271 research outputs found
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
- …