Geometrical coupling fields of a hypercomplex type

This paper presents an application of Laplace's equation obtained from a quaternionic function that satisfies the Cauchy-Riemann conditions determined earlier by Borges and Machado [#!BorgesZeMarcio!#]. Therefore, we show that it is possible to express in a single equation gravity, electric and magnetic potential fields, and this expression can only be provided due to a function that will be called here the coupling function.

Geometrical hypercomplex coupling between electric and gravitational fields

The present work shows a coupling of electrical and gravitational fields through Cauchy-Riemann conditions for quaternions present in a previous paper [1]. It is also obtained an extended version of the Laplace-like equations for quaternions, now written in terms of both electric and gravitational fields.

Tinkertoys for the twisted D-series

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Gaiotto duality for the twisted A(2N-1) series

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Normal Forms for Polynomial Differential Systems in R-3 Having an Invariant Quadric and a Darboux Invariant

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Multiseries Lie groups and asymptotic modules for characterizing and solving integrable models

A multiseries integrable model (MSIM) is defined as a family of compatible flows on an infinite-dimensional Lie group of N-tuples of formal series around N given poles on the Riemann sphere. Broad classes of solutions to a MSIM are characterized through modules over rings of rational functions, called asymptotic modules. Possible ways for constructing asymptotic modules are Riemann-Hilbert and ∂̄ problems. When MSIM's are written in terms of the group coordinates, some of them can be contracted into standard integrable models involving a small number of scalar functions only. Simple contractible MSIM's corresponding to one pole, yield the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. Two-pole contractible MSIM's are exhibited, which lead to a hierarchy of solvable systems of nonlinear differential equations consisting of (2 + 1) -dimensional evolution equations and of quite strong differential constraints. © 1989 American Institute of Physics.

Dark energy as a kinematic effect

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Constante cosmológica: algumas consequências algébricas e dinâmicas

Pós-graduação em Física - IFT

Mistura de sabor e violação de CP

Pós-graduação em Física - IFT

Topology Verification for Isosurface Extraction

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes.

Lyotropic mixture made of potassium laurate/1-undecanol/K2SO4/water presenting high birefringences and large biaxial nematic phase domain: a laser conoscopy study

The lyotropic liquid crystalline quaternary mixture made of potassium laurate (KL), potassium sulphate, 1-undecanol and water was investigated by experimental optical methods (optical microscopy and laser conoscopy). In a particular temperature and relative concentrations range, the three nematic phases (two uniaxial and one biaxial) were identified. The biaxial domain in the temperature/KL concentration surface is larger when compared to other lyotropic mixtures. Moreover, this new mixture gives nematic phases with higher birefringence than similar systems. The behavior of the symmetric tensor order parameter invariants sigma(3) and sigma(2) calculated from the measured optical birefringences supports that the uniaxial-to-biaxial transitions are of second order, described by a mean-field theory.

Generators of supersymmetric polynomials in positive characteristic

In Kantor and Trishin (1997) [3], Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m vertical bar n) and a related algebra A, of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A(s) was investigated earlier by Stembridge (1985) who in [9] called the elements of A(s) supersymmetric polynomials and determined generators of A(s). The case of positive characteristic p of the ground field K has been recently investigated by La Scala and Zubkov (in press) in [6]. We extend their work and give a complete description of generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m vertical bar n) and generators of A(s).

Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.

Database of diazotrophs in global ocean: abundances, biomass and nitrogen fixation rates

[EN] Marine N2 fixing microorganisms, termed diazotrophs, are a key functional group in marine pelagic ecosystems. The biological fixation of dinitrogen (N2) to bioavailable nitrogen provides an important new source of nitrogen for pelagic marine ecosystems 5 and influences primary productivity and organic matter export to the deep ocean. As one of a series of efforts to collect biomass and rates specific to different phytoplankton functional groups, we have constructed a database on diazotrophic organisms in the global pelagic upper ocean by compiling about 12 000 direct field measurements of cyanobacterial diazotroph abundances (based on microscopic cell counts or qPCR 10 assays targeting the nifH genes) and N2 fixation rates. Biomass conversion factors are estimated based on cell sizes to convert  abundance data to diazotrophic biomass. The database is limited spatially, lacking large regions of the ocean especially in the Indian Ocean. The data are approximately log-normal distributed, and large variances exist in most sub-databases with non-zero values differing 5 to 8 orders of magnitude. 15 Lower mean N2 fixation rate was found in the North Atlantic Ocean than the Pacific Ocean. Reporting the geometric mean and the range of one geometric standard error below and above the geometric mean, the pelagic N2 fixation rate in the global ocean is estimated to be 62 (53–73) TgNyr−1 and the pelagic diazotrophic biomass in the global ocean is estimated to be 4.7 (2.3–9.6) TgC from cell counts and to 89 (40–20 200) TgC from nifH-based abundances. Uncertainties related to biomass conversion factors can change the estimate of geometric mean pelagic diazotrophic biomass in the global ocean by about ±70 %. This evolving database can be used to study spatial and temporal distributions and variations of marine N2 fixation, to validate geochemical estimates and to parameterize and validate biogeochemical models. The database is 25 stored in PANGAEA (http://doi.pangaea.de/10.1594/PANGAEA.774851).

On existence and uniqueness of positive solutions to a class of fractional boundary value problems

[EN] The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fractional boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ′ ( 0 ) = 0 , where 2 < α ≤ 3 and D 0 + α is the Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem in partially ordered metric spaces. The autonomous case of this problem was studied in the paper [Zhao et al., Abs. Appl. Anal., to appear], but in Zhao et al. (to appear), the question of uniqueness of the solution is not treated. We also present some examples where we compare our results with the ones obtained in Zhao et al. (to appear). 2010 Mathematics Subject Classification: 34B15