3,728 research outputs found
Waves in the Skyrme--Faddeev model and integrable reductions
In the present article we show that the Skyrme--Faddeev model possesses
nonlinear wave solutions, which can be expressed in terms of elliptic
functions. The Whitham averaging method has been exploited in order to describe
slow deformation of periodic wave states, leading to a quasi-linear system. The
reduction to general hydrodynamic systems have been considered and it is
compared with other integrable reductions of the system.Comment: 16 pages, 5 figure
A Bayesian decision approach to rainfall thresholds based flood warning
International audienceOperational real time flood forecasting systems generally require a hydrological model to run in real time as well as a series of hydro-informatics tools to transform the flood forecast into relatively simple and clear messages to the decision makers involved in flood defense. The scope of this paper is to set forth the possibility of providing flood warnings at given river sections based on the direct comparison of the quantitative precipitation forecast with critical rainfall threshold values, without the need of an on-line real time forecasting system. This approach leads to an extremely simplified alert system to be used by non technical stakeholders and could also be used to supplement the traditional flood forecasting systems in case of system failures. The critical rainfall threshold values, incorporating the soil moisture initial conditions, result from statistical analyses using long hydrological time series combined with a Bayesian utility function minimization. In the paper, results of an application of the proposed methodology to the Sieve river, a tributary of the Arno river in Italy, are given to exemplify its practical applicability
Flood forecasting using a fully distributed model: application of the TOPKAPI model to the Upper Xixian Catchment
International audienceTOPKAPI is a physically-based, fully distributed hydrological model with a simple and parsimonious parameterisation. The original TOPKAPI is structured around five modules that represent evapotranspiration, snowmelt, soil water, surface water and channel water, respectively. Percolation to deep soil layers was ignored in the old version of the TOPKAPI model since it was not important in the basins to which the model was originally applied. Based on published literature, this study developed a new version of the TOPKAPI model, in which the new modules of interception, infiltration, percolation, groundwater flow and lake/reservoir routing are included. This paper presents an application study that makes a first attempt to derive information from public domains through the internet on the topography, soil and land use types for a case study Chinese catchment - the Upper Xixian catchment in Huaihe River with an area of about 10000 km2, and apply a new version of TOPKAPI to the catchment for flood simulation. A model parameter value adjustment was performed using six months of the 1998 dataset. Calibration did not use a curve fitting process, but was chiefly based upon moderate variations of parameter values from those estimated on physical grounds, as is common in traditional calibration. The hydrometeorological dataset of 2002 was then used to validate the model, both against the outlet discharge as well as at an internal gauging station. Finally, to complete the model performance analysis, parameter uncertainty and its effects on predictive uncertainty were also assessed by estimating a posterior parameter probability density via Bayesian inference
Abelian Chern-Simons Vortices and Holomorphic Burgers' Hierarchy
The Abelian Chern-Simons Gauge Field Theory in 2+1 dimensions and its
relation with holomorphic Burgers' Hierarchy is considered. It is shown that
the relation between complex potential and the complex gauge field as in
incompressible and irrotational hydrodynamics, has meaning of the analytic
Cole-Hopf transformation, linearizing the Burgers Hierarchy in terms of the
holomorphic Schr\"odinger Hierarchy. Then the motion of planar vortices in
Chern-Simons theory, appearing as pole singularities of the gauge field,
corresponds to motion of zeroes of the hierarchy. Using boost transformations
of the complex Galilean group of the hierarchy, a rich set of exact solutions,
describing integrable dynamics of planar vortices and vortex lattices in terms
of the generalized Kampe de Feriet and Hermite polynomials is constructed. The
results are applied to the holomorphic reduction of the Ishimori model and the
corresponding hierarchy, describing dynamics of magnetic vortices and
corresponding lattices in terms of complexified Calogero-Moser models.
Corrections on two vortex dynamics from the Moyal space-time non-commutativity
in terms of Airy functions are found.Comment: 15 pages, talk presented in Workshop `Nonlinear Physics IV: Theory
and Experiment`, 22-30 June 2006, Gallipoli, Ital
Classification of integrable Volterra type lattices on the sphere. Isotropic case
The symmetry approach is used for classification of integrable isotropic
vector Volterra lattices on the sphere. The list of integrable lattices
consists mainly of new equations. Their symplectic structure and associated PDE
of vector NLS-type are discussed.Comment: 16 page
The Darboux-Backlund transformation for the static 2-dimensional continuum Heisenberg chain
We construct the Darboux-Backlund transformation for the sigma model
describing static configurations of the 2-dimensional classical continuum
Heisenberg chain. The transformation is characterized by a non-trivial
normalization matrix depending on the background solution. In order to obtain
the transformation we use a new, more general, spectral problem.Comment: 12 page
Anti-self-dual Riemannian metrics without Killing vectors, can they be realized on K3?
Explicit Riemannian metrics with Euclidean signature and anti-self dual
curvature that do not admit any Killing vectors are presented. The metric and
the Riemann curvature scalars are homogenous functions of degree zero in a
single real potential and its derivatives. The solution for the potential is a
sum of exponential functions which suggests that for the choice of a suitable
domain of coordinates and parameters it can be the metric on a compact
manifold. Then, by the theorem of Hitchin, it could be a class of metrics on
, or on surfaces whose universal covering is .Comment: Misprints in eqs.(9-11) corrected. Submitted to Classical and Quantum
Gravit
Point Symmetries of Generalized Toda Field Theories II Applications of the Symmetries
The Lie symmetries of a large class of generalized Toda field theories are
studied and used to perform symmetry reduction. Reductions lead to generalized
Toda lattices on one hand, to periodic systems on the other. Boundary
conditions are introduced to reduce theories on an infinite lattice to those on
semi-infinite, or finite ones.Comment: 26 pages, no figure
Chern - Simons Gauge Field Theory of Two - Dimensional Ferromagnets
A Chern-Simons gauged Nonlinear Schr\"odinger Equation is derived from the
continuous Heisenberg model in 2+1 dimensions. The corresponding planar magnets
can be analyzed whithin the anyon theory. Thus, we show that static magnetic
vortices correspond to the self-dual Chern - Simons solitons and are described
by the Liouville equation. The related magnetic topological charge is
associated with the electric charge of anyons. Furthermore, vortex - antivortex
configurations are described by the sinh-Gordon equation and its conformally
invariant extension. Physical consequences of these results are discussed.Comment: 15 pages, Plain TeX, Lecce, June 199
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