Tidal friction in close-in satellites and exoplanets: The Darwin theory re-visited

This report is a review of Darwin`s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) capture into the 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.

An overview on a nonideal system with three and a half degrees of freedom

The present paper studies a system comprised of two blocks connected by springs and dampers, and a DC motor with limited power supply fixed on a block, characterizing a non-ideal problem. This DC motor exciting the system causes interactions between the motor and the structure supporting it. Because of that, the non-ideal mathematical formulation of the problem has one and a half extra degree of freedom than the ideal one. A suitable choice of physical parameters leads to internal resonance conditions, that is, its natural frequencies are multiple of each other, by a known integer quantity. The purpose here is to study the dynamic behavior of the system using an analytical method based on perturbation techniques. The literature shows that the averaging method is the more flexible method concerning non-ideal problems. Summarizing, an steady state solution in amplitude and phase coordinates was obtained with averaging method showing the dependence of the structure amplitudes with the rotation frequency of the motor. Moreover, this solution shows that on of the amplitude coordinates has influence in the determination of the stationary rotation frequency. The analytical solution obtained shows the presence of the rotation frequency in expressions representing the oscillations of the structure, and the presence of amplitude coordinates in expressions describing the dynamic motion of the DC motor. These characteristics show the influence not only of the motor on structure but also of the response of the structure on dynamical behavior of the motor. Copyright © 2005 by ASME.

Some developments on cup anemometer aerodynamics

In the present study the geometry of cups is experimentally studied through anemometer performance. This performance is analyzed in two different ways. On the one hand the anemometer transfer function between cases is compared. On the other hand the stationary rotation speed is decomposed into constant and harmonic terms, the comparison being established between the last ones. Results indicate that some cup shapes can improve the uniformity of anemometer rotation, this fact being important to reduce degradation due to ageing.

Selective neurodegeneration induced in rotation-mediated aggregate cell cultures by a transient switch to stationary culture conditions: a potential model to study ischemia-related pathogenic mechanisms.

Aggregating brain cell cultures at an advanced maturational stage (20-21 days in vitro) were subjected for 1-3 h to anaerobic (hypoxic) and/or stationary (ischemic) conditions. After restoration of the normal culture conditions, cell loss was estimated by measuring the release of lactate dehydrogenase as well as the irreversible decrease of cell type-specific enzyme activities, total protein and DNA content. Ischemia for 2 h induced significant neuronal cell death. Hypoxia combined with ischemia affected both neuronal and glial cells to different degrees (GABAergic neurons>cholinergic neurons>astrocytes). Hypoxic and ischemic conditions greatly stimulated the uptake of 2-deoxy-D-glucose, indicating increased glucose consumption. Furthermore, glucose restriction (5.5 mM instead of 25 mM) dramatically increased the susceptibility of neuronal and glial cells to hypoxic and ischemic conditions. Glucose media concentrations below 2 mM caused selective neuronal cell death in otherwise normal culture conditions. GABAergic neurons showed a particularly high sensitivity to glucose restriction, hypoxia, and ischemia. The pattern of ischemia-induced changes in vitro showed many similarities to in vivo findings, suggesting that aggregating brain cell cultures provide a useful in vitro model to study pathogenic mechanisms related to brain ischemia.

The effect of counterpoise correction and relaxation energy term to the internal rotation barriers: application to the BF3 ...NH3 and C2H4 ...SO2 dimers

The relevance of the fragment relaxation energy term and the effect of the basis set superposition error on the geometry of the BF3⋯NH3 and C2H4⋯SO2 van der Waals dimers have been analyzed. Second-order Møller-Plesset perturbation theory calculations with the d95(d,p) basis set have been used to calculate the counterpoise-corrected barrier height for the internal rotations. These barriers have been obtained by relocating the stationary points on the counterpoise-corrected potential energy surface of the processes involved. The fragment relaxation energy can have a large influence on both the intermolecular parameters and barrier height. The counterpoise correction has proved to be important for these systems

The effect of counterpoise correction and relaxation energy term to the internal rotation barriers: application to the BF3 ...NH3 and C2H4 ...SO2 dimers

The relevance of the fragment relaxation energy term and the effect of the basis set superposition error on the geometry of the BF3⋯NH3 and C2H4⋯SO2 van der Waals dimers have been analyzed. Second-order Møller-Plesset perturbation theory calculations with the d95(d,p) basis set have been used to calculate the counterpoise-corrected barrier height for the internal rotations. These barriers have been obtained by relocating the stationary points on the counterpoise-corrected potential energy surface of the processes involved. The fragment relaxation energy can have a large influence on both the intermolecular parameters and barrier height. The counterpoise correction has proved to be important for these systems

Dominant-non-dominant asymmetry of kicking a stationary and rolling ball in a futsal context

The aim of this study was to analyse the characteristics of the asymmetries in the dominant and non-dominant limbs when kicking stationary and rolling balls. Ten experienced Brazilian amateur futsal players participated in this study. Each participant performed kicks under two conditions (stationary ball vs. rolling ball) with the dominant and non-dominant limbs (five kicks per condition per limb). We analysed the kicking accuracy, ball and foot velocities, angular joint displacement and velocity. The asymmetry between the dominant and non-dominant limbs was analysed by symmetry index and two-way repeated measures ANOVA. The results did not reveal any interaction between the condition and limb for ball velocity, foot velocity and accuracy. However, kicking with the dominant limb in both kicks showed higher ball velocity (stationary ball: dominant - 24.27 ± 2.21 m · s(-1) and non-dominant - 21.62 ± 2.26 m · s(-1); rolling ball: dominant - 23.88 ± 2.71 m · s(-1) and non-dominant - 21.42 ± 2.25 m · s(-1)), foot velocity (stationary ball: dominant - 17.61 ± 1.87 m · s(-1) and non-dominant - 15.58 ± 2.69 m · s(-1); rolling ball: dominant - 17.25 ± 2.26 m · s(-1) and non-dominant - 14.77 ± 2.35 m · s(-1)) and accuracy (stationary ball: dominant - 1.17 ± 0.84 m and non-dominant - 1.56 ± 1.30 m; rolling ball: dominant - 1.31 ± 0.91 m and non-dominant - 1.97 ± 1.44 m). In addition, the angular joint adjustments were dependent on the limb in both kicks (the kicks with non-dominant limb showed lower hip external rotation than the kicks with the dominant limb), indicating that the hip joint is important in kick performance. In conclusion, the kicks with the non-dominant limb showed different angular adjustments in comparison to kicks with the dominant limb. In addition, kicking a rolling ball with the non-dominant limb showed higher asymmetry for accuracy, indicating that complex kicks are more asymmetric.

Aerodynamic Analysis of Cup Anemometers Performance: The Stationary Harmonic Response

The effect of cup anemometer shape parameters, such as the cups’ shape, their size, and their center rotation radius, was experimentally analyzed.This analysis was based on both the calibration constants of the transfer function and the most important harmonic termof the rotor’smovement,which due to the cup anemometer design is the third one.This harmonic analysis represents a new approach to study cup anemometer performances. The results clearly showed a good correlation between the average rotational speed of the anemometer’s rotor and the mentioned third harmonic term of its movement.

An Eulerian Immersed Boundary Method for flow simulations over stationary and moving rigid bodies

The fluid flow over bodies with complex geometry has been the subject of research of many scientists and widely explored experimentally and numerically. The present study proposes an Eulerian Immersed Boundary Method for flows simulations over stationary or moving rigid bodies. The proposed method allows the use of Cartesians Meshes. Here, two-dimensional simulations of fluid flow over stationary and oscillating circular cylinders were used for verification and validation. Four different cases were explored: the flow over a stationary cylinder, the flow over a cylinder oscillating in the flow direction, the flow over a cylinder oscillating in the normal flow direction, and a cylinder with angular oscillation. The time integration was carried out by a classical 4th order Runge-Kutta scheme, with a time step of the same order of distance between two consecutive points in x direction. High-order compact finite difference schemes were used to calculate spatial derivatives. The drag and lift coefficients, the lock-in phenomenon and vorticity contour plots were used for the verification and validation of the proposed method. The extension of the current method allowing the study of a body with different geometry and three-dimensional simulations is straightforward. The results obtained show a good agreement with both numerical and experimental results, encouraging the use of the proposed method.

Nonexistence of regular stationary solution in a metric nonsymmetric theory of gravitation

It is proven that the field equations of a previously studied metric nonsymmetric theory of gravitation do not admit any non-singular stationary solution which represents a field of non-vanishing total mass and non-vanishing total fermionic charge.

Quantification and source identification of atmospheric particulate polycyclic aromatic hydrocarbons and their dry deposition fluxes at three sites in Salvador Basin, Brazil, impacted by mobile and stationary sources

The present work has aimed to determine the 16 US EPA priority PAH atmospheric particulate matter levels present in three sites around Salvador, Bahia: (i) Lapa bus station, strongly impacted by heavy-duty diesel vehicles; (ii) Aratu harbor, impacted by an intense movement of goods, and (iii) Bananeira village on Maré Island, a non vehicle-influenced site with activities such as handcraft work and fisheries. Results indicated that BbF (0.130-6.85 ng m-3) is the PAH with highest concentration in samples from Aratu harbor and Bananeira and CRY (0.075-6.85 ng m-3) presented higher concentrations at Lapa station. PAH sources from studied sites were mainly of anthropogenic origin such as gasoline-fueled light-duty vehicles and diesel-fueled heavy-duty vehicles, discharges in the port, diesel burning from ships, dust ressuspension, indoor soot from cooking, and coal and wood combustion for energy production.

Rotation curve bifurcations as indicators of close recent galaxy encounters

Context. Rotation curves of interacting galaxies often show that velocities are either rising or falling in the direction of the companion galaxy. Aims. We seek to reproduce and analyse these features in the rotation curves of simulated equal-mass galaxies suffering a one-to-one encounter as possible indicators of close encounters. Methods. Using simulations of major mergers in 3D, we study the time evolution of these asymmetries in a pair of galaxies during the first passage. Results. Our main results are: (a) the rotation curve asymmetries appear right at pericentre of the first passage, (b) the significant disturbed rotation velocities occur within a small time interval, of similar to 0.5 Gyr h(-1), and, therefore, the presence of bifurcation in the velocity curve could be used as an indicator of the pericentre occurrence. These results are in qualitative agreement with previous findings for minor mergers and flybys.

Shared information in stationary states of stochastic processes

We present four estimators of the shared information (or interdepency) in ground states given that the coefficients appearing in the wave function are all real non-negative numbers and therefore can be interpreted as probabilities of configurations. Such ground states of Hermitian and non-Hermitian Hamiltonians can be given, for example, by superpositions of valence bond states which can describe equilibrium but also stationary states of stochastic models. We consider in detail the last case, the system being a classical not a quantum one. Using analytical and numerical methods we compare the values of the estimators in the directed polymer and the raise and peel models which have massive, conformal invariant and nonconformal invariant massless phases. We show that like in the case of the quantum problem, the estimators verify the area law with logarithmic corrections when phase transitions take place.

Generic hyperbolicity of stationary solutions for a reaction-diffusion system

In this paper, we study the generic hyperbolicity of equilibria of a reaction-diffusion system with respect to nonlinear terms in the set of C(2)-functions equipped with the Whitney Topology. To accomplish this, we combine Baire`s Lemma and the usual Transversality Theorem. (C) 2010 Elsevier Ltd. All rights reserved.

A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures

This paper addresses the development of a hybrid-mixed finite element formulation for the quasi-static geometrically exact analysis of three-dimensional framed structures with linear elastic behavior. The formulation is based on a modified principle of stationary total complementary energy, involving, as independent variables, the generalized vectors of stress-resultants and displacements and, in addition, a set of Lagrange multipliers defined on the element boundaries. The finite element discretization scheme adopted within the framework of the proposed formulation leads to numerical solutions that strongly satisfy the equilibrium differential equations in the elements, as well as the equilibrium boundary conditions. This formulation consists, therefore, in a true equilibrium formulation for large displacements and rotations in space. Furthermore, this formulation is objective, as it ensures invariance of the strain measures under superposed rigid body rotations, and is not affected by the so-called shear-locking phenomenon. Also, the proposed formulation produces numerical solutions which are independent of the path of deformation. To validate and assess the accuracy of the proposed formulation, some benchmark problems are analyzed and their solutions compared with those obtained using the standard two-node displacement/ rotation-based formulation.