14,074 research outputs found

    Geometrical Models for Substitutions

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    International audienceWe consider a substitution associated with the Arnoux-Yoccoz interval exchange transformation (IET) related to the tribonacci substitution. We construct the so-called stepped lines associated with the fixed points of the substitution in the abelianization (symbolic) space. We analyze various projections of the stepped line, recovering the Rauzy fractal, a Peano curve related to work in [Arnoux 88], another Peano curve related to the work of [McMullen 09] and [Lowenstein et al. 07], and also the interval exchange transformation itself

    Geometric Formulation of Edge and Nodal Finite Element Equations in Electromagnetics

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    Finite element equations for electromagnetic fields are examined, in particular nodal elements using scalar potential formulation and edge elements for vector potential formulation. It is shown how the equations usually obtained via variational approach may be more conveniently derived using integral methods employing a geometrical description of the interpolating functions of edge and facet elements. Moreover, the resultant equations describe the equivalent multi-branch circuit models

    Non-Smooth Spatio-Temporal Coordinates in Nonlinear Dynamics

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    This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of motion to the form, which is convenient for further use of analytical and numerical methods of analyses. Three different types of nonsmooth transformations are discussed as follows: positional coordinate transformation, state variables transformation, and temporal transformations. Illustrating examples are provided.Comment: 15 figure

    Symmetric intersections of Rauzy fractals

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    In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry considered is reflection through the origin. Given an unimodular irreducible Pisot substitution, we consider the intersection of its Rauzy fractal with the Rauzy fractal of the reverse substitution. This set is symmetric and it is obtained by the balanced pair algorithm associated with both substitutions

    Aperiodic and correlated disorder in XY-chains: exact results

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    We study thermodynamic properties, specific heat and susceptibility, of XY quantum chains with coupling constants following arbitrary substitution rules. Generalizing an exact renormalization group transformation, originally formulated for Ising quantum chains, we obtain exact relevance criteria of Harris-Luck type for this class of models. For two-letter substitution rules, a detailed classification is given of sequences leading to irrelevant, marginal or relevant aperiodic modulations. We find that the relevance of the same aperiodic sequence of couplings in general will be different for XY and Ising quantum chains. By our method, continuously varying critical exponents may be calculated exactly for arbitrary (two-letter) substitution rules with marginal aperiodicity. A number of examples are given, including the period-doubling, three-folding and precious mean chains. We also discuss extensions of the renormalization approach to a special class of long-range correlated random chains, generated by random substitutions.Comment: 19 page

    Collisional excitation of doubly and triply deuterated ammonia ND2_2H and ND3_3 by H2_2

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    The availability of collisional rate coefficients is a prerequisite for an accurate interpretation of astrophysical observations, since the observed media often harbour densities where molecules are populated under non--LTE conditions. In the current study, we present calculations of rate coefficients suitable to describe the various spin isomers of multiply deuterated ammonia, namely the ND2_2H and ND3_3 isotopologues. These calculations are based on the most accurate NH3_3--H2_2 potential energy surface available, which has been modified to describe the geometrical changes induced by the nuclear substitutions. The dynamical calculations are performed within the close--coupling formalism and are carried out in order to provide rate coefficients up to a temperature of TT = 50K. For the various isotopologues/symmetries, we provide rate coefficients for the energy levels below ∌\sim 100 cm−1^{-1}. Subsequently, these new rate coefficients are used in astrophysical models aimed at reproducing the NH2_2D, ND2_2H and ND3_3 observations previously reported towards the prestellar cores B1b and 16293E. We thus update the estimates of the corresponding column densities and find a reasonable agreement with the previous models. In particular, the ortho--to--para ratios of NH2_2D and NHD2_2 are found to be consistent with the statistical ratios

    Human-chimpanzee alignment: Ortholog Exponentials and Paralog Power Laws

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    Genomic subsequences conserved between closely related species such as human and chimpanzee exhibit an exponential length distribution, in contrast to the algebraic length distribution observed for sequences shared between distantly related genomes. We find that the former exponential can be further decomposed into an exponential component primarily composed of orthologous sequences, and a truncated algebraic component primarily composed of paralogous sequences.Comment: Main text: 31 pages, 13 figures, 1 table; Supplementary materials: 9 pages, 9 figures, 1 tabl

    Properties of Physical Systems: Transient Singularities on Borders and Surface Transitive Zones

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    Certain alternative properties of physical systems are describable by supports of arguments of response functions (e.g. light cone, borders of media) and expressed by projectors; corresponding equations of restraints lead to dispersion relations, theorems of counting, etc. As supports are measurable, their absolutely strict borders contradict the spirit of quantum theory and their quantum evolution leading to appearance of subtractions or certain needed flattening would be considered. Flattening of projectors introduce transitive zones that can be examined as a specification of adiabatic hypothesis or the Bogoliubov regulatory function in QED. For demonstration of their possibilities the phenomena of refraction and reflection of electromagnetic wave are considered; they show, in particular, the inevitable appearing of double electromagnetic layers on all surfaces that formerly were repeatedly postulated, etc. Quantum dynamics of projectors proves the neediness of subtractions that usually are artificially adding and express transient singularities and zones in squeezed forms.Comment: 12 p
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