Pendular behavior of public transport networks.

In this paper, we propose a methodology that bears close resemblance to the Fourier analysis of the first harmonic to study networks subjected to pendular behavior. In this context, pendular behavior is characterized by the phenomenon of people's dislocation from their homes to work in the morning and people's dislocation in the opposite direction in the afternoon. Pendular behavior is a relevant phenomenon that takes place in public transport networks because it may reduce the overall efficiency of the system as a result of the asymmetric utilization of the system in different directions. We apply this methodology to the bus transport system of Brasília, which is a city that has commercial and residential activities in distinct boroughs. We show that this methodology can be used to characterize the pendular behavior of this system, identifying the most critical nodes and times of the day when this system is in more severe demanded.

Analysis of etching at a solid-solid interface.

We present a method to derive an analytical expression for the roughness of an eroded surface whose dynamics are ruled by cellular automaton. Starting from the automaton, we obtain the time evolution of the height average and height variance (roughness). We apply this method to the etching model in 1+1 dimensions, and then we obtain the roughness exponent. Using this in conjunction with the Galilean invariance we obtain the other exponents, which perfectly match the numerical results obtained from simulations. These exponents are exact, and they are the same as those exhibited by the Kardar-Parisi-Zhang (KPZ) model for this dimension. Therefore, our results provide proof for the conjecture that the etching and KPZ models belong to the same universality class. Moreover, the method is general, and it can be applied to other cellular automata models.

Physiological aging as an infinitesimally ratcheted random walk.

The distribution of a population throughout the physiological age of the individuals is very relevant information in population studies. It has been modeled by the Langevin and the Fokker-Planck equations. A major problem with these equations is that they allow the physiological age to move back in time. This paper proposes an Infinitesimally ratcheted random walk as a way to solve that problem. Two mathematical representations are proposed. One of them uses a nonlocal scalar field. The other one is local, but involves a multicomponent field of speed states. These two formulations are compared to each other and to the Fokker-Planck equation. The relevant properties are discussed. The dynamics of the mean and variance of the population age resulting from the two proposed formulations are obtained.

Effects of receptor interaction in bacterial chemotaxis.

Signaling in bacterial chemotaxis is mediated by several types of transmembrane chemoreceptors. The chemoreceptors form tight polar clusters whose functions are of great biological interest. Here, we study the general properties of a chemotaxis model that includes interaction between neighboring chemoreceptors within a receptor cluster and the appropriate receptor methylation and demethylation dynamics to maintain (near) perfect adaptation. We find that, depending on the receptor coupling strength, there are two steady-state phases in the model: a stationary phase and an oscillatory phase. The mechanism for the existence of the two phases is understood analytically. Two important phenomena in transient response, the overshoot in response to a pulse stimulus and the high gain in response to sustained changes in external ligand concentrations, can be explained in our model, and the mechanisms for these two seemingly different phenomena are found to be closely related. The model also naturally accounts for several key in vitro response experiments and the recent in vivo fluorescence resonance energy transfer experiments for various mutant strains. Quantitatively, our study reveals possible choices of parameters for fitting the existing experiments and suggests future experiments to test the model predictions.