Locating invariant tori for a family of two-dimensional Hamiltonian mappings

The location of invariant tori for a two-dimensional Hamiltonian mapping exhibiting mixed phase space is discussed. The phase space of the mapping shows a large chaotic sea surrounding periodic islands and limited by a set of invariant tori. Given the mapping considered is parameterised by an exponent γ in one of the dynamical variables, a connection with the standard mapping near a transition from local to global chaos is used to estimate the position of the invariant tori limiting the size of the chaotic sea for different values of the parameter γ. © 2011 Elsevier B.V. All rights reserved.

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)

Propriedades de escala de um guia de ondas periodicamente corrugado

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelo estatístico de rede de resistores para o estudo de processos de condução em nanocompósitos poliméricos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dynamical properties of a dissipative discontinuous map: A scaling investigation

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

Time-dependent properties in two-dimensional and Hamiltonian mappings

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Scaling properties and universality in a ratchet system

Critical exponents that describe a transition from unlimited to limited diffusion for a ratchet system are obtained analytically and numerically. The system is described by a two dimensional nonlinear mapping with three relevant control parameters. Two of them control the non-linearity while the third one controls the intensity of the dissipation. Chaotic attractors appear in the phase space due to the dissipation and considering large non-linearity are characterised by the use of Lyapunov exponents. The critical exponents are used to overlap different curves of average momentum (dynamical variable) onto a single plot confirming a scale invariance. The formalism used is general and the procedure can be extended to different systems.

Expoentes de escala para mapeamentos discretos bidimensionais

Pós-graduação em Física - IGCE

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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Monte Carlo study of the anisotropic N=3 Ashkin-Teller model

The phase diagram of an asymmetric N = 3 Ashkin-Teller model is obtained by a numerical analysis which combines Monte Carlo renormalization group and reweighting techniques. Present results reveal several differences with those obtained by mean-field calculations and a Hamiltonian approach. In particular, we found Ising critical exponents along a line where Goldschmidt has located the Kosterlitz-Thouless multicritical point. On the other hand, we did find nonuniversal exponents along another transition line. Symmetry breaking in this case is very similar to the N = 2 case, since the symmetries associated to only two of the Ising variables are broken. However, for large values of the coupling constant ratio XW = W/K, when the only broken symmetry is of a hidden variable, we detected first-order phase transitions giving evidence supporting the existence of a multicritical point, as suggested by Goldschmidt, but in a different region of the phase diagram. © 2002 Elsevier Science B.V. All rights reserved.

Termodinâmica do modelo Bouncer: um gás unidimensional simplificado

Pós-graduação em Física - IGCE