuramoto Sivashinsky Equation

1993 ◽  
pp. 281-287
Author(s):  
C. M. Alfaro ◽  
R. D. Benguria ◽  
M. C. Depassier
Keyword(s):  
Sivashinsky Equation

scholarly journals LYAPUNOV EXPONENTS OF THE KURAMOTO–SIVASHINSKY PDE

2019 ◽  
Vol 61 (3) ◽  
pp. 270-285 ◽  
Author(s):  
RUSSELL A. EDSON ◽  
J. E. BUNDER ◽  
TRENT W. MATTNER ◽  
A. J. ROBERTS
Keyword(s):  
Differential Equation ◽  
Lyapunov Exponents ◽  
Chaotic Dynamics ◽  
Large Range ◽  
Nonlinear Partial Differential Equation ◽  
Bifurcation Parameter ◽  
One Dimensional ◽  
Lyapunov Spectra ◽  
Sivashinsky Equation

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.

scholarly journals The 3D Kuramoto-Sivashinsky Equation for Nonequilibrium Defects Interacting through Self-Consisting Strain and Nanostructuring of Solids

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
V. I. Emel’yanov
Keyword(s):  
Nonlocal Elasticity ◽  
Three Dimensional ◽  
Nonlocal Elasticity Theory ◽  
Simultaneous Formation ◽  
Self Consistent ◽  
Strain Modulation ◽  
Isotropic Solids ◽  
Sivashinsky Equation ◽  
Nanograin Size

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.

scholarly journals Lyapunov exponents of the Kuramoto--Sivashinsky PDE

2019 ◽  
Vol 61 ◽  
pp. 270-285
Author(s):  
Russell A. Edson ◽  
Judith E. Bunder ◽  
Trent W. Mattner ◽  
Anthony J. Roberts
Keyword(s):  
Differential Equation ◽  
Lyapunov Exponents ◽  
Chaotic Dynamics ◽  
Large Range ◽  
Nonlinear Partial Differential Equation ◽  
Bifurcation Parameter ◽  
One Dimensional ◽  
Lyapunov Spectra ◽  
Sivashinsky Equation

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

scholarly journals The Role of Scales in the Dynamics of Parameterization Uncertainties

2006 ◽  
Vol 63 (6) ◽  
pp. 1659-1671 ◽  
Author(s):  
S. Vannitsem
Keyword(s):  
Spectral Characteristics ◽  
Atmospheric Model ◽  
Model Error ◽  
Error Growth ◽  
Model Uncertainties ◽  
One Dimensional ◽  
Spatially Distributed ◽  
The One ◽  
Sivashinsky Equation

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.

Role of dactinomycin in the improved survival of children with Wilms' tumor

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

Role of the allergist in diagnosis and management of patients with uveitis

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

The power of norms to sway fused group members

2018 ◽  
Vol 41 ◽  
Author(s):  
Winnifred R. Louis ◽  
Craig McGarty ◽  
Emma F. Thomas ◽  
Catherine E. Amiot ◽  
Fathali M. Moghaddam
Keyword(s):  
Evolutionary Anthropology ◽  
Normative Systems ◽  
Violent Extremism ◽  
Identity Fusion ◽  
Group Members

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.

Elaborating the role of reflection and individual differences in the study of folk-economic beliefs

2018 ◽  
Vol 41 ◽  
Author(s):  
Kevin Arceneaux
Keyword(s):  
Decision Making ◽  
Individual Differences ◽  
Cognitive Processes ◽  
Evolutionary History ◽  
Behavioral Responses ◽  
History Of ◽  
Economic Beliefs

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.

The role of affect in feelings of obligation

2020 ◽  
Vol 43 ◽  
Author(s):  
Stefen Beeler-Duden ◽  
Meltem Yucel ◽  
Amrisha Vaish
Keyword(s):  
Positive Emotions ◽  
The Creation ◽  
Sense Of Obligation

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.

Refining our understanding of the “elephant in the room”

2020 ◽  
Vol 43 ◽  
Author(s):  
Andrew Whiten
Keyword(s):  
Social Cognition ◽  
Cultural Evolution ◽  
Cognitive Abilities ◽  
Critical Factors ◽  
Technological Culture

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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