One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization. © 2013 American Physical Society.

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.

Estruturas shrimp e propriedades dinâmicas no modelo dissipativo do acelerador de Fermi

Pós-graduação em Física - IGCE

Transições de fase nas dinâmicas de uma partícula se movendo em um poço ou barreira de potencial dependentes periodicamente do tempo

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bilhares dependentes do tempo: um mecanismo para suprimir aceleração de Fermi

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Conseqüencias do arrasto viscoso no modelo Fermi-Ulam

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

Aceleração de Fermi em bilhares com fronteiras dependentes do tempo descritas por osciladores não lineares: caso conservativo e dissipativo

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

Crises de fronteira em aceleradores de Fermi

Pós-graduação em Física - IGCE

A dissipative Fermi-Ulam model under two different kinds of dissipation

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

Propriedades estatísticas de bilhares abertos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Termodinâmica do modelo Bouncer: um gás unidimensional simplificado

Pós-graduação em Física - IGCE

Soliton propagation through a disordered system:statistics of the transmission delay

We have studied the soliton propagation through a segment containing random pointlike scatterers. In the limit of small concentration of scatterers when the mean distance between the scatterers is larger than the soliton width, a method has been developed for obtaining the statistical characteristics of the soliton transmission through the segment. The method is applicable for any classical particle traversing through a disordered segment with the given velocity transformation after each act of scattering. In the case of weak scattering and relatively short disordered segment the transmission time delay of a fast soliton is mostly determined by the shifts of the soliton center after each act of scattering. For sufficiently long segments the main contribution to the delay is due to the shifts of the amplitude and velocity of a fast soliton after each scatterer. Corresponding crossover lengths for both cases of light and heavy solitons have been obtained. We have also calculated the exact probability density function of the soliton transmission time delay for a sufficiently long segment. In the case of weak identical scatterers the latter is a universal function which depends on a sole parameter—the mean number of scatterers in a segment.

Gauge invariance and classical dynamics of noncommutative particle theory

We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed; in particular, the motion in the constant magnetic field is studied in detail. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3299296]

Classical motions from pseudoclassical spin-1/2 particle models

The classical trajectory and spin precessions of Bargmann, Michel, and Telegdi are deduced from a pseudoclassical model of a relativistic spin-(1/2) particle. The corresponding deduction from a non- relativistic model is also given.

Pseudoclassical description for a nonrelativistic spinning particle II. Classical content

The pure classical content of a pseudoclassical nonrelativistic model of a spinning particle is studied. The only physical meaningful world line is the one without "Zitterbewegung." Interactions with external electromagnetic fields are also studied.