J. S. Andrade

Laws of population growth

An important issue in the study of cities is defining a metropolitan area, because different definitions affect conclusions regarding the statistical distribution of urban activity. A commonly employed method of defining a metropolitan area is the Metropolitan Statistical Areas (MSAs), based on rules attempting to capture the notion of city as a functional economic region, and it is performed by using experience. The construction of MSAs is a time-consuming process and is typically done only for a subset (a few hundreds) of the most highly populated cities. Here, we introduce a method to designate metropolitan areas, denoted “City Clustering Algorithm” (CCA). The CCA is based on spatial distributions of the population at a fine geographic scale, defining a city beyond the scope of its administrative boundaries. We use the CCA to examine Gibrats law of proportional growth, which postulates that the mean and standard deviation of the growth rate of cities are constant, independent of city size. We find that the mean growth rate of a cluster by utilizing the CCA exhibits deviations from Gibrats law, and that the standard deviation decreases as a power law with respect to the city size. The CCA allows for the study of the underlying process leading to these deviations, which are shown to arise from the existence of long-range spatial correlations in population growth. These results have sociopolitical implications, for example, for the location of new economic development in cities of varied size.

Inertial Effects on Fluid Flow through Disordered Porous Media

We investigate the origin of the deviations from the classical Darcy law by numerical simulation of the Navier-Stokes equations in two-dimensional disordered porous media. We apply the Forchheimer equation as a phenomenological model to correlate the variations of the friction factor for different porosities and flow conditions. At sufficiently high Reynolds numbers, when inertia becomes relevant, we observe a transition from linear to nonlinear behavior which is typical of experiments. We find that such a transition can be understood and statistically characterized in terms of the spatial distribution of kinetic energy in the system. [S0031-9007(99)09541-1]

Towards Design Principles for Optimal Transport Networks

We investigate the optimal design of networks for a general transport system. Our network is built from a regular two-dimensional (d = 2) square lattice to be improved by adding long-range connections (shortcuts) with probability Pij ∼ r −α ij , where rij is the Euclidean distance between sites i and j, and α is a variable exponent. We introduce a cost constraint on the total length of the additional links and find optimal transport in the system for α = d + 1. Remarkably, this condition remains optimal, regardless of the strategy used for navigation, being based on local or global knowledge of the network structure, in sharp contrast with the results obtained for unconstrained navigation using global or local information, where the optimal conditions are α = 0 and α = d, respectively. The validity of our theoretical results is supported by data on the US airport network, for which α ≈ 3.0 was recently found [Bianconi et al., arXiv:0810.4412 (2008)].

Wind velocity and sand transport on a barchan dune

We present measurements of wind velocity and sand flux performed on the windward side of a large barchan dune in Jericoacoara, northeastern Brazil. From the measured profile, we calculate the air shear stress using an analytical approximation and treat the problem of flow separation by an heuristic model. We find that the results from this approach agree well with our field data. Moreover, using the calculated shear velocity, we predict the sand flux according to well-known equilibrium relations and with a phenomenological continuum saltation model that includes saturation transients and thus allows for nonequilibrium conditions. Based on the field data and theoretical predicted results, we indicate the principal differences between saturated and nonsaturated sand flux models. Finally, we show that the measured dune moves with invariant shape and predict its velocity from our data and calculations.

Spreading gossip in social networks

We study a simple model of information propagation in social networks, where two quantities are introduced: the spread factor, which measures the average maximal reachability of the neighbors of a given node that interchange information among each other, and the spreading time needed for the information to reach such a fraction of nodes. When the information refers to a particular node at which both quantities are measured, the model can be taken as a model for gossip propagation. In this context, we apply the model to real empirical networks of social acquaintances and compare the underlying spreading dynamics with different types of scale-free and small-world networks. We find that the number of friendship connections strongly influences the probability of being gossiped. Finally, we discuss how the spread factor is able to be applied to other situations.

Universality behind Basquin's Law of Fatigue

Basquins law of fatigue states that the lifetime of the system has a power-law dependence on the external load amplitude, tf approximately sigma 0- alpha, where the exponent alpha has a strong material dependence. We show that in spite of the broad scatter of the exponent alpha, the fatigue fracture of heterogeneous materials exhibits universal features. We propose a generic scaling form for the macroscopic deformation and show that at the fatigue limit the system undergoes a continuous phase transition. On the microlevel, the fatigue fracture proceeds in bursts characterized by universal power-law distributions. We demonstrate that the system dependent details are contained in Basquins exponent for time to failure, and once this is taken into account, remaining features of failure are universal.

Aeolian transport layer

We investigate the airborne transport of particles on a granular surface by the saltation mechanism through numerical simulation of particle motion coupled with turbulent flow. We determine the saturated flux q(s) and show that its behavior is consistent with classical empirical relations obtained from wind tunnel measurements. Our results also allow one to propose and explain a new relation valid for small fluxes, namely, q(s) = a(u*-u(t))alpha, where u* and u(t) are the shear and threshold velocities of the wind, respectively, and the scaling exponent is alpha approximately 2. We obtain an expression for the velocity profile of the wind distorted by the particle motion due to the feedback and discover a novel dynamical scaling relation. We also find a new expression for the dependence of the height of the saltation layer as a function of the wind velocity.

How to suppress undesired synchronization

Examples of synchronization can be found in a wide range of phenomena such as neurons firing, lasers cascades, chemical reactions, and opinion formation. However, in many situations the formation of a coherent state is not pleasant and should be mitigated. For example, the onset of synchronization can be the root of epileptic seizures, traffic congestion in networks, and the collapse of constructions. Here we propose the use of contrarians to suppress undesired synchronization. We perform a comparative study of different strategies, either requiring local or total knowledge, and show that the most efficient one solely requires local information. Our results also reveal that, even when the distribution of neighboring interactions is narrow, significant improvement is observed when contrarians sit at the highly connected elements. The same qualitative results are obtained for artificially generated networks and two real ones, namely, the Routers of the Internet and a neuronal network.

Breathing synchronization in interconnected networks

Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a time delay appears in the interaction which might obstruct synchronization. Here we study the synchronization properties of interconnected networks of oscillators with a time delay between networks and analyze the dynamics as a function of the couplings and communication lag. We discover a new breathing synchronization regime, where two groups appear in each network synchronized at different frequencies. Each group has a counterpart in the opposite network, one group is in phase and the other in anti-phase with their counterpart. For strong couplings, instead, networks are internally synchronized but a phase shift between them might occur. The implications of our findings on several socio-technical and biological systems are discussed.

Displacement operator for quantum systems with position-dependent mass

A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique commutation relation for x and p{sub {gamma}}. Such a formalism naturally leads to a Schroedinger-like equation that is reminiscent of wave equations typically used to model electrons with position-dependent (effective) masses propagating through abrupt interfaces in semiconductor heterostructures. The distinctive features of our approach are demonstrated through analytical solutions calculated for particles under null and constant potentials like infinite wells in one and two dimensions and potential barriers.