Exponential decay and scaling laws in noisy chaotic scattering

2008 ◽  
Vol 372 (2) ◽  
pp. 110-116 ◽  
Author(s):  
Jesús M. Seoane ◽  
Miguel A.F. Sanjuán
Keyword(s):  
Exponential Decay ◽  
Scaling Laws ◽  
Chaotic Scattering

ESCAPING DYNAMICS IN THE PRESENCE OF DISSIPATION AND NOISE IN SCATTERING SYSTEMS

2010 ◽  
Vol 20 (09) ◽  
pp. 2783-2793 ◽  
Author(s):  
JESÚS M. SEOANE ◽  
MIGUEL A. F. SANJUÁN
Keyword(s):  
Fractal Dimension ◽  
Decay Rate ◽  
Exponential Decay ◽  
Scaling Law ◽  
Scattering Function ◽  
Chaotic Scattering ◽  
Fundamental Interest ◽  
External Perturbations ◽  
Exponential Decay Rate ◽  
Scattering Systems

Chaotic scattering in open Hamiltonian systems is a problem of fundamental interest with applications in several branches of physics. In this paper we analyze the effects of adding external perturbations such as dissipation and noise in chaotic scattering phenomena. Our main result is the exponential decay rate of the particles in the scattering region when the system is affected by dissipation and noise. In the case of dissipation the particles escape more slowly from the scattering region than in the conservative case. However, in the noisy case, the particles escape faster from the scattering region as compared to the noiseless case. Moreover, we analyze the fractal dimension of the set of singularities of the scattering function for the dissipative and the conservative cases. As a result of our analysis we have found that a scaling law exists between the exponential decay rate of the particles and the dissipative parameter, and that the fractal dimension for the noisy case is the unity.

Siphon Flows in Stratified Coronal Loops

1994 ◽  
Vol 144 ◽  
pp. 185-187
Author(s):  
S. Orlando ◽  
G. Peres ◽  
S. Serio
Keyword(s):  
Heat Flux ◽  
Scaling Laws ◽  
Flow Model ◽  
Supersonic Flows ◽  
Coronal Loops ◽  
Characteristic Parameters

AbstractWe have developed a detailed siphon flow model for coronal loops. We find scaling laws relating the characteristic parameters of the loop, explore systematically the space of solutions and show that supersonic flows are impossible for realistic values of heat flux at the base of the upflowing leg.

Equilibrium scaling laws for layered spin glasses

1993 ◽  
Vol 3 (10) ◽  
pp. 2041-2062 ◽  
Author(s):  
M. J. Thill ◽  
H. J. Hilhorst
Keyword(s):  
Spin Glasses ◽  
Scaling Laws ◽  
Layered Spin

Analysis of shear bands in slow granular flows using a frictional Cosserat model

2000 ◽  
Vol 627 ◽  
Author(s):  
Prabhu R. Nott ◽  
K. Kesava Rao ◽  
L. Srinivasa Mohan
Keyword(s):  
Scaling Laws ◽  
Shear Bands ◽  
Shear Layers ◽  
Theoretical Description ◽  
Field Variable ◽  
Cosserat Continuum ◽  
Momentum Balance ◽  
Rigid Plastic ◽  
Independent Field ◽  
Cosserat Model

ABSTRACTThe slow flow of granular materials is often marked by the existence of narrow shear layers, adjacent to large regions that suffer little or no deformation. This behaviour, in the regime where shear stress is generated primarily by the frictional interactions between grains, has so far eluded theoretical description. In this paper, we present a rigid-plastic frictional Cosserat model that captures thin shear layers by incorporating a microscopic length scale. We treat the granular medium as a Cosserat continuum, which allows the existence of localised couple stresses and, therefore, the possibility of an asymmetric stress tensor. In addition, the local rotation is an independent field variable and is not necessarily equal to the vorticity. The angular momentum balance, which is implicitly satisfied for a classical continuum, must now be solved in conjunction with the linear momentum balances. We extend the critical state model, used in soil plasticity, for a Cosserat continuum and obtain predictions for flow in plane and cylindrical Couette devices. The velocity profile predicted by our model is in qualitative agreement with available experimental data. In addition, our model can predict scaling laws for the shear layer thickness as a function of the Couette gap, which must be verified in future experiments. Most significantly, our model can determine the velocity field in viscometric flows, which classical plasticity-based model cannot.

Scaling laws of cylindrical shells under lateral pressure

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1669-1671
Author(s):  
A. Tabiei ◽  
J. Sun ◽  
G. J. Simitses
Keyword(s):  
Scaling Laws ◽  
Lateral Pressure ◽  
Cylindrical Shells
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