9,011 research outputs found
Kinematics of a Spacetime with an Infinite Cosmological Constant
A solution of the sourceless Einstein's equation with an infinite value for
the cosmological constant \Lambda is discussed by using Inonu-Wigner
contractions of the de Sitter groups and spaces. When \Lambda --> infinity,
spacetime becomes a four-dimensional cone, dual to Minkowski space by a
spacetime inversion. This inversion relates the four-cone vertex to the
infinity of Minkowski space, and the four-cone infinity to the Minkowski
light-cone. The non-relativistic limit c --> infinity is further considered,
the kinematical group in this case being a modified Galilei group in which the
space and time translations are replaced by the non-relativistic limits of the
corresponding proper conformal transformations. This group presents the same
abstract Lie algebra as the Galilei group and can be named the conformal
Galilei group. The results may be of interest to the early Universe Cosmology.Comment: RevTex, 7 pages, no figures. Presentation changes, including a new
Title. Version to appear in Found. Phys. Let
Time-Reversal Symmetry Breaking and Decoherence in Chaotic Dirac Billiards
In this work, we perform a statistical study on Dirac Billiards in the
extreme quantum limit (a single open channel on the leads). Our numerical
analysis uses a large ensemble of random matrices and demonstrates the
preponderant role of dephasing mechanisms in such chaotic billiards. Physical
implementations of these billiards range from quantum dots of graphene to
topological insulators structures. We show, in particular, that the role of
finite crossover fields between the universal symmetries quickly leaves the
conductance to the asymptotic limit of unitary ensembles. Furthermore, we show
that the dephasing mechanisms strikingly lead Dirac billiards from the extreme
quantum regime to the semiclassical Gaussian regime
Foliations and Chern-Heinz inequalities
We extend the Chern-Heinz inequalities about mean curvature and scalar
curvature of graphs of -functions to leaves of transversally oriented
codimension one -foliations of Riemannian manifolds. That extends
partially Salavessa's work on mean curvature of graphs and generalize results
of Barbosa-Kenmotsu-Oshikiri \cite{barbosa-kenmotsu-Oshikiri} and
Barbosa-Gomes-Silveira \cite{barbosa-gomes-silveira} about foliations of
3-dimensional Riemannian manifolds by constant mean curvature surfaces. These
Chern-Heinz inequalities for foliations can be applied to prove
Haymann-Makai-Osserman inequality (lower bounds of the fundamental tones of
bounded open subsets in terms of its inradius)
for embedded tubular neighborhoods of simple curves of .Comment: This paper is an improvment of an earlier paper titled On Chern-Heinz
Inequalities. 8 Pages, Late
Characterizing neuromorphologic alterations with additive shape functionals
The complexity of a neuronal cell shape is known to be related to its
function. Specifically, among other indicators, a decreased complexity in the
dendritic trees of cortical pyramidal neurons has been associated with mental
retardation. In this paper we develop a procedure to address the
characterization of morphological changes induced in cultured neurons by
over-expressing a gene involved in mental retardation. Measures associated with
the multiscale connectivity, an additive image functional, are found to give a
reasonable separation criterion between two categories of cells. One category
consists of a control group and two transfected groups of neurons, and the
other, a class of cat ganglionary cells. The reported framework also identified
a trend towards lower complexity in one of the transfected groups. Such results
establish the suggested measures as an effective descriptors of cell shape
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