22,093 research outputs found
Kinematic cosmology in conformally flat spacetime
In a recent series of papers Endean examines the properties of spatially
homogeneous and isotropic (FLRW) cosmological models filled with dust in the
``conformally flat spacetime presentation of cosmology'' (CFS cosmology). This
author claims it is possible to resolve a certain number of the difficulties
the standard model exhibits when confronted to observations, if the theoretical
predictions are obtained in the special framework of CFS cosmology. As a
by-product of his analysis Endean claims that no initial (big-bang) nor final
(big-crunch) singularities occur in the closed FLRW model. In this paper we
show up the fallacious arguments leading to Endean's conclusions and we
consistently reject his CFS cosmology.Comment: 5 pages, LaTeX2e, aas2pp4.sty, cases.sty, to be published in the
Astrophysical Journa
Lattice symmetry breaking perturbations for spiral waves
Spiral waves in two-dimensional excitable media have been observed
experimentally and studied extensively. It is now well-known that the symmetry
properties of the medium of propagation drives many of the dynamics and
bifurcations which are experimentally observed for these waves. Also,
symmetry-breaking induced by boundaries, inhomogeneities and anisotropy have
all been shown to lead to different dynamical regimes as to that which is
predicted for mathematical models which assume infinite homogeneous and
isotropic planar geometry. Recent mathematical analyses incorporating the
concept of forced symmetry-breaking from the Euclidean group of all planar
translations and rotations have given model-independent descriptions of the
effects of media imperfections on spiral wave dynamics. In this paper, we
continue this program by considering rotating waves in dynamical systems which
are small perturbations of a Euclidean-equivariant dynamical system, but for
which the perturbation preserves only the symmetry of a regular square lattice
Orange Peels and Fresnel Integrals
There are two standard ways of peeling an orange: either cut the skin along
meridians, or cut it along a spiral. We consider here the second method, and
study the shape of the spiral strip, when unfolded on a table. We derive a
formula that describes the corresponding flattened-out spiral. Cutting the peel
with progressively thinner strip widths, we obtain a sequence of increasingly
long spirals. We show that, after rescaling, these spirals tends to a definite
shape, known as the Euler spiral. The Euler spiral has applications in many
fields of science. In optics, the illumination intensity at a point behind a
slit is computed from the distance between two points on the Euler spiral. The
Euler spiral also provides optimal curvature for train tracks between a
straight run and an upcoming bend. It is striking that it can be also obtained
with an orange and a kitchen knife
Distortion of imbeddings of groups of intermediate growth into metric spaces
For every metric space in which there exists a sequence of
finite groups of bounded-size generating set that does not embed coarsely, and
for every unbounded, increasing function , we produce a group of
subexponential word growth all of whose imbeddings in have
distortion worse than .
This applies in particular to any B-convex Banach space , such as
Hilbert space.Comment: Used to appear as first half of arXiv:1403.558
Growth Series and Random Walks on Some Hyperbolic Graphs
Consider the tesselation of the hyperbolic plane by m-gons, l per vertex. In
its 1-skeleton, we compute the growth series of vertices, geodesics, tuples of
geodesics with common extremities. We also introduce and enumerate "holly
trees", a family of reduced loops in these graphs. We then apply Grigorchuk's
result relating cogrowth and random walks to obtain lower estimates on the
spectral radius of the Markov operator associated with a symmetric random walk
on these graphs.Comment: 21 pages. to appear in monash. mat
Born Reciprocity in String Theory and the Nature of Spacetime
After many years, the deep nature of spacetime in string theory remains an
enigma. In this letter we incorporate the concept of Born reciprocity in order
to provide a new point of view on string theory in which spacetime is a derived
dynamical concept. This viewpoint may be thought of as a dynamical chiral phase
space formulation of string theory, in which Born reciprocity is implemented as
a choice of a Lagrangian submanifold of the phase space, and amounts to a
generalization of T-duality. In this approach the fundamental symmetry of
string theory contains phase space diffeomorphism invariance and the underlying
string geometry should be understood in terms of dynamical bi-Lagrangian
manifolds and an apparently new geometric structure, somewhat reminiscent of
para-quaternionic geometry, which we call Born geometry
Multi-dimensional metric approximation by primitive points
We refine metrical statements in the style of the Khintchine-Groshev Theorem
by requiring certain coprimality constraints on the coordinates of the integer
solutions
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