41,941 research outputs found
Numerical solution of boundary value problems for the eikonal equation in an anisotropic medium
A Dirichlet problem is considered for the eikonal equation in an anisotropic
medium. The nonlinear boundary value problem (BVP) formulated in the present
work is the limit of the diffusion-reaction problem with a reaction parameter
tending to infinity. To solve numerically the singularly perturbed
diffusion-reaction problem, monotone approximations are employed. Numerical
examples are presented for a two-dimensional BVP for the eikonal equation in an
anisotropic medium. The standard piecewise-linear finite-element approximation
in space is used in computations.Comment: 20 pages, 18 figure
Statistical Properties of Soft X-ray emission of solar flares
We present a statistical analysis of properties of Soft X-Ray (SXR) emission,
plasma temperature (T), and emission measure (EM), derived from GOES
observations of flares in 2002-2017. The temperature and emission measures are
obtained using the TEBBS algorithm (Ryan et al. 2012), which delivers reliable
results together with uncertainties even for weak B-class flare events. More
than 96% of flares demonstrate a sequential appearance of T, SXR, and EM
maxima, in agreement with the expected behavior of the chromospheric
evaporation process. The relative number of such flares increases with
increasing the SXR flux maximum. The SXR maximum is closer in time to the T
maximum for B-class flares than for >=C-class flares, while it is very close to
the EM maximum for M- and X-class flares. We define flares as "T-controlled" if
the time interval between the SXR and T maxima is at least two times shorter
than the interval between the EM and SXR maxima, and as "EM-controlled" if the
time interval between the EM and SXR maxima is at least two times shorter than
the interval between the SXR and T maxima. For any considered flare class
range, the T-controlled events compared to EM-controlled events have: a) higher
EM but lower T; b) longer durations and shorter relative growth times; c)
longer FWHM and characteristic decay times. Interpretation of these statistical
results based on analysis of a single loop dynamics suggests that for flares of
the same class range, the T-controlled events can be developed in longer loops
than the EM-controlled events.Comment: Accepted for publication in The Astrophysical Journal (26 pages, 6
figures, 2 tables
Pulsed ESR Measurement of Coherence Times in Si:P at Very Low Temperatures
A purpose built millikelvin pulsed x-band ESR system is used to measure spin
decoherence times of phosphorus donor spins in 99.92% isotopically pure 28
silicon. The isolated P spin T2 is estimated at 260 (50) ms at 4.2 K and 330
(100) ms at 0.9 K.Comment: 4 pages, 4 figures, 34th ANZIP condensed matter and materials meeting
201
Cohomological dimension, self-linking, and systolic geometry
Given a closed manifold M, we prove the upper bound of (n+d)/2 for the length
of a product of systoles that can form a curvature-free lower bound for the
total volume of M, in the spirit of M. Gromov's systolic inequalities. Here n
is the dimension of M, while d is the is the cohomological dimension of its
fundamental group. We apply this upper bound to show that, in the case of a
4-manifold, the Lusternik--Schnirelmann category is an upper bound for such
length. Furthermore we prove a systolic inequality on a manifold M with
b_1(M)=2 in the presence of a nontrivial self-linking class of the typical
fiber of its Abel--Jacobi map to the 2-torus.Comment: 15 pages; to appear in Israel Journal of Mathematic
Pion Distribution Amplitude and Photon-to-Pion Transition Form Factor in QCD
We discuss the status of the pion distribution amplitude (DA) in connection
with QCD sum rules and experimental data on the
transition form factor. Contents: (a) Pion DA in generalized QCD Sum Rules
(SRs); (b) Light Cone Sum Rules (LCSR) analysis of the CLEO data for the
transition form factor; (c) Recent lattice QCD data
for the pion DA; (d) BaBar data---a challenge for QCD?Comment: 6 pages, 3 figures, talk delivered by the first author at the
International Meeting "Excited QCD'', January 31--February 5, 2010, Tatranska
Lomnica (Slovakia
What is this thing called pion distribution amplitude? From theory to data
We discuss the status of the pion distribution amplitude (DA) from analyzing
the CLEO experimental data in the context of QCD sum-rule techniques and QCD
perturbation theory at the NLO accuracy. The constraints extracted this way for
the Gegenbauer coefficients a_2 and a_4 exclude \Phi_{CZ} at the 4\sigma level,
while \Phi_{asy} is outside the 3\sigma error ellipse. These data provide
strong support for the type of endpoint-suppressed, double-humped pion DA we
derived via QCD sum rules with nonlocal condensates and favor a value of the
vacuum quark virtuality \lambda_q^2 \simeq 0.4 GeV^2. This pion DA is in
agreement with the E791 data, though these experimental results should be
viewed carefully and further confirmation is necessary for a more accurate
judging of pion DAs from them.Comment: 6 pages, 4 figures, cernrep class. Talk presented at the LC03
Workshop "Hadrons and beyond
Accessing the pion distribution amplitude through the CLEO and E791 data
Using QCD perturbation theory in NLO and light-cone QCD sum rules, we extract
from the CLEO experimental data on the F^{\gamma^*\gamma\pi}(Q^{2} transition
form factor constraints on the Gegenbauer coefficients a_2 and a_4, as well as
on the inverse moment _{\pi} of the pion distribution amplitude. We
show that both the asymptotic and the Chernyak--Zhitnitsky pion distribution
amplitudes are excluded at the 3\sigma- and 4\sigma-level, respectively, while
the data confirms the end-point suppressed shape of the pion DA we previously
obtained with QCD sum rules and nonlocal condensates. These findings are also
supported by the data of the Fermilab E791 experiment on diffractive dijet
production.Comment: 9 pages, 7 figures. Talk given at NAPP2003, Dubrovnik, May 26--31,
2003; misprints fixe
Pion form factor in the QCD sum-rule approach with nonlocal condensates
We present results of a calculation of the electromagnetic pion form factor
within the framework of QCD Sum Rules with nonlocal condensates, using a
perturbative spectral density which includes contributions.Comment: 7 pages, 2 figures, talk presented by the first author at the
International Meeting "Excited QCD", February 8--14, 2009, Zakopane (Poland),
typos and references correcte
Dynamics of Turbulent Convection and Convective Overshoot in a Moderate Mass Star
Continued progress in observational stellar astrophysics requires a deep
understanding of the underlying convection dynamics. We present results of
realistic 3D radiative hydrodynamic simulations of the outer layers of a
moderate mass star (1.47 Msun), including the full convection zone, the
overshoot region, and the top layers of the radiative zone. The simulation
results show that the surface granulation has a broad range of scales, from 2
to 12 Mm, and that large granules are organized in well-defined clusters,
consisting of several granules. Comparison of the mean structure profiles from
3D simulations with the corresponding 1D standard stellar model shows an
increase of the stellar radius by ~800 km, as well as significant changes in
the thermodynamic structure and turbulent properties of the ionization zones.
Convective downdrafts in the intergranular lanes between granulation clusters
reach speeds of more than 20 km/s, penetrate through the whole convection zone,
hit the radiative zone, and form a 8 Mm thick overshoot layer. Contrary to
semi-empirical overshooting models, our results show that the 3D dynamic
overshoot region consists of two layers: a nearly adiabatic extension of the
convection zone and a deeper layer of enhanced subadiabatic stratification.
This layer is formed because of heating caused by the braking of the
overshooting convective plumes. This effect has to be taken into account in
stellar modeling and the interpretation of asteroseismology data. In
particular, we demonstrate that the 3D model can qualitatively explain
deviations from the standard solar model found by helioseismology.Comment: 14 pages, 5 figures, submitted to ApJ Letter
Small values of the Lusternik-Schnirelmann category for manifolds
We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have
free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and
Gonzalez-Acuna, by generalizing their result in dimension 3, to all higher
dimensions. We also obtain some general results on the relations between the
fundamental group of a closed manifold M, the dimension of M, and the
Lusternik-Schnirelmann category of M, and relate the latter to the systolic
category of M.Comment: 16 pages, to appear in Geometry and Topolog
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