1,048 research outputs found
Singularity, complexity, and quasi--integrability of rational mappings
We investigate global properties of the mappings entering the description of
symmetries of integrable spin and vertex models, by exploiting their nature of
birational transformations of projective spaces. We give an algorithmic
analysis of the structure of invariants of such mappings. We discuss some
characteristic conditions for their (quasi)--integrability, and in particular
its links with their singularities (in the 2--plane). Finally, we describe some
of their properties {\it qua\/} dynamical systems, making contact with
Arnol'd's notion of complexity, and exemplify remarkable behaviours.Comment: Latex file. 17 pages. To appear in CM
Delirium, thrombocytopenia, insomnia, and mild liver damage associated with MAOI withdrawal
International audienc
Baxterization, dynamical systems, and the symmetries of integrability
We resolve the `baxterization' problem with the help of the automorphism
group of the Yang-Baxter (resp. star-triangle, tetrahedron, \dots) equations.
This infinite group of symmetries is realized as a non-linear (birational)
Coxeter group acting on matrices, and exists as such, {\em beyond the narrow
context of strict integrability}. It yields among other things an unexpected
elliptic parametrization of the non-integrable sixteen-vertex model. It
provides us with a class of discrete dynamical systems, and we address some
related problems, such as characterizing the complexity of iterations.Comment: 25 pages, Latex file (epsf style). WARNING: Postscript figures are
BIG (600kB compressed, 4.3MB uncompressed). If necessary request hardcopy to
[email protected] and give your postal mail addres
Thermal noise properties of two aging materials
In this lecture we review several aspects of the thermal noise properties in
two aging materials: a polymer and a colloidal glass.
The measurements have been performed after a quench for the polymer and
during the transition from a fluid-like to a solid-like state for the gel. Two
kind of noise has been measured: the electrical noise and the mechanical noise.
For both materials we have observed that the electric noise is characterized
by a strong intermittency, which induces a large violation of the Fluctuation
Dissipation Theorem (FDT) during the aging time, and may persist for several
hours at low frequency. The statistics of these intermittent signals and their
dependance on the quench speed for the polymer or on sample concentration for
the gel are studied. The results are in a qualitative agreement with recent
models of aging, that predict an intermittent dynamics. For the mechanical
noise the results are unclear. In the polymer the mechanical thermal noise is
still intermittent whereas for the gel the violation of FDT, if it exists, is
extremely small.Comment: to be published in the Proceedings of the XIX Sitges Conference on
''Jammming, Yielding and Irreversible Deformation in Condensed Matter'',
M.-C.Miguel and M. Rubi eds.,Springer Verlag, Berli
On the Symmetries of Integrability
We show that the Yang-Baxter equations for two dimensional models admit as a
group of symmetry the infinite discrete group . The existence of
this symmetry explains the presence of a spectral parameter in the solutions of
the equations. We show that similarly, for three-dimensional vertex models and
the associated tetrahedron equations, there also exists an infinite discrete
group of symmetry. Although generalizing naturally the previous one, it is a
much bigger hyperbolic Coxeter group. We indicate how this symmetry can help to
resolve the Yang-Baxter equations and their higher-dimensional generalizations
and initiate the study of three-dimensional vertex models. These symmetries are
naturally represented as birational projective transformations. They may
preserve non trivial algebraic varieties, and lead to proper parametrizations
of the models, be they integrable or not. We mention the relation existing
between spin models and the Bose-Messner algebras of algebraic combinatorics.
Our results also yield the generalization of the condition so often
mentioned in the theory of quantum groups, when no parameter is available.Comment: 23 page
Integrability of one degree of freedom symplectic maps with polar singularities
In this paper, we treat symplectic difference equations with one degree of
freedom. For such cases, we resolve the relation between that the dynamics on
the two dimensional phase space is reduced to on one dimensional level sets by
a conserved quantity and that the dynamics is integrable, under some
assumptions. The process which we introduce is related to interval exchange
transformations.Comment: 10 pages, 2 figure
Foraging is determinant to improve smallholders’ food security in rural areas in Mali, West Africa
Studies on the enabling factors for household food security (HFS) most often used simplified econometric models looking into the links with a selected set of variables. In this research, a livelihood approach of HFS was used and aimed at determining the most significant livelihood assets for HFS in dryland agricultural systems. Elements of the five livelihood assets were assessed through questionnaire surveys with a random sample of 180 households, and six focus group discussions in three communities along the rural-urban continuum, in Southern Mali. The coping strategy index approach was used to evaluate household food security status. Non-parametric and parametric statistical tests were combined, as appropriate, to identify the most significant determinants of HFS status. Findings indicated that most determinant factors of HFS were the diversity of wild and cultivated food plants, and hunting (natural capital); access to clean water and irrigation (infrastructural capital); and off-farm employment (financial capital). HFS also improved along the urban-rural continuum and rural households with high natural capital seemed to be more food secure. Findings call for important investment to expand the natural capital (e.g., domestication of new crops and agricultural diversification) and infrastructural capital (irrigation facilities, clean water) of the rural households
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