3,176 research outputs found
A Bose-Einstein Approach to the Random Partitioning of an Integer
Consider N equally-spaced points on a circle of circumference N. Choose at
random n points out of on this circle and append clockwise an arc of
integral length k to each such point. The resulting random set is made of a
random number of connected components. Questions such as the evaluation of the
probability of random covering and parking configurations, number and length of
the gaps are addressed. They are the discrete versions of similar problems
raised in the continuum. For each value of k, asymptotic results are presented
when n,N both go to infinity according to two different regimes. This model may
equivalently be viewed as a random partitioning problem of N items into n
recipients. A grand-canonical balls in boxes approach is also supplied, giving
some insight into the multiplicities of the box filling amounts or spacings.
The latter model is a k-nearest neighbor random graph with N vertices and kn
edges. We shall also briefly consider the covering problem in the context of a
random graph model with N vertices and n (out-degree 1) edges whose endpoints
are no more bound to be neighbors
Semilinear mixed problems on Hilbert complexes and their numerical approximation
Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010),
281-354] that linear, mixed variational problems, and their numerical
approximation by mixed finite element methods, can be studied using the
powerful, abstract language of Hilbert complexes. In another recent article
[arXiv:1005.4455], we extended the Arnold-Falk-Winther framework by analyzing
variational crimes (a la Strang) on Hilbert complexes. In particular, this gave
a treatment of finite element exterior calculus on manifolds, generalizing
techniques from surface finite element methods and recovering earlier a priori
estimates for the Laplace-Beltrami operator on 2- and 3-surfaces, due to Dziuk
[Lecture Notes in Math., vol. 1357 (1988), 142-155] and later Demlow [SIAM J.
Numer. Anal., 47 (2009), 805-827], as special cases. In the present article, we
extend the Hilbert complex framework in a second distinct direction: to the
study of semilinear mixed problems. We do this, first, by introducing an
operator-theoretic reformulation of the linear mixed problem, so that the
semilinear problem can be expressed as an abstract Hammerstein equation. This
allows us to obtain, for semilinear problems, a priori solution estimates and
error estimates that reduce to the Arnold-Falk-Winther results in the linear
case. We also consider the impact of variational crimes, extending the results
of our previous article to these semilinear problems. As an immediate
application, this new framework allows for mixed finite element methods to be
applied to semilinear problems on surfaces.Comment: 22 pages; v2: major revision, particularly sharpening of error
estimates in Section
The effects of dietary fibre type on satiety-related hormones and voluntary food intake in dogs
Depending on type and inclusion level, dietary fibre may increase and maintain satiety and postpone the onset of hunger. This 7-week study evaluated the effect of fibre fermentability on physiological satiety-related metabolites and voluntary food intake (VFI) in dogs. Sixteen healthy adult dogs were fed a low-fermentable fibre (LFF) diet containing 8·5 % cellulose or a high-fermentable fibre (HFF) diet containing 8·5 % sugarbeet pulp and 2 % inulin. Large intestinal fibre degradation was evaluated by apparent faecal digestibility of nutrients and faecal SCFA and NH3 concentrations. Postprandial blood samples were obtained to determine postprandial plasma glucose, insulin, total peptide tyrosine–tyrosine (PYY), total glucagon-like peptide-1 (GLP-1) and total ghrelin concentrations. At the end of the study, the dogs were given a single meal of a dry dog food to determine VFI. Dogs fed the HFF diet had a significantly higher large intestinal fibre degradation and production of SCFA compared with the dogs fed the LFF diet. The HFF-fed dogs tended (P = 0·058) to show a lower VFI at the end of the study. No treatment effects were found for postprandial plasma glucose, PYY, GLP-1 and ghrelin responses. The concentrations of these metabolites could not be related to the observed difference in VFI. The inclusion of fermentable fibre in canine diets may contribute to the prevention or mitigation of obesity through its effects on satiety. The underlying mechanisms require further investigatio
Abundance of local actions for the vacuum Einstein equations
We exhibit large classes of local actions for the vacuum Einstein equations.
In presence of fermions, or more generally of matter which couple to the
connection, these actions lead to inequivalent equations revealing an arbitrary
number of parameters. Even in the pure gravitational sector, any corresponding
quantum theory would depend on these parameters.Comment: 10 pages. Final version to appear in Letters in Mathematical Physic
Black Holes and Wormholes in 2+1 Dimensions
A large variety of spacetimes---including the BTZ black holes---can be
obtained by identifying points in 2+1 dimensional anti-de Sitter space by means
of a discrete group of isometries. We consider all such spacetimes that can be
obtained under a restriction to time symmetric initial data and one asymptotic
region only. The resulting spacetimes are non-eternal black holes with
collapsing wormhole topologies. Our approach is geometrical, and we discuss in
detail: The allowed topologies, the shape of the event horizons, topological
censorship and trapped curves.Comment: 23 pages, LaTeX, 11 figure
A Spinning Anti-de Sitter Wormhole
We construct a 2+1 dimensional spacetime of constant curvature whose spatial
topology is that of a torus with one asymptotic region attached. It is also a
black hole whose event horizon spins with respect to infinity. An observer
entering the hole necessarily ends up at a "singularity"; there are no inner
horizons.
In the construction we take the quotient of 2+1 dimensional anti-de Sitter
space by a discrete group Gamma. A key part of the analysis proceeds by
studying the action of Gamma on the boundary of the spacetime.Comment: Latex, 28 pages, 7 postscript figures included in text, a Latex file
without figures can be found at http://vanosf.physto.se/~stefan/spinning.html
Replaced with journal version, minor change
Curvature condensation and bifurcation in an elastic shell
We study the formation and evolution of localized geometrical defects in an
indented cylindrical elastic shell using a combination of experiment and
numerical simulation. We find that as a symmetric localized indentation on a
semi-cylindrical shell increases, there is a transition from a global mode of
deformation to a localized one which leads to the condensation of curvature
along a symmetric parabolic crease. This process introduces a soft mode in the
system, converting a load-bearing structure into a hinged, kinematic mechanism.
Further indentation leads to twinning wherein the parabolic crease bifurcates
into two creases that move apart on either side of the line of symmetry. A
qualitative theory captures the main features of the phenomena and leads to
sharper questions about the nucleation of these defects.Comment: 4 pages, 5 figures, submitted to Physical Review Letter
Generalized Lagrangian of N = 1 supergravity and its canonical constraints with the real Ashtekar variable
We generalize the Lagrangian of N = 1 supergravity (SUGRA) by using an
arbitrary parameter , which corresponds to the inverse of Barbero's
parameter . This generalized Lagrangian involves the chiral one as a
special case of the value . We show that the generalized
Lagrangian gives the canonical formulation of N = 1 SUGRA with the real
Ashtekar variable after the 3+1 decomposition of spacetime. This canonical
formulation is also derived from those of the usual N = 1 SUGRA by performing
Barbero's type canonical transformation with an arbitrary parameter . We give some comments on the canonical formulation of the theory.Comment: 17 pages, LATE
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