Spinors in Higher Dimensional and Locally Anisotropic Spaces

The theory of spinors is developed for locally anisotropic (la) spaces, in brief la-spaces, which in general are modeled as vector bundles provided with nonlinear and distinguished connections and metric structures (such la-spaces contain as particular cases the Lagrange, Finsler and, for trivial nonlinear connections, Kaluza-Klein spaces). The la-spinor differential geometry is constructed. The distinguished spinor connections are studied and compared with similar ones on la-spaces. We derive the la-spinor expressions of curvatures and torsions and analyze the conditions when the distinguished torsion and nonmetricity tensors can be generated from distinguished spinor connections. The dynamical equations for gravitational and matter field la-interactions are formulated.Comment: 54 pages, Revtex, an extension of the paper published in J. Math. Phys. 37 (1996), 508--52

Matrix exponential via Clifford algebras

We use isomorphism $\varphi$ between matrix algebras and simple orthogonal Clifford algebras \cl(Q) to compute matrix exponential ${e}^{A}$ of a real, complex, and quaternionic matrix A. The isomorphic image $p=\varphi(A)$ in \cl(Q), where the quadratic form $Q$ has a suitable signature $(p,q),$ is exponentiated modulo a minimal polynomial of $p$ using Clifford exponential. Elements of \cl(Q) are treated as symbolic multivariate polynomials in Grassmann monomials. Computations in \cl(Q) are performed with a Maple package `CLIFFORD'. Three examples of matrix exponentiation are given

Temporal and vertical variations of aerosol physical and chemical properties over West Africa: AMMA aircraft campaign in summer 2006

While the Sahelian belt in West Africa stretches in the border between the global hot-spots of mineral dust and biomass burning aerosols, the presence of West African Monsoon is expected to create significant vertical and temporal variations in the regional aerosol properties through transport and mixing of particles from various sources (mineral dust, biomass burning, sulfates, sea salt). In order to improve our understanding of the evolution of the aerosol-cloud system over such region across the onset of the summer monsoon, the French ATR-42 research aircraft was deployed in Niamey, Niger (13°30' N, 02°05' E) in summer 2006, during the three special observation periods (SOPs) of the African Monsoon Multidisciplinary Analysis (AMMA) project. These three SOPs covered both dry and wet periods before and after the onset of the Western African Monsoon. <br><br> State of the art physico-chemical aerosol measurements on the ATR-42 showed a notable seasonal transition in averaged number size distributions where (i) the Aitken mode is dominating over the accumulation mode during the dry season preceding the monsoon arrival and (ii) the accumulation mode increasingly gained importance after the onset of the West African monsoon and even dominated the Aitken mode after the monsoon had fully developed. The parameters for the mean log-normal distributions observed in respective layers characterized by the different wind regimes (monsoon layer, SAL, free troposphere) are presented, together with the major particle compositions found in the accumulation mode particles. Thereby, results of this study should facilitate radiative transfer calculations, validation of satellite remote sensors, and detailed transport modeling by partners within and outside the AMMA community. <br><br> Extended analysis of the chemical composition of single aerosol particles by a transmission electron microscope (TEM) coupled to an energy dispersive X-ray spectrometer (EDX) revealed dominance of mineral dust (aluminosilicate) even in the submicron particle size range during the dry period, gradually replaced by prevailing biomass burning and sulfate particles, after the onset of the monsoon period. The spatial and temporal evolution from SOP1 to SOP2a1 and SOP2a2 of the particle physical and chemical properties and associated aerosol hygroscopic properties are remarkably consistent

Increase of the aerosol hygroscopicity by aqueous mixing in a mesoscale convective system: a case study from the AMMA campaign

International audienceAerosol properties were measured during an airborne campaign experiment that took place in July 2006 in West Africa within the framework of the African Monsoon Multidisciplinary Analyses (AMMA). The goal of the present study was to determine the main microphysical processes that affect the aerosols during the passage of a mesoscale convective system (MCS) over the region of Niamey in Niger. A main difference in the aerosol profiles measured before and after the passage of the MCS was found for a layer located between 1300 and 3000 m where the aerosol concentration has drastically decreased after the passage of the MCS. Concurrently, a significant increase of the cloud condensation nuclei fraction was also observed during the post-MCS period in the same layer. Moreover, the results of the elemental composition analyses of individual particles collected in this layer after the MCS passage have shown higher contributions of sulfate, nitrate and chloride to the total aerosol. A mesoscale atmospheric model with on-line dust parameterization and Lagrangian backtrajectories was used to interpret the impact of the MCS on the aerosol properties. The results of the simulation show that the MCS 1) generates dust particles at the surface in front of the system and washout particles behind, 2) modifies the aerosol mixing state through cloud processing, and 3) enhances CCN activity of particles through the coating of soluble material

A geometric basis for the standard-model gauge group

A geometric approach to the standard model in terms of the Clifford algebra Cl_7 is advanced. A key feature of the model is its use of an algebraic spinor for one generation of leptons and quarks. Spinor transformations separate into left-sided ("exterior") and right-sided ("interior") types. By definition, Poincare transformations are exterior ones. We consider all rotations in the seven-dimensional space that (1) conserve the spacetime components of the particle and antiparticle currents and (2) do not couple the right-chiral neutrino. These rotations comprise additional exterior transformations that commute with the Poincare group and form the group SU(2)_L, interior ones that constitute SU(3)_C, and a unique group of coupled double-sided rotations with U(1)_Y symmetry. The spinor mediates a physical coupling of Poincare and isotopic symmetries within the restrictions of the Coleman--Mandula theorem. The four extra spacelike dimensions in the model form a basis for the Higgs isodoublet field, whose symmetry requires the chirality of SU(2). The charge assignments of both the fundamental fermions and the Higgs boson are produced exactly.Comment: 17 pages, LaTeX requires iopart. Accepted for publication in J. Phys. A: Math. Gen. 9 Mar 2001. Typos correcte

Characterizing the impact of urban emissions on regional aerosol particles: airborne measurements during the MEGAPOLI experiment

The MEGAPOLI (Megacities: Emissions, urban, regional and Global Atmospheric POLlution and climate effects, and Integrated tools for assessment and mitigation) experiment took place in July 2009. The aim of this campaign was to study the aging and reactions of aerosol and gas-phase emissions in the city of Paris. Three ground-based measurement sites and several mobile platforms including instrument equipped vehicles and the ATR-42 aircraft were involved. We present here the variations in particle- and gas-phase species over the city of Paris, using a combination of high-time resolution measurements aboard the ATR-42 aircraft. Particle chemical composition was measured using a compact time-of-flight aerosol mass spectrometer (C-ToF-AMS), giving detailed information on the non-refractory submicron aerosol species. The mass concentration of black carbon (BC), measured by a particle absorption soot photometer (PSAP), was used as a marker to identify the urban pollution plume boundaries. Aerosol mass concentrations and composition were affected by air-mass history, with air masses that spent longest time over land having highest fractions of organic aerosol and higher total mass concentrations. The Paris plume is mainly composed of organic aerosol (OA), BC, and nitrate aerosol, as well as high concentrations of anthropogenic gas-phase species such as toluene, benzene, and NO_x. Using BC and CO as tracers for air-mass dilution, we observe the ratio of ΔOA / ΔBC and ΔOA / ΔCO increase with increasing photochemical age (−log(NO_x / NO_y)). Plotting the equivalent ratios of different organic aerosol species (LV-OOA, SV-OOA, and HOA) illustrate that the increase in OA is a result of secondary organic aerosol (SOA) formation. Within Paris the changes in the ΔOA / ΔCO are similar to those observed during other studies in London, Mexico City, and in New England, USA. Using the measured SOA volatile organic compounds (VOCs) species together with organic aerosol formation yields, we were able to predict ~50% of the measured organics. These airborne measurements during the MEGAPOLI experiment show that urban emissions contribute to the formation of OA and have an impact on aerosol composition on a regional scale

Positivity and conservation of superenergy tensors

Two essential properties of energy-momentum tensors T_{\mu\nu} are their positivity and conservation. This is mathematically formalized by, respectively, an energy condition, as the dominant energy condition, and the vanishing of their divergence \nabla^\mu T_{\mu\nu}=0. The classical Bel and Bel-Robinson superenergy tensors, generated from the Riemann and Weyl tensors, respectively, are rank-4 tensors. But they share these two properties with energy momentum tensors: the Dominant Property (DP) and the divergence-free property in the absence of sources (vacuum). Senovilla defined a universal algebraic construction which generates a basic superenergy tensor T{A} from any arbitrary tensor A. In this construction the seed tensor A is structured as an r-fold multivector, which can always be done. The most important feature of the basic superenergy tensors is that they satisfy automatically the DP, independently of the generating tensor A. In a previous paper we presented a more compact definition of T{A} using the r-fold Clifford algebra. This form for the superenergy tensors allowed to obtain an easy proof of the DP valid for any dimension. In this paper we include this proof. We explain which new elements appear when we consider the tensor T{A} generated by a non-degree-defined r-fold multivector A and how orthogonal Lorentz transformations and bilinear observables of spinor fields are included as particular cases of superenergy tensors. We find some sufficient conditions for the seed tensor A, which guarantee that the generated tensor T{A} is divergence-free. These sufficient conditions are satisfied by some physical fields, which are presented as examples.Comment: 19 pages, no figures. Language and minor changes. Published versio