scholarly journals Spatiotemporal Symmetries in the Disynaptic Canal-Neck Projection

2007 ◽  
Vol 67 (5) ◽  
pp. 1396-1417 ◽  
Author(s):  
Martin Golubitsky ◽  
LieJune Shiau ◽  
Ian Stewart
Keyword(s):  
Spatiotemporal Symmetries

scholarly journals Stability analysis of the elliptic cylinder wake

2014 ◽  
Vol 763 ◽  
pp. 302-321 ◽  
Author(s):  
Justin S. Leontini ◽  
David Lo Jacono ◽  
Mark C. Thompson
Keyword(s):  
Stability Analysis ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Cylinder Wake ◽  
Long Wavelength ◽  
Aspect Ratios ◽  
Numerical Stability Analysis ◽  
Spatiotemporal Symmetries ◽  
Three Dimensional Simulations

AbstractThis paper presents the results of numerical stability analysis of the wake of an elliptical cylinder. Aspect ratios where the ellipse is longer in the streamwise direction than in the transverse direction are considered. The focus is on the dependence on the aspect ratio of the ellipse of the various bifurcations to three-dimensional flow from the two-dimensional Kármán vortex street. It is shown that the three modes present in the wake of a circular cylinder (modes A, B and QP) are present in the ellipse wake, and that in general they are all stabilized by increasing the aspect ratio of the ellipse. Two new pertinent modes are found: one long-wavelength mode with similarities to mode A, and a second that is only unstable for aspect ratios greater than approximately 1.75, which has similar spatiotemporal symmetries to mode B but has a distinct spatial structure. Results from fully three-dimensional simulations are also presented confirming the existence and growth of these two new modes in the saturated wakes.

scholarly journals Bifurcation from relative periodic solutions

2001 ◽  
Vol 21 (2) ◽  
pp. 605-635 ◽  
Author(s):  
CLAUDIA WULFF ◽  
JEROEN S. W. LAMB ◽  
IAN MELBOURNE
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Systematic Approach ◽  
Local Bifurcation ◽  
Dimensional Problem ◽  
Continuous Symmetry ◽  
Finite Dimensional ◽  
Bundle Theorem ◽  
Spatiotemporal Symmetries

Relative periodic solutions are ubiquitous in dynamical systems with continuous symmetry. Recently, Sandstede, Scheel and Wulff derived a center bundle theorem, reducing local bifurcation from relative periodic solutions to a finite-dimensional problem. Independently, Lamb and Melbourne showed how to systematically study local bifurcation from isolated periodic solutions with discrete spatiotemporal symmetries.In this paper, we show how the center bundle theorem, when combined with certain group theoretic results, reduces bifurcation from relative periodic solutions to bifurcation from isolated periodic solutions. In this way, we obtain a systematic approach to the study of local bifurcation from relative periodic solutions.

CONTROL OF SPATIOTEMPORAL CHAOS IN NEURONAL NETWORKS

1996 ◽  
Vol 07 (04) ◽  
pp. 507-517 ◽  
Author(s):  
CARLOS LOURENÇO ◽  
AGNESSA BABLOYANTZ
Keyword(s):  
Chaos Control ◽  
Neuronal Networks ◽  
Spatiotemporal Chaos ◽  
High Dimensional ◽  
High Dimensions ◽  
Physical Systems ◽  
Control Techniques ◽  
Spatiotemporal Symmetries ◽  
Very High

Different strategies for the control of chaotic neuronal networks and physical systems are presented. The variables of the dynamics span phase-spaces with very high dimensions. Novel control techniques are introduced that handle these high-dimensional cases. Depending on the system, several orbits with different spatiotemporal symmetries may be stabilized out of the chaotic attractor. The role of chaos control in information processing is pointed out.

COLLECTIVE DIRECTIONAL TRANSPORT AND COUPLED BROWNIAN RATCHETS

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2498-2504 ◽  
Author(s):  
ZHIGANG ZHENG
Keyword(s):  
Coupled Systems ◽  
Spatial Symmetry ◽  
Substrate Potential ◽  
Cooperative Dynamics ◽  
Brownian Ratchets ◽  
Directional Transport ◽  
Spatiotemporal Symmetries

Recent progresses on collective directional transport in coupled systems are overviewed. By considering the mutual interactions among elements, the directed ratchet motion exhibits complicated and novel cooperative dynamics. The directional transport can be induced not only by breaking the spatial symmetry of the substrate potential, but also by breaking the coupling symmetry and the spatiotemporal symmetries.

scholarly journals Directed Transport of Atoms in a Hamiltonian Quantum Ratchet

Science ◽  
2009 ◽  
Vol 326 (5957) ◽  
pp. 1241-1243 ◽  
Author(s):  
Tobias Salger ◽  
Sebastian Kling ◽  
Tim Hecking ◽  
Carsten Geckeler ◽  
Luis Morales-Molina ◽  
...  
Keyword(s):  
Optical Lattice ◽  
Observation Time ◽  
Einstein Condensate ◽  
Transport Current ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Observation Times ◽  
Spatiotemporal Symmetries ◽  
Driving Potential ◽  
Full Quantum

Classical ratchet potentials, which alternate a driving potential with periodic random dissipative motion, can account for the operation of biological motors. We demonstrate the operation of a quantum ratchet, which differs from classical ratchets in that dissipative processes are absent within the observation time of the system (Hamiltonian regime). An atomic rubidium Bose-Einstein condensate is exposed to a sawtooth-like optical lattice potential, whose amplitude is periodically modulated in time. The ratchet transport arises from broken spatiotemporal symmetries of the driven potential, resulting in a desymmetrization of transporting eigenstates (Floquet states). The full quantum character of the ratchet transport was demonstrated by the measured atomic current oscillating around a nonzero stationary value at longer observation times, resonances occurring at positions determined by the photon recoil, and dependence of the transport current on the initial phase of the driving potential.

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