4,324 research outputs found
Gauge theory on nonassociative spaces
We show how to do gauge theory on the octonions and other nonassociative
algebras such as `fuzzy ' models proposed in string theory. We use the
theory of quasialgebras obtained by cochain twist introduced previously. The
gauge theory in this case is twisting-equivalent to usual gauge theory on the
underlying classical space. We give a general U(1)-Yang-Mills example for any
quasi-algebra and a full description of the moduli space of flat connections in
this theory for the cube and hence for the octonions. We also obtain
further results about the octonions themselves; an explicit Moyal-product
description of them as a nonassociative quantisation of functions on the cube,
and a characterisation of their cochain twist as invariant under Fourier
transform.Comment: 24 pages latex, two .eps figure
Braided Cyclic Cocycles and Non-Associative Geometry
We use monoidal category methods to study the noncommutative geometry of
nonassociative algebras obtained by a Drinfeld-type cochain twist. These are
the so-called quasialgebras and include the octonions as braided-commutative
but nonassociative coordinate rings, as well as quasialgebra versions
\CC_{q}(G) of the standard q-deformation quantum groups. We introduce the
notion of ribbon algebras in the category, which are algebras equipped with a
suitable generalised automorphism , and obtain the required
generalisation of cyclic cohomology. We show that this \emph{braided cyclic
cocohomology} is invariant under a cochain twist. We also extend to our
generalisation the relation between cyclic cohomology and differential calculus
on the ribbon quasialgebra. The paper includes differential calculus and cyclic
cocycles on the octonions as a finite nonassociative geometry, as well as the
algebraic noncommutative torus as an associative example.Comment: 36 pages latex, 9 figure
Irreducible actions and compressible modules
Any finite set of linear operators on an algebra yields an operator
algebra and a module structure on A, whose endomorphism ring is isomorphic
to a subring of certain invariant elements of . We show that if is
a critically compressible left -module, then the dimension of its
self-injective hull over the ring of fractions of is bounded by the
uniform dimension of and the number of linear operators generating .
This extends a known result on irreducible Hopf actions and applies in
particular to weak Hopf action. Furthermore we prove necessary and sufficient
conditions for an algebra A to be critically compressible in the case of group
actions, group gradings and Lie actions
Produção, teor e quantidade acumulada de nutrientes em rabanete cultivado em diferentes substratos.
O objetivo deste trabalho foi avaliar a produção, teor e quantidade acumulada de nutrientes em rabanete nos substratos areia, fibra de casca de coco (fcc) e mistura de areia com fibra de casca de coco.Resumo 963
On the electrical conductivity of composites with a polymeric matrix and a non-uniform concentration of carbon nanotubes
We present a multiscale modelling approach to explore the effects of a non-uniform concentration of carbon nanotubes (CNTs) on the electrical conductivity of CNT-polymer composites. Realistic three-dimensional representative volume elements (RVEs) are generated from a two-dimensional CNT concentration map, obtained via microscopy techniques. The RVEs capture the measured probability density function of the CNT concentration and include a length-scale to represent the details of the spatial distribution of the concentration. The homogenized conductivity of the RVEs is computed via multiscale FE analyses for different values of such length-scale, and it is compared to measurements. The modelling strategy is then used to explore the effects of the microstructural features of these materials on their electrical conductivity
Application of machine learning to predict the multiaxial strain-sensing response of CNT-polymer composites
We present predictive multiscale models of the multiaxial strain-sensing response of conductive CNT-polymer composites. Detailed physically-based finite element (FE) models at the micron scale are used to produce training data for an artificial neural network; the latter is then used, at macroscopic scale, to predict the electro-mechanical response of components of arbitrary shape subject to a non-uniform, multiaxial strain field, allowing savings in computational time of six orders of magnitude. We apply this methodology to explore the application of CNT-polymer composites to the construction of different types of sensors and to damage detection
Identification and selection rules of the spin-wave eigen-modes in a normally magnetized nano-pillar
We report on a spectroscopic study of the spin-wave eigen-modes inside an
individual normally magnetized two layers circular nano-pillar
(PermalloyCopperPermalloy) by means of a Magnetic Resonance Force
Microscope (MRFM). We demonstrate that the observed spin-wave spectrum
critically depends on the method of excitation. While the spatially uniform
radio-frequency (RF) magnetic field excites only the axially symmetric modes
having azimuthal index , the RF current flowing through the
nano-pillar, creating a circular RF Oersted field, excites only the modes
having azimuthal index . Breaking the axial symmetry of the
nano-pillar, either by tilting the bias magnetic field or by making the pillar
shape elliptical, mixes different -index symmetries, which can be excited
simultaneously by the RF current. Experimental spectra are compared to
theoretical prediction using both analytical and numerical calculations. An
analysis of the influence of the static and dynamic dipolar coupling between
the nano-pillar magnetic layers on the mode spectrum is performed
Working Group Report on the "TeV Particle Astrophysics and Physics Beyond the Standard Model"
This working group focused mainly on the complementarity among particle
physics and astrophysics. The analysis of data from both fields will better
constrain theoretical models. Much of the discussion focused on detecting dark
matter and susy particles, and on the potential of neutrino and gamma-ray
astrophysics for seeking or constraining new physics.Comment: Report on Working Group in the TeV Particle Astrophysics Workshop II
- Madison - Aug 200
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