Gravitational Capture of Asteroids by Gas Drag

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nebular gas drag and co-orbital system dynamics

Aims. We study trajectories of planetesimals whose orbits decay due to gas drag in a primordial solar nebula and are perturbed by the gravity of the secondary body on an eccentric orbit whose mass ratio takes values from mu(2) = 10(-7) to mu(2) = 10(-3) increasing ten times at each step. Each planetesimal ultimately suffers one of the three possible fates: (1) trapping in a mean motion resonance with the secondary body; (2) collision with the secondary body and consequent increase of its mass; or (3) diffusion after crossing the orbit of the secondary body.Methods. We take the Burlirsh-Stoer numerical algorithm in order to integrate the Newtonian equations of the planar, elliptical restricted three-body problem with the secondary body and the planetesimal orbiting the primary. It is assumed that there is no interaction among planetesimals, and also that the gas does not affect the orbit of the secondary body.Results. The results show that the optimal value of the gas drag constant k for the 1: 1 resonance is between 0.9 and 1.25, representing a meter size planetesimal for each AU of orbital radius. In this study, the conditions of the gas drag are such that in theory, L4 no longer exists in the circular case for a critical value of k that defines a limit size of the planetesimal, but for a secondary body with an eccentricity larger than 0.05 when mu(2) = 10(-6), it reappears. The decrease of the cutoff collision radius increase the difusions but does not affect the distribution of trapping. The contribution to the mass accretion of the secondary body is over 40% with a collision radius 0.05R(Hill) and less than 15% with 0.005R(Hill) for mu(2) = 10(-7). The trappings no longer occur when the drag constant k reachs 30. That means that the size limit of planetesimal trapping is 0.2 m per AU of orbital radius. In most cases, this accretion occurs for a weak gas drag and small secondary eccentricity. The diffusions represent most of the simulations showing that gas drag is an efficient process in scattering planetesimals and that the trapping of planetesimals in the 1: 1 resonance is a less probable fate. These results depend on the specific drag force chosen.

Can Drag Force Suppress Fermi Acceleration in a Bouncer Model?

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Non-uniform drag force on the Fermi accelerator model

Some dynamical properties of a particle suffering the action of a generic drag force are obtained for a dissipative Fermi Acceleration model. The dissipation is introduced via a viscous drag force, like a gas, and is assumed to be proportional to a power of the velocity: F alpha -nu(gamma). The dynamics is described by a two-dimensional nonlinear area-contracting mapping obtained via the solution of Newton's second law of motion. We prove analytically that the decay of high energy is given by a continued fraction which recovers the following expressions: (i) linear for gamma = 1; (ii) exponential for gamma = 2; and (iii) second-degree polynomial type for gamma = 1.5. Our results are discussed for both the complete version and the simplified version. The procedure used in the present paper can be extended to many different kinds of system, including a class of billiards problems.

How to drag with a worn-out mouse? Searching for social justice through collaboration

We consider what a concern for social justice in terms of social inclusion might mean for teacher education, both practising and prospective, with particular reference to the use of information and communication technology (ICT) in mathematics education taking place at a borderland school. Our discussion proceeds through the following steps: (1) We explore what a borderland position might denote to address what social inclusion might mean. (2) We consider the significance of mathematics education and the use of ICT for processes of social inclusion. (3) We briefly refer to the Interlink Network, as many of our observations emerge as reflections on this project. (4) We present different issues that will be of particular importance with respect to teacher education if we want to establish a mathematics education for social inclusion. These issues concern moving away from the comfort zone, establishing networks, identifying new approaches, moving beyond prototypical research, and getting in contact. This brings us to (5) final considerations, where we return to the notion of social justice. © Springer Science+Business Media B.V. 2009.

Nebular gas drag and planetary accretion with eccentric high-mass planets

Aims.We investigate the dynamics of pebbles immersed in a gas disk interacting with a planet on an eccentric orbit. The model has a prescribed gap in the disk around the location of the planetary orbit, as is expected for a giant planet with a mass in the range of 0.1-1 Jupiter masses. The pebbles with sizes in the range of 1 cm to 3 m are placed in a ring outside of the giant planet orbit at distances between 10 and 30 planetary Hill radii. The process of the accumulation of pebbles closer to the gap edge, its possible implication for the planetary accretion, and the importance of the mass and the eccentricity of the planet in this process are the motivations behind the present contribution. Methods. We used the Bulirsch-Stoer numerical algorithm, which is computationally consistent for close approaches, to integrate the Newtonian equations of the planar (2D), elliptical restricted three-body problem. The angular velocity of the gas disk was determined by the appropriate balance between the gravity, centrifugal, and pressure forces, such that it is sub-Keplerian in regions with a negative radial pressure gradient and super-Keplerian where the radial pressure gradient is positive. Results. The results show that there are no trappings in the 1:1 resonance around the L 4 and L5 Lagrangian points for very low planetary eccentricities (e2 < 0.07). The trappings in exterior resonances, in the majority of cases, are because the angular velocity of the disk is super-Keplerian in the gap disk outside of the planetary orbit and because the inward drift is stopped. Furthermore, the semi-major axis location of such trappings depends on the gas pressure profile of the gap (depth) and is a = 1.2 for a planet of 1 MJ. A planet on an eccentric orbit interacts with the pebble layer formed by these resonances. Collisions occur and become important for planetary eccentricity near the present value of Jupiter (e 2 = 0.05). The maximum rate of the collisions onto a planet of 0.1 MJ occurs when the pebble size is 37.5 cm ≤ s < 75 cm; for a planet with the mass of Jupiter, it is15 cm ≤ s < 30 cm. The accretion stops when the pebble size is less than 2 cm and the gas drag dominates the motion. © 2013 ESO.

Studying Close Approaches for a Cloud of Particles Considering Atmospheric Drag

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Arraste via fecal de nutrientes da ingestão produzido por bagaço de mandioca hidrolisado

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Desempenho operacional de um protótipo “aerossolo”

It is been a great deal of interest the studying of the operational performance of tractors and its machinery especially in work conditions. The present study had as objective to evaluate the operational performance of an Aerossolo prototype tracked with a Valtra BM100 4x2 TDA, with the engine power of 73.6 kW (100 cv). The prototype equipment is a drag type, hydraulically commanded, with telescopic heading for longitudinal adjustment, two lateral sections with 28 knifes in each one of them, concrete ballasts, wheels of transport and aggregate breaker coil. The work was conducted in the Department of Agricultural Engineering of the UNESP, Jaboticabal Campus, in a randomized blocks design, factorial 3 x 3, with four repetitions. The nine studied treatments were a combination for three ballast conditions (0; 960 and 1,307 kg) and three angles of the sections (0 degrees; 7 degrees and 14 degrees). The results indicate an increase in operational consumption (liters per hectare) of 32.4% in relation to the concrete ballast addition, and a 26.8% in relation to the angle variation between sections. The working depth, traction force and power demands were higher with the increases in the concrete ballast and the angle variation between sections.

Dynamical evolution of Saturn's F ring dust particles

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the dynamic behaviour of the "click" mechanism in dipteran flight

In this paper, the dynamic behaviour of the "click" mechanism is analysed. A more accurate model is used than in the past, in which the limits of movement due to the geometry of the flight mechanism are imposed. Moreover, the effects of different damping models are investigated. In previous work, the damping model was assumed to be of the linear viscous type for simplicity, but it is likely that the damping due to drag forces is nonlinear. Accordingly, a model of damping in which the damping force is proportional to the square of the velocity is used, and the results are compared with the simpler model of linear viscous damping. Because of the complexity of the model an analytical approach is not possible so the problem has been cast in terms of non-dimensional variables and solved numerically. The peak kinetic energy of the wing root per energy input in one cycle is chosen to study the effectiveness of the "click" mechanism compared with a linear resonant mechanism. It is shown that, the "click" mechanism has distinct advantages when it is driven below its resonant frequency. When the damping is quadratic, there are some further advantages compared to when the damping is linear and viscous, provided that the amplitude of the excitation force is large enough to avoid the erratic behaviour of the mechanism that occurs for small forces. (C) 2011 Elsevier Ltd. All rights reserved.

Fatores envolvidos na migração das endopróteses em pacientes submetidos ao tratamento endovascular do aneurisma da aorta abdominal

A migração da endoprótese é complicação do tratamento endovascular definida como deslocamento da ancoragem inicial. Para avaliação da migração, verifica-se a posição da endoprótese em relação a determinada região anatômica. Considerando o aneurisma da aorta abdominal infrarrenal, a área proximal de referência consiste na origem da artéria renal mais baixa e, na região distal, situa-se nas artérias ilíacas internas. Os pacientes deverão ser monitorizados por longos períodos, a fim de serem identificadas migrações, visto que estas ocorrem normalmente após 2 anos de implante. Para evitar migrações, forças mecânicas que propiciam fixação, determinadas por características dos dispositivos e incorporação da endoprótese, devem predominar sobre forças gravitacionais e hemodinâmicas que tendem a arrastar a prótese no sentido caudal. Angulação, extensão e diâmetro do colo, além da medida transversa do saco aneurismático, são importantes aspectos morfológicos do aneurisma relacionados à migração. Com relação à técnica, não se recomenda implante de endopróteses com sobredimensionamento excessivo (> 30%), por provocar dilatação do colo do aneurisma, além de dobras e vazamentos proximais que também contribuem para a migração. Por outro lado, endopróteses com mecanismos adicionais de fixação (ganchos, farpas e fixação suprarrenal) parecem apresentar menos migrações. O processo de incorporação das endopróteses ocorre parcialmente e parece não ser suficiente para impedir migrações tardias. Nesse sentido, estudos experimentais com endopróteses de maior porosidade e uso de substâncias que permitam maior fibroplasia e aderência da prótese à artéria vêm sendo realizados e parecem ser promissores. Esses aspectos serão discutidos nesta revisão.

Simultaneous recording of shadowgrams and schlieren images for the study of plasma assisted aerodynamics

This work describes an optical device for the simultaneous recording of shadowgrams and schlieren images, and some results are presented concerning its applications to the study of plasma assisted flow control in airfoil models. This approach offers many advantages in comparison to other methods, specially because the use of tracer particles (like smoke in wind tunnels) is not required for the experiments, thus avoiding contaminations in the electric discharges or air flows. Besides, while schlieren images reveal the refractive index gradients in the area of study, shadowgrams detect the second order spatial derivatives of the refractive indexes. Therefore, the simultaneous recording of these different images may give interesting information about the phenomena under study. In this paper, these images were used to confirm the existence of vortex structures in the flow induced by corona discharges on airfoil models. These structures are a possible explanation for the effects of drag reduction and lift force increasing, which have been reported in experiments of plasma assisted Aerodynamics.

Effect of a frictional force on the Fermi-Ulam model

The dynamical properties of a classical particle bouncing between two rigid walls, in the presence of a drag force, are studied for the case where one wall is fixed and the other one moves periodically in time. The system is described in terms of a two-dimensional nonlinear map obtained by solution of the relevant differential equations. It is shown that the structure of the KAM curves and the chaotic sea is destroyed as the drag force is introduced. At high energy, the velocity of the particle decreases linearly with increasing iteration number, but with a small superimposed sinusoidal modulation. If the motion passes near enough to a fixed point, the particle approaches it exponentially as the iteration number evolves, with a speed of approach that depends on the strength of the drag force. For a simplified version of the model it is shown that, at low energies corresponding to the region of the chaotic sea in the non-dissipative model, the particle wanders in a chaotic transient that depends on the strength of the drag coefficient. However, the KAM islands survive in the presence of dissipation. It is confirmed that the fixed points and periodic orbits go over smoothly into the orbits of the well-known (non-dissipative) Fermi-Ulam model as the drag force goes to zero.

Influences of the load centre of gravity on heavy vehicle acceleration

The aim of this paper is to analyse the influence of the load centre of gravity on heavy vehicle acceleration. This analysis is done through a method in which a vehicle centre of gravity map is used. A model for the driving force is presented for bus, truck and tractor-semi trailer combinations. The proposed model takes into consideration the resistance forces (drag, rolling resistance, translation and rotation acceleration, climbing resistance) and the 4 X 2 traction system. The positions of the vehicle centre of gravity as a function of the position of the load centre of gravity are determined. The vehicle acceleration is calculated based on the position of the load centre of gravity. This study analyses the acceleration of one of the Mercedes-Benz do Brasil tractor-semitrailer vehicle. A comparison of the acceleration for different maximum adhesion coefficients and ramps are presented, showing new results. An example showing the variations of the load centre of gravity position with the acceleration time and distance is provided. The load centre of gravity position is important for vehicle safety and the efficiency and economy in the transportation of the load.