161 research outputs found
Integrable lattice equations with vertex and bond variables
We present integrable lattice equations on a two dimensional square lattice
with coupled vertex and bond variables. In some of the models the vertex
dynamics is independent of the evolution of the bond variables, and one can
write the equations as non-autonomous "Yang-Baxter maps". We also present a
model in which the vertex and bond variables are fully coupled. Integrability
is tested with algebraic entropy as well as multidimensional consistencyComment: 15 pages, remarks added, other minor change
A modeling approach to assess the hydrological response of small mediterranean catchments to the variability of soil characteristics in a context of extreme events
This paper presents a modeling study aiming at quantifying the possible impact of soil characteristics on the hydrological response of small ungauged catchments in a context of extreme events. The study focuses on the September 2002 event in the Gard region (South-Eastern France), which led to catastrophic flash-floods. The proposed modeling approach is able to take into account rainfall variability and soil profiles variability. Its spatial discretization is determined using Digital Elevation Model (DEM) and a soil map. The model computes infiltration, ponding and vertical soil water distribution, as well as river discharge. In order to be applicable to ungauged catchments, the model is set up without any calibration and the soil parameter specification is based on an existing soil database. The model verification is based on a regional evaluation using 17 estimated discharges obtained from an extensive post-flood investigation. Thus, this approach provides a spatial view of the hydrological response across a large range of scales. To perform the simulations, radar rainfall estimations are used at a 1 km<sup>2</sup> and 5 min resolution. To specify the soil hydraulic properties, two types of pedotransfer function (PTF) are compared. It is shown that the PTF including information about soil structure reflects better the spatial variability that can be encountered in the field. The study is focused on four small ungauged catchments of less than 10 km<sup>2</sup>, which experienced casualties. Simulated specific peak discharges are found to be in agreement with estimations from a post-event in situ investigation. Examining the dynamics of simulated infiltration and saturation degrees, two different behaviors are shown which correspond to different runoff production mechanisms that could be encountered within catchments of less than 10 km<sup>2</sup>. They produce simulated runoff coefficients that evolve in time and highlight the variability of the infiltration capacity of the various soil types. Therefore, we propose a cartography distinguishing between areas prone to saturation excess and areas prone only to infiltration excess mechanisms. The questions raised by this modeling study will be useful to improve field observations, aiming at better understanding runoff generation for these extreme events and examine the possibility for early warning, even in very small ungauged catchments
Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm
The discrete-time Toda equation arises as a universal equation for the
relevant Hankel determinants associated with one-variable orthogonal
polynomials through the mechanism of adjacency, which amounts to the inclusion
of shifted weight functions in the orthogonality condition. In this paper we
extend this mechanism to a new class of two-variable orthogonal polynomials
where the variables are related via an elliptic curve. This leads to a `Higher
order Analogue of the Discrete-time Toda' (HADT) equation for the associated
Hankel determinants, together with its Lax pair, which is derived from the
relevant recurrence relations for the orthogonal polynomials. In a similar way
as the quotient-difference (QD) algorithm is related to the discrete-time Toda
equation, a novel quotient-quotient-difference (QQD) scheme is presented for
the HADT equation. We show that for both the HADT equation and the QQD scheme,
there exists well-posed -periodic initial value problems, for almost all
\s\in\Z^2. From the Lax-pairs we furthermore derive invariants for
corresponding reductions to dynamical mappings for some explicit examples.Comment: 38 page
On the complexity of some birational transformations
Using three different approaches, we analyze the complexity of various
birational maps constructed from simple operations (inversions) on square
matrices of arbitrary size. The first approach consists in the study of the
images of lines, and relies mainly on univariate polynomial algebra, the second
approach is a singularity analysis, and the third method is more numerical,
using integer arithmetics. Each method has its own domain of application, but
they give corroborating results, and lead us to a conjecture on the complexity
of a class of maps constructed from matrix inversions
The thermal-viscous disk instability model in the AGN context
Accretion disks in AGN should be subject to the same type of instability as
in cataclysmic variables (CVs) or in low-mass X-ray binaries (LMXBs), which
leads to dwarf nova and soft X-ray transient outbursts. It has been suggested
that this thermal/viscous instability can account for the long term variability
of AGNs. We test this assertion by presenting a systematic study of the
application of the disk instability model (DIM) to AGNs. We are using the
adaptative grid numerical code we have developed in the context of CVs,
enabling us to fully resolve the radial structure of the disk. We show that,
because in AGN disks the Mach numbers are very large, the heating and cooling
fronts are so narrow that they cannot be resolved by the numerical codes that
have been used until now. In addition, these fronts propagate on time scales
much shorter than the viscous time. As a result, a sequence of heating and
cooling fronts propagate back and forth in the disk, leading only to small
variations of the accretion rate onto the black hole, with short quiescent
states occurring for very low mass transfer rates only. Truncation of the inner
part of the disk by e.g. an ADAF does not alter this result, but enables longer
quiescent states. Finally we discuss the effects of irradiation by the central
X-ray source, and show that, even for extremely high irradiation efficiencies,
outbursts are not a natural outcome of the model.Comment: Astronomy & Astrophysics - in pres
Discrete integrable systems and Poisson algebras from cluster maps
We consider nonlinear recurrences generated from cluster mutations applied to
quivers that have the property of being cluster mutation-periodic with period
1. Such quivers were completely classified by Fordy and Marsh, who
characterised them in terms of the skew-symmetric matrix that defines the
quiver. The associated nonlinear recurrences are equivalent to birational maps,
and we explain how these maps can be endowed with an invariant Poisson bracket
and/or presymplectic structure.
Upon applying the algebraic entropy test, we are led to a series of
conjectures which imply that the entropy of the cluster maps can be determined
from their tropical analogues, which leads to a sharp classification result.
Only four special families of these maps should have zero entropy. These
families are examined in detail, with many explicit examples given, and we show
how they lead to discrete dynamics that is integrable in the Liouville-Arnold
sense.Comment: 49 pages, 3 figures. Reduced to satisfy journal page restrictions.
Sections 2.4, 4.5, 6.3, 7 and 8 removed. All other results remain, with minor
editin
Electronic Raman scattering in HgBa_{2}Ca_{2}Cu_{3}O_{8+\delta} single crystals. Analysis of the superconducting state
Electronic Raman scattering measurements have been performed on
single crystals in the superconducting
state. Pure electronic Raman spectra with no phonon structures hindering the
analysis of the electronic continuum have been obtained. As a consequence, the
spectra in the pure and symmetries are directly and
reliably analyzed and the pure contribution can be easily identified.
Below the critical temperature two electronic structures at and are clearly seen.
Both are observed simultaneously in pure symmetry, the highest energy
one being located at the energy of the maximum. These two maxima
disappear at and do not soften significantly as the temperature is
raised up to The low energy frequency dependence of the
electronic response is strongly linear, for various excitation lines in the
476.5 to 647.1 nm range. Such experimental data cannot be reconciled with a
pure symmetry. Instead, they strongly advocate in favor of
an anisotropic superconducting gap with two distinct gap maxima and of nodes
existing outside the [110] and [1,,0] directions in {\bf k}-space. We
discuss in detail the simplest order parameter compatible with our experimental
findings.Comment: 12 pages, revtex, 12 figure
The AVuPUR project (Assessing the Vulnerabiliy of Peri-Urbans Rivers): experimental set up, modelling strategy and first results
International audienceLe projet AVuPUR a pour objectif de progresser sur la comprĂ©hension et la modĂ©lisation des flux d'eau dans les bassins versants pĂ©ri-urbains. Il s'agit plus particuliĂšrement de fournir des outils permettant de quantifier l'impact d'objets anthropiques tels que zones urbaines, routes, fossĂ©s sur les rĂ©gimes hydrologiques des cours d'eau dans ces bassins. Cet article prĂ©sente la stratĂ©gie expĂ©rimentale et de collecte de donnĂ©es mise en Âœuvre dans le projet et les pistes proposĂ©es pour l'amĂ©lioration des outils de modĂ©lisation existants et le dĂ©veloppement d'outils novateurs. Enfin, nous prĂ©sentons comment ces outils seront utilisĂ©s pour simuler et quantifier l'impact des modifications d'occupation des sols et/ou du climat sur les rĂ©gimes hydrologiques des bassins Ă©tudiĂ©s. / The aim of the AVuPUR project is to enhance our understanding and modelling capacity of water fluxes within suburban watersheds. In particular, the objective is to deliver tools allowing to quantify the impact of anthropogenic elements such as urban areas, roads, ditches on the hydrological regime of suburban rivers. This paper presents the observation and data collection strategy set up by the project, and the directions for improving existing modelling tools or proposing innovative ones. Finally, we present how these tools will be used to simulate and quantify the impact of land use and climate changes on the hydrological regimes of the studied catchments
Magnetized Kelvin-Helmholtz instability in the presence of a radiation field
The purpose of this study is to analyze the dynamical role of a radiation
field on the growth rate of the unstable Kelvin - Helmholtz (KH) perturbations.
As a first step toward this purpose, the analyze is done in a general way,
irrespective of applying the model to a specific astronomical system. The
transition zone between the two layers of the fluid is ignored. Then, we
perform a linear analysis and by imposing suitable boundary conditions and
considering a radiation field, we obtain appropriate dispersion relation.
Unstable modes are studied by solving the dispersion equation numerically, and
then growth rates of them are obtained. By analyzing our dispersion relation,
we show that for a wide range of the input parameters, the radiation field has
a destabilizing effect on KH instability. In eruptions of the galaxies or
supermassive stars, the radiation field is dynamically important and because of
the enhanced KH growth rates in the presence of the radiation; these eruptions
can inject more momentum and energy into their environment and excite more
turbulent motions.Comment: Accepted for publication in Astrophysics and Space Scienc
- âŠ