Scaling properties of the regular dynamics for a dissipative bouncing ball model

Some scaling properties of the regular dynamics for a dissipative version of the one-dimensional Fermi accelerator model are studied. The dynamics of the model is given in terms of a two-dimensional nonlinear area contracting map. Our results show that the velocities of saddle fixed points (saddle velocities) can be described using scaling arguments for different values of the control parameter. (c) 2007 Elsevier B.V. All rights reserved.

The Feigenbaum's delta for a high dissipative bouncing ball model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A bouncing ball model with two nonlinearities: a prototype for Fermi acceleration

Some dynamical properties of a bouncing ball model under the presence of an external force modelled by two nonlinear terms are studied. The description of the model is made by the use of a two-dimensional nonlinear measure-preserving map on the variable's velocity of the particle and time. We show that raising the straight of a control parameter which controls one of the nonlinearities, the positive Lyapunov exponent decreases in the average and suffers abrupt changes. We also show that for a specific range of control parameters, the model exhibits the phenomenon of Fermi acceleration. The explanation of both behaviours is given in terms of the shape of the external force and due to a discontinuity of the moving wall's velocity.

On Ti-18Si-6B and Ti-7.5Si-22.5B powder alloys prepared by high-energy ball milling and sintering

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

Influence of ball-milled low purity boron powder on the superconductivity of MgB2

MgB2 samples were prepared using as-supplied commercial 96% boron with strong crystalline phase and the same 96% boron (B) after ball milling. The effects of the properties of the starting B powder on the superconductivity were evaluated. We observed that samples using ball-milled 96% B, in comparison with the one made from the as-supplied 96% B, were character- ized by small grain size, broadened full width at half maximum (FWHM), and enhanced magnetic critical current density (J(c)). J(c) reached 2 x 10(3) Acm(-2) at 5 K and 8 T. The improved pinning of these samples seems to be caused by enhanced grain boundary pinning at high field.

Bulk and high-energy ball-milled Gd5Si2Ge2: Comparative study of magnetic and magnetocaloric properties

High-energy ball milling was employed to produce small particles of Gd5Si2Ge2. Magnetic and magnetocaloric properties of the ball-milled and bulk Gd5Si2Ge2 samples were investigated through the magnetization measurements. When compared to the bulk material, a significant decrease in saturation magnetization and magnetocaloric effect (-Delta S-max = 4 vs. 20 J/kgK for Delta H = 0-5 T) is observed even after the relatively short ball milling time of 4 h which produced particles with an average size of ca. 0.5 mu m. The ball-milled samples appear to loose a first-order structural transition, present in bulk Gd5Si2Ge2, and display a superparamagnetic behaviour below the corresponding Curie temperatures. (C) 2010 Elsevier Masson SAS. All rights reserved.

Histological study of resection arthroplasty with and without tendon ball interposition in dogs

We studied an experimental model of resection arthroplasty with or without tendon ball interposition in the wrist of dogs. Animals were divided into two groups. Animals in group A were treated by resection of the os carpi radiale with interposition of a ball made from the tendon of the extensor carpi radialis and the group B underwent bone resection alone. Animals were assessed 1, 6, 12 and 24 weeks after operation. In all of them the wrist joint was stable and had good mobility, allowing walking supported by the operated limb. In both groups biological material filled the cavity created by bone resection. A progressive repair process resulted in fibroplasia with areas of fibrocartilaginous metaplasia. The tendon ball showed complete ischaemic necrosis at the end of the first week, which delayed the healing process. © 1999 The British Society for Surgery of the Hand.

Consequences of quadratic frictional force on the one dimensional bouncing ball model

Some dynamical properties of the one dimensional Fermi accelerator model, under the presence of frictional force are studied. The frictional force is assumed as being proportional to the square particle's velocity. The problem is described by use of a two dimensional non linear mapping, therefore obtained via the solution of differential equations. We confirm that the model experiences contraction of the phase space area and in special, we characterized the behavior of the particle approaching an attracting fixed point. © 2007 American Institute of Physics.

The feigenbaumes δ for a high dissipative bouncing ball model

We have studied a dissipative version of a one-dimensional Fermi accelerator model. The dynamics of the model is described in terms of a two-dimensional, nonlinear area-contracting map. The dissipation is introduced via inelastic collisions of the particle with the walls and we consider the dynamics in the regime of high dissipation. For such a regime, the model exhibits a route to chaos known as period doubling and we obtain a constant along the bifurcations so called the Feigenbaum's number 8.

Use of high energy ball milling on the sintering optimization of alumina ceramics

In this work, the effect of the milling time on the densification of the alumina ceramics with or without 5wt.%Y 2O 3, is evaluated, using high-energy ball milling. The milling was performed with different times of 0, 2, 5 or 10 hours. All powders, milled at different times, were characterized by X-Ray Diffraction presenting a reduction of the crystalline degree and crystallite size as function of the milling time increasing. The powders were compacted by cold uniaxial pressing and sintered at 1550°C-60min. Green density of the compacts presented an increasing as function of the milling time and sintered samples presented evolution on the densification as function of the reduction of the crystallite size of the milled powders. © (2010) Trans Tech Publications.

Effect of ball milling on structural and physicochemical characteristics of cassava and Peruvian carrot starches

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

Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities

Some dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent -2. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape. © 2013 Elsevier B.V. All rights reserved.

Estudo de um depósito de argila ball clay de Tambaú (SP), para aplicação na indústria cerâmica de revestimentos

Pós-graduação em Geologia Regional - IGCE

The rolling ball problem on the plane revisited

By a sequence of rollings without slipping or twisting along segments of a straight line of the plane, a spherical ball of unit radius has to be transferred from an initial state to an arbitrary final state taking into account the orientation of the ball. We provide a new proof that with at most 3 moves, we can go from a given initial state to an arbitrary final state. The first proof of this result is due to Hammersley ( 1983). His proof is more algebraic than ours which is more geometric. We also showed that generically no one of the three moves, in any elimination of the spin discrepancy, may have length equal to an integral multiple of 2 pi.

A theoretical characterization of scaling properties in a bouncing ball system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)