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

The dynamics of a driven stadium-like billiard is considered using the formalism of discrete mappings. The model presents a resonant velocity that depends on the rotation number around fixed points and external boundary perturbation which plays an important separation rule in the model. We show that particles exhibiting Fermi acceleration (initial velocity is above the resonant one) are scaling invariant with respect to the initial velocity and external perturbation. However, initial velocities below the resonant one lead the particles to decelerate therefore unlimited energy growth is not observed. This phenomenon may be interpreted as a specific Maxwell's Demon which may separate fast and slow billiard particles. (C) 2012 Elsevier B.V. All rights reserved.

Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard

The behavior of the average energy for an ensemble of non-interacting particles is studied using scaling arguments in a dissipative time-dependent stadium-like billiard. The dynamics of the system is described by a four dimensional nonlinear mapping. The dissipation is introduced via inelastic collisions between the particles and the moving boundary. For different combinations of initial velocities and damping coefficients, the long time dynamics of the particles leads them to reach different states of final energy and to visit different attractors, which change as the dissipation is varied. The decay of the average energy of the particles, which is observed for a large range of restitution coefficients and different initial velocities, is described using scaling arguments. Since this system exhibits unlimited energy growth in the absence of dissipation, our results for the dissipative case give support to the principle that Fermi acceleration seems not to be a robust phenomenon. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3699465]

Scaling invariance for the escape of particles from a periodically corrugated waveguide

The escape dynamics of a classical light ray inside a corrugated waveguide is characterised by the use of scaling arguments. The model is described via a two-dimensional nonlinear and area preserving mapping. The phase space of the mapping contains a set of periodic islands surrounded by a large chaotic sea that is confined by a set of invariant tori. When a hole is introduced in the chaotic sea, letting the ray escape, the histogram of frequency of the number of escaping particles exhibits rapid growth, reaching a maximum value at n(p) and later decaying asymptotically to zero. The behaviour of the histogram of escape frequency is characterised using scaling arguments. The scaling formalism is widely applicable to critical phenomena and useful in characterisation of phase transitions, including transitions from limited to unlimited energy growth in two-dimensional time varying billiard problems. (C) 2011 Elsevier B.V. All rights reserved.

O desenho no processo projetivo: estudo das representações gráficas de projetos de Paulo Mendes da Rocha

Há anos vem-se questionando o papel da representação gráfica na arquitetura, diante das novas tecnologias gráficas computacionais e novos processos projetivos delas decorrentes. Entretanto, o desenho à mão livre ainda se mostra atuante no processo projetivo, marcado por um olhar atento, uma percepção individual e um tempo de execução que permite imersão, entrega e reflexão. Este artigo apresenta uma análise a partir de um olhar mais atento ao desenho de projetos do arquiteto Paulo Mendes da Rocha, como contribuição para a discussão sobre o papel do desenho analógico no processo projetivo. Foram selecionados alguns projetos do arquiteto: Projeto para o Concurso de remodelação do centro urbano de Santiago (Chile); Estádio Serra Dourada; Edifício Jaraguá, Caetano de Campos; Ginásio do Clube Atlético Paulistano (1958); Residência no Butantã (1964); residência Fernando Millan (1970) e Museu Brasileiro da Escultura (1986). Este artigo apresenta estudos de leitura sobre os desenhos originais do arquiteto com o objetivo de detectar as intenções projetuais, conceitos e características do projeto. Foram feitas marcações gráficas sobre os desenhos originais, evidenciando uma leitura particular do pesquisador que permitiu uma melhor compreensão dos projetos.