147 research outputs found
Complexity spectrum of some discrete dynamical systems
We first study birational mappings generated by the composition of the matrix
inversion and of a permutation of the entries of matrices. We
introduce a semi-numerical analysis which enables to compute the Arnold
complexities for all the possible birational transformations. These
complexities correspond to a spectrum of eighteen algebraic values. We then
drastically generalize these results, replacing permutations of the entries by
homogeneous polynomial transformations of the entries possibly depending on
many parameters. Again it is shown that the associated birational, or even
rational, transformations yield algebraic values for their complexities.Comment: 1 LaTex fil
Separation, for Analytical Purpose, of Np Traces from different Solutions of Fuel Reprocessing
AbstractFour separation methods were developed for performance control of hydrometallurgical extraction processes as COEX™ or advanced PUREX. These methods used implemented the operations of radionuclides oxidation state adjustment and chromatographic separation using TEVA resin. Concerning FP raffinate, the method consisted in reducing Np traces to the valence IV by a mixture of ferrous sulfamate and ascorbic acid, to fix Np(IV) on “TEVA” resin and to eluate it by a nitrohydrofluoric acid solution. The Np recovery yield is 100%. The decontamination of Np is sufficiently high to allow its analysis by FXL (Zr/Np < 1). The study also showed that in presence of Zr and Tc, Pu behaved like Np. The mixture of ferrous sulfamate and ascorbic acid had surprisingly no action on Pu(IV). Concerning plutonium solution ([Pu] > 10g/L) and uranium solution ([U] > 100g/L), the same method used for Np recovery from FP raffinate led to an eluate containing 100% of the initial Np ([Np]: 10mg/L). The low concentration of U and Pu (< 100mg/L) allows the determination of Np by FXL. Concerning Pu(III)-U(IV) solution, the method, included 2 redox stages, the first one to oxidize all actinides to oxidation state VI et the second one to reduce Np and Pu respectively to IV and III oxidation state. Then Np(IV) was fixed on TEVA resin. The eluate contains 100% of the initial Np ([Np]: 10mg/L) and a low concentration of U and Pu ([U] < 20mg/L, [Pu] < 10mg/L). The next experiments will consist in consolidating these good results by working with real solutions of fuel reprocessing
Birational Mappings and Matrix Sub-algebra from the Chiral Potts Model
We study birational transformations of the projective space originating from
lattice statistical mechanics, specifically from various chiral Potts models.
Associating these models to \emph{stable patterns} and \emph{signed-patterns},
we give general results which allow us to find \emph{all} chiral -state
spin-edge Potts models when the number of states is a prime or the square
of a prime, as well as several -dependent family of models. We also prove
the absence of monocolor stable signed-pattern with more than four states. This
demonstrates a conjecture about cyclic Hadamard matrices in a particular case.
The birational transformations associated to these lattice spin-edge models
show complexity reduction. In particular we recover a one-parameter family of
integrable transformations, for which we give a matrix representationComment: 22 pages 0 figure The paper has been reorganized, splitting the
results into two sections : results pertaining to Physics and results
pertaining to Mathematic
A classification of four-state spin edge Potts models
We classify four-state spin models with interactions along the edges
according to their behavior under a specific group of symmetry transformations.
This analysis uses the measure of complexity of the action of the symmetries,
in the spirit of the study of discrete dynamical systems on the space of
parameters of the models, and aims at uncovering solvable ones. We find that
the action of these symmetries has low complexity (polynomial growth, zero
entropy). We obtain natural parametrizations of various models, among which an
unexpected elliptic parametrization of the four-state chiral Potts model, which
we use to localize possible integrability conditions associated with high genus
curves.Comment: 5 figure
Symmetry, complexity and multicritical point of the two-dimensional spin glass
We analyze models of spin glasses on the two-dimensional square lattice by
exploiting symmetry arguments. The replicated partition functions of the Ising
and related spin glasses are shown to have many remarkable symmetry properties
as functions of the edge Boltzmann factors. It is shown that the applications
of homogeneous and Hadamard inverses to the edge Boltzmann matrix indicate
reduced complexities when the elements of the matrix satisfy certain
conditions, suggesting that the system has special simplicities under such
conditions. Using these duality and symmetry arguments we present a conjecture
on the exact location of the multicritical point in the phase diagram.Comment: 32 pages, 6 figures; a few typos corrected. To be published in J.
Phys.
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
Determination of Total Antioxidant Content in Various Drinks by Amperometry
In the present work the total content of phenolic antioxidants in juice of some fruit and vegetables, in wines, water extracts of tea and herb were measured by amperometry. Efficiency of the method allowed determining the total antioxidant content in their binary and multimixes, including processes of frosting-defrosting and juice diluting as well. The deviation of experimentally received values of the total antioxidant content in some drink mixes from the values calculated proceeding from the additivity principle of the antioxidant content in separate drinks has been revealed
Random Matrix Theory and higher genus integrability: the quantum chiral Potts model
We perform a Random Matrix Theory (RMT) analysis of the quantum four-state
chiral Potts chain for different sizes of the chain up to size L=8. Our
analysis gives clear evidence of a Gaussian Orthogonal Ensemble statistics,
suggesting the existence of a generalized time-reversal invariance.
Furthermore a change from the (generic) GOE distribution to a Poisson
distribution occurs when the integrability conditions are met. The chiral Potts
model is known to correspond to a (star-triangle) integrability associated with
curves of genus higher than zero or one. Therefore, the RMT analysis can also
be seen as a detector of ``higher genus integrability''.Comment: 23 pages and 10 figure
- …