A new approach to the vakonomic mechanics

The aim of this paper is to show that the Lagrange-d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them, here we consider the generalization of the Hamiltonian principle for nonholonomic systems with nonzero transpositional relations. By applying this variational principle which takes into the account transpositional relations different from the classical ones we deduce the equations of motion for the nonholonomic systems with constraints that in general are nonlinear in the velocity. These equations of motion coincide, except perhaps in a zero Lebesgue measure set, with the classical differential equations deduced with d'Alembert-Lagrange principle. We provide a new point of view on the transpositional relations for the constrained mechanical systems: the virtual variations can produce zero or non-zero transpositional relations. In particular the independent virtual variations can produce non-zero transpositional relations. For the unconstrained mechanical systems the virtual variations always produce zero transpositional relations. We conjecture that the existence of the nonlinear constraints in the velocity must be sought outside of the Newtonian model. All our results are illustrated with precise examples

The Galactic plane at faint X-ray fluxes - II. Stacked X-ray spectra of a sample of serendipitous XMM-Newton sources

We have investigated the X-ray spectral properties of a sample of 138 X-ray sources detected serendipitously in $XMM-Newton$ observations of the Galactic plane, at an intermediate to faint flux level. We divide our sample into 5 subgroups according to the spectral hardness of the sources, and stack (i.e. co-add) the individual source spectra within each subgroup. As expected these stacked spectra show a softening trend from the hardest to the softest subgroups, which is reflected in the inferred line-of-sight column density. The spectra of the three hardest subgroups are characterized by a hard continuum plus superimpose Fe-line emission in the 6--7 keV bandpass. The average equivalent width (EW) of the 6.7-keV He-like Fe-K$\alpha$ line is 170$^{+35}_{-32}$ eV, whereas the 6.4-keV Fe-K fluorescence line from neutral iron and the 6.9-keV H-like Fe-Ly$\alpha$ line have EWs of 89$^{+26}_{-25}$ eV and 81$^{+30}_{-29}$ eV respectively, i.e. roughly half that of the 6.7-keV line. The remaining subgroups exhibit soft thermal spectra. Virtually all of the spectrally-soft X-ray sources can be associated with relatively nearby coronally-active late-type stars, which are evident as bright near-infrared (NIR) objects within the X-ray error circles. On a similar basis only a minority of the spectrally-hard X-ray sources have likely NIR identifications. The average continuum and Fe-line properties of the spectrally-hard sources are consistent with those of magnetic cataclysmic variables but the direct identification of large numbers of such systems in Galactic X-ray surveys, probing intermediate to faint flux levels, remains challenging.Comment: 14 pages, 9 figures, 4 tables, accepted for publication in MNRA

Sharp-Interface Limit of a Fluctuating Phase-Field Model

We present a derivation of the sharp-interface limit of a generic fluctuating phase-field model for solidification. As a main result, we obtain a sharp-interface projection which presents noise terms in both the diffusion equation and in the moving boundary conditions. The presented procedure does not rely on the fluctuation-dissipation theorem, and can therefore be applied to account for both internal and external fluctuations in either variational or non-variational phase-field formulations. In particular, it can be used to introduce thermodynamical fluctuations in non-variational formulations of the phase-field model, which permit to reach better computational efficiency and provide more flexibility for describing some features of specific physical situations. This opens the possibility of performing quantitative phase-field simulations in crystal growth while accounting for the proper fluctuations of the system.Comment: 21 pages, 1 figure, submitted to Phys. Rev.

The Complex Demographic History and Evolutionary Origin of the Western Honey Bee, Apis Mellifera.

The western honey bee, Apis mellifera, provides critical pollination services to agricultural crops worldwide. However, despite substantial interest and prior investigation, the early evolution and subsequent diversification of this important pollinator remain uncertain. The primary hypotheses place the origin of A. mellifera in either Asia or Africa, with subsequent radiations proceeding from one of these regions. Here, we use two publicly available whole-genome data sets plus newly sequenced genomes and apply multiple population genetic analysis methods to investigate the patterns of ancestry and admixture in native honey bee populations from Europe, Africa, and the Middle East. The combination of these data sets is critical to the analyses, as each contributes samples from geographic locations lacking in the other, thereby producing the most complete set of honey bee populations available to date. We find evidence supporting an origin of A. mellifera in the Middle East or North Eastern Africa, with the A and Y lineages representing the earliest branching lineages. This finding has similarities with multiple contradictory hypotheses and represents a disentangling of genetic relationships, geographic proximity, and secondary contact to produce a more accurate picture of the origins of A. mellifera. We also investigate how previous studies came to their various conclusions based on incomplete sampling of populations, and illustrate the importance of complete sampling in understanding evolutionary processes. These results provide fundamental knowledge about genetic diversity within Old World honey bee populations and offer insight into the complex history of an important pollinator

Implementation of min–max MPC using hinging hyperplanes. Application to a heat exchanger

Min–max model predictive control (MMMPC) is one of the few control techniques able to cope with modelling errors or uncertainties in an explicit manner. The implementation of MMMPC suffers a large computational burden due to the numerical min–max problem that has to be solved at every sampling time. This fact severely limits the range of processes to which this control structure can be applied. An implementation scheme based on hinging hyperplanes that overcome these problems is presented here. Experimental results obtained when applying the controller to the heat exchanger of a pilot plant are given.Ministerio de Ciencia y Tecnología DPI2001-2380-C02-01Ministerio de Ciencia y Tecnología DPI2002-04375-C03-0