5,152 research outputs found
Bifurcations of periodic orbits with spatio-temporal symmetries
Motivated by recent analytical and numerical work on two- and three-dimensional convection with imposed spatial periodicity, we analyse three examples of bifurcations from a continuous group orbit of spatio-temporally symmetric periodic solutions of partial differential equations. Our approach is based on centre manifold reduction for maps, and is in the spirit of earlier work by Iooss (1986) on bifurcations of group orbits of spatially symmetric equilibria. Two examples, two-dimensional pulsating waves (PW) and three-dimensional alternating pulsating waves (APW), have discrete spatio-temporal symmetries characterized by the cyclic groups Z_n, n=2 (PW) and n=4 (APW). These symmetries force the Poincare' return map M to be the nth iterate of a map G: M=G^n. The group orbits of PW and APW are generated by translations in the horizontal directions and correspond to a circle and a two-torus, respectively. An instability of pulsating waves can lead to solutions that drift along the group orbit, while bifurcations with Floquet multiplier +1 of alternating pulsating waves do not lead to drifting solutions. The third example we consider, alternating rolls, has the spatio-temporal symmetry of alternating pulsating waves as well as being invariant under reflections in two vertical planes. This leads to the possibility of a doubling of the marginal Floquet multiplier and of bifurcation to two distinct types of drifting solutions. We conclude by proposing a systematic way of analysing steady-state bifurcations of periodic orbits with discrete spatio-temporal symmetries, based on applying the equivariant branching lemma to the irreducible representations of the spatio-temporal symmetry group of the periodic orbit, and on the normal form results of Lamb (1996). This general approach is relevant to other pattern formation problems, and contributes to our understanding of the transition from ordered to disordered behaviour in pattern-forming systems
Structure in the nucleus of NGC 1068 at 10 microns
New 8 to 13 micron array camera images of the central kiloparsec of Seyfert 2 galaxy NGC 1068 resolve structure that is similar to that observed at visible and radio wavelengths. The images reveal an infrared source which is extended and asymmetric, with its long axis oriented at P.A. 33 deg. Maps of the spatial distribution of 8 to 13 micron color temperature and warm dust opacity are derived from the multiwavelength infrared images. The results suggest that there exist two pointlike luminosity sources in the central regions of NGC 1068, with the brighter source at the nucleus and the fainter one some 100 pc to the northeast. This geometry strengthens the possibility that the 10 micron emission observed from grains in the nucleus is powered by a nonthermal source. In the context of earlier visible and radio studies, these results considerably strengthen the case for jet induced star formation in NGC 1068
The 8.3 and 12.4 micron imaging of the Galactic Center source complex with the Goddard infrared array camera
A 30 x 30 arcsec field at the Galactic Center (1.5 x 1.5 parsec) was mapped at 8.3 microns and 12.41 microns with high spatial resolution and accurate relative astrometry, using the 16 x 16 Si:Bi accumulation mode charge injection device Goddard infrared array camera. The design and performance of the array camera detector electronics system and image data processing techniques are discussed. Color temperature and dust opacity distributions derived from the spatially accurate images indicate that the compact infrared sources and the large scale ridge structure are bounded by warmer, more diffuse material. None of the objects appear to be heated appreciably by internal luminosity sources. These results are consistent with the model proposing that the complex is heated externally by a strong luminosity source at the Galactic Center, which dominates the energetics of the inner few parsecs of the galaxy
Hydrodynamics of confined colloidal fluids in two dimensions
We apply a hybrid Molecular Dynamics and mesoscopic simulation technique to
study the dynamics of two dimensional colloidal discs in confined geometries.
We calculate the velocity autocorrelation functions, and observe the predicted
long time hydrodynamic tail that characterizes unconfined fluids, as
well as more complex oscillating behavior and negative tails for strongly
confined geometries. Because the tail of the velocity autocorrelation
function is cut off for longer times in finite systems, the related diffusion
coefficient does not diverge, but instead depends logarithmically on the
overall size of the system.Comment: RevTex 13 pages, 9 figure
A systematically coarse-grained model for DNA, and its predictions for persistence length, stacking, twist, and chirality
We introduce a coarse-grained model of DNA with bases modeled as rigid-body
ellipsoids to capture their anisotropic stereochemistry. Interaction potentials
are all physicochemical and generated from all-atom simulation/parameterization
with minimal phenomenology. Persistence length, degree of stacking, and twist
are studied by molecular dynamics simulation as functions of temperature, salt
concentration, sequence, interaction potential strength, and local position
along the chain, for both single- and double-stranded DNA where appropriate.
The model of DNA shows several phase transitions and crossover regimes in
addition to dehybridization, including unstacking, untwisting, and collapse
which affect mechanical properties such as rigidity and persistence length. The
model also exhibits chirality with a stable right-handed and metastable
left-handed helix.Comment: 30 pages, 20 figures, Supplementary Material available at
http://www.physics.ubc.ca/~steve/publications.htm
Fresnel Representation of the Wigner Function: An Operational Approach
We present an operational definition of the Wigner function. Our method
relies on the Fresnel transform of measured Rabi oscillations and applies to
motional states of trapped atoms as well as to field states in cavities. We
illustrate this technique using data from recent experiments in ion traps [D.
M. Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996)] and in cavity QED [B.
Varcoe et al., Nature 403, 743 (2000)]. The values of the Wigner functions of
the underlying states at the origin of phase space are W(0)=+1.75 for the
vibrational ground state and W(0)=-1.4 for the one-photon number state. We
generalize this method to wave packets in arbitrary potentials.Comment: 4 pages include 4 figures, submitted to PR
Anomalous translational velocity of vortex ring with finite-amplitude Kelvin waves
We consider finite-amplitude Kelvin waves on an inviscid vortex assuming that
the vortex core has infinitesimal thickness. By numerically solving the
governing Biot-Savart equation of motion, we study how the frequency of the
Kelvin waves and the velocity of the perturbed ring depend on the Kelvin wave
amplitude. In particular, we show that, if the amplitude of the Kelvin waves is
sufficiently large, the perturbed vortex ring moves backwards.Comment: 6 pages, 5 figures, v2: minor changes, v3: typos correcte
Overcritical Rotation of a Trapped Bose-Einstein Condensate
The rotational motion of an interacting Bose-Einstein condensate confined by
a harmonic trap is investigated by solving the hydrodynamic equations of
superfluids, with the irrotationality constraint for the velocity field. We
point out the occurrence of an overcritical branch where the system can rotate
with angular velocity larger than the oscillator frequencies. We show that in
the case of isotropic trapping the system exhibits a bifurcation from an
axisymmetric to a triaxial configuration, as a consequence of the interatomic
forces. The dynamical stability of the rotational motion with respect to the
dipole and quadrupole oscillations is explicitly discussed.Comment: 6 pages, 3 postscript figure
Three-dimensional gravity-capillary solitary waves in water of finite depth and related problems
Colloquium: Theory of Drag Reduction by Polymers in Wall Bounded Turbulence
The flow of fluids in channels, pipes or ducts, as in any other wall-bounded
flow (like water along the hulls of ships or air on airplanes) is hindered by a
drag, which increases many-folds when the fluid flow turns from laminar to
turbulent. A major technological problem is how to reduce this drag in order to
minimize the expense of transporting fluids like oil in pipelines, or to move
ships in the ocean. It was discovered in the mid-twentieth century that minute
concentrations of polymers can reduce the drag in turbulent flows by up to 80%.
While experimental knowledge had accumulated over the years, the fundamental
theory of drag reduction by polymers remained elusive for a long time, with
arguments raging whether this is a "skin" or a "bulk" effect. In this
colloquium review we first summarize the phenomenology of drag reduction by
polymers, stressing both its universal and non-universal aspects, and then
proceed to review a recent theory that provides a quantitative explanation of
all the known phenomenology. We treat both flexible and rod-like polymers,
explaining the existence of universal properties like the Maximum Drag
Reduction (MDR) asymptote, as well as non-universal cross-over phenomena that
depend on the Reynolds number, on the nature of the polymer and on its
concentration. Finally we also discuss other agents for drag reduction with a
stress on the important example of bubbles.Comment: Invited Colloquium Paper for Reviews of Modern Physics, 24 pages, 18
Figs., submitte
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