Darboux-Egoroff metrics, rational Landau-Ginzburg potentials and the Painleve VI equation

We present a class of three-dimensional integrable structures associated with the Darboux-Egoroff metric and classical Euler equations of free rotations of a rigid body. They are obtained as canonical structures of rational Landau-Ginzburg potentials and provide solutions to the Painleve VI equation.

Signatures of primordial non-Gaussianities in the matter power-spectrum and bispectrum: the time-RG approach

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

On certain new exact solutions of a diffusive predator-prey system

We construct exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the G'/G expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained. © 2012 Elsevier B.V.

Aplicação da transformada integral generalizada no escoamento potencial em contrações

Pós-graduação em Engenharia Mecânica - FEIS

Simulação numérica de escoamentos hipersônicos sobre corpos rombudos pelo método de elementos finitos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelagem matemática e análise dinâmica da torre de um pulverizador de pomares

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Análise da estabilidade do movimento rotacional de satélites artificiais com quatérnions e sob a influência de torques externos

The aim of this work is to analyze the stability of the rotational motion’s artificial satellite using the Routh Hurwitz Algorithm (CRH) and the quaternions to describe the satellite’s attitude. This algorithm allows the investigation of the stability of the motion using the coefficients of the characteristic equation associated with the equation of the rotational motion in the linear form. The equations of the rotational motion are given by the four cinematic equations for the quaternion and the three equations of Euler for the spin velocity’s components. In the Euler equations are included the components of the gravity gradient torque (TGG) and the solar radiation torque (TRS). The TGG is generated by the difference of the Earth gravity force direction and intensity actuating on each satellite mass element and it depends on the mass distribution and the form of the satellite. The TRS is created by changing of the linear momentum, which happens due to the interactions of solar photons with the satellite surface. The equilibrium points are gotten by the equation of rotational motion and the CRH is applied in the linear form of these equations. Simulations are developed for small and medium satellites, but the gotten equilibrium points are not stable by CRH. However, when some of the eigenvalues of the characteristic equation are analyzed, it is found some equilibrium points which can be pointed out as stables for an interval of the time, due to small magnitude of the real part of these eigenvalue

Processing optimized for symmetry in the problem of evasive maneuvers

The increasing number of space debris in operating regions around the earth constitutes a real threat to space missions. The goal of the research is to establish appropriate scientific-technological conditions to prevent the destruction and/or impracticability of spacecraft in imminent collision in these regions. A definitive solution to this problem has not yet been reached with the degree of precision that the dynamics of spatial objects (vehicle and debris) requires mainly due to the fact that collisions occur in chains and fragmentation of these objects in the space environment. This fact threatens the space missions on time and with no prospects for a solution in the near future. We present an optimization process in finding the initial conditions (CIC) to collisions, considering the symmetry of the distributions of maximum relative positions between spatial objects with respect to the spherical angles. For this, we used the equations of the dynamics on the Clohessy-Witshire, representing a limit of validation that is highly computationally costly. We simulate different maximum relative positions values of the corresponding initial conditions given in terms of spherical angles. Our results showed that there are symmetries that significantly reduce operating costs, such that the search of the CIC is advantageously carried out up to 4 times the initial processing routine. Knowledge of CIC allows the propulsion system operating vehicle implement evasive maneuvers before impending collisions with space debris.

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.

Notes on Newton-Euler formulation of robotic manipulators

The equations corresponding to Newton-Euler iterative method for the determination of forces and moments acting on the rigid links of a robotic manipulator are given a new treatment using composed vectors for the representation of both kinematical and dynamical quantities. It is shown that Lagrange equations for the motion of a holonomic system are easily found from the composed vectors defined in this note. Application to a simple model of an industrial robot shows that the method developed in these notes is efficient in solving the dynamics of a robotic manipulator. An example is developed, where it is seen that with the application of appropriate control moments applied to each arm of the robot, starting from a given initial position, it is possible to reach equilibrium in a final pre-assigned position.

Nonlinear Schrodinger equation for a superfluid Bose gas from weak coupling to unitarity: Study of vortices

We introduce a nonlinear Schrodinger equation to describe the dynamics of a superfluid Bose gas in the crossover from the weak-coupling regime, where an(1/3)<<1 with a the interatomic s-wave scattering length and n the bosonic density, to the unitarity limit, where a ->+infinity. We call this equation the unitarity Schrodinger equation (USE). The zero-temperature bulk equation of state of this USE is parametrized by the Lee-Yang-Huang low-density expansion and Jastrow calculations at unitarity. With the help of the USE we study the profiles of quantized vortices and vortex-core radius in a uniform Bose gas. We also consider quantized vortices in a Bose gas under cylindrically symmetric harmonic confinement and study their profile and chemical potential using the USE and compare the results with those obtained from the Gross-Pitaevskii-type equations valid in the weak-coupling limit. Finally, the USE is applied to calculate the breathing modes of the confined Bose gas as a function of the scattering length.

Fluid dynamics of air in a packed bed: velocity profiles and the continuum model assumption

Air flow through packed beds was analyzed experimentally under conditions ranging from those that reinforce the effect of the wall on the void fraction to those that minimize it. The packing was spherical particles, with a tube-to-particle diameter ratio (D/dp) between 3 and 60. Air flow rates were maintained between 1.3 and 4.44 m3/min, and gas velocity was measured with a Pitot tube positioned above the bed exit. Measurements were made at various radial and angular coordinate values, allowing the distribution of air flow across the bed to be described in detail. Comparison of the experimentally observed radial profiles with those derived from published equations revealed that at high D/dp ratios the measured and calculated velocity profiles behaved similarly. At low ratios, oscillations in the velocity profiles agreed with those in the voidage profiles, signifying that treating the porous medium as a continuum medium is questionable in these cases.

The dynamics of bright matter wave solitons in a quasi one-dimensional Bose-Einstein condensate with a rapidly varying trap

The dynamics of a bright matter wave soliton in a quasi one-dimensional Bose-Einstein condensate (BEC) with a periodically rapidly varying time trap is considered. The governing equation is based on averaging the fast modulations of the Gross-Pitaevskii (GP) equation. This equation has the form of a GP equation with an effective potential of a more complicated structure than an unperturbed trap. In the case of an inverted (expulsive) quadratic trap corresponding to an unstable GP equation, the effective potential can be stable. For the bounded space trap potential it is showed that bifurcation exists, i.e. the single-well potential bifurcates to the triple-well effective potential. The stabilization of a BEC cloud on-site state in the temporary modulated optical lattice is found. This phenomenon is analogous to the Kapitza stabilization of an inverted pendulum. The analytical predictions of the averaged GP equation are confirmed by numerical simulations of the full GP equation with rapid perturbations.

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

We consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski- reactive like equation; for the particle's momentum density, a generalized Ohm's-like equation; and for the particle's energy density, a MaxwellCattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles. © 2011 Elsevier B.V. All rights reserved.

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.