3,886 research outputs found
Stable periodic waves in coupled Kuramoto-Sivashinsky - Korteweg-de Vries equations
Periodic waves are investigated in a system composed of a
Kuramoto-Sivashinsky - Korteweg-de Vries (KS-KdV) equation, which is linearly
coupled to an extra linear dissipative equation. The model describes, e.g., a
two-layer liquid film flowing down an inclined plane. It has been recently
shown that the system supports stable solitary pulses. We demonstrate that a
perturbation analysis, based on the balance equation for the field momentum,
predicts the existence of stable cnoidal waves (CnWs) in the same system. It is
found that the mean value U of the wave field u in the main subsystem, but not
the mean value of the extra field, affects the stability of the periodic waves.
Three different areas can be distinguished inside the stability region in the
parameter plane (L,U), where L is the wave's period. In these areas, stable
are, respectively, CnWs with positive velocity, constant solutions, and CnWs
with negative velocity. Multistability, i.e., the coexistence of several
attractors, including the waves with several maxima per period, appears at
large value of L. The analytical predictions are completely confirmed by direct
simulations. Stable waves are also found numerically in the limit of vanishing
dispersion, when the KS-KdV equation goes over into the KS one.Comment: a latex text file and 16 eps files with figures. Journal of the
Physical Society of Japan, in pres
Travelling-waves consistent with turbulence-driven secondary flow in a square duct
We present numerically determined travelling-wave solutions for
pressure-driven flow through a straight duct with a square cross-section. This
family of solutions represents typical coherent structures (a staggered array
of counter-rotating streamwise vortices and an associated low-speed streak) on
each wall. Their streamwise average flow in the cross-sectional plane
corresponds to an eight vortex pattern much alike the secondary flow found in
the turbulent regime
Stabilized Kuramoto-Sivashinsky system
A model consisting of a mixed Kuramoto - Sivashinsky - KdV equation, linearly
coupled to an extra linear dissipative equation, is proposed. The model applies
to the description of surface waves on multilayered liquid films. The extra
equation makes its possible to stabilize the zero solution in the model,
opening way to the existence of stable solitary pulses (SPs). Treating the
dissipation and instability-generating gain in the model as small
perturbations, we demonstrate that balance between them selects two
steady-state solitons from their continuous family existing in the absence of
the dissipation and gain. The may be stable, provided that the zero solution is
stable. The prediction is completely confirmed by direct simulations. If the
integration domain is not very large, some pulses are stable even when the zero
background is unstable. Stable bound states of two and three pulses are found
too. The work was supported, in a part, by a joint grant from the Israeli
Minsitry of Science and Technology and Japan Society for Promotion of Science.Comment: A text file in the latex format and 20 eps files with figures.
Physical Review E, in pres
Stable two-dimensional solitary pulses in linearly coupled dissipative Kadomtsev-Petviashvili equations
A two-dimensional (2D) generalization of the stabilized Kuramoto -
Sivashinsky (KS) system is presented. It is based on the Kadomtsev-Petviashvili
(KP) equation including dissipation of the generic (Newell -- Whitehead --
Segel, NWS) type and gain. The system directly applies to the description of
gravity-capillary waves on the surface of a liquid layer flowing down an
inclined plane, with a surfactant diffusing along the layer's surface.
Actually, the model is quite general, offering a simple way to stabilize
nonlinear waves in media combining the weakly-2D dispersion of the KP type with
gain and NWS dissipation. Parallel to this, another model is introduced, whose
dissipative terms are isotropic, rather than of the NWS type. Both models
include an additional linear equation of the advection-diffusion type, linearly
coupled to the main KP-NWS equation. The extra equation provides for stability
of the zero background in the system, opening a way to the existence of stable
localized pulses. The consideration is focused on the case when the dispersive
part of the system of the KP-I type, admitting the existence of 2D localized
pulses. Treating the dissipation and gain as small perturbations and making use
of the balance equation for the field momentum, we find that the equilibrium
between the gain and losses may select two 2D solitons, from their continuous
family existing in the conservative counterpart of the model (the latter family
is found in an exact analytical form). The selected soliton with the larger
amplitude is expected to be stable. Direct simulations completely corroborate
the analytical predictions.Comment: a latex text file and 16 eps files with figures; Physical Review E,
in pres
Radial velocity eclipse mapping of exoplanets
Planetary rotation rates and obliquities provide information regarding the
history of planet formation, but have not yet been measured for evolved
extrasolar planets. Here we investigate the theoretical and observational
perspective of the Rossiter-McLauglin effect during secondary eclipse (RMse)
ingress and egress for transiting exoplanets. Near secondary eclipse, when the
planet passes behind the parent star, the star sequentially obscures light from
the approaching and receding parts of the rotating planetary surface. The
temporal block of light emerging from the approaching (blue-shifted) or
receding (red-shifted) parts of the planet causes a temporal distortion in the
planet's spectral line profiles resulting in an anomaly in the planet's radial
velocity curve. We demonstrate that the shape and the ratio of the
ingress-to-egress radial velocity amplitudes depends on the planetary
rotational rate, axial tilt and impact factor (i.e. sky-projected planet
spin-orbital alignment). In addition, line asymmetries originating from
different layers in the atmosphere of the planet could provide information
regarding zonal atmospheric winds and constraints on the hot spot shape for
giant irradiated exoplanets. The effect is expected to be most-pronounced at
near-infrared wavelengths, where the planet-to-star contrasts are large. We
create synthetic near-infrared, high-dispersion spectroscopic data and
demonstrate how the sky-projected spin axis orientation and equatorial velocity
of the planet can be estimated. We conclude that the RMse effect could be a
powerful method to measure exoplanet spins.Comment: 7 pages, 3 figures, 1 table, accepted for publication in ApJ on 2015
June 1
Extracting Multidimensional Phase Space Topology from Periodic Orbits
We establish a hierarchical ordering of periodic orbits in a strongly coupled
multidimensional Hamiltonian system. Phase space structures can be
reconstructed quantitatively from the knowledge of periodic orbits alone. We
illustrate our findings for the hydrogen atom in crossed electric and magnetic
fields.Comment: 4 pages, 5 figures, accepted for publication in Phys. Rev. Let
Studies of Phase Turbulence in the One Dimensional Complex Ginzburg-Landau Equation
The phase-turbulent (PT) regime for the one dimensional complex
Ginzburg-Landau equation (CGLE) is carefully studied, in the limit of large
systems and long integration times, using an efficient new integration scheme.
Particular attention is paid to solutions with a non-zero phase gradient. For
fixed control parameters, solutions with conserved average phase gradient
exist only for less than some upper limit. The transition from phase to
defect-turbulence happens when this limit becomes zero. A Lyapunov analysis
shows that the system becomes less and less chaotic for increasing values of
the phase gradient. For high values of the phase gradient a family of
non-chaotic solutions of the CGLE is found. These solutions consist of
spatially periodic or aperiodic waves travelling with constant velocity. They
typically have incommensurate velocities for phase and amplitude propagation,
showing thereby a novel type of quasiperiodic behavior. The main features of
these travelling wave solutions can be explained through a modified
Kuramoto-Sivashinsky equation that rules the phase dynamics of the CGLE in the
PT phase. The latter explains also the behavior of the maximal Lyapunov
exponents of chaotic solutions.Comment: 16 pages, LaTeX (Version 2.09), 10 Postscript-figures included,
submitted to Phys. Rev.
Phylogeny of the Hawkmoth tribe Ambulycini: mitogenomes from museum specimens resolve major relationships
Ambulycini are a cosmopolitan tribe of the moth family Sphingidae, comprised of ten genera, three of which are found in tropical Asia, four in the Neotropics, one in Africa, one in the Middle East and one restricted to the islands of New Caledonia. Recent phylogenetic analyses of the tribe have yielded conflicting results, and some have suggested a close relationship of the monobasic New Caledonian genus Compsulyx Holloway, 1979 to the Neotropical ones, despite being found on opposite sides of the Pacific Ocean. Here we investigate relationships within the tribe using full mitochondrial genomes, mainly derived from dry-pinned museum collections material. Mitogenomic data were obtained for 19 species representing nine of the ten Ambulycini genera. Phylogenetic trees are in agreement with a tropical Asian origin for the tribe. Furthermore, results indicate that the Neotropical genus Adhemarius Oiticica Filho, 1939 is paraphyletic and support the notion that Orecta Rothschild & Jordan 1903 and Trogolegnum Rothschild & Jordan, 1903 may need to be synonymized. Finally, in our analysis the Neotropical genera do not collectively form a monophyletic group, due to a clade comprising the New Caledonian genus Compsulyx and the African genus Batocnema Rothschild & Jordan, 1903 being placed as sister to the Neotropical genus Protambulyx Rothschild & Jordan, 1903. This finding implies a complex biogeographic history and suggests the evolution of the tribe involved at least two long-distance dispersal events
Low regularity solutions of two fifth-order KdV type equations
The Kawahara and modified Kawahara equations are fifth-order KdV type
equations and have been derived to model many physical phenomena such as
gravity-capillary waves and magneto-sound propagation in plasmas. This paper
establishes the local well-posedness of the initial-value problem for Kawahara
equation in with and the local well-posedness
for the modified Kawahara equation in with .
To prove these results, we derive a fundamental estimate on dyadic blocks for
the Kawahara equation through the multiplier norm method of Tao
\cite{Tao2001} and use this to obtain new bilinear and trilinear estimates in
suitable Bourgain spaces.Comment: 17page
Beyond a pale blue dot : how to search for possible bio-signatures on earth-like planets
The Earth viewed from outside the Solar system would be identified merely
like a pale blue dot, as coined by Carl Sagan. In order to detect possible
signatures of the presence of life on a second earth among several terrestrial
planets discovered in a habit-able zone, one has to develop and establish a
methodology to characterize the planet as something beyond a mere pale blue
dot. We pay particular attention to the periodic change of the color of the dot
according to the rotation of the planet. Because of the large-scale
inhomogeneous distribution of the planetary surface, the reflected light of the
dot comprises different color components corresponding to land, ocean, ice, and
cloud that cover the surface of the planet. If we decompose the color of the
dot into several principle components, in turn, one can identify the presence
of the different surface components. Furthermore, the vegetation on the earth
is known to share a remarkable reflection signature; the reflection becomes
significantly enhanced at wave-lengths longer than 760nm, which is known as a
red-edge of the vegetation. If one can identify the corresponding color
signature in a pale blue dot, it can be used as a unique probe of the presence
of life. I will describe the feasibility of the methodology for future space
missions, and consider the direction towards astrobiology from an
astrophysicist's point of view.Comment: 11 pages, 5 figures, published in Yamagishi A., Kakegawa T., Usui T.
(eds) Astrobiology. Springer, Singapore (2019
- …