4,673 research outputs found
Integrable discretizations of a two-dimensional Hamiltonian system with a quartic potential
In this paper, we propose integrable discretizations of a two-dimensional
Hamiltonian system with quartic potentials. Using either the method of
separation of variables or the method based on bilinear forms, we construct the
corresponding integrable mappings for the first three among four integrable
cases
Hypergeometric solutions to Schr\"odinger equations for the quantum Painlev\'e equations
We consider Schr\"odinger equations for the quantum Painlev\'e equations. We
present hypergeometric solutions of the Schr\"odinger equations for the quantum
Painlev\'e equations, as particular solutions. We also give a representation
theoretic correspondence between Hamiltonians of the Schr\"odinger equations
for the quantum Painlev\'e equations and those of the KZ equation or the
confluent KZ equations.Comment: 17 pages; Journal of Mathematical Physics (Vol.52, Issue 8) 201
Intertidal finger bars at El Puntal, Bay of Santander, Spain: observation and forcing analysis
A system of 15 small-scale finger bars has been observed, by using video
imagery, between 23 June 2008 and 2 June 2010. The bar system is located in
the intertidal zone of the swell-protected beaches of El Puntal Spit, in the
Bay of Santander (northern coast of Spain). The bars appear on a planar beach
(slope = 0.015) with fine, uniform sand (<i>D</i><sub>50</sub> = 0.27 mm) and
extend 600 m alongshore. The cross-shore span of the bars is
determined by the tidal horizontal excursion (between 70 and 130 m).
They have an oblique orientation with respect to the low-tide shoreline;
specifically, they are down-current-oriented with respect to the dominant
sand transport computed (mean angle of 26° from the shore normal).
Their mean wavelength is 26 m and their amplitude varies between 10
and 20 cm. The full system slowly migrates to the east (sand
transport direction) with a mean speed of 0.06 m day<sup>-1</sup>, a maximum
speed in winter (up to 0.15 m day<sup>-1</sup>) and a minimum speed in
summer. An episode of merging has been identified as bars with larger
wavelength seem to migrate more slowly than shorter bars. The wind blows
predominantly from the west, generating waves that transport sediment across
the bars during high-tide periods. This is the main candidate to explain the
eastward migration of the system. In particular, the wind can generate waves
of up to 20 cm (root-mean-squared wave height) over a fetch that can
reach 4.5 km at high tide. The astronomical tide seems to be
important in the bar dynamics, as the tidal level changes the fetch and also
determines the time of exposure of the bars to the surf-zone waves and
currents. Furthermore, the river discharge could act as input of suspended
sediment in the bar system and play a role in the bar dynamics
On spectral scaling laws for incompressible anisotropic MHD turbulence
A heuristic model is given for anisotropic magnetohydrodynamics (MHD)
turbulence in the presence of a uniform external magnetic field B_0 {\bf {\hat
e}_{\pa}}. The model is valid for both moderate and strong and is able
to describe both the strong and weak wave turbulence regimes as well as the
transition between them. The main ingredient of the model is the assumption of
constant ratio at all scales between \add{the} linear wave period and \add{the}
nonlinear turnover timescale. Contrary to the model of critical balance
introduced by Goldreich and Sridhar [P. Goldreich and S. Sridhar, ApJ {\bf
438}, 763 (1995)], it is not assumed in addition that this ratio be equal to
unity at all scales which allows us to use the Iroshnikov-Kraichnan
phenomenology. It is then possible to recover the widely observed anisotropic
scaling law \kpa \propto \kpe^{2/3} between parallel and perpendicular
wavenumbers (with reference to B_0 {\bf {\hat e}_{\pa}}) and to obtain the
universal prediction, , for the total energy spectrum
E(\kpe,\kpa) \sim \kpe^{-\alpha} \kpa^{-\beta}. In particular, with such a
prediction the weak Alfv\'en wave turbulence constant-flux solution is
recovered and, for the first time, a possible explanation to its precursor
found numerically by Galtier et al [S. Galtier et al., J. Plasma Phys. {\bf
63}, 447 (2000)] is given
Integrating Species Traits into Species Pools
Despite decades of research on the speciesâpool concept and the recent explosion of interest in traitâbased frameworks in ecology and biogeography, surprisingly little is known about how spatial and temporal changes in speciesâpool functional diversity (SPFD) influence biodiversity and the processes underlying community assembly. Current traitâbased frameworks focus primarily on community assembly from a static regional species pool, without considering how spatial or temporal variation in SPFD alters the relative importance of deterministic and stochastic assembly processes. Likewise, speciesâpool concepts primarily focus on how the number of species in the species pool influences local biodiversity. However, species pools with similar richness can vary substantially in functionalâtrait diversity, which can strongly influence community assembly and biodiversity responses to environmental change. Here, we integrate recent advances in community ecology, traitâbased ecology, and biogeography to provide a more comprehensive framework that explicitly considers how variation in SPFD, among regions and within regions through time, influences the relative importance of community assembly processes and patterns of biodiversity. First, we provide a brief overview of the primary ecological and evolutionary processes that create differences in SPFD among regions and within regions through time. We then illustrate how SPFD may influence fundamental processes of local community assembly (dispersal, ecological drift, niche selection). Higher SPFD may increase the relative importance of deterministic community assembly when greater functional diversity in the species pool increases niche selection across environmental gradients. In contrast, lower SPFD may increase the relative importance of stochastic community assembly when high functional redundancy in the species pool increases the influence of dispersal history or ecological drift. Next, we outline experimental and observational approaches for testing the influence of SPFD on assembly processes and biodiversity. Finally, we highlight applications of this framework for restoration and conservation. This speciesâpool functional diversity framework has the potential to advance our understanding of how localâ and regionalâscale processes jointly influence patterns of biodiversity across biogeographic regions, changes in biodiversity within regions over time, and restoration outcomes and conservation efforts in ecosystems altered by environmental change
Symmetry breaking induced by random fluctuations for Bose-Einstein condensates in a double-well trap
This paper is devoted to the study of the dynamics of two weakly-coupled
Bose-Einstein condensates confined in a double-well trap and perturbed by
random external forces. Energy diffusion due to random forcing allows the
system to visit symmetry-breaking states when the number of atoms exceeds a
threshold value. The energy distribution evolves to a stationary distribution
which depends on the initial state of the condensate only through the total
number of atoms. This loss of memory of the initial conditions allows a simple
and complete description of the stationary dynamics of the condensate which
randomly visits symmetric and symmetry-breaking states.Comment: 12 pages, 6 figure
Generation and nonlinear evolution of shore-oblique/transverse sand bars
The coupling between topography, waves and currents in the surf zone may selforganize
to produce the formation of shore-transverse or shore-oblique sand bars on
an otherwise alongshore uniform beach. In the absence of shore-parallel bars, this has
been shown by previous studies of linear stability analysis, but is now extended to the
finite-amplitude regime. To this end, a nonlinear model coupling wave transformation
and breaking, a shallow-water equations solver, sediment transport and bed updating
is developed. The sediment flux consists of a stirring factor multiplied by the depthaveraged
current plus a downslope correction. It is found that the cross-shore profile
of the ratio of stirring factor to water depth together with the wave incidence angle
primarily determine the shape and the type of bars, either transverse or oblique to
the shore. In the latter case, they can open an acute angle against the current (upcurrent
oriented) or with the current (down-current oriented). At the initial stages of
development, both the intensity of the instability which is responsible for the formation
of the bars and the damping due to downslope transport grow at a similar rate with
bar amplitude, the former being somewhat stronger. As bars keep on growing, their
finite-amplitude shape either enhances downslope transport or weakens the instability
mechanism so that an equilibrium between both opposing tendencies occurs, leading
to a final saturated amplitude. The overall shape of the saturated bars in plan view
is similar to that of the small-amplitude ones. However, the final spacings may be
up to a factor of 2 larger and final celerities can also be about a factor of 2 smaller
or larger. In the case of alongshore migrating bars, the asymmetry of the longshore
sections, the lee being steeper than the stoss, is well reproduced. Complex dynamics
with merging and splitting of individual bars sometimes occur. Finally, in the case of
shore-normal incidence the rip currents in the troughs between the bars are jet-like
while the onshore return flow is wider and weaker as is observed in nature
Identification of input-output LPV models
This chapter presents an overview of the available methods for identifying input-output LPV models both in discrete time and continuous time with the main focus on noise modeling issues. First, a least-squares approach and an instrumental variable method are presented for dealing with LPV-ARX models. Then, a refined instrumental variable approach is discussed to address more sophisticated noise models like Box-Jenkins in the LPV context. This latter approach is also introduced in continuous time and efficient solutions are proposed for both the problem of time-derivative approximation and the issue of continuous-time modeling of the noise
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