A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems

In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time-independent case. On one hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution in the time-periodic case, while it was shown by Fathi and Mather that there is no such convergence of the Lax-Oleinik semigroup. On the other hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution faster than the Lax-Oleinik semigroup in the time-independent case.Comment: We give a new definition of Lax-Oleinik type operator; add some reference

Weak KAM for commuting Hamiltonians

For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax-Oleinik semi-groups, a result of Barles and Tourin ([BT01]), using a direct geometrical method (Stoke's theorem). We also obtain a "generalization" of a theorem of Maderna ([Mad02]). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton-Jacobi equation) for G and for H are the same. As a corrolary we obtain the equality of the Aubry sets, of the Peierls barrier and of flat parts of Mather's $\alpha$ functions. This is also related to works of Sorrentino ([Sor09]) and Bernard ([Ber07b]).Comment: 23 pages, accepted for publication in NonLinearity (january 29th 2010). Minor corrections, fifth part added on Mather's $\alpha$ function (or effective Hamiltonian

Arnold diffusion in the dynamics of a 4-machine power system undergoing a large fault

We focus on the seemingly complicated dynamics of a four-machine power system which is undergoing a sudden fault. Adopting a Hamiltonian (energy) formulation, we consider the system as an interconnection of (one degree of freedom) subsystems. Under certain configuration (a star network) and parameter values we establish the presence of Arnold diffusion which entails periodic, almost periodic, and complicated nonperiodic dyanmics all simultaneously present; and erratic transfer of energies between the subsystems. In section 1 we introduce the transient stability problem in a mathematical setting and explain what our results mean in the power systems context. Section 2 provides insights into Arnold diffusion and summarizes its mathematical formulation as in [8], [1]. Section 3 gives conditions for which Arnold diffusion arises on certain energy levels of the swing equations. These conditions are verified analytically in the case when all but one subsystem (machine) undergo relatively small oscillations

The ratio of pattern speeds in double-barred galaxies

We have obtained two-dimensional velocity fields in the ionized gas of a set of 8 double-barred galaxies, at high spatial and spectral resolution, using their H$\alpha$ emission fields measured with a scanning Fabry-Perot spectrometer. Using the technique by which phase reversals in the non-circular motion indicate a radius of corotation, taking advantage of the high angular and velocity resolution we have obtained the corotation radii and the pattern speeds of both the major bar and the small central bar in each of the galaxies; there are few such measurements in the literature. Our results show that the inner bar rotates more rapidly than the outer bar by a factor between 3.3 and 3.6.Comment: 5 pages, 1 figure, 1 tabl

Boron-doped nanocrystalline silicon thin films for solar cells

This article reports on the structural, electronic, and optical properties of boron-doped hydrogenated nanocrystalline silicon (nc-Si: H) thin films. The films were deposited by plasma-enhanced chemical vapour deposition (PECVD) at a substrate temperature of 150 degrees C. Crystalline volume fraction and dark conductivity of the films were determined as a function of trimethylboron-to-silane flow ratio. Optical constants of doped and undoped nc-Si: H were obtained from transmission and reflection spectra. By employing p(+) nc-Si: H as a window layer combined with a p' a-SiC buffer layer, a-Si: H-based p-p'-i-n solar cells on ZnO:Al-coated glass substrates were fabricated. Device characteristics were obtained from current-voltage and spectral-response measurements. (C) 2011 Elsevier B. V. All rights reserved

Nuclear spirals as feeding channels to the Supermassive Black Hole: the case of the galaxy NGC 6951

We report the discovery of gas streaming motions along nuclear spiral arms towards the LINER nucleus of the galaxy NGC 6951. The observations, obtained using the GMOS integral field spectrograph on the Gemini North telescope, yielded maps of the flux distributions and gas kinematics in the Halpha, [NII]6584 and [SII]6717,31 emission lines of the inner 7x5 arcsec^2 of the galaxy. This region includes a circumnuclear star-forming ring with radius 500pc, a nuclear spiral inside the ring and the LINER nucleus. The kinematics of the ionized gas is dominated by rotation, but subtraction of a kinematic model of a rotating exponential disk reveals deviations from circular rotation within the nuclear ring which can be attributed to (1) streaming motions along the nuclear spiral arms and (2) a bipolar outflow which seems to be associated to a nuclear jet. On the basis of the observed streaming velocities and geometry of the spiral arms we estimate a mass inflow rate of ionized gas of 3x10^(-4) Msun/yr, which is of the order of the accretion rate necessary to power the LINER nucleus of NGC 6951. Similar streaming motions towards the nucleus of another galaxy with LINER nucleus -- NGC 1097 -- have been reported by our group in a previous paper. Taken together, these results support a scenario in which nuclear spirals are channels through which matter is transferred from galactic scales to the nuclear region to feed the supermassive black hole.Comment: 25 pages, 6 eps figures, accepted for publication in Ap