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 $\gamma^*\gamma^\to \pi^0$ 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 $\gamma^*\gamma\to\pi^{0}$ 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 $O(\alpha_s)$ 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