151 research outputs found
On Vanishing Theorems For Vector Bundle Valued p-Forms And Their Applications
Let be a strictly increasing function
with . We unify the concepts of -harmonic maps, minimal
hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and
introduce -Yang-Mills fields, -degree, -lower degree, and generalized
Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on
manifolds. When and
the -Yang-Mills field becomes an ordinary Yang-Mills field,
-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the plus
sign, and a generalized Yang-Mills-Born-Infeld field with the minus sign on a
manifold respectively. We also introduce the energy functional (resp.
-Yang-Mills functional) and derive the first variational formula of the
energy functional (resp. -Yang-Mills functional) with
applications. In a more general frame, we use a unified method to study the
stress-energy tensors that arise from calculating the rate of change of various
functionals when the metric of the domain or base manifold is changed. These
stress-energy tensors, linked to -conservation laws yield monotonicity
formulae. A "macroscopic" version of these monotonicity inequalities enables us
to derive some Liouville type results and vanishing theorems for forms with
values in vector bundles, and to investigate constant Dirichlet boundary value
problems for 1-forms. In particular, we obtain Liouville theorems for
harmonic maps (e.g. -harmonic maps), and Yang-Mills fields (e.g.
generalized Yang-Mills-Born-Infeld fields on manifolds). We also obtain
generalized Chern type results for constant mean curvature type equations for
forms on and on manifolds with the global doubling property
by a different approach. The case and is due to Chern.Comment: 1. This is a revised version with several new sections and an
appendix that will appear in Communications in Mathematical Physics. 2. A
"microscopic" approach to some of these monotonicity formulae leads to
celebrated blow-up techniques and regularity theory in geometric measure
theory. 3. Our unique solution of the Dirichlet problems generalizes the work
of Karcher and Wood on harmonic map
-minimal surface and manifold with positive -Bakry-\'{E}mery Ricci curvature
In this paper, we first prove a compactness theorem for the space of closed
embedded -minimal surfaces of fixed topology in a closed three-manifold with
positive Bakry-\'{E}mery Ricci curvature. Then we give a Lichnerowicz type
lower bound of the first eigenvalue of the -Laplacian on compact manifold
with positive -Bakry-\'{E}mery Ricci curvature, and prove that the lower
bound is achieved only if the manifold is isometric to the -shpere, or the
-dimensional hemisphere. Finally, for compact manifold with positive
-Bakry-\'{E}mery Ricci curvature and -mean convex boundary, we prove an
upper bound for the distance function to the boundary, and the upper bound is
achieved if only if the manifold is isometric to an Euclidean ball.Comment: 15 page
Possible origins of macroscopic left-right asymmetry in organisms
I consider the microscopic mechanisms by which a particular left-right (L/R)
asymmetry is generated at the organism level from the microscopic handedness of
cytoskeletal molecules. In light of a fundamental symmetry principle, the
typical pattern-formation mechanisms of diffusion plus regulation cannot
implement the "right-hand rule"; at the microscopic level, the cell's
cytoskeleton of chiral filaments seems always to be involved, usually in
collective states driven by polymerization forces or molecular motors. It seems
particularly easy for handedness to emerge in a shear or rotation in the
background of an effectively two-dimensional system, such as the cell membrane
or a layer of cells, as this requires no pre-existing axis apart from the layer
normal. I detail a scenario involving actin/myosin layers in snails and in C.
elegans, and also one about the microtubule layer in plant cells. I also survey
the other examples that I am aware of, such as the emergence of handedness such
as the emergence of handedness in neurons, in eukaryote cell motility, and in
non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue.
Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in
Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec
The solution to the Tullock rent-seeking game when R > 2: mixed-strategy equilibria and mean dissipation rates
In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium exists when R>2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete, and show that full rent dissipation occurs when the strategy space is continuous. Our results are shown to be consistent with recent experimental evidence on the dissipation of rents.
An earlier version of this paper circulated under the title, No, Virginia, There is No Overdissipation of Rents. We are grateful to Dave Furth and Frans van Winden for stimulating conversations, and for comments provided by workshop participants from the CORE-ULB-KUL IUAP project, Purdue University, Pennsylvania State University, Rijksuniversiteit Limburg, and Washington State University. We also thank Max van de Sande Bakhuyzen and Ben Heijdra for useful discussions, and Geert Gielens for computational assistance. An earlier version of the paper was presented at the ESEM 1992 in Brussels and the Mid-West Mathematical Economics Conference in Pittsburgh. All three authors would like to thank CentER for its hospitality during the formative stages of the paper. The second author has also benefited from the financial support of the Katholieke Universitieit Leuven and the Jay N. Ross Young Faculty Scholar Award at Purdue University. The third author benefitted from visiting IGIER where part of the paper was written. The third author also benefitted from grant IUAP 26 of the Belgian Government
Anisotropy studies around the galactic centre at EeV energies with the Auger Observatory
Data from the Pierre Auger Observatory are analyzed to search for
anisotropies near the direction of the Galactic Centre at EeV energies. The
exposure of the surface array in this part of the sky is already significantly
larger than that of the fore-runner experiments. Our results do not support
previous findings of localized excesses in the AGASA and SUGAR data. We set an
upper bound on a point-like flux of cosmic rays arriving from the Galactic
Centre which excludes several scenarios predicting sources of EeV neutrons from
Sagittarius . Also the events detected simultaneously by the surface and
fluorescence detectors (the `hybrid' data set), which have better pointing
accuracy but are less numerous than those of the surface array alone, do not
show any significant localized excess from this direction.Comment: Matches published versio
Update on the correlation of the highest energy cosmic rays with nearby extragalactic matter
Data collected by the Pierre Auger Observatory through 31 August 2007 showed
evidence for anisotropy in the arrival directions of cosmic rays above the
Greisen-Zatsepin-Kuz'min energy threshold, \nobreak{eV}. The
anisotropy was measured by the fraction of arrival directions that are less
than from the position of an active galactic nucleus within 75 Mpc
(using the V\'eron-Cetty and V\'eron catalog). An updated
measurement of this fraction is reported here using the arrival directions of
cosmic rays recorded above the same energy threshold through 31 December 2009.
The number of arrival directions has increased from 27 to 69, allowing a more
precise measurement. The correlating fraction is , compared
with expected for isotropic cosmic rays. This is down from the early
estimate of . The enlarged set of arrival directions is
examined also in relation to other populations of nearby extragalactic objects:
galaxies in the 2 Microns All Sky Survey and active galactic nuclei detected in
hard X-rays by the Swift Burst Alert Telescope. A celestial region around the
position of the radiogalaxy Cen A has the largest excess of arrival directions
relative to isotropic expectations. The 2-point autocorrelation function is
shown for the enlarged set of arrival directions and compared to the isotropic
expectation.Comment: Accepted for publication in Astroparticle Physics on 31 August 201
Atmospheric effects on extensive air showers observed with the Surface Detector of the Pierre Auger Observatory
Atmospheric parameters, such as pressure (P), temperature (T) and density,
affect the development of extensive air showers initiated by energetic cosmic
rays. We have studied the impact of atmospheric variations on extensive air
showers by means of the surface detector of the Pierre Auger Observatory. The
rate of events shows a ~10% seasonal modulation and ~2% diurnal one. We find
that the observed behaviour is explained by a model including the effects
associated with the variations of pressure and density. The former affects the
longitudinal development of air showers while the latter influences the Moliere
radius and hence the lateral distribution of the shower particles. The model is
validated with full simulations of extensive air showers using atmospheric
profiles measured at the site of the Pierre Auger Observatory.Comment: 24 pages, 9 figures, accepted for publication in Astroparticle
Physic
The exposure of the hybrid detector of the Pierre Auger Observatory
The Pierre Auger Observatory is a detector for ultra-high energy cosmic rays.
It consists of a surface array to measure secondary particles at ground level
and a fluorescence detector to measure the development of air showers in the
atmosphere above the array. The "hybrid" detection mode combines the
information from the two subsystems. We describe the determination of the
hybrid exposure for events observed by the fluorescence telescopes in
coincidence with at least one water-Cherenkov detector of the surface array. A
detailed knowledge of the time dependence of the detection operations is
crucial for an accurate evaluation of the exposure. We discuss the relevance of
monitoring data collected during operations, such as the status of the
fluorescence detector, background light and atmospheric conditions, that are
used in both simulation and reconstruction.Comment: Paper accepted by Astroparticle Physic
The Fluorescence Detector of the Pierre Auger Observatory
The Pierre Auger Observatory is a hybrid detector for ultra-high energy
cosmic rays. It combines a surface array to measure secondary particles at
ground level together with a fluorescence detector to measure the development
of air showers in the atmosphere above the array. The fluorescence detector
comprises 24 large telescopes specialized for measuring the nitrogen
fluorescence caused by charged particles of cosmic ray air showers. In this
paper we describe the components of the fluorescence detector including its
optical system, the design of the camera, the electronics, and the systems for
relative and absolute calibration. We also discuss the operation and the
monitoring of the detector. Finally, we evaluate the detector performance and
precision of shower reconstructions.Comment: 53 pages. Submitted to Nuclear Instruments and Methods in Physics
Research Section
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