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

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>₅₀ = 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^-1, a maximum speed in winter (up to 0.15 m day^-1) 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

Integrating Species Traits into Species Pools

Despite decades of research on the species‐pool concept and the recent explosion of interest in trait‐based frameworks in ecology and biogeography, surprisingly little is known about how spatial and temporal changes in species‐pool functional diversity (SPFD) influence biodiversity and the processes underlying community assembly. Current trait‐based 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, species‐pool 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 functional‐trait diversity, which can strongly influence community assembly and biodiversity responses to environmental change. Here, we integrate recent advances in community ecology, trait‐based 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 species‐pool functional diversity framework has the potential to advance our understanding of how local‐ and regional‐scale 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

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

Teacher feedback, writing assignment quality, and third-grade students' revision in lower- and higher-achieving urban schools

The relation of the quality of writing assignments and written instructor responses to student writings to the quality of subsequent student work was investigated in 29 urban third-grade classrooms in 8 schools. Writing assignments were generally of a higher quality in the 4 schools that served primarily middle-class, higher-achieving students, most of whom were white or Asian, versus the 4 schools that served primarily low-income and lower-achieving students, the majority of whom were Latino. Across all classrooms, however, teachers focused on standardizing students' written output, which led to marked improvement in the writing mechanics of students' work. Results of regression analyses indicated that the amount and type of feedback students received predicted a significant, although small, proportion of the variance in the quality of the content, organization, and mechanics of students' final drafts. The quality of the writing assignments predicted a small but significant proportion of the variance in the quality of the content of students' final drafts only. These findings raise questions about the implementation of broad educational policies in classrooms, such as using the writing process approach, and indicate a need for professional development for teachers

Fluctuation theorems for harmonic oscillators

We study experimentally the thermal fluctuations of energy input and dissipation in a harmonic oscillator driven out of equilibrium, and search for Fluctuation Relations. We study transient evolution from the equilibrium state, together with non equilibrium steady states. Fluctuations Relations are obtained experimentally for both the work and the heat, for the stationary and transient evolutions. A Stationary State Fluctuation Theorem is verified for the two time prescriptions of the torque. But a Transient Fluctuation Theorem is satisfied for the work given to the system but not for the heat dissipated by the system in the case of linear forcing. Experimental observations on the statistical and dynamical properties of the fluctuation of the angle, we derive analytical expressions for the probability density function of the work and the heat. We obtain for the first time an analytic expression of the probability density function of the heat. Agreement between experiments and our modeling is excellent