1,567 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
Steady state fluctuation relations for systems driven by an external random force
We experimentally study the fluctuations of the work done by an external
Gaussian random force on two different stochastic systems coupled to a thermal
bath: a colloidal particle in an optical trap and an atomic force microscopy
cantilever. We determine the corresponding probability density functions for
different random forcing amplitudes ranging from a small fraction to several
times the amplitude of the thermal noise. In both systems for sufficiently weak
forcing amplitudes the work fluctuations satisfy the usual steady state
fluctuation theorem. As the forcing amplitude drives the system far from
equilibrium, deviations of the fluctuation theorem increase monotonically. The
deviations can be recasted to a single master curve which only depends on the
kind of stochastic external force.Comment: 6 pages, submitted to EP
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
High titers of transmissible spongiform encephalopathy infectivity associated with extremely low levels of PrP in vivo
Rona Barron - ORCID: 0000-0003-4512-9177 https://orcid.org/0000-0003-4512-9177Diagnosis of transmissible spongiform encephalopathy (TSE) disease in humans and ruminants relies on the detection in post-mortem brain tissue of the protease-resistant form of the host glycoprotein PrP. The presence of this abnormal isoform (PrPSc) in tissues is taken as indicative of the presence of TSE infectivity. Here we demonstrate conclusively that high titers of TSE infectivity can be present in brain tissue of animals that show clinical and vacuolar signs of TSE disease but contain low or undetectable levels of PrPSc. This work questions the correlation between PrPSc level and the titer of infectivity and shows that tissues containing little or no proteinase K-resistant PrP can be infectious and harbor high titers of TSE infectivity. Reliance on protease-resistant PrPSc as a sole measure of infectivity may therefore in some instances significantly underestimate biological properties of diagnostic samples, thereby undermining efforts to contain and eradicate TSEs.https://doi.org/10.1074/jbc.M704329200282pubpub4
Singularity confinement and algebraic integrability
Two important notions of integrability for discrete mappings are algebraic
integrability and singularity confinement, have been used for discrete
mappings. Algebraic integrability is related to the existence of sufficiently
many conserved quantities whereas singularity confinement is associated with
the local analysis of singularities. In this paper, the relationship between
these two notions is explored for birational autonomous mappings. Two types of
results are obtained: first, algebraically integrable mappings are shown to
have the singularity confinement property. Second, a proof of the non-existence
of algebraic conserved quantities of discrete systems based on the lack of
confinement property is given.Comment: 18 pages, no figur
Higher loop renormalization of a supersymmetric field theory
Using Dyson--Schwinger equations within an approach developed by Broadhurst
and Kreimer and the renormalization group, we show how high loop order of the
renormalization group coefficients can be efficiently computed in a
supersymmetric model.Comment: 8 pages, 2 figure
New Gauge Invariant Formulation of the Chern-Simons Gauge Theory: Classical and Quantal Analysis
Recently proposed new gauge invariant formulation of the Chern-Simons gauge
theory is considered in detail. This formulation is consistent with the gauge
fixed formulation. Furthermore it is found that the canonical (Noether)
Poincar\'e generators are not gauge invariant even on the constraints surface
and do not satisfy the Poincar\'e algebra contrast to usual case. It is the
improved generators, constructed from the symmetric energy-momentum tensor,
which are (manifestly) gauge invariant and obey the quantum as well as
classical Poincar\'e algebra. The physical states are constructed and it is
found in the Schr\"odinger picture that unusual gauge invariant longitudinal
mode of the gauge field is crucial for constructing the physical wavefunctional
which is genuine to (pure) Chern-Simons theory. In matching to the gauge fixed
formulation, we consider three typical gauges, Coulomb, axial and Weyl gauges
as explicit examples. Furthermore, recent several confusions about the effect
of Dirac's dressing function and the gauge fixings are clarified. The analysis
according to old gauge independent formulation a' la Dirac is summarized in an
appendix.Comment: No figures, 44 page
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
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