7,152 research outputs found
Geometric auxetics
We formulate a mathematical theory of auxetic behavior based on one-parameter
deformations of periodic frameworks. Our approach is purely geometric, relies
on the evolution of the periodicity lattice and works in any dimension. We
demonstrate its usefulness by predicting or recognizing, without experiment,
computer simulations or numerical approximations, the auxetic capabilities of
several well-known structures available in the literature. We propose new
principles of auxetic design and rely on the stronger notion of expansive
behavior to provide an infinite supply of planar auxetic mechanisms and several
new three-dimensional structures
Liftings and stresses for planar periodic frameworks
We formulate and prove a periodic analog of Maxwell's theorem relating
stressed planar frameworks and their liftings to polyhedral surfaces with
spherical topology. We use our lifting theorem to prove deformation and
rigidity-theoretic properties for planar periodic pseudo-triangulations,
generalizing features known for their finite counterparts. These properties are
then applied to questions originating in mathematical crystallography and
materials science, concerning planar periodic auxetic structures and ultrarigid
periodic frameworks.Comment: An extended abstract of this paper has appeared in Proc. 30th annual
Symposium on Computational Geometry (SOCG'14), Kyoto, Japan, June 201
SUSY Quantum Hall Effect on Non-Anti-Commutative Geometry
We review the recent developments of the SUSY quantum Hall effect
[hep-th/0409230, hep-th/0411137, hep-th/0503162, hep-th/0606007,
arXiv:0705.4527]. We introduce a SUSY formulation of the quantum Hall effect on
supermanifolds. On each of supersphere and superplane, we investigate SUSY
Landau problem and explicitly construct SUSY extensions of Laughlin
wavefunction and topological excitations. The non-anti-commutative geometry
naturally emerges in the lowest Landau level and brings particular physics to
the SUSY quantum Hall effect. It is shown that SUSY provides a unified picture
of the original Laughlin and Moore-Read states. Based on the charge-flux
duality, we also develop a Chern-Simons effective field theory for the SUSY
quantum Hall effect.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Second Hopf map and Yang-Coulomb system on 5d (pseudo)sphere
Using the second Hopf map, we perform the reduction of the eight-dimensional
(pseudo)spherical (Higgs)oscillator to a five-dimensional system interacting
with a Yang monopole. Then, using a standard trick, we obtain, from the latter
system, the pseudospherical and spherical generalizations of the Yang-Coulomb
system (the five dimensional analog of MICZ-Kepler system). We present the
whole set of its constants of motions, including the hidden symmetry generators
given by the analog of Runge-Lenz vector. In the same way, starting from the
eight-dimensional anisotropic inharmonic Higgs oscillator, we construct the
integrable (pseudo)spherical generalization of the Yang-Coulomb system with the
Stark term.Comment: 10 pages, PACS: 03.65.-w, 02.30.Ik, 14.80.H
A Pseudoclassical Model for Invariant Planar Fermions
A pseudoclassical model is proposed for the description of planar
invariant massive fermions. The quantization of the model leads to the
(2+1)-dimensional invariant fermion model used recently in
conserving theories of high-T superconductors. The rich symmetry of
the quantum model is elucidated through the analysis of the canonical structure
of its pseudoclassical counterpart. We show that both the quantum
invariant planar massive fermion model and the proposed pseudoclassical
model --- for a particular choice of the parameter appearing in the Lagrangian
--- have a U(1,1) dynamical symmetry as well as an supersymmetry. The
hidden supersymmetry leads to a non-standard superextension of the
(2+1)-dimensional Poincar\'e group. In the quantum theory the one particle
states provide an irreducible representation of the extended supergroup
labelled by the zero eigenvalue of the superspin. We discuss the gauge
modification of the pseudoclassical model and compare our results with those
obtained from the standard pseudoclassical model for massive planar fermions.Comment: 24 pages, LaTeX, minor stylistic corrections, to appear in Nucl.
Phys.
Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
We propose the integrable (pseudo)spherical generalization of the
four-dimensional anisotropic oscillator with additional nonlinear potential.
Performing its Kustaanheimo-Stiefel transformation we then obtain the
pseudospherical generalization of the MICZ-Kepler system with linear and
potential terms. We also present the generalization of the
parabolic coordinates, in which this system admits the separation of variables.
Finally, we get the spherical analog of the presented MICZ-Kepler-like system.Comment: 7 page
Topological Entropy of Braids on the Torus
A fast method is presented for computing the topological entropy of braids on
the torus. This work is motivated by the need to analyze large braids when
studying two-dimensional flows via the braiding of a large number of particle
trajectories. Our approach is a generalization of Moussafir's technique for
braids on the sphere. Previous methods for computing topological entropies
include the Bestvina--Handel train-track algorithm and matrix representations
of the braid group. However, the Bestvina--Handel algorithm quickly becomes
computationally intractable for large braid words, and matrix methods give only
lower bounds, which are often poor for large braids. Our method is
computationally fast and appears to give exponential convergence towards the
exact entropy. As an illustration we apply our approach to the braiding of both
periodic and aperiodic trajectories in the sine flow. The efficiency of the
method allows us to explore how much extra information about flow entropy is
encoded in the braid as the number of trajectories becomes large.Comment: 19 pages, 44 figures. SIAM journal styl
Auxetic regions in large deformations of periodic frameworks
In materials science, auxetic behavior refers to lateral widening upon
stretching. We investigate the problem of finding domains of auxeticity in
global deformation spaces of periodic frameworks. Case studies include planar
periodic mechanisms constructed from quadrilaterals with diagonals as periods
and other frameworks with two vertex orbits. We relate several geometric and
kinematic descriptions.Comment: Presented at the International Conference on "Interdisciplinary
Applications of Kinematics" (IAK18), Lima, Peru, March 201
Fractional quantum Hall effect on the two-sphere: a matrix model proposal
We present a Chern-Simons matrix model describing the fractional quantum Hall
effect on the two-sphere. We demonstrate the equivalence of our proposal to
particular restrictions of the Calogero-Sutherland model, reproduce the quantum
states and filling fraction and show the compatibility of our result with the
Haldane spherical wavefunctions.Comment: 26 pages, LaTeX, no figures, references adde
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