Dynamical Casimir effect for a massless scalar field between two concentric spherical shells with mixed boundary conditions

In this work we analyze the dynamical Casimir effect for a massless scalar field confined between two concentric spherical shells considering mixed boundary conditions. We thus generalize a previous result in literature [Phys. Rev. A 78, 032521 (2008)], where the same problem is approached for the field constrained to the Dirichlet-Dirichlet boundary conditions. A general expression for the average number of particle creation is deduced considering an arbitrary law of radial motion of the spherical shells. This expression is then applied to harmonic oscillations of the shells, and the number of particle production is analyzed and compared with the results previously obtained under Dirichlet-Dirichlet boundary conditions.

Number of particle creation and decoherence in the nonideal dynamical Casimir effect at finite temperature

In this work we investigate the dynamical Casimir effect in a nonideal cavity by deriving an effective Hamiltonian. We first compute a general expression for the average number of particle creation, applicable for any law of motion of the cavity boundary, under the only restriction of small velocities. We also compute a general expression for the linear entropy of an arbitrary state prepared in a selected mode, also applicable for any law of motion of a slow moving boundary. As an application of our results we have analyzed both the average number of particle creation and linear entropy within a particular oscillatory motion of the cavity boundary. On the basis of these expressions we develop a comprehensive analysis of the resonances in the number of particle creation in the nonideal dynamical Casimir effect. We also demonstrate the occurrence of resonances in the loss of purity of the initial state and estimate the decoherence times associated with these resonances. Since our results were obtained in the framework of the perturbation theory, they are restricted, under resonant conditions, to a short-time approximation. (C) 2009 Elsevier Inc. All rights reserved.

Fenômeno de interferência na densidade de energia em cavidades com duas fronteiras oscilantes

O primeiro objetivo do presente trabalho é calcular a força quântica exata que atua sobre as fronteiras de uma cavidade, bem como o comportamento exato da densidade de energia numa cavidade não estática, onde ambas as fronteiras executam movimentos prescritos arbitrários. O modelo considerado é o do campo escalar não massivo em 1 + 1 dimensões, sendo que o campo obedece à condição de Dirichlet em cada uma das fronteiras. Considerando o vácuo como estado inicial do campo, nós mostramos que a densidade de energia em um dado ponto do espaço-tempo pode ser obtida através do traçado de uma sequência de linhas nulas, conectando o valor da densidade de energia nesse ponto a um certo valor conhecido da densidade de energia em um ponto das “zonas estáticas”. O segundo objetivo é mostrar que para movimentos específicos das fronteiras, particularmente para os quais ambas voltam às suas posições iniciais em instantes múltiplos do comprimento inicial da cavidade, o método exato por nós obtido permite encontrar soluções analíticas escritas como uma expansão em série na variável que controla as amplitudes de movimento das fronteiras. Os resultados analíticos por nós obtidos são aplicáveis a uma vasta classe de movimentos, a qual inclui a grande maioria dos casos ressonantes estudados na literatura. O terceiro objetivo do presente trabalho é investigar, através dos métodos de cálculos desenvolvidos aqui, o fenômeno da interferência na energie e na densidade de energia em cavidades com duas fronteiras móveis, obtendo fórmulas genéricas para os termos de interferência respectivos.

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.

Intercepting moving targets: does memory from practice in a specific condition of target displacement affect movement timing?

This investigation aimed at assessing the extent to which memory from practice in a specific condition of target displacement modulates temporal errors and movement timing of interceptive movements. We compared two groups practicing with certainty of future target velocity either in unchanged target velocity or in target velocity decrease. Following practice, both experimental groups were probed in the situations of unchanged target velocity and target velocity decrease either under the context of certainty or uncertainty about target velocity. Results from practice showed similar improvement of temporal accuracy between groups, revealing that target velocity decrease did not disturb temporal movement organization when fully predictable. Analysis of temporal errors in the probing trials indicated that both groups had higher timing accuracy in velocity decrease in comparison with unchanged velocity. Effect of practice was detected by increased temporal accuracy of the velocity decrease group in situations of decreased velocity; a trend consistent with the expected effect of practice was observed for temporal errors in the unchanged velocity group and in movement initiation at a descriptive level. An additional point of theoretical interest was the fast adaptation in both groups to a target velocity pattern different from that practiced. These points are discussed under the perspective of integration of vision and motor control by means of an internal forward model of external motion.

Use of peripheral vision in the interception of moving targets

Use of peripheral vision to organize and reorganize an interceptive action was investigated in young adults. Temporal errors and kinematic variables were evaluated in the interception of a virtual moving target, in situations in which its initial velocity was kept unchanged or was unexpectedly decreased. Observation of target approach was made through continuous visual pursuit (focal vision) or keeping visual focus at the origin of the trajectory or at the contact spot (peripheral vision). Results showed that visual focus at the contact spot led to temporal errors similar to focal vision, although showing a distinct kinematic profile, while focus at the origin led to an impoverished performance

Constraints on the spatiotemporal accuracy of interceptive action: effects of target size on hitting a moving object

Results of two experiments are reported that examined how people respond to rectangular targets of different sizes in simple hitting tasks. If a target moves in a straight line and a person is constrained to move along a linear track oriented perpendicular to the targetrsquos motion, then the length of the target along its direction of motion constrains the temporal accuracy and precision required to make the interception. The dimensions of the target perpendicular to its direction of motion place no constraints on performance in such a task. In contrast, if the person is not constrained to move along a straight track, the targetrsquos dimensions may constrain the spatial as well as the temporal accuracy and precision. The experiments reported here examined how people responded to targets of different vertical extent (height): the task was to strike targets that moved along a straight, horizontal path. In experiment 1 participants were constrained to move along a horizontal linear track to strike targets and so target height did not constrain performance. Target height, length and speed were co-varied. Movement time (MT) was unaffected by target height but was systematically affected by length (briefer movements to smaller targets) and speed (briefer movements to faster targets). Peak movement speed (Vmax) was influenced by all three independent variables: participants struck shorter, narrower and faster targets harder. In experiment 2, participants were constrained to move in a vertical plane normal to the targetrsquos direction of motion. In this task target height constrains the spatial accuracy required to contact the target. Three groups of eight participants struck targets of different height but of constant length and speed, hence constant temporal accuracy demand (different for each group, one group struck stationary targets = no temporal accuracy demand). On average, participants showed little or no systematic response to changes in spatial accuracy demand on any dependent measure (MT, Vmax, spatial variable error). The results are interpreted in relation to previous results on movements aimed at stationary targets in the absence of visual feedback.

Hitting a moving target: Perception and action in the timing of rapid interceptions

Different interceptive tasks and modes of interception (hitting or capturing) do not necessarily involve similar control processes. Control based on preprogramming of movement parameters is possible for actions with brief movement times but is now widely rejected; continuous perceptuomotor control models are preferred for all types of interception. The rejection of preprogrammed control and acceptance of continuous control is evaluated for the timing of rapidly executed, manual hitting actions. It is shown that a preprogrammed control model is capable of providing a convincing account of observed behavior patterns that avoids many of the arguments that have been raised against it. Prominent continuous perceptual control models are analyzed within a common framework and are shown to be interpretable as feedback control strategies. Although these models can explain observations of on-line adjustments to movement, they offer only post hoc explanations for observed behavior patterns in hitting tasks and are not directly supported by data. It is proposed that rapid manual hitting tasks make up a class of interceptions for which a preprogrammed strategy is adopted-a strategy that minimizes the role of visual feedback. Such a strategy is effective when the task demands a high degree of temporal accuracy.

Intercepting a moving target: effects of temporal precision constraints and movement amplitude

The effects of temporal precision constraints and movement amplitude on performance of an interceptive aiming task were examined. Participants were required to strike a moving target object with a 'bat' by moving the bat along a straight path (constrained by a linear slide) perpendicular to the path of the target. Temporal precision constraints were defined in terms of the time period (or window) within which contact with the target was possible. Three time windows were used (approx. 35, 50 and 65 ms) and these were achieved either by manipulating the size of the bat (experiment 1a), the size of the target (experiment 1b) or the speed of the target (experiment 2). In all experiments, movement time (MT) increased in proportion to movement amplitude but was only affected by differences in the temporal precision constraint if this was achieved by variation in the target's speed. In this case the MT was approximately inversely proportional to target speed. Peak movement speed was affected by temporal accuracy constraints in all three experiments: participants reached higher speeds when the temporal precision required was greater. These results are discussed with reference to the speed-accuracy trade-off observed for temporally constrained aiming movements. It is suggested that the MT and speed of interceptive aiming movements may be understood as responses to the spatiotemporal constraints of the task.

Solution of adsorption problems involving steep moving profiles

The moving finite element collocation method proposed by Kill et al. (1995) Chem. Engng Sci. 51 (4), 2793-2799 for solution of problems with steep gradients is further developed to solve transient problems arising in the field of adsorption. The technique is applied to a model of adsorption in solids with bidisperse pore structures. Numerical solutions were found to match the analytical solution when it exists (i.e. when the adsorption isotherm is linear). The method is simple yet sufficiently accurate for use in adsorption problems, where global collocation methods fail. (C) 1998 Elsevier Science Ltd. All rights reserved.

Beach water table fluctuations due to spring-neap tides: moving boundary effects

Tidal water table fluctuations in a coastal aquifer are driven by tides on a moving boundary that varies with the beach slope. One-dimensional models based on the Boussinesq equation are often used to analyse tidal signals in coastal aquifers. The moving boundary condition hinders analytical solutions to even the linearised Boussinesq equation. This paper presents a new perturbation approach to the problem that maintains the simplicity of the linearised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection-diffusion equation) with an oscillating velocity. The perturbation method is applied to the propagation of spring-neap tides (a bichromatic tidal system with the fundamental frequencies wt and wt) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the two primary tidal oscillations, generating a slowly damped water table fluctuation of frequency omega(1) - omega(2), i.e., the spring-neap tidal water table fluctuation. The analytical predictions are found to be consistent with recently published field observations. (C) 2000 Elsevier Science Ltd. All rights reserved.

On the solute coupling at the moving solid/liquid interface during equiaxed solidification

Integral mass conservation was widely accepted for the solute coupling to solve solute redistribution during equiaxed solidification so far. The present study revealed that the integral form was invalid for moving boundary problems as it could not represent the mass balance at the moving interface. Accordingly, differential mass conservation at the solid/liquid interface was used to solve solute diffusion for spherical geometry. The model was applied for hydrogen diffusion in solidification to validate that the hydrogen enrichment was significant and depended on the growth rate. (c) 2006 American Institute of Physics.