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.

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.

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.

A theoretical characterization of scaling properties in a bouncing ball system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Transport and dynamical properties for a bouncing ball model with regular and stochastic perturbations

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

Global ballistic acceleration in a bouncing-ball model

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

Breaking down the Fermi acceleration with inelastic collisions

The phenomenon of Fermi acceleration is addressed for a dissipative bouncing ball model with external stochastic perturbation. It is shown that the introduction of energy dissipation (inelastic collisions of the particle with the moving wall) is a sufficient condition to break down the process of Fermi acceleration. The phase transition from bounded to unbounded energy growth in the limit of vanishing dissipation is characterized.

Parameter space for a dissipative Fermi-Ulam model

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

Preparation of Ni-Ti-Mo and Ni-Ti-Mo-Zr Alloys by High-Energy Ball Milling and Subsequent Hot Pressing

This work discusses on the preparation of Ni-45Ti-5Mo, Ni-40Ti-10Mo and Ni-46Ti-2Mo-2Zr (at-%) alloys by high-energy ball milling and hot pressing, which are potentially attractive for dental and medical applications. The milling process was performed in stainless steel balls (19mm diameter) and vials (225 mL) using a rotary speed of 300rpm and a ball-to-powder weight ratio of 10:1. Hot pressing under vacuum was performed in a BN-coated graphite crucible at 900 degrees C for 1 h using a load of 20 MPa. The milled and hot-pressed materials were characterized by X-ray diffraction, electron scanning microscopy, and electron dispersive spectrometry. Peaks of B2-NiTi and Ni4Ti3 were identified in XRD patterns of Ni-45Ti-5Mo, Ni-40Ti-10Mo and Ni-46Ti-2Mo-2Zr powders milled for 1h. The NiTi compound dissolved small Mo amounts lower than 4 at%, which were measured by EDS analysis. Moreover, it was identified the existence of an unknown Mo-rich phase in microstructures of the hot-pressed Ni-Ti-Mo alloys.

Preparation of Al2TiO5-Al2O3 and Al2TiO5-Al2O3-TiO2 Ceramics by High-Energy Ball Milling and Sintering

The present work reports on the preparation of Al2O3-TiO2 ceramics by high-energy ball milling and sintering, varying the molar fraction in 1:1 and 3:1. The powder mixtures were processed in a planetary Fritsch P-5 ball mill using silicon nitride balls (10 mm diameter) and vials (225 mL), rotary speed of 250 rpm and a ball-to-powder weight ratio of 5:1. Samples were collected into the vial after different milling times. The milled powders were uniaxially compacted and sintered at 1300 and 1500 degrees C for 4h. The milled and sintered materials were characterized by X-ray diffraction and electron scanning microscopy (SEM). Results indicated that the intensity of Al2O3 and TiO2 peaks were reduced for longer milling times, suggesting that nanosized particles can be achieved. The densification of Al2O3-TiO2 ceramics was higher than 98% over the relative density in samples sintered at 1500 degrees C for 4h, which presented the formation of Al2TiO5.

Effect of acid-ethanol treatment followed by ball milling on structural and physicochemical characteristics of cassava starch

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

GLOBAL DYNAMICS IN THE POINCARE BALL of THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)