Saddle points and rare collisions under scaling approach in a Fermi accelerator with two nonlinear terms

Rare collisions of a classical particle bouncing between two walls are studied. The dynamics is described by a two-dimensional, nonlinear and area-preserving mapping in the variables velocity and time at the instant that the particle collides with the moving wall. The phase space is of mixed type preventing diffusion of the particle to high energy. Successive and therefore rare collisions are shown to have a histogram of frequency which is scaling invariant with respect to the control parameters. The saddle fixed points are studied and shown to be scaling invariant with respect to the control parameters too. © 2012 Elsevier B.V. All rights reserved.

Separation of particles leading either to decay or unlimited growth of energy in a driven stadium-like billiard

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Convergence towards asymptotic state in 1-D mappings: a scaling investigation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A simple method for choosing the parameters of a two degree-of-freedom tuned vibration absorber

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

Influence of the Connector and Implant Design on the Implant-Tooth-Connected Prostheses

Purpose:The purpose of this study was to evaluate stress transfer patterns between implant-tooth-connected prostheses comparing rigid and semirigid connectors and internal and external hexagon implants.Materials and Methods:Two models were made of photoelastic resin PL-2, with an internal hexagon implant of 4.00 x 13 mm and another with an external hexagon implant of 4.00 x 13 mm. Three denture designs were fabricated for each implant model, incorporating one type of connection in each one to connect implants and teeth: 1) welded rigid connection; 2) semirigid connection; and 3) rigid connection with occlusal screw. The models were placed in the polariscope, and 100-N axial forces were applied on fixed points on the occlusal surface of the dentures.Results:There was a trend toward less intensity in the stresses on the semirigid connection and solid rigid connection in the model with the external hexagon; among the three types of connections in the model with the internal hexagon implant, the semirigid connection was the most unfavorable one; in the tooth-implant association, it is preferable to use the external hexagon implant.Conclusions:The internal hexagon implant establishes a greater depth of hexagon retention and an increase in the level of denture stability in comparison with the implant with the external hexagon. However, this greater stability of the internal hexagon generated greater stresses in the abutment structures. Therefore, when this association is necessary, it is preferable to use the external hexagon implant.

Which kind of miniplate to use in mandibular sagittal split osteotomy? An in vitro study

This study verified the resistance to displacement of six miniplate fixation methods after sagittal split osteotomy (SSO). SSO was performed in 30 polyurethane synthetic mandible replicas. The distal segments were advanced (4 mm) and specimens were grouped according to the fixation method: four-hole standard miniplate; four-hole locking miniplate; six-hole standard miniplate; six-hole locking miniplate; six-hole standard sagittal miniplate; six-hole locking sagittal miniplate. Biomechanical evaluation was performed by applying compression loads to three points on the second molar region, using an Instron universal testing machine until a 3 mm displacement of the segments occurred. Compression loads able to produce 3 mm displacement were recorded in kN and subjected to analysis of variance (P < 0.01) and Tukey's tests for comparison between groups (P < 0.05). The locking sagittal miniplate showed higher resistance to displacement than the regular four- and six-hole locking and standard miniplates. No significant differences were observed between the locking sagittal miniplate and the regular sagittal or the four-hole locking miniplates. Two of the three groups with the best results had locking plate fixation methods. Fixation of SSO with a single miniplate is better accomplished using six-hole locking sagittal miniplates, six-hole standard sagittal miniplates, or four-hole locking miniplates; these methods are more resistant to displacement.

Prospective study of soft tissue contour changes following chin bone graft harvesting

This study sought to evaluate changes in the soft tissue contour after chin bone graft harvesting. Thirty selected patients underwent chin bone graft harvesting and evaluations were made using lateral cephalograms preoperatively and postoperatively at 30 and 180 days. Fixed points and lines were established on cephalometric tracings and used to measure the selected vertical and sagittal parameters. Results showed statistically significant alterations to the vertical position values of the vermilion (V-VPV) which increased from 9.70 to 11.01 and the exposure of lower incisors (V-ELI) which increased from 1.85 to 3.5, showing an increase in their distance from the plane of reference and a lowering of their position, the clinical equivalent of a labial ptosis condition. None of the sagittal parameters analysed showed any statistically significant variation in the final evaluation. The study concluded that the alterations to patients' soft tissue contours resulted mainly from failure to ensure precise reattachment of the mentalis muscles and identified the need for further investigation of that aspect.

Effect of a frictional force on the Fermi-Ulam model

The dynamical properties of a classical particle bouncing between two rigid walls, in the presence of a drag force, are studied for the case where one wall is fixed and the other one moves periodically in time. The system is described in terms of a two-dimensional nonlinear map obtained by solution of the relevant differential equations. It is shown that the structure of the KAM curves and the chaotic sea is destroyed as the drag force is introduced. At high energy, the velocity of the particle decreases linearly with increasing iteration number, but with a small superimposed sinusoidal modulation. If the motion passes near enough to a fixed point, the particle approaches it exponentially as the iteration number evolves, with a speed of approach that depends on the strength of the drag force. For a simplified version of the model it is shown that, at low energies corresponding to the region of the chaotic sea in the non-dissipative model, the particle wanders in a chaotic transient that depends on the strength of the drag coefficient. However, the KAM islands survive in the presence of dissipation. It is confirmed that the fixed points and periodic orbits go over smoothly into the orbits of the well-known (non-dissipative) Fermi-Ulam model as the drag force goes to zero.

A peculiar Maxwell's Demon observed in a time-dependent stadium-like billiard

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

Shrimp-shape domains in a dissipative kicked rotator

Some dynamical properties for a dissipative kicked rotator are studied. Our results show that when dissipation is taken into account a drastic change happens in the structure of the phase space in the sense that the mixed structure is modified and attracting fixed points and chaotic attractors are observed. A detailed numerical investigation in a two-dimensional parameter space based on the behavior of the Lyapunov exponent is considered. Our results show the existence of infinite self-similar shrimp-shaped structures corresponding to periodic attractors, embedded in a large region corresponding to the chaotic regime. (C) 2011 American Institute of Physics. [doi:10.1063/1.3657917]

Parameter space for a dissipative Fermi-Ulam model

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

Designing a modified Hopfield network to solve an Economic Dispatch problem with nonlinear cost function

Economic Dispatch (ED) problems have recently been solved by artificial neural networks approaches. In most of these dispatch models, the cost function must be linear or quadratic. Therefore, functions that have several minimum points represent a problem to the simulation since these approaches have not accepted nonlinear cost function. Another drawback pointed out in the literature is that some of these neural approaches fail to converge efficiently towards feasible equilibrium points. This paper discusses the application of a modified Hopfield architecture for solving ED problems defined by nonlinear cost function. The internal parameters of the neural network adopted here are computed using the valid-subspace technique, which guarantees convergence to equilibrium points that represent a solution for the ED problem. Simulation results and a comparative analysis involving a 3-bus test system are presented to illustrate efficiency of the proposed approach.

The defocusing mechanism of isochronous resonances

We present a numerical study concerning the defocusing mechanism of isochronous resonance island chains in the presence of two permanent robust tori. The process is initialized and concluded through bifurcations of fixed points located on the robust tori. Our approach is based on a Hamiltonian system derived from the resonant normal form. Choosing a convenient parameter in this system, we are able to depict a comprehensive analysis of the dynamics of the problem. (c) 2004 Elsevier B.V. All rights reserved.

Foraging, diet and community structure in an epigaeic ant (Hymenoptera: Formicidae) assemblage: the role of recruitment

The significance of recruitment systems for community structure of epigaeic ants in a tropical upland forest in southern Brazil was evaluated by examining patterns of spatial occurrence at fixed points. Normal exploratory activity was evaluated with pitfall traps, while the effect of recruitment and diet was evaluated by using honey and sardine baits at the same points. Through techniques developed for environmental impact assessment, the significance of recruitment was evaluated following perturbation, or the placement of bait. Of the 46 species encountered, 15 were sufficiently frequent to study. Of these, only 6 showed significant spatial frequency changes at baits when compared with pitfall trap collections. In one analysis, monthly differences were important for a few smaller species, suggesting thermic limitations, while bait types either increased or decreased spatial point usage. The magnitude of spatial point variation is an index for the strength of recruitment in community organization. Bait types suggest nutritional possibilities of each species. Both recruitment and diet are probably functions of the species composition of the ant community.

Stable two-dimensional dispersion-managed soliton

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schrodinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct partial differential equation (PDE) and ordinary differential equation (ODE) simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown.