44,081 research outputs found
Scarred Patterns in Surface Waves
Surface wave patterns are investigated experimentally in a system geometry
that has become a paradigm of quantum chaos: the stadium billiard. Linear waves
in bounded geometries for which classical ray trajectories are chaotic are
known to give rise to scarred patterns. Here, we utilize parametrically forced
surface waves (Faraday waves), which become progressively nonlinear beyond the
wave instability threshold, to investigate the subtle interplay between
boundaries and nonlinearity. Only a subset (three main types) of the computed
linear modes of the stadium are observed in a systematic scan. These correspond
to modes in which the wave amplitudes are strongly enhanced along paths
corresponding to certain periodic ray orbits. Many other modes are found to be
suppressed, in general agreement with a prediction by Agam and Altshuler based
on boundary dissipation and the Lyapunov exponent of the associated orbit.
Spatially asymmetric or disordered (but time-independent) patterns are also
found even near onset. As the driving acceleration is increased, the
time-independent scarred patterns persist, but in some cases transitions
between modes are noted. The onset of spatiotemporal chaos at higher forcing
amplitude often involves a nonperiodic oscillation between spatially ordered
and disordered states. We characterize this phenomenon using the concept of
pattern entropy. The rate of change of the patterns is found to be reduced as
the state passes temporarily near the ordered configurations of lower entropy.
We also report complex but highly symmetric (time-independent) patterns far
above onset in the regime that is normally chaotic.Comment: 9 pages, 10 figures (low resolution gif files). Updated and added
references and text. For high resolution images:
http://physics.clarku.edu/~akudrolli/stadium.htm
In-Plane Focusing of Terahertz Surface Waves on a Gradient Index Metamaterial Film
We designed and implemented a gradient index metasurface for the in-plane
focusing of confined terahertz surface waves. We measured the spatial
propagation of the surface waves by two-dimensional mapping of the complex
electric field using a terahertz near-field spectroscope. The surface waves
were focused to a diameter of 500 \micro m after a focal length of approx. 2
mm. In the focus, we measured a field amplitude enhancement of a factor of 3.Comment: 6 pages, 4 figure
Superlattice Patterns in Surface Waves
We report novel superlattice wave patterns at the interface of a fluid layer
driven vertically. These patterns are described most naturally in terms of two
interacting hexagonal sublattices. Two frequency forcing at very large aspect
ratio is utilized in this work. A superlattice pattern ("superlattice-I")
consisting of two hexagonal lattices oriented at a relative angle of 22^o is
obtained with a 6:7 ratio of forcing frequencies. Several theoretical
approaches that may be useful in understanding this pattern have been proposed.
In another example, the waves are fully described by two superimposed hexagonal
lattices with a wavelength ratio of sqrt(3), oriented at a relative angle of
30^o. The time dependence of this "superlattice-II" wave pattern is unusual.
The instantaneous patterns reveal a time-periodic stripe modulation that breaks
the 6-fold symmetry at any instant, but the stripes are absent in the time
average. The instantaneous patterns are not simply amplitude modulations of the
primary standing wave. A transition from the superlattice-II state to a 12-fold
quasi-crystalline pattern is observed by changing the relative phase of the two
forcing frequencies. Phase diagrams of the observed patterns (including
superlattices, quasicrystalline patterns, ordinary hexagons, and squares) are
obtained as a function of the amplitudes and relative phases of the driving
accelerations.Comment: 15 pages, 14 figures (gif), to appear in Physica
Two-dimensional surface waves in magnetohydrodynamics
The study of nonlinear waves in water has a long history beginning with the seminal paper by Korteweg & de Vries (Phil. Mag., vol. 39, 1895, p. 240) and more recently for magnetohydrodynamics Danov & Ruderman (Fluid Dyn., vol. 18, 1983, pp. 751–756). The appearance of a Hilbert transform in the nonlinear equation for magnetohydrodynamics (MHD) distinguishes it from the water wave model description. In this paper, we are interested in examining weakly nonlinear interfacial waves in dimensions. First, we determine the wave solution in the linear case. Next, we derive the corresponding generalisation for the Kadomtsev–Petviashvili (KP) equation with the inclusion of an equilibrium magnetic field. The derived governing equation is a generalisation of the Benjamin–Ono (BO) equation called the Benjamin equation first derived in Benjamin (J. Fluid Mech., vol. 245, 1992, pp. 401–411) and in the higher-dimensional context in Kim & Akylas (J. Fluid Mech., vol. 557, 2006, pp. 237–256)
Diffraction-Free Bloch Surface Waves
In this letter, we demonstrate a novel diffraction-free Bloch surface wave
(DF-BSW) sustained on all-dielectric multilayers that does not diffract after
being passed through three obstacles or across a single mode fiber. It can
propagate in a straight line for distances longer than 110 {\mu}m at a
wavelength of 633 nm and could be applied as an in-plane optical virtual probe,
both in air and in an aqueous environment. The ability to be used in water, its
long diffraction-free distance, and its tolerance to multiple obstacles make
this DF-BSW ideal for certain applications in areas such as the biological
sciences, where many measurements are made on glass surfaces or for which an
aqueous environment is required, and for high-speed interconnections between
chips, where low loss is necessary. Specifically, the DF-BSW on the dielectric
multilayer can be used to develop novel flow cytometry that is based on the
surface wave, but not the free space beam, to detect the surface-bound targets
Surface waves enhance particle dispersion
We study the horizontal dispersion of passive tracer particles on the free
surface of gravity waves in deep water. For random linear waves with the
JONSWAP spectrum, the Lagrangian particle trajectories are computed using an
exact nonlinear model known as the John--Sclavounos equation. We show that the
single-particle dispersion exhibits an unusual super-diffusive behavior. In
particular, for large times , the variance of the tracer increases as a quadratic function of time, i.e., . This dispersion is markedly faster than Taylor's
single-particle dispersion theory which predicts that the variance of passive
tracers grows linearly with time for large . Our results imply that the wave
motion significantly enhances the dispersion of fluid particles. We show that
this super-diffusive behavior is a result of the long-term correlation of the
Lagrangian velocities of fluid parcels on the free surface
Dispersion and damping of potential surface waves in a degenerate plasma
Potential (electrostatic) surface waves in plasma half-space with degenerate
electrons are studied using the quasi-classical mean-field kinetic model. The
wave spectrum and the collisionless damping rate are obtained numerically for a
wide range of wavelengths. In the limit of long wavelengths, the wave frequency
approaches the cold-plasma limit with
being the plasma frequency, while at short wavelengths, the wave
spectrum asymptotically approaches the spectrum of zero-sound mode propagating
along the boundary. It is shown that the surface waves in this system remain
weakly damped at all wavelengths (in contrast to strongly damped surface waves
in Maxwellian electron plasmas), and the damping rate nonmonotonically depends
on the wavelength, with the maximum (yet small) damping occuring for surface
waves with wavelength of , where is the
Thomas-Fermi length.Comment: 22 pages, 6 figure
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