Physical origin of oscillations in the three‐dimensional collision amplitudes of heavy–light–heavy systems. Semiclassical quantization of chaotic scattering

1993 ◽  
Vol 98 (5) ◽  
pp. 3929-3944 ◽  
Author(s):  
Beverly B. Grayce ◽  
Rex T. Skodje ◽  
Jeremy M. Hutson
Keyword(s):  
Three Dimensional ◽  
Physical Origin ◽  
Chaotic Scattering ◽  
Semiclassical Quantization

CHAOTIC SCATTERING IN TIME-DEPENDENT HAMILTONIAN SYSTEMS

1991 ◽  
Vol 01 (03) ◽  
pp. 667-679 ◽  
Author(s):  
YING-CHENG LAI ◽  
CELSO GREBOGI
Keyword(s):  
Phase Space ◽  
Measure Zero ◽  
Invariant Set ◽  
Time Dependent ◽  
Invariant Sets ◽  
Physical Origin ◽  
Chaotic Scattering ◽  
Periodic Oscillations ◽  
Surface Of Section ◽  
Oscillating Potential

We consider the classical scattering of particles in a one-degree-of-freedom, time-dependent Hamiltonian system. We demonstrate that chaotic scattering can be induced by periodic oscillations in the position of the potential. We study the invariant sets on a surface of section for different amplitudes of the oscillating potential. It is found that for small amplitudes, the phase space consists of nonescaping KAM islands and an escaping set. The escaping set is made up of a nonhyperbolic set that gives rise to chaotic scattering and remains of KAM islands. For large amplitudes, the phase space contains a Lebesgue measure zero invariant set that gives rise to chaotic scattering. In this regime, we also discuss the physical origin of the Cantor set responsible for the chaotic scattering and calculate its fractal dimension.

scholarly journals Localized Kaluza-Klein 6-brane

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Tetsuji Kimura ◽  
Shin Sasaki ◽  
Kenta Shiozawa
Keyword(s):  
Gauge Theory ◽  
Sigma Model ◽  
Three Dimensional ◽  
Linear Sigma Model ◽  
Physical Origin ◽  
Fundamental String ◽  
Extended Space ◽  
Instanton Effect ◽  
M Theory ◽  
Kaluza Klein

Abstract We study the membrane wrapping mode corrections to the Kaluza-Klein (KK) 6-brane in eleven dimensions. We examine the localized KK6-brane in the extended space in E7(7) exceptional field theory. In order to discuss the physical origin of the localization in the extended space, we consider a probe M2-brane in eleven dimensions. We show that a three-dimensional $$ \mathcal{N} $$ N = 4 gauge theory is naturally interpreted as a membrane generalization of the two-dimensional $$ \mathcal{N} $$ N = (4, 4) gauged linear sigma model for the fundamental string. We point out that the vector field in the $$ \mathcal{N} $$ N = 4 model is identified as a dual coordinate of the KK6-brane geometry. We find that the BPS vortex in the gauge theory gives rise to the violation of the isometry along the dual direction. We then show that the vortex corrections are regarded as an instanton effect in M-theory induced by the probe M2-brane wrapping around the M-circle.

scholarly journals Physical origin of the high energy optical response of three dimensional photonic crystals

2007 ◽  
Vol 15 (26) ◽  
pp. 17754 ◽  
Author(s):  
Luis A. Dorado ◽  
Ricardo A. Depine ◽  
Gabriel Lozano ◽  
Hernán Míguez
Keyword(s):  
Photonic Crystals ◽  
Three Dimensional ◽  
Optical Response ◽  
High Energy ◽  
Physical Origin

Three-dimensional transverse instabilities in detached boundary layers

2007 ◽  
Vol 571 ◽  
pp. 221-233 ◽  
Author(s):  
FRANÇOIS GALLAIRE ◽  
MATTHIEU MARQUILLIE ◽  
UWE EHRENSTEIN
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Linear Analysis ◽  
Navier Stokes ◽  
Physical Origin ◽  
Viscous Effects ◽  
Global Mode ◽  
Navier Stokes Equations ◽  
Recirculation Bubble

A direct numerical simulation of the incompressible Navier–Stokes equations of the flow over a bump shows a stationary longitudinal instability at a Reynolds number of Re = 400. A three-dimensional global mode linear analysis is used to interpret these results and shows that the most unstable eigenmode is steady and localized in the recirculation bubble, with spanwise wavelength of approximately ten bump heights. An inviscid geometrical optics analysis along closed streamlines is then proposed and modified to account for viscous effects. This motivates a final discussion regarding the physical origin of the observed instability.

Anisotropic, Adaptive, and Asymmetric Multi-Stability From Origami Folding

2017 ◽  
Author(s):  
Suyi Li
Keyword(s):  
Three Dimensional ◽  
Stable State ◽  
Physical Origin ◽  
Stable States ◽  
Stability Properties ◽  
Dimensional Shape ◽  
Multiple Stable States ◽  
Three Dimensional Shape ◽  
Unstable States ◽  
Lower Dimensional

This study investigates the elastic multi-stability properties originated from origami folding. Specifically, it focuses on a space-filling architecture consisting of stacked Miura-ori sheets, which exhibits multiple stable states corresponding to different internal folding configurations. The fundamentally three-dimensional shape transformations from origami folding impart several unique properties that are unachievable from the lower dimensional mechanisms. They are (1) anisotropy-arrangement of the stable and unstable states fundamentally differs along different principle axes; (2) adaptability-stable states can be generated or eliminated via simple pressurization; and (3) asymmetry-the energy barrier of switching from one stable state to another can be significantly higher than the opposite switch, even though the two stable states have the same energy level. These unique stability properties could be harnessed to create a wide variety of adaptive functionalities, such as programmable stiffness, impulsive actuation, and mechanical diode effect. The purpose of this paper is to examine the physical origin of the three stability properties and their correlations to the origami design. Results of this of study can foster the creation of novel multi-functional structures and materials based on origami.

Semiclassical quantization of three-dimensional quasi-Landau resonances under strong-field mixing

1987 ◽  
Vol 6 (4) ◽  
pp. 295-302 ◽  
Author(s):  
J. Main ◽  
A. Holle ◽  
G. Wiebusch ◽  
K. H. Welge
Keyword(s):  
Strong Field ◽  
Three Dimensional ◽  
Semiclassical Quantization

Three-dimensional optical billiard chaotic scattering

2001 ◽  
Vol 154 (3-4) ◽  
pp. 207-218 ◽  
Author(s):  
David Sweet ◽  
Benjamin W. Zeff ◽  
Edward Ott ◽  
Daniel P. Lathrop
Keyword(s):  
Three Dimensional ◽  
Chaotic Scattering

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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