Fourier analysis of finite element preconditioned collocation schemes

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes

R-local Delaunay inhibition model

Let us consider the local specification system of Gibbs point process with inhib ition pairwise interaction acting on some Delaunay subgraph specifically not con taining the edges of Delaunay triangles with circumscribed circle of radius grea ter than some fixed positive real value $R$. Even if we think that there exists at least a stationary Gibbs state associated to such system, we do not know yet how to prove it mainly due to some uncontrolled "negative" contribution in the expression of the local energy needed to insert any number of points in some large enough empty region of the space. This is solved by introducing some subgraph, called the $R$-local Delaunay graph, which is a slight but tailored modification of the previous one. This kind of model does not inherit the local stability property but satisfies s ome new extension called $R$-local stability. This weakened property combined with the local property provides the existence o f Gibbs state.Comment: soumis \`{a} Journal of Statistical Physics 27 page

Preliminary results from the STEPHI2009 campaign on the open cluster NGC 1817

We present preliminary observational results of the multi-site STEPHI campaign on the cluster NGC 1817. The three observatories involved are San Pedro Martir (Mexico), Xing Long (China) and the Observatorio del Teide (Spain) - giving an ideal combination to maximise the duty cycle. The cluster has 12 known delta Scuti stars and at least two detached eclipsing binary systems. This combination of characteristics is ideal for extracting information about global parameters of the targets, which will in turn impose strict constraints on the stellar models. From an initial comparison with stellar models using the known fundamental parameters, and just the observed pulsation frequencies and measured effective temperatures, it appears that a lower value of initial helium mass fraction will most likely explain the observations of these stars.Comment: 4 pages, proceedings from HELAS IV meeting 2010, Lanzarot

About the Algebraic Solutions of Smallest Enclosing Cylinders Problems

Given n points in Euclidean space E^d, we propose an algebraic algorithm to compute the best fitting (d-1)-cylinder. This algorithm computes the unknown direction of the axis of the cylinder. The location of the axis and the radius of the cylinder are deduced analytically from this direction. Special attention is paid to the case d=3 when n=4 and n=5. For the former, the minimal radius enclosing cylinder is computed algebrically from constrained minimization of a quartic form of the unknown direction of the axis. For the latter, an analytical condition of existence of the circumscribed cylinder is given, and the algorithm reduces to find the zeroes of an one unknown polynomial of degree at most 6. In both cases, the other parameters of the cylinder are deduced analytically. The minimal radius enclosing cylinder is computed analytically for the regular tetrahedron and for a trigonal bipyramids family with a symmetry axis of order 3.Comment: 13 pages, 0 figure; revised version submitted to publication (previous version is a copy of the original one of 2010

Investigation of grapevine root distribution by in situ minirhizotron observation

Root observations of Vitis berlandieri x Vitis riparia were conducted in two experimental sets using minirhizotron technique. Experiment 1 was a field experiment carried out on a 12 years old Riesling/5C vineyard. On six plants three minirhizotrons were installed at different angles (90°, 60°, 45°) and two directions per tube were used for observation. The maximum of root length density (RLD) was found in soil depths of 600-800 mm with high variation mainly due to plant x angle interaction. Observation direction did not influence the estimates of RLD. The installation angle of the tubes did not lead to any consistent effect on root observation. Experiment 2 was a pot trial of six pots with four vines each. Tubes were installed horizontally. RLD in the pot experiment according to the monolith method and the estimated RLD according to the minirhizotron method did not correlate, so the quantification of Vitis RLD distribution using minirhizotron is difficult.

Root dynamics and pattern of 'Riesling' on 5C rootstock using minirhizotrons

Root length density (RLD) in the years from 1994-1997 was estimated using minirhizotrons. The field experiment was conducted on six 'Riesling' vines in Rheingau (Germany). The majority of root distribution was found in soil depths of 60-100 cm with considerable variations between the plants. Roots dynamics showed a periodicity with one or two maxima, depending on year and vine plant. The first peak of RLD was observed around veraison, the second peak appeared after harvest. The rate of root length death was estimated. In the deeper layer the turnover of roots was 60% of the total RLD every year.

The CoRoT target HD 49933: 2- Comparison of theoretical mode amplitudes with observations

From the seismic data obtained by CoRoT for the star HD 49933 it is possible, as for the Sun, to constrain models of the excitation of acoustic modes by turbulent convection. We compare a stochastic excitation model described in Paper I (arXiv:0910.4027) with the asteroseismology data for HD 49933, a star that is rather metal poor and significantly hotter than the Sun. Using the mode linewidths measured by CoRoT for HD 49933 and the theoretical mode excitation rates computed in Paper I, we derive the expected surface velocity amplitudes of the acoustic modes detected in HD 49933. Using a calibrated quasi-adiabatic approximation relating the mode amplitudes in intensity to those in velocity, we derive the expected values of the mode amplitude in intensity. Our amplitude calculations are within 1-sigma error bars of the mode surface velocity spectrum derived with the HARPS spectrograph. The same is found with the mode amplitudes in intensity derived for HD 49933 from the CoRoT data. On the other hand, at high frequency, our calculations significantly depart from the CoRoT and HARPS measurements. We show that assuming a solar metal abundance rather than the actual metal abundance of the star would result in a larger discrepancy with the seismic data. Furthermore, calculations that assume the ``new'' solar chemical mixture are in better agreement with the seismic data than those that assume the ``old'' solar chemical mixture. These results validate, in the case of a star significantly hotter than the Sun and Alpha Cen A, the main assumptions in the model of stochastic excitation. However, the discrepancies seen at high frequency highlight some deficiencies of the modelling, whose origin remains to be understood.Comment: 8 pages, 3 figures (B-W and color), accepted for publication in Astronomy & Astrophysics. Corrected typo in Eq. (4). Updated references. Language improvement

Dynamical transitions in correlated driven diffusion in a periodic potential

The diffusion of a two-dimensional array of particles driven by a constant force in the presence of a periodic external potential exhibits a hierarchy of dynamical phase transitions when the driving force is varied. This behavior can be explained by a simple phenomenological approach which reduces the system of strongly interacting particles to weakly interacting quasi-particles (kinks). The richness of the strongly coupled system is however not lost because, contrary to a single-Brownian particle, the array shows an hysteretic behavior even at non-zero temperature. The present investigation can be viewed as a first step toward understanding nanotribology.Comment: 4 pages, 3 pictures, revtex to appear in Phys Rev. Let