Moving constraints as stabilizing controls in classical mechanics

The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms which are linear or quadratic w.r.t.time derivatives of the control functions. After reviewing the basic equations, we explain the significance of the quadratic terms, related to geodesics orthogonal to a given foliation. We then study the problem of stabilization of the system to a given point, by means of oscillating controls. This problem is first reduced to the weak stability for a related convex-valued differential inclusion, then studied by Lyapunov functions methods. In the last sections, we illustrate the results by means of various mechanical examples.Comment: 52 pages, 4 figure

The boundary Riemann solver coming from the real vanishing viscosity approximation

We study a family of initial boundary value problems associated to mixed hyperbolic-parabolic systems: v^{\epsilon} _t + A (v^{\epsilon}, \epsilon v^{\epsilon}_x ) v^{\epsilon}_x = \epsilon B (v^{\epsilon} ) v^{\epsilon}_{xx} The conservative case is, in particular, included in the previous formulation. We suppose that the solutions $v^{\epsilon}$ to these problems converge to a unique limit. Also, it is assumed smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $A$ can be $0$. Second, we take into account the possibility that $B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.Comment: 84 pages, 6 figures. Text changes in Sections 1 and 3.2.3. Added Section 3.1.2. Minor changes in other section

Spectro-photometric Evolution of Elliptical Galaxies. II. Models with infall

In this paper we present new chemo-spectro-photometric models of elliptical galaxies in which infall of primordial gas is allowed to occur. They aim to simulate the collapse of a galaxy made of two components, i.e. luminous material and dark matter. The mass of the dark component is assumed to be constant in time, whereas that of the luminous material is supposed to accrete at a suitable rate. They also include the effect of galactic winds powered by supernova explosions and stellar winds from massive, early-type stars. The models are constrained to match a number of properties of elliptical galaxies, i.e. the slope and mean colours of the colour-magnitude relation (CMR), V versus (V--K), the UV excess as measured by the colour (1550--V) together with the overall shape of the integrated spectral energy distribution (ISED) in the ultraviolet, the relation between the Mg2 index and (1550--V), the mass to blue luminosity ratio M/Lb as a function of the B luminosity, and finally the broad-band colours (U--B), (B--V), (V--I), (V--K), etc.Comment: pages 22, 20 postscript figures, 2 external table (tab2_infall using supertabular.sty and tab5_infall using supertabular1.sty

Some Results on the Boundary Control of Systems of Conservation Laws

This note is concerned with the study of the initial boundary value problem for systems of conservation laws from the point of view of control theory, where the initial data is fixed and the boundary data are regarded as control functions. We first consider the problem of controllability at a fixed time for genuinely nonlinear Temple class systems, and present a description of the set of attainable configurations of the corresponding solutions in terms of suitable Oleinik-type estimates. We next present a result concerning the asymptotic stabilization near a constant state for general $n\times n$ systems. Finally we show with an example that in general one cannot achieve exact controllability to a constant state in finite time.Comment: 10 pages, 4 figures, conferenc

Effects of dark matter annihilation on the first stars

We study the evolution of the first stars in the universe (Population III) from the early pre-Main Sequence until the end of helium burning in the presence of WIMP dark matter annihilation inside the stellar structure. The two different mechanisms that can provide this energy source are the contemporary contraction of baryons and dark matter, and the capture of WIMPs by scattering off the gas with subsequent accumulation inside the star. We find that the first mechanism can generate an equilibrium phase, previously known as a "dark star", which is transient and present in the very early stages of pre-MS evolution. The mechanism of scattering and capture acts later, and can support the star virtually forever, depending on environmental characteristic of the dark matter halo and on the specific WIMP model.Comment: Proceedings of the IAU Symposium 255, "Low-Metallicity Star Formation: From the First Stars to Dwarf Galaxies"; L.K. Hunt, S. Madden and R. Schneider ed

Suppression of Fusarium moniforme by Streptomyces spp. isolates in relation to dose- response relationship

Suplemento. Edição do IX International Congress of Plant Pathology, 2008, Torino. Abstracts on invited and offered papers