Scaling dynamics for a particle in a time-dependent potential well

Some dynamical properties for a classical particle confined in an infinitely deep box of potential containing a periodically oscillating square well are studied. The dynamics of the system is described by using a two-dimensional non-linear area-preserving map for the variables energy and time. The phase space is mixed and the chaotic sea is described using scaling arguments. Scaling exponents are obtained as a function of all the control parameters, extending the previous results obtained in the literature. (c) 2012 Elsevier B.V. All rights reserved.

Boundary crisis and suppression of Fermi acceleration in a dissipative two-dimensional non-integrable time-dependent billiard

Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non-dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time-dependent billiards. (C) 2010 Elsevier B.V. All rights reserved.

CRITICAL EXPONENTS and SCALING PROPERTIES FOR THE CHAOTIC DYNAMICS of A PARTICLE IN A TIME-DEPENDENT POTENTIAL BARRIER

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

Robust tori-like Lagrangian coherent structures

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

Comparison between the complete Bayesian method and empirical Bayesian method for ARCH models using Brazilian financial time series

In this work we compared the estimates of the parameters of ARCH models using a complete Bayesian method and an empirical Bayesian method in which we adopted a non-informative prior distribution and informative prior distribution, respectively. We also considered a reparameterization of those models in order to map the space of the parameters into real space. This procedure permits choosing prior normal distributions for the transformed parameters. The posterior summaries were obtained using Monte Carlo Markov chain methods (MCMC). The methodology was evaluated by considering the Telebras series from the Brazilian financial market. The results show that the two methods are able to adjust ARCH models with different numbers of parameters. The empirical Bayesian method provided a more parsimonious model to the data and better adjustment than the complete Bayesian method.

Time analysis for temporary gravitational capture - Stable orbits

In a previous work, Vieira Neto & Winter (2001) numerically explored the capture times of particles as temporary satellites of Uranus. The study was made in the framework of the spatial, circular, restricted three-body problem. Regions of the initial condition space whose trajectories are apparently stable were determined. The criterion adopted was that the trajectories do not escape from the planet during an integration of 10(5) years. These regions occur for a wide range of orbital initial inclinations (i). In the present work it is studied the reason for the existence of such stable regions. The stability of the planar retrograde trajectories is due to a family of simple periodic orbits and the associated quasi-periodic orbits that oscillate around them. These planar stable orbits had already been studied (Henon 1970; Huang & Innanen 1983). Their results are reviewed using Poincare surface of sections. The stable non-planar retrograde trajectories, 110 degrees less than or equal to i < 180, are found to be tridimensional quasi-periodic orbits around the same family of periodic orbits found for the planar case (i = 180 degrees). It was not found any periodic orbit out of the plane associated to such quasi-periodic orbits. The largest region of stable prograde trajectories occurs at i = 60 degrees. Trajectories in such region are found to behave as quasi-periodic orbits evolving similarly to the stable retrograde trajectories that occurs at i = 120 degrees.

Effect of denture fabrication and wear on closest speaking space and interocclusal distance during deglutition

Statement of problem. The accuracy of assessing maxillomandibular relationships for trial bases and dentures using phonetic and swallowing methods has not been compared to that observed with definitive prostheses. Thus, there is no evidence to prove whether measurements obtained through such methods remain the same after adaptation to dentures.Purpose. This study investigated changes in the closest speaking space, interocclusal rest space, and interocclusal distance during deglutition in edentulous patients during and after complete denture treatment.Material and methods. Eighteen edentulous subjects participated in this study and measurements were performed after 7 Intervals of time: (1) with occlusion rims and record bases following creation of the maxillomandibular relationship record, (2) with trial dentures, (3) at Insertion of definitive complete dentures, (4) 1 week, (5) 2 weeks, (6) 1 month, and (7) 3 months after insertion. Recordings of interocclusal distances were made with a mandibular kinesiograph. Closest speaking space was measured during the pronunciation of the word 'seis'. The distance between postural rest position and centric occlusion, or interocclusal rest space, was measured using a kinesiograph. Interocclusal distance during deglutition was tested by recording the closest mandibular position recorded during swallowing of 20 mL of water. Data were analyzed using repeated-measure ANOVA, followed by the Student-Newman-Keuls test (alpha=.05).Results. A significant (P <.01)reduction in the mean closest speaking space was found when it was evaluated using occlusion rims and record bases (4.6 mm) compared with other stages (3.0 to 3.4 mm). No significant differences were found in mean interocclusal rest space and interocclusal distance during deglutition among the time periods evaluated.Conclusions. The presence of occlusion rims can influence mandibular position during pronunciation of the /s/ sound. The arrangement of artificial teeth changes the closest speaking space. However, rest position and deglutition were not affected, either during denture fabrication or short-term use.

Dynamics in discrete phase spaces and time interval operators

The von Neumann-Liouville time evolution equation is represented in a discrete quantum phase space. The mapped Liouville operator and the corresponding Wigner function are explicitly written for the problem of a magnetic moment interacting with a magnetic field and the precessing solution is found. The propagator is also discussed and a time interval operator, associated to a unitary operator which shifts the energy levels in the Zeeman spectrum, is introduced. This operator is associated to the particular dynamical process and is not the continuous parameter describing the time evolution. The pair of unitary operators which shifts the time and energy is shown to obey the Weyl-Schwinger algebra. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Genetic Algorithms (Binary and Real Codes) for the Optimisation of a Fermentation Process for Butanol Production

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

Escape of particles in a time-dependent potential well

We investigate the escape of an ensemble of noninteracting particles inside an infinite potential box that contains a time-dependent potential well. The dynamics of each particle is described by a two-dimensional nonlinear area-preserving mapping for the variables energy and time, leading to a mixed phase space. The chaotic sea in the phase space surrounds periodic islands and is limited by a set of invariant spanning curves. When a hole is introduced in the energy axis, the histogram of frequency for the escape of particles, which we observe to be scaling invariant, grows rapidly until it reaches a maximum and then decreases toward zero at sufficiently long times. A plot of the survival probability of a particle in the dynamics as function of time is observed to be exponential for short times, reaching a crossover time and turning to a slower-decay regime, due to sticky regions observed in the phase space.

A recursive approach to space resection using straight lines

An approach using straight lines as features to solve the photogrammetric space resection problem is presented. An explicit mathematical model relating straight lines, in both object and image space, is used. Based on this model, Kalman Filtering is applied to solve the space resection problem. The recursive property of the filter is used in an iterative process which uses the sequentially estimated camera location parameters to feedback to the feature extraction process in the image. This feedback process leads to a gradual reduction of the image space for feature searching, and consequently eliminates the bottleneck due to the high computational cost of the image segmentation phase. It also enables feature extraction and the determination of feature correspondence in image and object space in an automatic way, i.e., without operator interference. Results obtained from simulated and real data show that highly accurate space resection parameters are obtained as well as a progressive processing time reduction. The obtained accuracy, the automatic correspondence process, and the short related processing time show that the proposed approach can be used in many real-time machine vision systems, making possible the implementation of applications not feasible until now.

Épocas de consórcio de alho com beterraba perante três manejos do mato sobre a produtividade e o lucro

The research was carried out with intercropped cultivation of garlic and beet, in Caçador, SC, Brazil. Four seeding epochs for beet (0, 15, 30 and 45 days after garlic planting) and three management systems for weeds (with herbicides, without control and with frequent weeding) were tested. It was hoped to determine the effects of this intercropping, in time and space, seeking the benefits in .weed control, efficient land use, productivity, commercial quality, and profitability. The randomized block design was in split-plots. The epochs represented the plots, and the management, the subplots, with four replicates. Napromide at 750 g/ha did not cause symptoms of intoxication in the garlic plants, nor in the beet. All the treatments in epochs at the initiation of intercropping, in three management systems for weeds, presented efficient land use values greater than 1. The profitability of the intercropping of garlic and beet only became evident in the management involving frequent weeding; in all epochs, profits were greater than for the respective epochs of monoculture of beet and monoculture of garlic.

Numerical study of the spherically symmetric Gross-Pitaevskii equation in two space dimensions

The Gross-Pitaevskii equation for Bose-Einstein condensation (BEC) in two space dimensions under the action of a harmonic oscillator trap potential for bosonic atoms with attractive and repulsive interparticle interactions was numerically studied by using time-dependent and time-independent approaches. In both cases, numerical difficulty appeared for large nonlinearity. Nonetheless, the solution of the time-dependent approach exhibited intrinsic oscillation with time iteration which is independent of space and time steps used in discretization.

The effect of changing the mode of ventilation on the arterial-to-end-tidal CO2 difference and physiological dead space in laterally and dorsally recumbent horses during halothane anesthesia

Objective - To evaluate the effect of changing the mode of ventilation from spontaneous to controlled on the arterial-to-end-tidal CO2 difference [P(a-ET)CO2] and physiological dead space (VD(phys)/VT) in laterally and dorsally recumbent halothane-anesthetized horses. Study Design - Prospective, experimental, nonrandomized trial. Animals - Seven mixed breed adult horses (1 male and 6 female) weighing 320 ± 11 kg. Methods - Horses were anesthetized in 2 positions - right lateral and dorsal recumbency - with a minimum interval of 1 month. Anesthesia was maintained with halothane in oxygen for 180 minutes. Spontaneous ventilation (SV) was used for 90 minutes followed by 90 minutes of controlled ventilation (CV). The same ventilator settings were used for both laterally and dorsally recumbent horses. Arterial blood gas analysis was performed every 30 minutes during anesthesia. End-tidal CO2 (PETCO2) was measured continuously. P(a-ET)CO2 and VD(phys)/VT were calculated. Statistical analysis included analysis of variance for repeated measures over time, followed by Student-Newman-Keuls test. Comparison between groups was performed using a paired t test; P < .05 was considered significant. Results - P(a-ET)CO2 and VD(phys)/VT increased during SV, whereas CV reduced these variables. The variables did not change significantly throughout mechanical ventilation in either group. Dorsally recumbent horses showed greater P(a-ET)CO2 and VD(phys)/VT values throughout. PaCO2 was greater during CV in dorsally positioned horses. Conclusions and Clinical Relevance - Changing the mode of ventilation from spontaneous to controlled was effective in reducing P(a-ET)CO2 and physiological dead space in both laterally and dorsally recumbent halothane-anesthetized horses. Dorsal recumbency resulted in greater impairment of effective ventilation. Capnometry has a limited value for accurate estimation of PaCO, in anesthetized horses, although it may be used to evaluate pulmonary function when paired with arterial blood gas analysis. © Copyright 2000 by The American College of Veterinary Surgeons.

Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

The Bose-Einstein condensate of several types of trapped bosons at ultralow temperature was described using the coupled time dependent Gross-Pitaevskii equation. Both the stationary and time evolution problems were analyzed using this approach. The ground state stationary wave functions were found to be sharply peaked near the origin for attractive interatomic interaction for larger nonlinearity while for a repulsive interatomic interaction the wave function extends over a larger region of space.