scholarly journals Euler equations are not exactly controllable by a finite-dimensional external force

2008 ◽  
Vol 237 (10-12) ◽  
pp. 1317-1323 ◽  
Author(s):  
Armen Shirikyan
Keyword(s):  
Euler Equations ◽  
External Force ◽  
Finite Dimensional

Instabilities of exact, time-periodic solutions of the incompressible Euler equations

2000 ◽  
Vol 404 ◽  
pp. 269-287 ◽  
Author(s):  
JOSEPH A. BIELLO ◽  
KENNETH I. SALDANHA ◽  
NORMAN R. LEBOVITZ
Keyword(s):  
Periodic Solutions ◽  
Linear Stability ◽  
Euler Equations ◽  
Parameter Space ◽  
Spatial Scales ◽  
Inviscid Flow ◽  
Steady Flows ◽  
Periodic Flows ◽  
Finite Dimensional ◽  
Time Periodic Solutions

We consider the linear stability of exact, temporally periodic solutions of the Euler equations of incompressible, inviscid flow in an ellipsoidal domain. The problem of linear stability is reduced, without approximation, to a hierarchy of finite-dimensional Floquet problems governing fluid-dynamical perturbations of differing spatial scales and symmetries. We study two of these Floquet problems in detail, emphasizing parameter regimes of special physical significance. One of these regimes includes periodic flows differing only slightly from steady flows. Another includes long-period flows representing the nonlinear outcome of an instability of steady flows. In both cases much of the parameter space corresponds to instability, excepting a region adjacent to the spherical configuration. In the second case, even if the ellipsoid departs only moderately from a sphere, there are filamentary regions of instability in the parameter space. We relate this and other features of our results to properties of reversible and Hamiltonian systems, and compare our results with related studies of periodic flows.

EULER EQUATIONS ON FINITE-DIMENSIONAL LIE GROUPS

1978 ◽  
Vol 12 (2) ◽  
pp. 371-389 ◽  
Author(s):  
A S Miščenko ◽  
A T Fomenko
Keyword(s):  
Lie Groups ◽  
Euler Equations ◽  
Finite Dimensional

scholarly journals The onset of thermalization in finite-dimensional equations of hydrodynamics: insights from the Burgers equation

2017 ◽  
Vol 473 (2197) ◽  
pp. 20160585 ◽  
Author(s):  
Divya Venkataraman ◽  
Samriddhi Sankar Ray
Keyword(s):  
Energy Spectrum ◽  
Numerical Simulations ◽  
Euler Equations ◽  
Burgers Equation ◽  
Three Dimensional ◽  
Direct Numerical Simulations ◽  
Infinite Dimensional ◽  
Localized Structures ◽  
Finite Dimensional ◽  
Incompressible Euler

Solutions to finite-dimensional (all spatial Fourier modes set to zero beyond a finite wavenumber K G ), inviscid equations of hydrodynamics at long times are known to be at variance with those obtained for the original infinite dimensional partial differential equations or their viscous counterparts. Surprisingly, the solutions to such Galerkin-truncated equations develop sharp localized structures, called tygers (Ray et al. 2011 Phys. Rev. E 84 , 016301 ( doi:10.1103/PhysRevE.84.016301 )), which eventually lead to completely thermalized states associated with an equipartition energy spectrum. We now obtain, by using the analytically tractable Burgers equation, precise estimates, theoretically and via direct numerical simulations, of the time τ c at which thermalization is triggered and show that τ c ∼ K G ξ , with ξ = − 4 9 . Our results have several implications, including for the analyticity strip method, to numerically obtain evidence for or against blow-ups of the three-dimensional incompressible Euler equations.

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

The Unassailable Self: Freud's Image Among Post-war American Intellectuals

2017 ◽  
Vol 19 (1) ◽  
pp. 55-75 ◽  
Author(s):  
Katherine Jenness
Keyword(s):  
World War Ii ◽  
Cold War ◽  
External Force ◽  
Sigmund Freud ◽  
Human Being ◽  
World War ◽  
The Us ◽  
Post War ◽  
The Cold War ◽  
The Way

This paper explores the way American intellectuals depicted Sigmund Freud during the peak of popularity and prestige of psychoanalysis in the US, roughly the decade and a half following World War II. These intellectuals insisted upon the unassailability of Freud's mind and personality. He was depicted as unsusceptible to any external force or influence, a trait which was thought to account for Freud's admirable comportment as a scientist, colleague and human being. This post-war image of Freud was shaped in part by the Cold War anxiety that modern individuality was imperilled by totalitarian forces, which could only be resisted by the most rugged of selves. It was also shaped by the unique situation of the intellectuals themselves, who were eager to position themselves, like the Freud they imagined, as steadfastly independent and critical thinkers who would, through the very clarity of their thought, lead America to a more robust democracy.

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