In this paper we test the hypothesis that q-exponential distribution fits better on distributions arising from lattices with a heterogeneous topology than a homogeneous topology. We compare two lattices: the first is the typical square lattice with a constant occupation density p (the lattice used in standard percolation theory), and the second is a lattice constructed with a gradient of p. In the homogeneous lattice the occupied number of neighbors of each cell is the same (on average) for the full lattice, otherwise in the p-gradient lattice this number changes along the lattice. In this sense the p-gradient lattice shows a more complex topology than the homogeneous lattice. We fit the q-exponential and the stretched exponential distribution on the cluster size distribution that arises in the lattices. We observe that the q-exponential fits better on the p-gradient lattice than on a constant p lattice. On the other hand, the stretched exponential distribution fits equally well on both lattices.

En este trabajo se prueba la hipotesis de que la distribución q-exponencial se adapta mejor en distribuciones derivadas de redes con una topología heterogenea que en una topología homogenea. Se comparan dos redes: la primera es la típica red cuadrada con una densidad de ocupación constante p (la red estandar de la percolación), y la segunda es una red construida con un gradiente de ocupación p. En la red homogénea, el número de vecinos ocupados de cada celda es el mismo (en promedio), pero por otro lado, en la red con p-gradiente, este número sufre cambio a lo largo de la red. En este sentido, la p-gradiente red muestra una topología mas compleja que la red homegénea. Nos ajustamos la q-exponencial y la distribucion exponencial estirada sobre la distribución de clusters de las redes. Observamos que la q-exponencial encaja mejor en la red p-gradiente que en una red con p constante. Por otro lado, la distribución exponencial estirada encaja bien en ambas redes.

We use a set of evoked words to define the vertices of a network. The connections between vertices are established by individuals in a population that evoke these words. The resulting graph is called an Evoked Words Network, EWN. The data of evoked words comes from an epidemiological research in odontological public health. In this research we consider three concept themes or evocative words: mouth, disease, and health. We investigate these words in two populations: an upper middle class and a poor district of the city of Natal. We compare and analyze six EWNs. The distribution of connectivities of all of these EWNs indicates a scale-free structure, with the data fitting a power law. The analyzed quantities of the EWNs depend more on the concept theme than on the income of population. This conclusion is discussed in the context of language-based networks.

Recently a multifractal object, Qmf, was proposed to allow the study of percolation properties in a multifractal support. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. The value of the probability of occupation at the percolation threshold, p c, is a function of r, a parameter of Qmf which is related to its anisotropy. We investigate the relation between p c and the average number of neighbors of the blocks as well as the anisotropy of Qmf.

Neste trabalho desenvolvemos um programa educativo versando sobre modos normais em uma cadeia de osciladores acoplados. O usuário do programa pode simular a evolução dinâmica de uma cadeia de osciladores escolhendo condições iniciais tanto em coordenadas cartesianas como em coordenadas normais. Focalizamos o efeito do desacoplamento do sistema de equações diferenciais (passagem de coordenadas cartesianas para coordenadas normais) sobre as trajetórias dos osciladores do ponto de vista da dinâmica qualitativa. Através das características da evolução dinâmica, quase-periodicidade ou periodicidade, o estudante ganha intuição sobre o significado das formas normais.

In this work we develop an educational software about normal modes in a chain of coupled oscillators. The software simulates the dynamical evolution of the system allowing to choose initial conditions in cartesian coordinates or in normal modes. We focus on the effect of decoupling the system of differential equations (transition from cartesian coordinates to normal modes) in the qualitative dynamics of the oscillators, either in the quasiperiodic or in the periodic regime. The purpose is to give the student some insights about the meaning of the normal modes.