New high order sufficient conditions for configuration tracking

In this paper, we propose new conditions guaranteeing that the trajectories of a mechanical control system can track any curve on the configuration manifold. We focus on systems that can be represented as forced affine connection control systems and we generalize the sufficient conditions for tracking known in the literature. The new results are proved by a combination of averaging procedures by highly oscillating controls with the notion of kinematic reduction.Comment: arXiv admin note: text overlap with arXiv:0911.536

Radiative non-isothermal Bondi accretion onto a massive black hole

In this paper, we present the classical Bondi accretion theory for the case of non-isothermal accretion processes onto a supermassive black hole (SMBH), including the effects of X-ray heating and the radiation force due to electron scattering and spectral lines. The radiation field is calculated by considering an optically thick, geometrically thin, standard accretion disk as the emitter of UV photons and a spherical central object as a source of X-ray emission. In the present analysis, the UV emission from the accretion disk is assumed to have an angular dependence, while the X-ray/central object radiation is assumed to be isotropic. This allows us to build streamlines in any angular direction we need to. The influence of both types of radiation is evaluated for different flux fractions of the X-ray and UV emissions with and without the effects of spectral line driving. We find that the radiation emitted near the SMBH interacts with the infalling matter and modifies the accretion dynamics. In the presence of line driving, a transition resembles from pure type 1 & 2 to type 5 solutions (see Fig2.1 of Frank etal. 2002), which takes place regardless of whether or not the UV emission dominates over the X-ray emission. We compute the radiative factors at which this transition occurs, and discard type 5 solution from all our models. Estimated values of the accretion radius and accretion rate in terms of the classical Bondi values are also given. The results are useful for the construction of proper initial conditions for time-dependent hydrodynamical simulations of accretion flows onto SMBH at the centre of galaxies.Comment: 10 pages, 10 figures, Accepted to be published in A&

Controllability of spin-boson systems

In this paper we study the so-called spin-boson system, namely {a two-level system} in interaction with a distinguished mode of a quantized bosonic field. We give a brief description of the controlled Rabi and Jaynes--Cummings models and we discuss their appearance in the mathematics and physics literature. We then study the controllability of the Rabi model when the control is an external field acting on the bosonic part. Applying geometric control techniques to the Galerkin approximation and using perturbation theory to guarantee non-resonance of the spectrum of the drift operator, we prove approximate controllability of the system, for almost every value of the interaction parameter

Sub-Finsler Structures from the Time-Optimal Control Viewpoint for some Nilpotent Distributions

In this paper, we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions. Motivated by problems in geometric group theory, we characterize extremal curves, discuss their optimality, and calculate the metric spheres, proving their Euclidean rectifiability. © 2016, Springer Science+Business Media New York

Longitudinal oscillations in density stratified and expanding solar waveguides

Waves and oscillations can provide vital information about the internal structure of waveguides they propagate in. Here, we analytically investigate the effects of density and magnetic stratification on linear longitudinal magnetohydrodynamic (MHD) waves. The focus of this paper is to study the eigenmodes of these oscillations. It is our specific aim is to understand what happens to these MHD waves generated in flux tubes with non-constant (e.g., expanding or magnetic bottle) cross-sectional area and density variations. The governing equation of the longitudinal mode is derived and solved analytically and numerically. In particular, the limit of the thin flux tube approximation is examined. The general solution describing the slow longitudinal MHD waves in an expanding magnetic flux tube with constant density is found. Longitudinal MHD waves in density stratified loops with constant magnetic field are also analyzed. From analytical solutions, the frequency ratio of the first overtone and fundamental mode is investigated in stratified waveguides. For small expansion, a linear dependence between the frequency ratio and the expansion factor is found. From numerical calculations it was found that the frequency ratio strongly depends on the density profile chosen and, in general, the numerical results are in agreement with the analytical results. The relevance of these results for solar magneto-seismology is discussed.Comment: 10 pages, 5 figures, published in ApJ, uses emulateap

The seed laser system of the FERMI free-electron laser: design, performance and near future upgrades

Abstract An important trend in extreme ultraviolet and soft X-ray free-electron laser (FEL) development in recent years has been the use of seeding by an external laser, aimed to improve the coherence and stability of the generated pulses. The high-gain harmonic generation seeding technique was first implemented at FERMI and provided FEL radiation with high coherence as well as intensity and wavelength stability comparable to table-top ultrafast lasers. At FERMI, the seed laser has another very important function: it is the source of external laser pulses used in pump–probe experiments allowing one to achieve a record-low timing jitter. This paper describes the design, performance and operational modes of the FERMI seed laser in both single- and double-cascade schemes. In addition, the planned upgrade of the system to meet the challenges of the upgrade to echo-enabled harmonic generation mode is presented