15,741 research outputs found
Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids
We present a set of explicit conditions, involving the components of the elastic stiffness tensor, which are necessary and sufficient to ensure the strong ellipticity of an orthorhombic incompressible medium. The derivation is based on the procedure developed by Zee & Sternberg (Arch. Rat. Mech. Anal., 83, 53-90 (1983)) and, consequently, is also applicable to the case of the homogeneously pre-stressed incompressible isotropic solids. This allows us to reformulate the results by Zee & Sternberg in terms of components of the incremental stiffness tensor. In addition, the resulting conditions are specialized to higher symmetry classes and compared with strong ellipticity conditions for plane strain, commonly used in the literature.The first author’s work and the second author’s visit to Brunel University were partly supported by
Brunel University’s ‘BRIEF’ award scheme
Estimating the masses of extra-solar planets
All extra-solar planet masses that have been derived spectroscopically are
lower limits since the inclination of the orbit to our line-of-sight is unknown
except for transiting systems. It is, however, possible to determine the
inclination angle, i, between the rotation axis of a star and an observer's
line-of-sight from measurements of the projected equatorial velocity (v sin i),
the stellar rotation period (P_rot) and the stellar radius (R_star). This
allows the removal of the sin i dependency of spectroscopically derived
extra-solar planet masses under the assumption that the planetary orbits lie
perpendicular to the stellar rotation axis. We have carried out an extensive
literature search and present a catalogue of v sin i, P_rot, and R_star
estimates for exoplanet host stars. In addition, we have used Hipparcos
parallaxes and the Barnes-Evans relationship to further supplement the R_star
estimates obtained from the literature. Using this catalogue, we have obtained
sin i estimates using a Markov-chain Monte Carlo analysis. This allows proper
1-sigma two-tailed confidence limits to be placed on the derived sin i's along
with the transit probability for each planet to be determined. While a small
proportion of systems yield sin i's significantly greater than 1, most likely
due to poor P_rot estimations, the large majority are acceptable. We are
further encouraged by the cases where we have data on transiting systems, as
the technique indicates inclinations of ~90 degrees and high transit
probabilities. In total, we estimate the true masses of 133 extra-solar
planets. Of these, only 6 have revised masses that place them above the 13
Jupiter mass deuterium burning limit. Our work reveals a population of
high-mass planets with low eccentricities and we speculate that these may
represent the signature of different planetary formation mechanisms at work.Comment: 40 pages, 6 tables, 2 figures. Accepted for publication in the
Monthly Notices of the Royal Astronomical Society after editing of Tables 1 &
6 for electronic publication. Html abstract shortened for astro-ph submissio
Anisotropic magnetoresistance of bulk carbon nanotube sheets
We have measured the magnetoresistance of stretched sheets of carbon
nanotubes in temperatures ranging from 2 K to 300 K and in magnetic fields up
to 9 T, oriented either perpendicular or parallel to the plane of the sheets.
The samples have been partially aligned by post-fabrication stretching, such
that the direction of stretching was either parallel or perpendicular to the
direction of applied electric current. We have observed large differences
between the magnetoresistance measured under the two field orientations, most
pronounced at the lowest temperatures, highest fields, and for the
laterally-aligned sample. Treatment of the sheets with nitric acid affects this
anisotropy. We analyzed the results within the theoretical framework of weak
and strong localization and concluded that the anisotropy bears the mark of a
more unusual phenomenon, possibly magnetically-induced mechanical strain.Comment: 34 pages, 10 figure
Ultra-high energy cosmic rays from Quark Novae
We explore acceleration of ions in the Quark Nova (QN) scenario, where a
neutron star experiences an explosive phase transition into a quark star (born
in the propeller regime). In this picture, two cosmic ray components are
isolated: one related to the randomized pulsar wind and the other to the
propelled wind, both boosted by the ultra-relativistic Quark Nova shock. The
latter component acquires energies while
the former, boosted pulsar wind, achieves ultra-high energies
eV. The composition is dominated by ions present in the pulsar wind in the
energy range above eV, while at energies below eV the
propelled ejecta, consisting of the fall-back neutron star crust material from
the explosion, is the dominant one. Added to these two components, the
propeller injects relativistic particles with Lorentz factors , later to be accelerated by galactic supernova shocks. The
QN model appears to be able to account for the extragalactic cosmic rays above
the ankle and to contribute a few percent of the galactic cosmic rays below the
ankle. We predict few hundred ultra-high energy cosmic ray events above
eV for the Pierre Auger detector per distant QN, while some thousands
are predicted for the proposed EUSO and OWL detectors.Comment: 20 pages, 1 figure. Major revisions in the text. Accepted for
publication in the Astrophysical Journa
Ill-posedness of degenerate dispersive equations
In this article we provide numerical and analytical evidence that some
degenerate dispersive partial differential equations are ill-posed.
Specifically we study the K(2,2) equation and
the "degenerate Airy" equation . For K(2,2) our results are
computational in nature: we conduct a series of numerical simulations which
demonstrate that data which is very small in can be of unit size at a
fixed time which is independent of the data's size. For the degenerate Airy
equation, our results are fully rigorous: we prove the existence of a compactly
supported self-similar solution which, when combined with certain scaling
invariances, implies ill-posedness (also in )
Investigating seasonal patterns in enteric infections: a systematic review of time series methods
Foodborne and waterborne gastrointestinal infections and their associated outbreaks are preventable, yet still result in significant morbidity, mortality, and revenue loss. Many enteric infections demonstrate seasonality, or annual systematic periodic fluctuations in incidence, associated with climatic and environmental factors. Public health professionals use statistical methods and time series models to describe, compare, explain, and predict seasonal patterns. However, descriptions and estimates of seasonal features, such as peak timing, depend on how researchers define seasonality for research purposes and how they apply time series methods. In this review, we outline the advantages and limitations of common methods for estimating seasonal peak timing. We provide recommendations improving reporting requirements for disease surveillance systems. Greater attention to how seasonality is defined, modeled, interpreted, and reported is necessary to promote reproducible research and strengthen proactive and targeted public health policies, intervention strategies, and preparedness plans to dampen the intensity and impacts of seasonal illnesses. © 2022 Cambridge University Press. All rights reserved
Illuminating dark matter and primordial black holes with interstellar antiprotons
Interstellar antiproton fluxes can arise from dark matter annihilating or
decaying into quarks or gluons that subsequently fragment into antiprotons.
Evaporation of primordial black holes also can produce a significant antiproton
cosmic-ray flux. Since the background of secondary antiprotons from spallation
has an interstellar energy spectrum that peaks at \sim 2\gev and falls
rapidly for energies below this, low-energy measurements of cosmic antiprotons
are useful in the search for exotic antiproton sources. However, measurement of
the flux near the earth is challenged by significant uncertainties from the
effects of the solar wind. We suggest evading this problem and more effectively
probing dark-matter signals by placing an antiproton spectrometer aboard an
interstellar probe currently under discussion. We address the experimental
challenges of a light, low-power-consuming detector, and present an initial
design of such an instrument. This experimental effort could significantly
increase our ability to detect, and have confidence in, a signal of exotic,
nonstandard antiproton sources. Furthermore, solar modulation effects in the
heliosphere would be better quantified and understood by comparing results to
inverse modulated data derived from existing balloon and space-based detectors
near the earth.Comment: 18 pages, 3 figure
Quantized Rotation of Atoms From Photons with Orbital Angular Momentum
We demonstrate the coherent transfer of the orbital angular momentum of a
photon to an atom in quantized units of hbar, using a 2-photon stimulated Raman
process with Laguerre-Gaussian beams to generate an atomic vortex state in a
Bose-Einstein condensate of sodium atoms. We show that the process is coherent
by creating superpositions of different vortex states, where the relative phase
between the states is determined by the relative phases of the optical fields.
Furthermore, we create vortices of charge 2 by transferring to each atom the
orbital angular momentum of two photons.Comment: New version, 4 pages and 3 figures, accepted for publication in
Physical Review Letter
Spectral Analysis for Matrix Hamiltonian Operators
In this work, we study the spectral properties of matrix Hamiltonians
generated by linearizing the nonlinear Schr\"odinger equation about soliton
solutions. By a numerically assisted proof, we show that there are no embedded
eigenvalues for the three dimensional cubic equation. Though we focus on a
proof of the 3d cubic problem, this work presents a new algorithm for verifying
certain spectral properties needed to study soliton stability. Source code for
verification of our comptuations, and for further experimentation, are
available at http://www.math.toronto.edu/simpson/files/spec_prop_code.tgz.Comment: 57 pages, 22 figures, typos fixe
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