31,530,766 research outputs found
Equilibria of biological aggregations with nonlocal repulsive-attractive interactions
We consider the aggregation equation in , where the interaction potential
incorporates short-range Newtonian repulsion and long-range power-law
attraction. We study the global well-posedness of solutions and investigate
analytically and numerically the equilibrium solutions. We show that there
exist unique equilibria supported on a ball of . By using the
method of moving planes we prove that such equilibria are radially symmetric
and monotone in the radial coordinate. We perform asymptotic studies for the
limiting cases when the exponent of the power-law attraction approaches
infinity and a Newtonian singularity, respectively. Numerical simulations
suggest that equilibria studied here are global attractors for the dynamics of
the aggregation model
Measurement of the multi-TeV neutrino cross section with IceCube using Earth absorption
Neutrinos interact only very weakly, so they are extremely penetrating.
However, the theoretical neutrino-nucleon interaction cross section rises with
energy such that, at energies above 40 TeV, neutrinos are expected to be
absorbed as they pass through the Earth. Experimentally, the cross section has
been measured only at the relatively low energies (below 400 GeV) available at
neutrino beams from accelerators \cite{Agashe:2014kda, Formaggio:2013kya}. Here
we report the first measurement of neutrino absorption in the Earth, using a
sample of 10,784 energetic upward-going neutrino-induced muons observed with
the IceCube Neutrino Observatory. The flux of high-energy neutrinos transiting
long paths through the Earth is attenuated compared to a reference sample that
follows shorter trajectories through the Earth. Using a fit to the
two-dimensional distribution of muon energy and zenith angle, we determine the
cross section for neutrino energies between 6.3 TeV and 980 TeV, more than an
order of magnitude higher in energy than previous measurements. The measured
cross section is (stat.) (syst.)
times the prediction of the Standard Model \cite{CooperSarkar:2011pa},
consistent with the expectation for charged and neutral current interactions.
We do not observe a dramatic increase in the cross section, expected in some
speculative models, including those invoking new compact dimensions
\cite{AlvarezMuniz:2002ga} or the production of leptoquarks
\cite{Romero:2009vu}.Comment: Preprint version of Nature paper 10.1038/nature2445
Unoriented D-brane instantons
We give a pedagogical introduction to D-brane instanton effects in vacuum
configurations with open and unoriented strings. We focus on quiver gauge
theories for unoriented D-branes at orbifold singularities and describe in some
detail the Z_3 case, where both `gauge' and `exotic' instantons can generate
non-perturbative super potentials, and the Z_5 case, where supersymmetry
breaking may arise from the combined effect of `gauge' instantons and a FI
D-term.Comment: 12 pages, 1 figure. Proceedings of the "XVII European Workshop on
String Theory 2011", Padova, Italy, 5-9 September 201
The gamma-ray burst monitor for Lobster-ISS
Lobster-ISS is an X-ray all-sky monitor experiment selected by ESA two years
ago for a Phase A study (now almost completed) for a future flight (2009)
aboard the Columbus Exposed Payload Facility of the International Space
Station. The main instrument, based on MCP optics with Lobster-eye geometry,
has an energy passband from 0.1 to 3.5 keV, an unprecedented daily sensitivity
of 2x10^{-12} erg cm^{-2}s$^{-1}, and it is capable to scan, during each orbit,
the entire sky with an angular resolution of 4--6 arcmin. This X-ray telescope
is flanked by a Gamma Ray Burst Monitor, with the minimum requirement of
recognizing true GRBs from other transient events. In this paper we describe
the GRBM. In addition to the minimum requirement, the instrument proposed is
capable to roughly localize GRBs which occur in the Lobster FOV (162x22.5
degrees) and to significantly extend the scientific capabilities of the main
instrument for the study of GRBs and X-ray transients. The combination of the
two instruments will allow an unprecedented spectral coverage (from 0.1 up to
300/700 keV) for a sensitive study of the GRB prompt emission in the passband
where GRBs and X-Ray Flashes emit most of their energy. The low-energy spectral
band (0.1-10 keV) is of key importance for the study of the GRB environment and
the search of transient absorption and emission features from GRBs, both goals
being crucial for unveiling the GRB phenomenon. The entire energy band of
Lobster-ISS is not covered by either the Swift satellite or other GRB missions
foreseen in the next decade.Comment: 6 pages, 4 figures. Paper presented at the COSPAR 2004 General
Assembly (Paris), accepted for publication in Advances in Space Research in
June 2005 and available on-line at the Journal site
(http://www.sciencedirect.com/science/journal/02731177), section "Articles in
press
Nonequilibrium candidate Monte Carlo: A new tool for efficient equilibrium simulation
Metropolis Monte Carlo simulation is a powerful tool for studying the
equilibrium properties of matter. In complex condensed-phase systems, however,
it is difficult to design Monte Carlo moves with high acceptance probabilities
that also rapidly sample uncorrelated configurations. Here, we introduce a new
class of moves based on nonequilibrium dynamics: candidate configurations are
generated through a finite-time process in which a system is actively driven
out of equilibrium, and accepted with criteria that preserve the equilibrium
distribution. The acceptance rule is similar to the Metropolis acceptance
probability, but related to the nonequilibrium work rather than the
instantaneous energy difference. Our method is applicable to sampling from both
a single thermodynamic state or a mixture of thermodynamic states, and allows
both coordinates and thermodynamic parameters to be driven in nonequilibrium
proposals. While generating finite-time switching trajectories incurs an
additional cost, driving some degrees of freedom while allowing others to
evolve naturally can lead to large enhancements in acceptance probabilities,
greatly reducing structural correlation times. Using nonequilibrium driven
processes vastly expands the repertoire of useful Monte Carlo proposals in
simulations of dense solvated systems
The Gap-Tooth Method in Particle Simulations
We explore the gap-tooth method for multiscale modeling of systems
represented by microscopic physics-based simulators, when coarse-grained
evolution equations are not available in closed form. A biased random walk
particle simulation, motivated by the viscous Burgers equation, serves as an
example. We construct macro-to-micro (lifting) and micro-to-macro (restriction)
operators, and drive the coarse time-evolution by particle simulations in
appropriately coupled microdomains (teeth) separated by large spatial gaps. A
macroscopically interpolative mechanism for communication between the teeth at
the particle level is introduced. The results demonstrate the feasibility of a
closure-on-demand approach to solving hydrodynamics problems
Cusps of Hilbert modular varieties
Motivated by a question of Hirzebruch on the possible topological types of
cusp cross-sections of Hilbert modular varieties, we give a necessary and
sufficient condition for a manifold M to be diffeomorphic to a cusp
cross-section of a Hilbert modular variety. Specialized to Hilbert modular
surfaces, this proves that every Sol 3-manifold is diffeomorphic to a cusp
cross-section of a (generalized) Hilbert modular surface. We also deduce an
obstruction to geometric bounding in this setting. Consequently, there exist
Sol 3-manifolds that cannot arise as a cusp cross-section of a 1-cusped
nonsingular Hilbert modular surface.Comment: To appear in Mathematical Proceedings Cambridge Philosophical Societ
An analysis of the field theoretic approach to the quasi-continuum method
Using the orbital-free density functional theory as a model theory, we
present an analysis of the field theoretic approach to quasi-continuum method.
In particular, by perturbation method and multiple scale analysis, we provide a
formal justification for the validity of the coarse-graining of various fields,
which is central to the quasi-continuum reduction of field theories. Further,
we derive the homogenized equations that govern the behavior of electronic
fields in regions of smooth deformations. Using Fourier analysis, we determine
the far-field solutions for these fields in the presence of local defects, and
subsequently estimate cell-size effects in computed defect energies.Comment: 26 pages, 1 figur
Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions
We establish the stability under the formations of infimum and of convex
combinations of subsolutions of convex Hamilton-Jacobi equations, some
comparison and existence results for convex and coercive Hamilton-Jacobi
equations with the Neumann type boundary condition as well as existence results
for the Skorokhod problem. We define the Aubry-Mather set associated with the
Neumann type boundary problem and establish some properties of the Aubry-Mather
set including the existence results for the ``calibrated'' extremals for the
corresponding action functional (or variational problem).Comment: 39 pages, 1 figur
Pathwise Accuracy and Ergodicity of Metropolized Integrators for SDEs
Metropolized integrators for ergodic stochastic differential equations (SDE)
are proposed which (i) are ergodic with respect to the (known) equilibrium
distribution of the SDE and (ii) approximate pathwise the solutions of the SDE
on finite time intervals. Both these properties are demonstrated in the paper
and precise strong error estimates are obtained. It is also shown that the
Metropolized integrator retains these properties even in situations where the
drift in the SDE is nonglobally Lipschitz, and vanilla explicit integrators for
SDEs typically become unstable and fail to be ergodic.Comment: 46 pages, 5 figure
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