The influence of gyroscopic forces on the dynamic behavior and flutter of rotating blades

The structural dynamics of a cantilever turbomachine blade mounted on a spinning and precessing rotor are investigated. Both stability and forced vibration are considered with a blade model that increases in complexity (and verisimilitude) from a spring-restrained point mass, to a uniform cantilever, to a twisted uniform cantilever turbomachine blade mounted on a spinning and precessing rotor are investigated. Both stability and forced vibration are considered with a blade model that increases in complexity (and verisimilitude) from a spring-restrained point mass, to a uniform cantilever, to a twisted uniform cantilever, to a tapered twisted cantilever of arbitrary cross-section. In every instance the formulation is from first principles using a finite element based on beam theory. Both ramp-type and periodic-type precessional angular displacements are considered. In concluding, forced vibrating and flutter are studied using the final and most sophisticated structural model. The analysis of stability is presented and a number of numerical examples are worked out

Extending higher dimensional quasi-cocycles

Let G be a group admitting a non-elementary acylindrical action on a Gromov hyperbolic space (for example, a non-elementary relatively hyperbolic group, or the mapping class group of a closed hyperbolic surface, or Out(F_n) for n>1). We prove that, in degree 3, the bounded cohomology of G with real coefficients is infinite-dimensional. Our proof is based on an extension to higher degrees of a recent result by Hull and Osin. Namely, we prove that, if H is a hyperbolically embedded subgroup of G and V is any G-module, then any n-quasi cocycle on H with values in V may be extended to G. Also, we show that our extensions detect the geometry of the embedding of hyperbolically embedded subgroups, in a suitable sense.Comment: Minor revisions. This version has been accepted for publication by the Journal of Topolog

Dynamical evolution of escaped plutinos, another source of Centaurs

It was shown in previous works the existence of weakly chaotic orbits in the plutino population that diffuse very slowly. These orbits correspond to long-term plutino escapers and then represent the plutinos that are escaping from the resonance at present. In this paper we perform numerical simulations in order to explore the dynamical evolution of plutinos recently escaped from the resonance. The numerical simulations were divided in two parts. In the first one we evolved 20,000 test particles in the resonance in order to detect and select the long-term escapers. In the second one, we numerically integrate the selected escaped plutinos in order to study their dynamical post escaped behavior. Our main results include the characterization of the routes of escape of plutinos and their evolution in the Centaur zone. We obtained a present rate of escape of plutinos between 1 and 10 every 10 years. The escaped plutinos have a mean lifetime in the Centaur zone of 108 Myr and their contribution to the Centaur population would be a fraction of less than 6 % of the total Centaur population. In this way, escaped plutinos would be a secondary source of Centaurs.Comment: Accepted for publication in A&

Origin of craters on Phoebe: comparison with Cassini's data

Phoebe is one of the irregular satellites of Saturn; the images taken by Cassini-Huygens spacecraft allowed us to analyze its surface and the craters on it. We study the craters on Phoebe produced by Centaur objects from the Scattered Disk (SD) and plutinos escaped from the 3:2 mean motion resonance with Neptune and compare our results with the observations by Cassini. We use previous simulations on trans-Neptunian Objects and a method that allows us to obtain the number of craters and the cratering rate on Phoebe. We obtain the number of craters and the greatest crater on Phoebe produced by Centaurs in the present configuration of the Solar System. Moreover, we obtain a present normalized rate of encounters of Centaurs with Saturn of $\dot F = 7.1 \times 10^{-11}$ per year, from which we can infer the current cratering rate on Phoebe for each crater diameter. Our study and the comparison with the observations suggest that the main crater features on Phoebe are unlikely to have been produced in the present configuration of the Solar System and that they must have been acquired when the SD were depleted in the early Solar System. If this is what happened and the craters were produced when Phoebe was a satellite of Saturn, then it had to be captured, very early in the evolution of the Solar System.Comment: Accepted for publication in Astronomy & Astrophysic

Effects of an eccentric inner Jupiter on the dynamical evolution of icy body reservoirs in a planetary scattering scenario

Aims. We analyze the dynamics of small body reservoirs under the effects of an eccentric inner giant planet resulting from a planetary scattering event around a 0.5 M⊙ star. Methods. First, we used a semi-analytical model to define the properties of the protoplanetary disk that lead to the formation of three Jupiter-mass planets. Then, we carried out N-body simulations assuming that the planets are close to their stability limit together with an outer planetesimal disk. In particular, the present work focused on the analysis of N-body simulations in which a single Jupiter-mass planet survives after the dynamical instability event. Results. Our simulations produce outer small body reservoirs with particles on prograde and retrograde orbits, and other ones whose orbital plane flips from prograde to retrograde and back again along their evolution (“Type-F particles”). We find strong correlations between the inclination i and the ascending node longitude Ω of Type-F particles. First, Ω librates around 90° or/and 270°. This property represents a necessary and sufficient condition for the flipping of an orbit. Moreover, the libration periods of i and Ω are equal and they are out to phase by a quarter period. We also remark that the larger the libration amplitude of i, the larger the libration amplitude of Ω. We analyze the orbital parameters of Type-F particles immediately after the instability event (post IE orbital parameters), when a single Jupiter-mass planet survives in the system. Our results suggest that the orbit of a particle can flip for any value of its post IE eccentricity, although we find only two Type-F particles with post IE inclinations i ≲ 17°. Finally, our study indicates that the minimum value of the inclination of the Type-F particles in a given system decreases with an increase in the eccentricity of the giant planet.Fil: Zanardi, Macarena. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: de Elia, Gonzalo Carlos. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: Di Sisto, Romina Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Naoz, S.. University of California at Los Angeles; Estados UnidosFil: Li, G.. Harvard-Smithsonian Center for Astrophysics; Estados UnidosFil: Guilera, O. M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Brunini, A.. Universidad Nacional de la Patagonia Austral; Argentin

A non self-referential expression of Tsallis' probability distribution function

The canonical probability distribution function (pdf) obtained by optimizing the Tsallis entropy under the linear mean energy constraint (first formalism) or the escort mean energy constraint (third formalism) suffer self-referentiality. In a recent paper [Phys. Lett. A {\bf335} (2005) 351-362] the authors have shown that the pdfs obtained in the two formalisms are equivalent to the pdf in non self-referential form. Based on this result we derive an alternative expression, which is non self-referential, for the Tsallis distributions in both first and third formalisms.Comment: 3 page

Safe abstractions of data encodings in formal security protocol models

When using formal methods, security protocols are usually modeled at a high level of abstraction. In particular, data encoding and decoding transformations are often abstracted away. However, if no assumptions at all are made on the behavior of such transformations, they could trivially lead to security faults, for example leaking secrets or breaking freshness by collapsing nonces into constants. In order to address this issue, this paper formally states sufficient conditions, checkable on sequential code, such that if an abstract protocol model is secure under a Dolev-Yao adversary, then a refined model, which takes into account a wide class of possible implementations of the encoding/decoding operations, is implied to be secure too under the same adversary model. The paper also indicates possible exploitations of this result in the context of methods based on formal model extraction from implementation code and of methods based on automated code generation from formally verified model