1,162 research outputs found
Unstable periodic orbits in a chaotic meandering jet flow
We study the origin and bifurcations of typical classes of unstable periodic
orbits in a jet flow that was introduced before as a kinematic model of chaotic
advection, transport and mixing of passive scalars in meandering oceanic and
atmospheric currents. A method to detect and locate the unstable periodic
orbits and classify them by the origin and bifurcations is developed. We
consider in detail period-1 and period-4 orbits playing an important role in
chaotic advection. We introduce five classes of period-4 orbits: western and
eastern ballistic ones, whose origin is associated with ballistic resonances of
the fourth order, rotational ones, associated with rotational resonances of the
second and fourth orders, and rotational-ballistic ones associated with a
rotational-ballistic resonance. It is a new kind of nonlinear resonances that
may occur in chaotic flow with jets and/or circulation cells. Varying the
perturbation amplitude, we track out the origin and bifurcations of the orbits
for each class
Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling
Small lattices of nearest neighbor coupled excitable FitzHugh-Nagumo
systems, with time-delayed coupling are studied, and compared with systems of
FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of
equilibria in N=2 case are studied analytically, and it is then numerically
confirmed that the same bifurcations are relevant for the dynamics in the case
. Bifurcations found include inverse and direct Hopf and fold limit cycle
bifurcations. Typical dynamics for different small time-lags and coupling
intensities could be excitable with a single globally stable equilibrium,
asymptotic oscillatory with symmetric limit cycle, bi-stable with stable
equilibrium and a symmetric limit cycle, and again coherent oscillatory but
non-symmetric and phase-shifted. For an intermediate range of time-lags inverse
sub-critical Hopf and fold limit cycle bifurcations lead to the phenomenon of
oscillator death. The phenomenon does not occur in the case of FitzHugh-Nagumo
oscillators with the same type of coupling.Comment: accepted by Phys.Rev.
A New High Resolution CO Map of the inner 2.'5 of M51 I. Streaming Motions and Spiral Structure
[Abridged] The Owens Valley mm-Array has been used to map the CO 1--0
emission in the inner 2'.5 of the grand design spiral galaxy M51 at 2''-3''
resolution. The molecular spiral arms are revealed with unprecedented clarity:
supermassive cloud complexes, Giant Molecular Associations, are for the first
time resolved both along and perpendicular to the arms. Major complexes occur
symmetrically opposite each other in the two major arms. Streaming motions can
be studied in detail along the major and minor axes of M51. The streaming
velocities are very large, 60-150 km/s. For the first time, sufficient
resolution to resolve the structure in the molecular streaming motions is
obtained. Our data support the presence of galactic shocks in the arms of M51.
In general, velocity gradients across arms are higher by a factor of 2-10 than
previously found. They vary in steepness along the spiral arms, becoming
particularly steep in between GMAs. The steep gradients cause conditions of
strong reverse shear in several regions in the arms, and thus the notion that
shear is generally reduced by streaming motions in spiral arms will have to be
modified. Of the three GMAs studied on the SW arm, only one shows reduced
shear. We find an expansion in the NE molecular arm at 25'' radius SE of the
center. This broadening occurs right after the end of the NE arm at the Inner
Lindblad Resonance. Bifurcations in the molecular spiral arm structure, at a
radius of 73'', may be evidence of a secondary compression of the gas caused by
the 4/1 ultraharmonic resonance. Inside the radius of the ILR, we detect narrow
(~ 5'') molecular spiral arms possibly related to the K-band arms found in the
same region. We find evidence of non-circular motions in the inner 20'' which
are consistent with gas on elliptical orbits in a bar.Comment: 29 pages, 15 figures, uses latex macros for ApJ; accepted for
publication in Ap
Hydrodynamic instabilities in gaseous detonations: comparison of Euler, Navier–Stokes, and large-eddy simulation
A large-eddy simulation is conducted to investigate the transient structure of an unstable detonation wave in two dimensions and the evolution of intrinsic hydrodynamic instabilities. The dependency of the detonation structure on the grid resolution is investigated, and the structures obtained by large-eddy simulation are compared with the predictions from solving the Euler and Navier–Stokes equations directly. The results indicate that to predict irregular detonation structures in agreement with experimental observations the vorticity generation and dissipation in small scale structures should be taken into account. Thus, large-eddy simulation with high grid resolution is required. In a low grid resolution scenario, in which numerical diffusion dominates, the structures obtained by solving the Euler or Navier–Stokes equations and large-eddy simulation are qualitatively similar. When high grid resolution is employed, the detonation structures obtained by solving the Euler or Navier–Stokes equations directly are roughly similar yet equally in disagreement with the experimental results. For high grid resolution, only the large-eddy simulation predicts detonation substructures correctly, a fact that is attributed to the increased dissipation provided by the subgrid scale model. Specific to the investigated configuration, major differences are observed in the occurrence of unreacted gas pockets in the high-resolution Euler and Navier–Stokes computations, which appear to be fully combusted when large-eddy simulation is employed
A short proof of chaos in an atmospheric system
We will prove the presence of chaotic motion in the Lorenz five-component
atmospheric system model using the Melnikov function method developed by Holmes
and Marsden for Hamiltonian systems on Lie Groups.Comment: PACS: 02.20.Sv; 02.30.Hg; 02.40.-k; 92.60.-e. 5 page
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