14,074 research outputs found
Geometrical Models for Substitutions
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
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
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
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
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 NDH and ND by H
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 NDH and ND isotopologues. These calculations are based on
the most accurate NH--H 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 = 50K. For the various
isotopologues/symmetries, we provide rate coefficients for the energy levels
below 100 cm. Subsequently, these new rate coefficients are used
in astrophysical models aimed at reproducing the NHD, NDH and ND
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 NHD and NHD are found to be consistent with
the statistical ratios
Human-chimpanzee alignment: Ortholog Exponentials and Paralog Power Laws
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
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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