839 research outputs found
Experimental investigation of the mechanical stiffness of periodic framework-patterned elastomers
Recent advances in the cataloguing of three-dimensional nets mean a systematic search for framework structures with specific properties is now feasible. Theoretical arguments about the elastic deformation of frameworks suggest characteristics of mechanically isotropic networks. We explore these concepts on both isotropic and anisotropic networks by manufacturing porous elastomers with three different periodic net geometries. The blocks of patterned elastomers are subjected to a range of mechanical tests to determine the dependence of elastic moduli on geometric and topological parameters. We report results from axial compression experiments, three-dimensional X-ray computed tomography imaging and image-based finite-element simulations of elastic properties of framework-patterned elastomers
An algorithm to identify automorphisms which arise from self-induced interval exchange transformations
We give an algorithm to determine if the dynamical system generated by a
positive automorphism of the free group can also be generated by a self-induced
interval exchange transformation. The algorithm effectively yields the interval
exchange transformation in case of success.Comment: 26 pages, 8 figures. v2: the article has been reorganized to make for
a more linear read. A few paragraphs have been added for clarit
Critical connectedness of thin arithmetical discrete planes
An arithmetical discrete plane is said to have critical connecting thickness
if its thickness is equal to the infimum of the set of values that preserve its
-connectedness. This infimum thickness can be computed thanks to the fully
subtractive algorithm. This multidimensional continued fraction algorithm
consists, in its linear form, in subtracting the smallest entry to the other
ones. We provide a characterization of the discrete planes with critical
thickness that have zero intercept and that are -connected. Our tools rely
on the notion of dual substitution which is a geometric version of the usual
notion of substitution acting on words. We associate with the fully subtractive
algorithm a set of substitutions whose incidence matrix is provided by the
matrices of the algorithm, and prove that their geometric counterparts generate
arithmetic discrete planes.Comment: 18 pages, v2 includes several corrections and is a long version of
the DGCI extended abstrac
Cross sections for geodesic flows and \alpha-continued fractions
We adjust Arnoux's coding, in terms of regular continued fractions, of the
geodesic flow on the modular surface to give a cross section on which the
return map is a double cover of the natural extension for the \alpha-continued
fractions, for each in (0,1]. The argument is sufficiently robust to
apply to the Rosen continued fractions and their recently introduced
\alpha-variants.Comment: 20 pages, 2 figure
Structure and evolution of the magnetochrome domains: no longer alone
Magnetotactic bacteria (MTB) can swim along Earth's magnetic field lines, thanks to the alignment of dedicated cytoplasmic organelles. These organelles, termed magnetosomes, are proteolipidic vesicles filled by a 35–120 nm crystal of either magnetite or greigite. The formation and alignment of magnetosomes are mediated by a group of specific genes, the mam genes, encoding the magnetosome-associated proteins. The whole process of magnetosome biogenesis can be divided into four sequential steps; (i) cytoplasmic membrane invagination, (ii) magnetosomes alignment, (iii) iron crystal nucleation and (iv) species-dependent mineral size and shape control. Since both magnetite and greigite are a mix of iron (III) and iron (II), iron redox state management within the magnetosome vesicle is a key issue. Recently, studies have started pointing out the importance of a MTB-specific c-type cytochrome domain found in several magnetosome-associated proteins (MamE, P, T, and X). This magnetochrome (MCR) domain is almost always found in tandem, and this tandem is either found alone (MamT), in combination with a PDZ domain (MamP), a domain of unknown function (MamX) or with a trypsin combined to one or two PDZ domains (MamE). By taking advantage of new genomic data available on MTB and a recent structural study of MamP, which helped define the MCR domain boundaries, we attempt to retrace the evolutionary history within and between the different MCR-containing proteins. We propose that the observed tandem repeat of MCR is the result of a convergent evolution and attempt to explain why this domain is rarely found alone
Optical Coatings as Mirrors for Optical Diagnostics
The aim of this work was to provide a comprehensive insight concerning coated films which might be used for first mirrors in ITER. The influence of the mirror crystallite size has been addressed as well as the coating techniques to provide nanocrystalline films. Tests of coated mirrors both in laboratories and in tokamaks are reviewed. For the tokamak tests a wide angle camera system has been installed in JET-ILW which is composed of a mirror box with 3 stainless steel mirrors coated with rhodium viewing the torus through a conically shaped aperture. The system delivered the required image quality for plasma monitoring and wall protection. No or insignificant degradation of the optical transmittance has been observed during the experimental campaign in 2014 with about 3000 plasma pulses in different magnetic field configurations
Generalized quasiperiodic Rauzy tilings
We present a geometrical description of new canonical -dimensional
codimension one quasiperiodic tilings based on generalized Fibonacci sequences.
These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual
Penrose and icosahedral tilings. Thanks to a natural indexing of the sites
according to their local environment, we easily write down, for any
approximant, the sites coordinates, the connectivity matrix and we compute the
structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change
Subset currents on free groups
We introduce and study the space of \emph{subset currents} on the free group
. A subset current on is a positive -invariant locally finite
Borel measure on the space of all closed subsets of consisting of at least two points. While ordinary geodesic currents
generalize conjugacy classes of nontrivial group elements, a subset current is
a measure-theoretic generalization of the conjugacy class of a nontrivial
finitely generated subgroup in , and, more generally, in a word-hyperbolic
group. The concept of a subset current is related to the notion of an
"invariant random subgroup" with respect to some conjugacy-invariant
probability measure on the space of closed subgroups of a topological group. If
we fix a free basis of , a subset current may also be viewed as an
-invariant measure on a "branching" analog of the geodesic flow space for
, whose elements are infinite subtrees (rather than just geodesic lines)
of the Cayley graph of with respect to .Comment: updated version; to appear in Geometriae Dedicat
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