Nonlinear Sciences

We demonstrate that a local mapping f in a space of bisequences over {0,1} which conserves the number of nonzero sites can be viewed as a deterministic particle system evolving according to a local mapping in a space of increasing bisequences over Z. We present an algorithm for determination of the local mapping in the space of particle coordinates corresponding to the local mapping f.

Using a stochastic cellular automaton model for urban traffic flow, we study and compare Macroscopic Fundamental Diagrams (MFDs) of arterial road networks governed by different types of adaptive traffic signal systems, under various boundary conditions. In particular, we simulate realistic signal systems that include signal linking and adaptive cycle times, and compare their performance against a highly adaptive system of self-organizing traffic signals which is designed to uniformly distribute the network density. We find that for networks with time-independent boundary conditions, well-defined stationary MFDs are observed, whose shape depends on the particular signal system used, and also on the level of heterogeneity in the system. We find that the spatial heterogeneity of both density and flow provide important indicators of network performance. We also study networks with time-dependent boundary conditions, containing morning and afternoon peaks. In this case, intricate hysteresis loops are observed in the MFDs which are strongly correlated with the density heterogeneity. Our results show that the MFD of the self-organizing traffic signals lies above the MFD for the realistic systems, suggesting that by adaptively homogenizing the network density, overall better performance and higher capacity can be achieved.

Based on complex network theory, we propose a computational methodology that addresses the spatial distribution of fuel breaks for the inhibition of the spread and size of wildland fires on heterogeneous landscapes. This is a two-tire approach where the dynamics of fire spread are modeled as a random Markov field process on a directed network whose edge weights, are provided by a state-of-the-art cellular automata model that integrates detailed GIS, landscape and meteorological data. Within this framework, the spatial distribution of fuel breaks is reduced to the problem of finding the network nodes among which the fire spreads faster, thus their removal favours the inhibition of the fire propagation. Here this is accomplished exploiting the information centrality statistics. We illustrate the proposed approach through (a) an artificial forest of randomly distributed density of vegetation, and (b) a real-world case concerning the island of Rhodes in Greece whose a major part of its forest burned in 2008. Simulation results show that the methodology outperforms significantly the benchmark tactic of random distribution of fuel breaks.

The nature of distributed computation has often been described in terms of the component operations of universal computation: information storage, transfer and modification. We review the first complete framework that quantifies each of these individual information dynamics on a local scale within a system, and describes the manner in which they interact to create non-trivial computation where "the whole is greater than the sum of the parts". We describe the application of the framework to cellular automata, a simple yet powerful model of distributed computation. This is an important application, because the framework is the first to provide quantitative evidence for several important conjectures about distributed computation in cellular automata: that blinkers embody information storage, particles are information transfer agents, and particle collisions are information modification events. The framework is also shown to contrast the computations conducted by several well-known cellular automata, highlighting the importance of information coherence in complex computation. The results reviewed here provide important quantitative insights into the fundamental nature of distributed computation and the dynamics of complex systems, as well as impetus for the framework to be applied to the analysis and design of other systems.

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.

A one-dimensional two-state number-conserving cellular automaton (NCCA) is a cellular automaton whose states are 0 or 1 and where cells take states 0 and 1 and updated their states by the rule which keeps overall sum of states constant. It can be regarded as a kind of particle based modeling of physical systems and has another intuitive representation, motion representation, based on the movement of each particle. We introduced a kind of hierarchical interpretation of motion representations to understand the necessary pattern size to each motion. We show any NCCA of its neighborhood size n can be hierarchically represented by NCCAs of their neighborhood size from n-1 to 1.

We propose a novel multi-layered nonlinear model that is able to capture and predict the housing-demographic dynamics of the real-state market by simulating the transitions of owners among price-based house layers. This model allows us to determine which parameters are most effective to smoothen the severity of a potential market crisis. The International Monetary Fund (IMF) has issued severe warnings about the current real-state bubble in the United States, the United Kingdom, Ireland, the Netherlands, Australia and Spain in the last years. Madrid (Spain), in particular, is an extreme case of this bubble. It is, therefore, an excellent test case to analyze housing dynamics in the context of the empirical data provided by the Spanish National Institute of Statistics and other sources of data. The model is able to predict the mean house occupancy, and shows that i) the house market conditions in Madrid are unstable but not critical; and ii) the regulation of the construction rate is more effective than interest rate changes. Our results indicate that to accommodate the construction rate to the total population of first-time buyers is the most effective way to maintain the system near equilibrium conditions. In addition, we show that to raise interest rates will heavily affect the poorest housing bands of the population while the middle class layers remain nearly unaffected.

Through an extension of the ultradiscretization for the optimal velocity (OV) model, we introduce an ultradiscretizable traffic flow model, which is a hybrid of the OV and the slow-to-start (s2s) models. Its ultradiscrete limit gives a generalization of a special case of the ultradiscrete OV (uOV) model recently proposed by Takahashi and Matsukidaira. A phase transition from free to jam phases as well as the existence of multiple metastable states are observed in numerically obtained fundamental diagrams for cellular automata (CA), which are special cases of the ultradiscrete limit of the hybrid model.

An approach based on a lattice version of the Boltzmann kinetic equation for describing multi-phase flows in nano- and micro-corrugated devices is proposed. We specialize it to describe the wetting/dewetting transition of fluids in presence of nanoscopic grooves etched on the boundaries. This approach permits to retain the essential supra-molecular details of fluid-solid interactions without surrendering -actually boosting- the computational efficiency of continuum methods. The mesoscopic method is first validated quantitatively against Molecular Dynamics (MD) results of Cottin-Bizonne et al. [Nature Mater. 2, 237 (2003)] and then applied to more complex situations which are hardly accessible to MD simulations. The resulting analysis confirms that surface roughness and capillary effects may conspire to promote a counter-intuitive but significant reduction of the flow drag with substantial enhancement in the mass flow rates and slip-lengths in the micrometric range for highly hydrophobic surfaces.

A new kind of cellular automaton (CA) for the study of the dynamics of urban systems is proposed. The state of a cell is not described using a finite set, but by means of continuum variables. A population sector is included, taking into account migration processes from and towards the external world. The transport network is considered through an integration index describing the capability of the network to interconnect the different parts of the city. The time evolution is given by Poisson distributed stochastic jumps affecting the dynamical variables, with intensities depending on the configuration of the system in a suitable set of neighbourhoods. The intensities of the Poisson processes are given in term of a set of potentials evaluated applying fuzzy logic to a practical method frequently used in Switzerland to evaluate the attractiveness of a terrain for different land uses and the related rents. The use of a continuum state space enables one to write a system of differential equations for the time evolution of the CA and thus to study the system from a dynamical systems theory perspective. This makes it possible, in particular, to look systematically for bifurcations and phase transitions in CA based models of urban systems.