Aspectos dinâmicos de espalhamento caótico clássico / Dynamical aspects of classical scattering

AUTOR(ES)
DATA DE PUBLICAÇÃO

2009

RESUMO

In this thesis we study different scattering systems with chaos. Chaotic scattering, present in a large variety of physical systems, is a type of transient chaos. While the phase-space of such systems is unbounded, irregular motion occurs only in a bounded area, called the scattering region. Still, any (nontrivial) scattering function relating initial conditions to asymptotic variables contains fractal structures, resulting in a very sharp sensitivity to initial conditions. Our first work shows that bifurcations leading to chaos manifest themselves through an infinitely fine-scale structure of rainbow singularities in the cross section. These singularities appear as cascades, mirroring the bifurcation cascade undergone by the chaotic saddle. The second work shows that the presence of dissipation in scattering systems can limit the auto-similarity of originally fractal structures. Depending on the value of their energy, particles scattered by repulsive potentials find forbidden regions in the space-phase. These regions determinate the structure of the chaotic saddle. With friction, the scenario of trapped orbits changes and, depending on the ammount dissipation, scattering functions follow a truncated fractal structure. Our third study concerns the presence of chaotic advection in blood flows. Typically, circulatory diseases are due to sudden changes on the geometry of vessel walls. These deformations can generate chaotic scattering of blood particles carried by the flow. We show, with numerical simulations, that chaos can occur in blood flows and thus form a hazardous cycle in the further developing of circulatory anomalies.

ASSUNTO(S)

dinamical systems physics chaos hamiltonian systems sistemas hamiltonianos sistemas dinâmicos física caos

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