1,315 research outputs found
Fermi-Frenet coordinates for space-like curves
We generalize Fermi coordinates, which correspond to an adapted set of
coordinates describing the vicinity of an observer's worldline, to the
worldsheet of an arbitrary spatial curve in a static spacetime. The spatial
coordinate axes are fixed using a covariant Frenet triad so that the metric can
be expressed using the curvature and torsion of the spatial curve. As an
application of Fermi-Frenet coordinates, we show that they allow covariant
inertial forces to be expressed in a simple and physically intuitive way.Comment: 7 page
Active swarms on a sphere
Here we show that coupling to curvature has profound effects on collective
motion in active systems, leading to patterns not observed in flat space.
Biological examples of such active motion in curved environments are numerous:
curvature and tissue folding are crucial during gastrulation, epithelial and
endothelial cells move on constantly growing, curved crypts and vili in the
gut, and the mammalian corneal epithelium grows in a steady-state vortex
pattern. On the physics side, droplets coated with actively driven microtubule
bundles show active nematic patterns. We study a model of self-propelled
particles with polar alignment on a sphere. Hallmarks of these motion patterns
are a polar vortex and a circulating band arising due to the incompatibility
between spherical topology and uniform motion - a consequence of the hairy ball
theorem. We present analytical results showing that frustration due to
curvature leads to stable elastic distortions storing energy in the band.Comment: 5 pages, 4 figures plus Supporting Informatio
Sistemas de produção de caprinos leiteiros e perfil de produtores associados às cooperativas de Jussara e Valente na Bahia.
Resumo: Este trabalho foi realizado com o objetivo de caracterizar os sistemas de produção aplicados a caprinos leiteiros criados por produtores associados às cooperativas de Jussara e Valente; na Bahia. Utilizaram-se dados retirados de entrevistas com 45 produtores que utilizavam o leite para consumo próprio ou venda; realizando-se estatística descritiva para descrever a natureza das variáveis estudadas. As propriedades possuíram; como mediana; 20 hectares. A maior utilização da terra correspondeu à forragem cultivada buffel (Cenchrus ciliaris) e à caatinga bruta. O rebanho de caprinos constou de 28 cabeças e a mediana de cabras em lactação foi de oito cabeças por dia. Em 42% das propriedades; os animais se alimentavam em áreas de terras devolutas. O sistema de produção animal pôde ser caracterizado como um sistema misto. A mediana de produção obtida foi de cinco litros ao dia e a mediana da produção comercializada mensalmente foi de 250 litros. Apenas 31;11% dos produtores faziam alguma anotação com relação ao seu rebanho. Dos produtores; 20% realizavam monta natural controlada e 11;11% realizavam estação de monta. Os reprodutores mais utilizados foram os SRD; sendo que 46;66% dos produtores os escolhiam sem objetivos de melhorar alguma característica. Com relação às matrizes; a mediana de partos por cabra por ano foi de um; sendo que 55;56% dos produtores descartavam as matrizes quando as mesmas apresentavam problemas produtivos e reprodutivos e somente 33;33% observavam alguma característica ao escolherem a matriz. Observou-se uma grande variabilidade dos fatores de produção e comercialização.Dissertação (Mestrado em Produção Animal) - Universidade Federal de Minas Gerais, Belo Horizonte. Orientador: Iran Borges (UFMG); Co-orientador: Evandro Vasconcelos Holanda, Embrapa Caprinos (CNPC)
Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice
We investigate the phase diagram of a discrete version of the Maier-Saupe
model with the inclusion of additional degrees of freedom to mimic a
distribution of rodlike and disklike molecules. Solutions of this problem on a
Bethe lattice come from the analysis of the fixed points of a set of nonlinear
recursion relations. Besides the fixed points associated with isotropic and
uniaxial nematic structures, there is also a fixed point associated with a
biaxial nematic structure. Due to the existence of large overlaps of the
stability regions, we resorted to a scheme to calculate the free energy of
these structures deep in the interior of a large Cayley tree. Both
thermodynamic and dynamic-stability analyses rule out the presence of a biaxial
phase, in qualitative agreement with previous mean-field results
Magnetovac Cylinder to Magnetovac Torus
A method for mapping known cylindrical magnetovac solutions to solutions in
torus coordinates is developed. Identification of the cylinder ends changes
topology from R1 x S1 to S1 x S1. An analytic Einstein-Maxwell solution for a
toroidal magnetic field in tori is presented. The toroidal interior is matched
to an asymptotically flat vacuum exterior, connected by an Israel boundary
layer.Comment: to appear in Class. Quant. Gra
Circular Orbits in Einstein-Gauss-Bonnet Gravity
The stability under radial and vertical perturbations of circular orbits
associated to particles orbiting a spherically symmetric center of attraction
is study in the context of the n-dimensional: Newtonian theory of gravitation,
Einstein's general relativity, and Einstein-Gauss-Bonnet theory of gravitation.
The presence of a cosmological constant is also considered. We find that this
constant as well as the Gauss-Bonnet coupling constant are crucial to have
stability for .Comment: 11 pages, 4 figs, RevTex, Phys. Rev. D, in pres
On the embedding of spacetime in five-dimensional Weyl spaces
We revisit Weyl geometry in the context of recent higher-dimensional theories
of spacetime. After introducing the Weyl theory in a modern geometrical
language we present some results that represent extensions of Riemannian
theorems. We consider the theory of local embeddings and submanifolds in the
context of Weyl geometries and show how a Riemannian spacetime may be locally
and isometrically embedded in a Weyl bulk. We discuss the problem of classical
confinement and the stability of motion of particles and photons in the
neighbourhood of branes for the case when the Weyl bulk has the geometry of a
warped product space. We show how the confinement and stability properties of
geodesics near the brane may be affected by the Weyl field. We construct a
classical analogue of quantum confinement inspired in theoretical-field models
by considering a Weyl scalar field which depends only on the extra coordinate.Comment: 16 pages, new title and references adde
Riemannian Geometry of Noncommutative Surfaces
A Riemannian geometry of noncommutative n-dimensional surfaces is developed
as a first step towards the construction of a consistent noncommutative
gravitational theory. Historically, as well, Riemannian geometry was recognized
to be the underlying structure of Einstein's theory of general relativity and
led to further developments of the latter. The notions of metric and
connections on such noncommutative surfaces are introduced and it is shown that
the connections are metric-compatible, giving rise to the corresponding Riemann
curvature. The latter also satisfies the noncommutative analogue of the first
and second Bianchi identities. As examples, noncommutative analogues of the
sphere, torus and hyperboloid are studied in detail. The problem of covariance
under appropriately defined general coordinate transformations is also
discussed and commented on as compared with other treatments.Comment: 28 pages, some clarifications, examples and references added, version
to appear in J. Math. Phy
Minimal resonances in annular non-Euclidean strips
Differential growth processes play a prominent role in shaping leaves and
biological tissues. Using both analytical and numerical calculations, we
consider the shapes of closed, elastic strips which have been subjected to an
inhomogeneous pattern of swelling. The stretching and bending energies of a
closed strip are frustrated by compatibility constraints between the curvatures
and metric of the strip. To analyze this frustration, we study the class of
"conical" closed strips with a prescribed metric tensor on their center line.
The resulting strip shapes can be classified according to their number of
wrinkles and the prescribed pattern of swelling. We use this class of strips as
a variational ansatz to obtain the minimal energy shapes of closed strips and
find excellent agreement with the results of a numerical bead-spring model.
Within this class of strips, we derive a condition under which a strip can have
vanishing mean curvature along the center line.Comment: 14 pages, 13 figures. Published version. Updated references and added
2 figure
Statistical models of mixtures with a biaxial nematic phase
We consider a simple Maier-Saupe statistical model with the inclusion of
disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like
and disc-like molecules. A quenched distribution of shapes leads to the
existence of a stable biaxial nematic phase, in qualitative agreement with
experimental findings for some ternary lyotropic liquid mixtures. An annealed
distribution, however, which is more adequate to liquid mixtures, precludes the
stability of this biaxial phase. We then use a two-temperature formalism, and
assume a separation of relaxation times, to show that a partial degree of
annealing is already sufficient to stabilize a biaxial nematic structure.Comment: 11 pages, 2 figure
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