169 research outputs found
Symmetry perspectives on some auxetic body-bar frameworks
Scalar mobility counting rules and their symmetry extensions are reviewed for
finite frameworks and also for infinite periodic frameworks of the bar-and-joint, body-joint
and body-bar types. A recently published symmetry criterion for the existence of equiauxetic
character of an infinite framework is applied to two long known but apparently little
studied hinged-hexagon frameworks, and is shown to detect auxetic behaviour in both. In
contrast, for double-link frameworks based on triangular and square tessellations, other affine
deformations can mix with the isotropic expansion mode.P.W. Fowler acknowledges support from the Royal Society/Leverhulme Trust in the form of a Senior
Research Fellowship for 2013. T. Tarnai is grateful for financial support under OKTA grant K81146.This is the final published version distributed under a Creative Commons Attribution License, which can also be found on the publisher's website at: http://www.mdpi.com/2073-8994/6/2/36
Symmetry as a sufficient condition for a finite flex
We show that if the joints of a bar and joint framework are
positioned as `generically' as possible subject to given symmetry constraints
and possesses a `fully-symmetric' infinitesimal flex (i.e., the
velocity vectors of the infinitesimal flex remain unaltered under all symmetry
operations of ), then also possesses a finite flex which
preserves the symmetry of throughout the path. This and other related
results are obtained by symmetrizing techniques described by L. Asimov and B.
Roth in their paper `The Rigidity Of Graphs' from 1978 and by using the fact
that the rigidity matrix of a symmetric framework can be transformed into a
block-diagonalized form by means of group representation theory. The finite
flexes that can be detected with these symmetry-based methods can in general
not be found with the analogous non-symmetric methods.Comment: 26 pages, 10 figure
Equiauxetic Hinged Archimedean Tilings
There is increasing interest in two-dimensional and quasi-two-dimensional materials and metamaterials for applications in chemistry, physics and engineering. Some of these applications are driven by the possible auxetic properties of such materials. Auxetic frameworks expand along one direction when subjected to a perpendicular stretching force. An equiauxetic framework has a unique mechanism of expansion (an equiauxetic mode) where the symmetry forces a Poisson’s ratio of −1. Hinged tilings offer opportunities for the design of auxetic and equiauxetic frameworks in 2D, and generic auxetic behaviour can often be detected using a symmetry extension of the scalar counting rule for mobility of periodic body-bar systems. Hinged frameworks based on Archimedean tilings of the plane are considered here. It is known that the regular hexagonal tiling, {63}, leads to an equiauxetic framework for both single-link and double-link connections between the tiles. For single-link connections, three Archimedean tilings considered as hinged body-bar frameworks are found here to be equiauxetic: these are {3.122}, {4.6.12}, and {4.82}. For double-link connections, three Archimedean tilings considered as hinged body-bar frameworks are found to be equiauxetic: these are {34.6}, {32.4.3.4}, and {3.6.3.6}.NKFI
Charge distribution in two-dimensional electrostatics
We examine the stability of ringlike configurations of N charges on a plane
interacting through the potential . We interpret the equilibrium distributions in terms of a shell
model and compare predictions of the model with the results of numerical
simulations for systems with up to 100 particles.Comment: LaTe
The orbit rigidity matrix of a symmetric framework
A number of recent papers have studied when symmetry causes frameworks on a
graph to become infinitesimally flexible, or stressed, and when it has no
impact. A number of other recent papers have studied special classes of
frameworks on generically rigid graphs which are finite mechanisms. Here we
introduce a new tool, the orbit matrix, which connects these two areas and
provides a matrix representation for fully symmetric infinitesimal flexes, and
fully symmetric stresses of symmetric frameworks. The orbit matrix is a true
analog of the standard rigidity matrix for general frameworks, and its analysis
gives important insights into questions about the flexibility and rigidity of
classes of symmetric frameworks, in all dimensions.
With this narrower focus on fully symmetric infinitesimal motions, comes the
power to predict symmetry-preserving finite mechanisms - giving a simplified
analysis which covers a wide range of the known mechanisms, and generalizes the
classes of known mechanisms. This initial exploration of the properties of the
orbit matrix also opens up a number of new questions and possible extensions of
the previous results, including transfer of symmetry based results from
Euclidean space to spherical, hyperbolic, and some other metrics with shared
symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure
Nuclear dependence of the transverse single-spin asymmetry in the production of charged hadrons at forward rapidity in polarized , Al, and Au collisions at GeV
We report on the nuclear dependence of transverse single-spin asymmetries
(TSSAs) in the production of positively-charged hadrons in polarized
, Al and Au collisions at
GeV. The measurements have been performed at forward
rapidity () over the range of GeV and
. We observed a positive asymmetry for
positively-charged hadrons in \polpp collisions, and a significantly reduced
asymmetry in + collisions. These results reveal a nuclear
dependence of charged hadron in a regime where perturbative techniques
are relevant. These results provide new opportunities to use \polpA collisions
as a tool to investigate the rich phenomena behind TSSAs in hadronic collisions
and to use TSSA as a new handle in studying small-system collisions.Comment: 303 authors from 66 institutions, 9 pages, 2 figures, 1 table. v1 is
version accepted for publication in Physical Review Letters. Plain text data
tables for the points plotted in figures for this and previous PHENIX
publications are (or will be) publicly available at
http://www.phenix.bnl.gov/papers.htm
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