Canard Cycles and Poincar\'e Index of Non-Smooth Vector Fields on the Plane

This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a subclass of non-smooth vector fields we provide necessary and sufficient conditions for the existence of canard kind solutions. By means of a regularization we prove that the canard cycles are singular orbits of singular perturbation problems which are limit periodic sets of a sequence of limit cycles. Moreover, we generalize the Poincar\'e Index for non-smooth vector fields.Comment: 20 pages, 25 figure

Mean mutual information and symmetry breaking for finite random fields

International audienc

Equilibrium states for potentials with \sup\phi - \inf\phi < \htop(f)

In the context of smooth interval maps, we study an inducing scheme approach to prove existence and uniqueness of equilibrium states for potentials $\phi$ with he `bounded range' condition \sup \phi - \inf \phi < \htop, first used by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of Perron-Frobenius operators. We demonstrate that this `bounded range' condition on the potential is important even if the potential is H\"older continuous. We also prove analyticity of the pressure in this context.Comment: Added Lemma 6 to deal with the disparity between leading eigenvalues and operator norms. Added extra references and corrected some typo

Cutting and Shuffling a Line Segment: Mixing by Interval Exchange Transformations

We present a computational study of finite-time mixing of a line segment by cutting and shuffling. A family of one-dimensional interval exchange transformations is constructed as a model system in which to study these types of mixing processes. Illustrative examples of the mixing behaviors, including pathological cases that violate the assumptions of the known governing theorems and lead to poor mixing, are shown. Since the mathematical theory applies as the number of iterations of the map goes to infinity, we introduce practical measures of mixing (the percent unmixed and the number of intermaterial interfaces) that can be computed over given (finite) numbers of iterations. We find that good mixing can be achieved after a finite number of iterations of a one-dimensional cutting and shuffling map, even though such a map cannot be considered chaotic in the usual sense and/or it may not fulfill the conditions of the ergodic theorems for interval exchange transformations. Specifically, good shuffling can occur with only six or seven intervals of roughly the same length, as long as the rearrangement order is an irreducible permutation. This study has implications for a number of mixing processes in which discontinuities arise either by construction or due to the underlying physics.Comment: 21 pages, 10 figures, ws-ijbc class; accepted for publication in International Journal of Bifurcation and Chao

Monitoring of river contamination derived from acid mine drainage using airborne imaging spectroscopy (HyMap data, South-West Spain)

Imaging spectroscopy is used in this work as an essential mapping tool to monitor changes in contaminated river sediments. Multidate hyperspectral image data (HyMap) are utilized to identify spatial mineral patterns, to detect temporal changes in mineralogy and to link these changes with geochemical processes and short-term climate characteristics. River sediments contaminated by acid mine drainage are covered by crusts with variably hydrated iron sulphate. The mineralogy of the crusts and the grain size of the underlying fluvial sediments overlap. The spectra used to build up maps from HyMap data are diagnosed mineralogically with archive spectral libraries from pyrite oxidation minerals from well-known sequences of minerals. The maps compiled from hyperspectral imagery display generalized oxidation shown by the coatings over river sediments following warm and dry periods with low water level. After the wet periods, the area covered by oxidized mineralogical phases recedes in favour of hydrated sulphate. The iteration of image processing algorithms and the mineralogical and potential contamination in a geological context are described. Change detection of the mineral crusts on the river sediments by mapping using hyperspectral remote sensing data may thus enable a quantitative and qualitative environmental evaluation by the regulators

Detection of radiation pressure acting on 2009 BD

We report the direct detection of radiation pressure on the asteroid 2009 BD, one of the smallest multi-opposition near-Earth objects currently known, with H ~ 28.4. Under the purely gravitational model of NEODyS the object is currently considered a possible future impactor, with impact solutions starting in 2071. The detection of a radiation-related acceleration allows us to estimate an Area to Mass Ratio (AMR) for the object, that can be converted (under some assumptions) into a range of possible values for its average density. Our result AMR = (2.97 \pm 0.33) x 10^(-4) m^2 kg^(-1) is compatible with the object being of natural origin, and it is narrow enough to exclude a man-made nature. The possible origin of this object, its future observability, and the importance of radiation pressure in the impact monitoring process, are also discussed.Comment: To be submitted for refereed publication. Preliminary analysis based on the 2009-2010 data, published on arXiv because of the current observability window of the targe

Closed-Loop Control of Local Magnetic Actuation for Robotic Surgical Instruments

We propose local magnetic actuation (LMA) as an approach to robotic actuation for surgical instruments. An LMA actuation unit consists of a pair of diametrically magnetized single-dipole cylindrical magnets, working as magnetic gears across the abdominal wall. In this study, we developed a dynamic model for an LMA actuation unit by extending the theory proposed for coaxial magnetic gears. The dynamic model was used for closed-loop control, and two alternative strategies-using either the angular velocity at the motor or at the load as feedback parameter-were compared. The amount of mechanical power that can be transferred across the abdominal wall at different intermagnetic distances was also investigated. The proposed dynamic model presented a relative error below 7.5% in estimating the load torque from the system parameters. Both the strategies proposed for closed-loop control were effective in regulating the load speed with a relative error below 2% of the desired steady-state value. However, the load-side closed-loop control approach was more precise and allowed the system to transmit larger values of torque, showing, at the same time, less dependence from the angular velocity. In particular, an average value of 1.5 mN·m can be transferred at 7 cm, increasing up to 13.5 mN·m as the separation distance is reduced down to 2 cm. Given the constraints in diameter and volume for a surgical instrument, the proposed approach allows for transferring a larger amount of mechanical power than what would be possible to achieve by embedding commercial dc motors

Cartografía geomorfológica y procesos de activos en la cuenca media-alta del río Eria mediante técnicas de SIG.( Provincia de León, España)

El objetivo es la elaboración de la cartografía geomorfológica y de procesos geológicos activos de un tramo del curso medio de la cuenca del río Eria, en el sector suroccidental de la provincia de León utilizando técnicas de SIG. El trabajo se ha basado en la fotointerpretación de fotos aéreas en visión estereoscópica, estudio bibliográfico y aplicación de técnicas de SIG para el análisis de modelos digitales de terreno y mapas derivados (pendientes, alturas…) y para la representación cartográfica. Como resultado se distinguen tres dominios de relieve caracterizados por diferentes procesos geológicos: dominio de los relieves sobre sustrato paleozoico, dominio de los relieves de origen fluvial y dominio de las formas de origen antrópico. En el primero tienen gran relevancia las formas del relieve relacionadas con la estructura geológica hercínica, en donde aparecen procesos activos ligados a procesos gravitacionales, originando formas del relieve como canchales, coluviones, depósitos de piedemonte y. Debido a lo escarpado de este dominio, apenas existen infraestructuras humanas, por lo que la interferencia de los procesos activos con las mismas es baja. En el segundo dominio aparecen formas del relieve originadas por procesos activos relacionados con el encajamiento de la red fluvial y de sedimentación, pudiendo afectar a infraestructuras humanas. En el tercero aparecen actuaciones susceptibles de interferir con los procesos activos naturales, provocando efectos adversos para la población. La información cartográfica obtenida supone la base para un análisis de susceptibilidad espacial de los distintos peligros de origen geológico, útil para la planificación territorial.The aim of this work is to represent by means of GIS techniques the geomorphological and active geological processes map of the middle course of the Eria river, located in the southwestern León province, Spain. This study is based on aerial photointerpretation, bibliographic analysis of previous works, and on the application of GIS techniques. These techniques were used for the representation of the mapping units, and for analyzing a DTM and derived maps (slop, aspect, etc.), creating a spatial and attribute database.Three main relief domains were differentiated based on the predominant active geological processes: the domain of landforms developed on the Palaeozoic metamorphic rocks, the domain of fluvial landforms, and the domain of anthropogenic landforms. The first one is mainly related to active gravitational processes, but because of the low human occupation, the interaction with human infrastructures is almost negligible. The second one is mainly related to incision and sedimentation of the drainage network, interacting with some human infrastructures developed on the floodplains, alluvial fans and close to the river side. The third one is formed by human elements affecting and modifying at different levels the strength of the active geological processes. The resulting map act as a basis for further spatial susceptibility for geological hazards analysis, which is useful for land use planning

The effect of anterior cruciate ligament recontruction on lower extremity relative phase dynamics during walking and running

The purpose of this investigation was to use relative phase dynamics to evaluate gait in individuals with a reconstructed anterior cruciate ligament (ACL) during walking and running. Relative phase dynamics can describe the coordination strategies between the interacting segments at the lower extremity. Ten subjects who had undergone ACL reconstruction using the central third of their patellar tendon and ten healthy controls walked and ran on a treadmill at a self-selected pace. Relative phase dynamics were calculated for the foot–shank and shank–thigh coordinative relation- ships. Statistical differences between the groups were noted for the foot– shank relationship (p\u3c0.05) during both walking and running and for the shank–thigh relationship (p\u3c0.05) during walking. Our results indicate that current ACL reconstructive techniques may result in altered relative phase dynamics. These changes in relative phase dynamics could be related to a loss of sensory information about joint position and velocity that is typically provided by the intact ACL. Additionally, relative phase adaptations could be a learned response from the early stages of postsurgical rehabilitation. Relative phase dynamics provide quantitative information about the dynamic status of the ACL-reconstructed knee that cannot be gained from the conventional time-series evaluation of gait analysis data. Relative phase dynamics measures should supplement the conventional gait analysis measures that are used today for the clinical evaluation of the functional dynamic stability of the reconstructed knee. The examination of relative phase dynamics could be clinically important for the quantification of new ACL surgical interventions and of patient performance at various stages of rehabilitation. Further research should incorporate relative phase dynamics to understand the influence of ACL reconstruction on coordination and functional patient outcomes