Gauge theory on nonassociative spaces

We show how to do gauge theory on the octonions and other nonassociative algebras such as `fuzzy $R^4$' 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 $Z_2^3$ 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 $\sigma$, 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 $A$ yields an operator algebra $B$ and a module structure on A, whose endomorphism ring is isomorphic to a subring $A^B$ of certain invariant elements of $A$. We show that if $A$ is a critically compressible left $B$-module, then the dimension of its self-injective hull $A$ over the ring of fractions of $A^B$ is bounded by the uniform dimension of $A$ and the number of linear operators generating $B$. 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 (Permalloy$|$Copper$|$Permalloy) 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 $\ell=0$, the RF current flowing through the nano-pillar, creating a circular RF Oersted field, excites only the modes having azimuthal index $\ell=+1$. Breaking the axial symmetry of the nano-pillar, either by tilting the bias magnetic field or by making the pillar shape elliptical, mixes different $\ell$-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