Poisson structures for reduced non-holonomic systems

Borisov, Mamaev and Kilin have recently found certain Poisson structures with respect to which the reduced and rescaled systems of certain non-holonomic problems, involving rolling bodies without slipping, become Hamiltonian, the Hamiltonian function being the reduced energy. We study further the algebraic origin of these Poisson structures, showing that they are of rank two and therefore the mentioned rescaling is not necessary. We show that they are determined, up to a non-vanishing factor function, by the existence of a system of first-order differential equations providing two integrals of motion. We generalize the form of that Poisson structures and extend their domain of definition. We apply the theory to the rolling disk, the Routh's sphere, the ball rolling on a surface of revolution, and its special case of a ball rolling inside a cylinder.Comment: 22 page

The use of an automated flight test management system in the development of a rapid-prototyping flight research facility

An automated flight test management system (ATMS) and its use to develop a rapid-prototyping flight research facility for artificial intelligence (AI) based flight systems concepts are described. The ATMS provides a flight test engineer with a set of tools that assist in flight planning and simulation. This system will be capable of controlling an aircraft during the flight test by performing closed-loop guidance functions, range management, and maneuver-quality monitoring. The rapid-prototyping flight research facility is being developed at the Dryden Flight Research Facility of the NASA Ames Research Center (Ames-Dryden) to provide early flight assessment of emerging AI technology. The facility is being developed as one element of the aircraft automation program which focuses on the qualification and validation of embedded real-time AI-based systems

Conservation of energy and momenta in nonholonomic systems with affine constraints

We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their `gauge-like' generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution

Quasi-Chaplygin Systems and Nonholonimic Rigid Body Dynamics

We show that the Suslov nonholonomic rigid body problem can be regarded almost everywhere as a generalized Chaplygin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a Hamiltonian form by means of Chaplygin reducing multiplier. Since we deal with Chaplygin systems in the local sense, the invariant manifolds of the integrable examples are not necessary tori.Comment: minor changes, to appear in Letters in Mathematical Physic

Employment in Personality Disorders and the Effectiveness of Individual Placement and Support:Outcomes from a Secondary Data Analysis

Purpose Personality disorders (PDs) are associated with severe functional impairment and subsequent high societal costs, increasing the need to improve occupational functioning in PD. Individual placement and support (IPS) is an effective, evidence-based method of supported employment, which so far has been tested in various mixed patient populations with severe mental illness (SMI, including PDs). However, the effectiveness of IPS for PDs per se remains uninvestigated. Methods Data from the SCION trial were used, including 31 SMI patients with PDs and 115 SMI patients with other primary diagnoses (primarily psychotic disorders). First, the interaction effect of diagnosis (PD vs other SMI) and intervention (IPS vs traditional vocational rehabilitation) was studied. Second, in the IPS condition, difference between diagnostic groups in time to first job was studied. Results We did not find evidence of a moderating effect of PD diagnosis on the primary effect of IPS (proportion who started in regular employment) (OR = 0.592, 95% CI 0.80–4.350, p = 0.606) after 30 months. Also, PD diagnosis did not moderate the effect of time until first job in IPS. Conclusions From the present explorative analysis we did not find evidence for a moderating effect of PD diagnosis on the effectiveness of IPS among PD participants. This indicates that IPS could be as effective in gaining employment in participants with PD as it is in participants with other SMI. Future studies, implementing larger numbers, should confirm whether IPS is equally effective in PDs and study whether augmentations or alterations to the standard IPS model might be beneficiary for PD

Macroscopic Equations of Motion for Two Phase Flow in Porous Media

The established macroscopic equations of motion for two phase immiscible displacement in porous media are known to be physically incomplete because they do not contain the surface tension and surface areas governing capillary phenomena. Therefore a more general system of macroscopic equations is derived here which incorporates the spatiotemporal variation of interfacial energies. These equations are based on the theory of mixtures in macroscopic continuum mechanics. They include wetting phenomena through surface tensions instead of the traditional use of capillary pressure functions. Relative permeabilities can be identified in this approach which exhibit a complex dependence on the state variables. A capillary pressure function can be identified in equilibrium which shows the qualitative saturation dependence known from experiment. In addition the new equations allow to describe the spatiotemporal changes of residual saturations during immiscible displacement.Comment: 15 pages, Phys. Rev. E (1998), in prin

Formation of Solar Filaments by Steady and Nonsteady Chromospheric Heating

It has been established that cold plasma condensations can form in a magnetic loop subject to localized heating of the footpoints. In this paper, we use grid-adaptive numerical simulations of the radiative hydrodynamic equations to parametrically investigate the filament formation process in a pre-shaped loop with both steady and finite-time chromospheric heating. Compared to previous works, we consider low-lying loops with shallow dips, and use a more realistic description for the radiative losses. We demonstrate for the first time that the onset of thermal instability satisfies the linear instability criterion. The onset time of the condensation is roughly \sim 2 hr or more after the localized heating at the footpoint is effective, and the growth rate of the thread length varies from 800 km hr-1 to 4000 km hr-1, depending on the amplitude and the decay length scale characterizing this localized chromospheric heating. We show how single or multiple condensation segments may form in the coronal portion. In the asymmetric heating case, when two segments form, they approach and coalesce, and the coalesced condensation later drains down into the chromosphere. With a steady heating, this process repeats with a periodicity of several hours. While our parametric survey confirms and augments earlier findings, we also point out that steady heating is not necessary to sustain the condensation. Once the condensation is formed, it can keep growing also when the localized heating ceases. Finally, we show that the condensation can survive continuous buffeting by perturbations resulting from the photospheric p-mode waves.Comment: 43 pages, 18 figure

Geometric aspects of nonholonomic field theories

A geometric model for nonholonomic Lagrangian field theory is studied. The multisymplectic approach to such a theory as well as the corresponding Cauchy formalism are discussed. It is shown that in both formulations, the relevant equations for the constrained system can be recovered by a suitable projection of the equations for the underlying free (i.e. unconstrained) Lagrangian system.Comment: 29 pages; typos remove

The enigmatic nature of the circumstellar envelope and bow shock surrounding Betelgeuse as revealed by Herschel. I. Evidence of clumps, multiple arcs, and a linear bar-like structure

Context. The interaction between stellar winds and the interstellar medium (ISM) can create complex bow shocks. The photometers on board the Herschel Space Observatory are ideally suited to studying the morphologies of these bow shocks. Aims. We aim to study the circumstellar environment and wind-ISM interaction of the nearest red supergiant, Betelgeuse. Methods. Herschel PACS images at 70, 100, and 160 micron and SPIRE images at 250, 350, and 500 micron were obtained by scanning the region around Betelgeuse. These data were complemented with ultraviolet GALEX data, near-infrared WISE data, and radio 21 cm GALFA-HI data. The observational properties of the bow shock structure were deduced from the data and compared with hydrodynamical simulations. Results. The infrared Herschel images of the environment around Betelgeuse are spectacular, showing the occurrence of multiple arcs at 6-7 arcmin from the central target and the presence of a linear bar at 9 arcmin. Remarkably, no large-scale instabilities are seen in the outer arcs and linear bar. The dust temperature in the outer arcs varies between 40 and 140 K, with the linear bar having the same colour temperature as the arcs. The inner envelope shows clear evidence of a non-homogeneous clumpy structure (beyond 15 arcsec), probably related to the giant convection cells of the outer atmosphere. The non-homogeneous distribution of the material even persists until the collision with the ISM. A strong variation in brightness of the inner clumps at a radius of 2 arcmin suggests a drastic change in mean gas and dust density some 32 000 yr ago. Using hydrodynamical simulations, we try to explain the observed morphology of the bow shock around Betelgeuse. Conclusions: [abbreviated]Comment: 26 page

Was the "naked burst" GRB 050421 really naked ?

A few long gamma-ray bursts such as GRB 050421 show no afterglow emission beyond the usual initial steep decay phase. It has been suggested that these events correspond to "naked" bursts that occur in a very low density environment. We reconsider this possibility in the context of various scenarios for the origin of the afterglow. In the standard model where the afterglow results from the forward shock as well as in the alternative model where the afterglow comes from the reverse shock, we aim to obtain constraints on the density of the environment, the microphysics parameters, or the Lorentz factor of the ejecta, which are imposed by the absence of a detected afterglow. For the two models we compute the afterglow evolution for different values of the external density (uniform or wind medium) and various burst parameters. We then compare our results to the Swift data of GRB 050421, which is the best example of a long burst without afterglow. In the standard model we show that consistency with the data imposes that the external density does not exceed 1E-5 cm-3 or that the microphysics parameters are very small with epsilon_e <~ 1E-2 and epsilon_B <~ 1E-4. If the afterglow is caused by the reverse shock, we find that its contribution can be strongly reduced if the central source has mainly emitted fast-moving material (with less than 10 - 30 % of the kinetic energy at Gamma<100 and was located in a dense environment. The two considered scenarios therefore lead to opposite constraints on the circumburst medium. The high-density environment, favored by the reverse shock model, better corresponds to what is expected if the burst progenitor was a massive star.Comment: 6 pages, 3 figures, 1 table, to appear in A&