2,362 research outputs found
Broken symmetries and pattern formation in two-frequency forced Faraday waves
We exploit the presence of approximate (broken) symmetries to obtain general
scaling laws governing the process of pattern formation in weakly damped
Faraday waves. Specifically, we consider a two-frequency forcing function and
trace the effects of time translation, time reversal and Hamiltonian structure
for three illustrative examples: hexagons, two-mode superlattices, and two-mode
rhomboids. By means of explicit parameter symmetries, we show how the size of
various three-wave resonant interactions depends on the frequency ratio m:n and
on the relative temporal phase of the two driving terms. These symmetry-based
predictions are verified for numerically calculated coefficients, and help
explain the results of recent experiments.Comment: 4 pages, 6 figure
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
Super-lattice, rhombus, square, and hexagonal standing waves in magnetically driven ferrofluid surface
Standing wave patterns that arise on the surface of ferrofluids by (single
frequency) parametric forcing with an ac magnetic field are investigated
experimentally. Depending on the frequency and amplitude of the forcing, the
system exhibits various patterns including a superlattice and subharmonic
rhombuses as well as conventional harmonic hexagons and subharmonic squares.
The superlattice arises in a bicritical situation where harmonic and
subharmonic modes collide. The rhombic pattern arises due to the non-monotonic
dispersion relation of a ferrofluid
"It All Ended in an Unsporting Way": Serbian Football and the Disintegration of Yugoslavia, 1989-2006
Part of a wider examination into football during the collapse of Eastern European Communism between 1989 and 1991, this article studies the interplay between Serbian football and politics during the period of Yugoslavia's demise. Research utilizing interviews with individuals directly involved in the Serbian game, in conjunction with contemporary Yugoslav media sources, indicates that football played an important proactive role in the revival of Serbian nationalism. At the same time the Yugoslav conflict, twinned with a complex transition to a market economy, had disastrous consequences for football throughout the territories of the former Yugoslavia. In the years following the hostilities the Serbian game has suffered decline, major financial hardship and continuing terrace violence, resulting in widespread nostalgia for the pre-conflict era
Nonlinear Competition Between Small and Large Hexagonal Patterns
Recent experiments by Kudrolli, Pier and Gollub on surface waves,
parametrically excited by two-frequency forcing, show a transition from a small
hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We
show that generically the hexagons and the superlattice wave patterns bifurcate
simultaneously from the flat surface state as the forcing amplitude is
increased, and that the experimentally-observed transition can be described by
considering a low-dimensional bifurcation problem. A number of predictions come
out of this general analysis.Comment: 4 pages, RevTex, revised, to appear in Phys. Rev. Let
Pattern formation in 2-frequency forced parametric waves
We present an experimental investigation of superlattice patterns generated
on the surface of a fluid via parametric forcing with 2 commensurate
frequencies. The spatio-temporal behavior of 4 qualitatively different types of
superlattice patterns is described in detail. These states are generated via a
number of different 3--wave resonant interactions. They occur either as
symmetry--breaking bifurcations of hexagonal patterns composed of a single
unstable mode or via nonlinear interactions between the two primary unstable
modes generated by the two forcing frequencies. A coherent picture of these
states together with the phase space in which they appear is presented. In
addition, we describe a number of new superlattice states generated by 4--wave
interactions that arise when symmetry constraints rule out 3--wave resonances.Comment: The paper contains 34 pages and 53 figures and provides an extensive
review of both the theoretical and experimental work peformed in this syste
Phenoconversion from probable rapid eye movement sleep behavior disorder to mild cognitive impairment to dementia in a population-based sample
© 2017 The Authors Introduction Rapid eye movement sleep behavior disorder (RBD) is strongly associated with synucleinopathies. In 2012, we reported an increased risk of mild cognitive impairment (MCI) and Parkinson disease (PD) in cognitively normal Olmsted County, Minnesota, residents, aged 70 to 89 years with probable RBD. Here, we examine their progression to dementia and other neurodegenerative phenotypes. Methods Fifteen participants with RBD who were diagnosed with either MCI or PD were longitudinally followed, and their subsequent clinical courses were reviewed. Results Over 6.4 ± 2.9 years, six of the 14 participants with MCI developed additional neurodegenerative signs, five of whom had Lewy body disease features. Four of them progressed to dementia at a mean age 84.8 ± 4.9 years, three of whom met the criteria for probable dementia with Lewy bodies. One subject with PD developed MCI, but not dementia. Discussion Our findings from the population-based sample of Olmsted County, Minnesota, residents suggest that a substantial number of RBD patients tend to develop overt synucleinopathy features over time, and RBD patients who develop MCI and subsequent dementia have clinical features most consistent with dementia with Lewy bodies
Coherent motion of stereocilia assures the concerted gating of hair-cell transduction channels
The hair cell's mechanoreceptive organelle, the hair bundle, is highly
sensitive because its transduction channels open over a very narrow range of
displacements. The synchronous gating of transduction channels also underlies
the active hair-bundle motility that amplifies and tunes responsiveness. The
extent to which the gating of independent transduction channels is coordinated
depends on how tightly individual stereocilia are constrained to move as a
unit. Using dual-beam interferometry in the bullfrog's sacculus, we found that
thermal movements of stereocilia located as far apart as a bundle's opposite
edges display high coherence and negligible phase lag. Because the mechanical
degrees of freedom of stereocilia are strongly constrained, a force applied
anywhere in the hair bundle deflects the structure as a unit. This feature
assures the concerted gating of transduction channels that maximizes the
sensitivity of mechanoelectrical transduction and enhances the hair bundle's
capacity to amplify its inputs.Comment: 24 pages, including 6 figures, published in 200
Faraday waves on a viscoelastic liquid
We investigate Faraday waves on a viscoelastic liquid. Onset measurements and
a nonlinear phase diagram for the selected patterns are presented. By virtue of
the elasticity of the material a surface resonance synchronous to the external
drive competes with the usual subharmonic Faraday instability. Close to the
bicriticality the nonlinear wave interaction gives rise to a variety of novel
surface states: Localised patches of hexagons, hexagonal superlattices,
coexistence of hexagons and lines. Theoretical stability calculations and
qualitative resonance arguments support the experimental observations.Comment: 4 pages, 4figure
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