Effect of sodium dodecylbenzene sulfonate on the motion of three-phase contact lines on the Wilhelmy plate surface

The combined approach of the molecular-kinetic and hydrodynamic theories for description of the motion of three-phase gas-liquid-solid contact lines has been examined using the Wilhelmy plate method. The whole dynamic meniscus has been divided into molecular, hydrodynamic, and static-like regions. The Young-Laplace equation and the molecular-kinetic and hydrodynamic dewetting theories have been applied to describe the meniscus profiles and contact angle. The dissipative forces accompanying the dynamic dewetting have also been investigated. The experiments with a Wilhelmy plate made from an acrylic polymer sheet were carried out using a computerized apparatus for contact angle analysis (OCA 20, DataPhysics, Germany). The extrapolated dynamic contact angle versus velocity of the three-phase contact line for Milli-Q water and 5 x 10(-4) M SDBS solution was experimentally obtained and compared with the combined MHD models with low and moderate Reynolds numbers. The models predict similar results for the extrapolated contact angle. SDBS decreases the equilibrium contact angle and increases the molecular jumping length but does not affect the molecular frequency significantly. The hydrodynamic deformation of the meniscus, viscous dissipation, and friction were also influenced by the SDBS surfactant. (c) 2005 Elsevier Inc. All rights reserved.

Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

Modelling the secular evolution of migrating planet pairs

The subject of this paper is the secular behaviour of a pair of planets evolving under dissipative forces. In particular, we investigate the case when dissipative forces affect the planetary semimajor axes and the planets move inwards/outwards the central star, in a process known as planet migration. To perform this investigation, we introduce fundamental concepts of conservative and dissipative dynamics of the three-body problem. Based on these concepts, we develop a qualitative model of the secular evolution of the migrating planetary pair. Our approach is based on the analysis of the energy and the orbital angular momentum exchange between the two-planet system and an external medium; thus no specific kind of dissipative forces is invoked. We show that, under the assumption that dissipation is weak and slow, the evolutionary routes of the migrating planets are traced by the Mode I and Mode II stationary solutions of the conservative secular problem. The ultimate convergence and the evolution of the system along one of these secular modes of motion are determined uniquely by the condition that the dissipation rate is sufficiently smaller than the proper secular frequency of the system. We show that it is possible to reassemble the starting configurations and the migration history of the systems on the basis of their final states and consequently to constrain the parameters of the physical processes involved.

Orbital evolution of the mu and nu dust ring particles of Uranus

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

Some comments on the F ring-Prometheus-Pandora environment

The system formed by the F ring and two close satellites, Prometheus and Pandora, has been analysed since the time that Voyager visited the planet Saturn. During the ring plane crossing in 1995 the satellites were found in different positions as predicted by the Voyager data. Besides the mutual effects of Prometheus and Pandora, they are also disturbed by a massive F ring. Showalter et al. [Icarus 100 (1992) 394] proposed that, the core of the ring has a mass which corresponds to a moonlet varying in size from 15 to 70 kin in radius which can prevent the ring from spreading due to dissipative forces, such as Poynting-Robertson drag and collisions. We have divided this work into two parts. Firstly we analysed the secular interactions between Prometheus-Pandora and a massive F ring using the secular theory. Our results show the variation in eccentricity and inclination of the satellites and the F ring taking into account a massive ring corresponding to a moonlet of different sizes. There is also a population of dust particles in the ring in the company of moonlets at different sizes [Icarus 109 (1997) 304]. We also analysed the behaviour of these particles under the effects of the Poynting-Robertson drag and radiation pressure. Our results show that the time scale proposed for a dust particle to leave the ring is much shorter than predicted before even in the presence of a coorbital moonlet. This result does not agree with the confinement model proposed by Dermott et al. [Nature 284 (1980) 309]. In 2004, Cassini mission will perform repeated observations of the whole system, including observations of the satellites and the F ring environment. These data will help us to better understand this system. (C) 2003 COSPAR. Published by Elsevier Ltd. All rights reserved.

The non-ideal problem behavior using a dynamic vibration absorber with nonlinear essential stiffness and timedependent damping properties

The purpose of this study is to develop a dynamic vibration absorber using viscoelastic material with nonlinear essential stiffness and time-dependent damping properties for a non-ideal vibrating system with Sommerfeld effect, resonance capture, and jump phenomenon. The absorber is a mass-bar subsystem that consists of a viscoelastic bar with memory attached to mass, in which the internal dissipative forces depend on current, deformations, and its operational frequency varies with limited temperature. The non-ideal vibrating system consists of a linear (nonlinear) oscillator (plane frame structure) under excitation, via spring connector, of a DC-motor with limited power supply. A viscoelastic dynamic absorber modeled with elastic stiffness essentially nonlinearities was developed to further reduce the Sommerfeld effect and the response of the structure. The numerical results show the performance of the absorber on the non-ideal system response through the resonance curves, time histories, and Poincarésections. Furthermore, the structure responses using the viscoelastic damper with and without memory were studied. © IMechE 2012.

Dynamical properties for a mixed Fermi accelerator model

The behavior of the decay of velocity in a semi-dissipative one-dimensional Fermi accelerator model is considered. Two different kinds of dissipative forces were considered: (i) F-v and; (ii) F-v2. We prove the decay of velocity is linear for (i) and exponential for (ii). During the decay, the particles move along specific corridors which are constructed by the borders of the stable manifolds of saddle points. These corridors organize themselves in a very complicated way in the phase space leading the basin of attraction of the sinks to be seemingly of fractal type. © 2013 Elsevier B.V. All rights reserved.

Dinâmica dos anéis de poeira e satélites de Urano e do anel F de Saturno

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

Records of migration in the exoplanet configurations

When compared to our Solar System, many exoplanet systems exhibit quite unusual planet configurations; some of these are hot Jupiters, which orbit their central stars with periods of a few days, others are resonant systems composed of two or more planets with commensurable orbital periods. It has been suggested that these configurations can be the result of a migration processes originated by tidal interactions of the planets with disks and central stars. The process known as planet migration occurs due to dissipative forces which affect the planetary semi-major axes and cause the planets to move towards to, or away from, the central star. In this talk, we present possible signatures of planet migration in the distribution of the hot Jupiters and resonant exoplanet pairs. For this task, we develop a semi-analytical model to describe the evolution of the migrating planetary pair, based on the fundamental concepts of conservative and dissipative dynamics of the three-body problem. Our approach is based on an analysis of the energy and the orbital angular momentum exchange between the two-planet system and an external medium; thus no specific kind of dissipative forces needs to be invoked. We show that, under assumption that dissipation is weak and slow, the evolutionary routes of the migrating planets are traced by the stationary solutions of the conservative problem (Birkhoff, Dynamical systems, 1966). The ultimate convergence and the evolution of the system along one of these modes of motion are determined uniquely by the condition that the dissipation rate is sufficiently smaller than the roper frequencies of the system. We show that it is possible to reassemble the starting configurations and migration history of the systems on the basis of their final states, and consequently to constrain the parameters of the physical processes involved.

Tratamiento consistente de restricciones e impacto en dinámica de sistemas multicuerpo

Esta tesis está enmarcada en el estudio de diferentes procedimientos numéricos para resolver la dinámica de un sistema multicuerpo sometido a restricciones e impacto, que puede estar compuesto por sólidos rígidos y deformables conectados entre sí por diversos tipos de uniones. Dentro de los métodos numéricos analizados se presta un especial interés a los métodos consistentes, los cuales tienen por objetivo que la energía calculada en cada paso de tiempo, para un sistema mecánico, tenga una evolución coherente con el comportamiento teórico de la energía. En otras palabras, un método consistente mantiene constante la energía total en un problema conservativo, y en presencia de fuerzas disipativas proporciona un decremento positivo de la energía total. En esta línea se desarrolla un algoritmo numérico consistente con la energía total para resolver las ecuaciones de la dinámica de un sistema multicuerpo. Como parte de este algoritmo se formulan energéticamente consistentes las restricciones y el contacto empleando multiplicadores de Lagrange, penalización y Lagrange aumentado. Se propone también un método para el contacto con sólidos rígidos representados mediante superficies implícitas, basado en una restricción regularizada que se adaptada adecuadamente para el cumplimiento exacto de la restricción de contacto y para ser consistente con la conservación de la energía total. En este contexto se estudian dos enfoques: uno para el contacto elástico puro (sin deformación) formulado con penalización y Lagrange aumentado; y otro basado en un modelo constitutivo para el contacto con penetración. En el segundo enfoque se usa un potencial de penalización que, en ausencia de componentes disipativas, restaura la energía almacenada en el contacto y disipa energía de forma consistente con el modelo continuo cuando las componentes de amortiguamiento y fricción son consideradas. This thesis focuses on the study of several numerical procedures used to solve the dynamics of a multibody system subjected to constraints and impact. The system may be composed by rigid and deformable bodies connected by different types of joints. Within this framework, special attention is paid to consistent methods, which preserve the theoretical behavior of the energy at each time step. In other words, a consistent method keeps the total energy constant in a conservative problem, and provides a positive decrease in the total energy when dissipative forces are present. A numerical algorithm has been developed for solving the dynamical equations of multibody systems, which is energetically consistent. Energetic consistency in contacts and constraints is formulated using Lagrange multipliers, penalty and augmented Lagrange methods. A contact methodology is proposed for rigid bodies with a boundary represented by implicit surfaces. The method is based on a suitable regularized constraint formulation, adapted both to fulfill exactly the contact constraint, and to be consistent with the conservation of the total energy. In this context two different approaches are studied: the first applied to pure elastic contact (without deformation), formulated with penalty and augmented Lagrange; and a second one based on a constitutive model for contact with penetration. In this second approach, a penalty potential is used in the constitutive model, that restores the energy stored in the contact when no dissipative effects are present. On the other hand, the energy is dissipated consistently with the continuous model when friction and damping are considered.

Altered stability of pulmonary surfactant in SP-C-deficient mice

The surfactant protein C (SP-C) gene encodes an extremely hydrophobic, 4-kDa peptide produced by alveolar epithelial cells in the lung. To discern the role of SP-C in lung function, SP-C-deficient (−/−) mice were produced. The SP-C (−/−) mice were viable at birth and grew normally to adulthood without apparent pulmonary abnormalities. SP-C mRNA was not detected in the lungs of SP-C (−/−) mice, nor was mature SP-C protein detected by Western blot of alveolar lavage from SP-C (−/−) mice. The levels of the other surfactant proteins (A, B, D) in alveolar lavage were comparable to those in wild-type mice. Surfactant pool sizes, surfactant synthesis, and lung morphology were similar in SP-C (−/−) and SP-C (+/+) mice. Lamellar bodies were present in SP-C (−/−) type II cells, and tubular myelin was present in the alveolar lumen. Lung mechanics studies demonstrated abnormalities in lung hysteresivity (a term used to reflect the mechanical coupling between energy dissipative forces and tissue-elastic properties) at low, positive-end, expiratory pressures. The stability of captive bubbles with surfactant from the SP-C (−/−) mice was decreased significantly, indicating that SP-C plays a role in the stabilization of surfactant at low lung volumes, a condition that may accompany respiratory distress syndrome in infants and adults.

Complete spin and orbital evolution of close-in bodies using a Maxwell viscoelastic rheology

In this paper, we present a formalism designed to model tidal interaction with a viscoelastic body made of Maxwell material. Our approach remains regular for any spin rate and orientation, and for any orbital configuration including high eccentricities and close encounters. The method is to integrate simultaneously the rotation and the position of the planet as well as its deformation. We provide the equations of motion both in the body frame and in the inertial frame. With this study, we generalize preexisting models to the spatial case and to arbitrary multipole orders using a formalism taken from quantum theory. We also provide the vectorial expression of the secular tidal torque expanded in Fourier series. Applying this model to close-in exoplanets, we observe that if the relaxation time is longer than the revolution period, the phase space of the system is characterized by the presence of several spin-orbit resonances, even in the circular case. As the system evolves, the planet spin can visit different spin-orbit configurations. The obliquity is decreasing along most of these resonances, but we observe a case where the planet tilt is instead growing. These conclusions derived from the secular torque are successfully tested with numerical integrations of the instantaneous equations of motion on HD 80606 b. Our formalism is also well adapted to close-in super-Earths in multiplanet systems which are known to have non-zero mutual inclinations.

Formulação lagrangiana para sistemas dissipativos através do cálculo fracionário

Neste trabalho, generalizamos o Princípio da Mínima Ação proposto por Riewe para sistemas não conservativos, contendo forças dissipativas lineares dependentes de derivadas temporais de qualquer ordem. A Ação generalizada é construída a partir de funções Lagrangianas dependentes de derivadas de ordem inteira e fracionária. Diferente de outras formulações, o uso de derivadas fracionárias permite a construção de Lagrangianas físicas para sistemas não conservativos. Uma Lagrangiana é dita física se fornece relações fisicamente consistentes para o momentum e o Hamiltoniano do sistema. Neste Princípio da Mínima Ação generalizado, as equações de movimento são obtidas a partir da equação de Euler-Lagrange e, tomando-se o limite indo à zero para o intervalo de tempo definindo a Ação. Finalmente, como exemplo de aplicação, formulamos pela primeira vez uma Lagrangiana física para o problema da carga pontual acelerada.

Secular and tidal evolution of circumbinary systems

We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin–orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star–planet–satellite systems and triple stellar systems.

On the 'downward control' of extratropical diabatic circulations by eddy-induced mean zonal forces

The situation considered is that of a zonally symmetric model of the middle atmosphere subject to a given quasi-steady zonal force F̄, conceived to be the result of irreversible angular momentum transfer due to the upward propagation and breaking of Rossby and gravity waves together with any other dissipative eddy effects that may be relevant. The model's diabatic heating is assumed to have the qualitative character of a relaxation toward some radiatively determined temperature field. To the extent that the force F̄ may be regarded as given, and the extratropical angular momentum distribution is realistic, the extratropical diabatic mass flow across a given isentropic surface may be regarded as controlled exclusively by the F̄ distribution above that surface (implying control by the eddy dissipation above that surface and not, for instance, by the frequency of tropopause folding below). This “downward control” principle expresses a critical part of the dynamical chain of cause and effect governing the average rate at which photochemical products like ozone become available for folding into, or otherwise descending into, the extratropical troposphere. The dynamical facts expressed by the principle are also relevant, for instance, to understanding the seasonal-mean rate of upwelling of water vapor to the summer mesopause, and the interhemispheric differences in stratospheric tracer transport. The robustness of the principle is examined when F̄ is time-dependent. For a global-scale, zonally symmetric diabatic circulation with a Brewer-Dobson-like horizontal structure given by the second zonally symmetric Hough mode, with Rossby height HR = 13 km in an isothermal atmosphere with density scale height H = 7 km, the vertical partitioning of the unsteady part of the mass circulation caused by fluctuations in F̄ confined to a shallow layer LF̄ is always at least 84% downward. It is 90% downward when the force fluctuates sinusoidally on twice the radiative relaxation timescale and 95% if five times slower. The time-dependent adjustment when F̄ is changed suddenly is elucidated, extending the work of Dickinson (1968), when the atmosphere is unbounded above and below. Above the forcing, the adjustment is characterized by decay of the meridional mass circulation cell at a rate proportional to the radiative relaxation rate τr−1 divided by {1 + (4H2/HR2)}. This decay is related to the boundedness of the angular momentum that can be taken up by the finite mass of air above LF̄ without causing an ever-increasing departure from thermal wind balance. Below the forcing, the meridional mass circulation cell penetrates downward at a speed τr−1 HR2/H. For the second Hough mode, the time for downward penetration through one density scale height is about 6 days if the radiative relaxation time is 20 days, the latter being representative of the lower stratosphere. At any given altitude, a steady state is approached. The effect of a rigid lower boundary on the time-dependent adjustment is also considered. If a frictional planetary boundary layer is present then a steady state is ultimately approached everywhere, with the mass circulation extending downward from LF̄ and closing via the boundary layer. Satellite observations of temperature and ozone are used in conjunction with a radiative transfer scheme to estimate the altitudes from which the lower stratospheric diabatic vertical velocity is controlled by the effective F̄ in the real atmosphere. The data appear to indicate that about 80% of the effective control is usually exerted from below 40 km but with significant exceptions up to 70 km (in the high latitude southern hemispheric winter). The implications for numerical modelling of chemical transport are noted.