Time analysis for temporary gravitational capture: Satellites of Uranus

We study the problem of gravitational capture in the framework of the Sun-Uranus-particle system. Part of the space of initial conditions is systematically explored, and the duration of temporary gravitational capture is measured. The location and size of different capture-time regions are given in terms of diagrams of initial semimajor axis versus eccentricity. The other initial orbital elements - inclination (i), longitude of the node (Ω), argument of pericenter (ω), and time of pericenter passage (τ) - are first taken to be zero. Then we investigate the cases with ω = 90°, 180°, and 270°. We also present a sample of results for Ω = 90°, considering the cases i = 60°, 120°, 150°, and 180°. Special attention is given to the influence of the initial orbital inclination, taking orbits initially in opposition at pericenter. In this case, the initial inclination is varied from 0° to 180° in steps of 10°. The success of the final stage of the capture problem, which involves the transformation of temporary captures into permanent ones, is highly dependent on the initial conditions associated with the longest capture times. The largest regions of the initial-conditions space with the longest capture times occur at inclinations of 60°-70° and 160°. The regions of possible stability as a function of initial inclination are also delimited. These regions include not only a known set of retrograde orbits, but also a new sort of prograde orbit with inclinations greater than zero.

Chaotic oscillation in an attractive Bose-Einstein condensate under an impulsive force

The chaotic oscillation in an attractive Bose-Einstein condensate (BEC) under an impulsive force was discussed using mean-field Gross-Pitaevskii (GP) equation. It was found that sustained chaotic oscillation resulted in a BEC under the action of an impulsive force generated by suddenly changing the interatomic scattering length or the harmonic oscillator trapping potential. The analysis suggested that the final state interatomic attraction played an important role in the generation of the chaotic dynamics.

Energy and angular momentum of the gravitational field in the teleparallel geometry

The Hamiltonian formulation of the teleparallel equivalent of general relativity is considered. Definitions of energy, momentum and angular momentum of the gravitational field arise from the integral form of the constraint equations of the theory. In particular, the gravitational energy-momentum is given by the integral of scalar densities over a three-dimensional spacelike hypersurface. The definition for the gravitational energy is investigated in the context of the Kerr black hole. In the evaluation of the energy contained within the external event horizon of the Kerr black hole, we obtain a value strikingly close to the irreducible mass of the latter. The gravitational angular momentum is evaluated for the gravitational field of a thin, slowly rotating mass shell. © 2002 The American Physical Society.

Gravitational energy of Kerr and Kerr anti-de Sitter space-times in the teleparallel geometry

In the context of the hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of the black holes. © SISSA/ISAS 2003.

Gravity and the quantum: Are they reconcilable?

General relativity and quantum mechanics are not consistent with each other. This conflict stems from the very fundamental principles on which these theories are grounded. General relativity, on one hand, is based on the equivalence principle, whose strong version establishes the local equivalence between gravitation and inertia. Quantum mechanics, on the other hand, is fundamentally based on the uncertainty principle, which is essentially nonlocal. This difference precludes the existence of a quantum version of the strong equivalence principle, and consequently of a quantum version of general relativity. Furthermore, there are compelling experimental evidences that a quantum object in the presence of a gravitational field violates the weak equivalence principle. Now it so happens that, in addition to general relativity, gravitation has an alternative, though equivalent, description, given by teleparallel gravity, a gauge theory for the translation group. In this theory torsion, instead of curvature, is assumed to represent the gravitational field. These two descriptions lead to the same classical results, but are conceptually different. In general relativity, curvature geometrizes the interaction while torsion, in teleparallel gravity, acts as a force, similar to the Lorentz force of electrodynamics. Because of this peculiar property, teleparallel gravity describes the gravitational interaction without requiring any of the equivalence principle versions. The replacement of general relativity by teleparallel gravity may, in consequence, lead to a conceptual reconciliation of gravitation with quantum mechanics. © 2006 American Institute of Physics.

Charge density alterations in human hair fibers: An investigation using electrostatic force microscopy

A new method for high-resolution analyses of hair surface charge density under ambient conditions is presented in this paper. Electrostatic force microscopy (EFM) is used here to analyze changes in surface charge density in virgin hair, bleached hair, and hair treated with a cationic polymer. The atomic force microscopy technique is used concomitantly to analyze morphological changes in hair roughness and thickness. The EFM images depict exactly how the polymer is distributed on the surface of the hair fiber. The EFM's powerful analytical tools enabled us to evaluate the varying degrees of interaction between the hair fiber surface charge density and the cationic polymer. The surface charge density and the polymer's distribution in the hair fibers are presented in the light of EFM measurements. © 2006 Society of Cosmetic Scientists and the Socièété Française de Cosmétologie.

Is the equivalence principle doomed forever to Dante's Inferno on account of quantum mechanics?

It is commonly assumed that the equivalence principle can coexist without conflict with quantum mechanics. We shall argue here that, contrary to popular belief, this principle does not hold in quantum mechanics. We illustrate this point by computing the second-order correction for the scattering of a massive scalar boson by a weak gravitational field, treated as an external field. The resulting cross-section turns out to be mass-dependent. A way out of this dilemma would be, perhaps, to consider gravitation without the equivalence principle. At first sight, this seems to be a too much drastic attitude toward general relativity. Fortunately, the teleparallel version of general relativity - a description of the gravitational interaction by a force similar to the Lorentz force of electromagnetism and that, of course, dispenses with the equivalence principle - is equivalent to general relativity, thus providing a consistent theory for gravitation in the absence of the aforementioned principle. © World Scientific Publishing Company.

Experimental study of the centripetal force

We describe an experimental set-up for studying and determining the centripetal force acting on a body whose mass and radius of circular trajectory are known. The experimental behaviour is determined and compared with theoretical predictions by using a system that allows for the evaluation of the angular velocity by means of electric current measurements, and by assuming a potential dependence of the force on the body mass, radius and angular velocity. © 2007 IOP Publishing Ltd.

Effects of taper on swimming force and swimmer performance after an experimental ten-week training program

Papoti, M., L.E.B. Martins, S.A. Cunha, A.M. Zagatto, and C.A. Gobatto. Effects of taper on swimming force and swimmer performance after an experimental ten-week training program. J. Strength Cond. Res. 21(2):538-542. 2007.- The purpose of this research was to examine how an 11-day taper after an 8.5-week experimental training cycle affected lactate levels during maximal exercise, mean force, and performance in training swimmers, independent of shaving, psychological changes, and postcompetition effects. Fourteen competition swimmers with shaved legs and torsos were recruited from the São Paulo Aquatic Federation. The training cycle consisted of a basic training period (endurance and quality phases) of 8.5 weeks, with 5,800 m·d -1 mean training volume and 6 d·wk -1 frequency; and a taper period (TP) of 1.5 weeks' duration that incorporated a 48% reduction in weekly volume without altering intensity. Attained swimming force (SF) and maximal performance over 200m maximal swim (Pmax) before and after taper were measured. After taper, SF and Pmax improved 3.6 and 1.6%, respectively (p < 0.05). There were positive correlations (p < 0.05) between SF and Pmax before (r = 0.86) and after (r = 0.83) the taper phase. Peak lactate concentrations after SF were unaltered before (6.79 ± 1.2 mM) and after (7.15 ± 1.8 mM) TP. Results showed that TP improved mean swimming velocity, but not in the same proportion as force after taper, suggesting that there are other factors influencing performance in faster swimming. © 2007 National Strength & Conditioning Association.

Consequences of quadratic frictional force on the one dimensional bouncing ball model

Some dynamical properties of the one dimensional Fermi accelerator model, under the presence of frictional force are studied. The frictional force is assumed as being proportional to the square particle's velocity. The problem is described by use of a two dimensional non linear mapping, therefore obtained via the solution of differential equations. We confirm that the model experiences contraction of the phase space area and in special, we characterized the behavior of the particle approaching an attracting fixed point. © 2007 American Institute of Physics.

An interplanetary mission to Neptune system: Gravitational capture and maneuvers around triton

The gravitational capture was initially used to understand the capture of planetary satellites. However, in the 90's decade, this phenomenon was applied in spacecraft trajectories. Belbruno and Miller studied missions in the Earth-Moon system that uses this technique to save fuel during the insertion of the spacecraft in its final orbit around the Moon. Using a parameter defined as twice the two-body energy of the planet-particle system, Yamakawa also studied the gravitational capture in the Earth-Moon system. In the present paper, this technique is used to study a mission that goes to the Neptune system and perform a gravitational capture in the satellite Triton. The results show direct and retrograde trajectories, for different values of the initial conditions.

Assessment of force decay in orthodontic elastomeric chains: An in vitro study

Introduction: Elastomeric materials are considered important sources of orthodontic forces. Objective: To assess force degradation over time of four commercially available orthodontic elastomeric chains (Morelli, Ormco, TP and Unitek). Methods: The synthetic elastics were submerged in 37 oC synthetic saliva and stretched by a force of 150 g (15 mm - Morelli and TP; 16mm - Unitek and Ormco). With a dynamometer, the delivered force was evaluated at different intervals: 30 minutes, 7 days, 14 days and 21 days. The results were subjected to ANOVA and Tukey's test. Results: There was a force decay between 19% to 26.67% after 30 minutes, and 36.67% to 57% after 21 days of activation. Conclusions: TP elastomeric chains exhibited the smallest percentage of force decay, with greater stability at all time intervals tested. Meanwhile, the Unitek chains displayed the highest percentage of force degradation, and no statically significant difference was found in force decay between Ormco and Morelli elastomeric chains during the study period.

Forced oscillations with continuum models of atomic force microscopy

The dynamics of the AFM-atomic force microscope follows a model based in a Timoshenko cantilever beam with a tip attached at the free end and acting with the surface of a sample. General boundary conditions arise when the tip is either in contact or non-contact with the surface. The governing equations are given in matrix conservative form subject to localized loads. The eigenanalysis is done with a fundamental matrix response of a damped second-order matrix differential equation. Forced responses are found by using a Galerkin approximation of the matrix impulse response. Simulations results with harmonic and pulse forcing show the filtering character and the effects of the tip-sample interaction at the end of the beam. © 2012 American Institute of Physics.

Fatigue and rapid hamstring/quadriceps force capacity in professional soccer players

The aim of this study was to investigate the effect of fatigue induced by an exhaustive laboratory-based soccer-specific exercise on different hamstrings/quadriceps (H:Q) ratios of soccer players. Twenty-two male professional soccer players (23·1 ± 3·4 year) performed maximal eccentric (ecc) and concentric (con) contractions for knee extensors (KE) and flexors (KF) at 60° s-1 and 180° s-1 to assess conventional (Hcon:Qcon) and functional (Hecc:Qcon) ratios. Additionally, they performed maximal voluntary isometric contraction for KE and KF, from which the maximal muscle strength, rate of force development (RFD) and RFD H:Q strength ratio (RFDH:Q) were extracted. Thereafter, subjects were performed an exhaustive laboratory-based soccer-specific exercise and a posttest similar to the pretest. There was significant reduction in Hcon:Qcon (0·60 ± 0·06 versus 0·58 ± 0·06, P<0·05) and in Hecc:Qcon (1·29 ± 0·2 versus 1·16 ± 0·2, P<0·01) after the soccer-specific exercise. However, no significant difference between Pre and Post exercise conditions was found for RFDH:Q at 0-50 (0·53 ± 0·23 versus 0·57 ± 0·24, P>0·05) and 0-100 ms (0·53 ± 0·17 versus 0·55 ± 0·17, P>0·05). In conclusion, H:Q strength ratios based on peak force values are more affected by fatigue than RFDH:Q obtained during early contraction phase. Thus, fatigue induced by soccer-specific intermittent protocol seems not reduce the potential for knee joint stabilization during the initial phase of voluntary muscle contraction. copy; 2012 Scandinavian Society of Clinical Physiology and Nuclear Medicine.