1,721,461 research outputs found
Cellular models for river networks
No full textA cellular model introduced for the evolution of the fluvial landscape is revisited using extensive numerical and scaling analyses. The basic network shapes and their recurrence especially in the aggregation structure are then addressed. The roles of boundary and initial conditions are carefully analyzed as well as the key effect of quenched disorder embedded in random pinning of the landscape surface. It is found that the above features strongly affect the scaling behavior of key morphological quantities. In particular, we conclude that randomly pinned regions (whose structural disorder bears much physical meaning mimicking uneven landscape-forming rainfall events, geological diversity or heterogeneity in surficial properties like vegetation, soil cover or type) play a key role for the robust emergence of aggregation patterns bearing much resemblance to real river networks
Mean field theory for ordinary and hot sandpiles
No full textA mean field theory is discussed for a sandpile model, a cellular automaton prototype of systems showing self-organized criticality. The previous formulation of the mean field does not take into account the dissipation effects that take place on boundaries. This gives rise to some inconsistencies that are eliminated by carefully considering the boundaries effects, as it is shown in this paper. We present here a revised version of the MF equations. The main result is that criticality arises in the thermodynamic limit for sandpile systems, confirming numerical observations on the behavior of the order parameter.
The mean field approach is also generalized by applying it to the more general case of sandpiles in thermal equilibrium where a temperature-like parameter T is introduced. In this case we show that criticality is not destroyed at T> 0
Complex Networks: Principles, Methods and Applications by Vito Latora, Vincenzo Nicosia and Giovanni Russo
No full textInvasion percolation and the time scaling behavior of a queuing model of human dynamics
No full textIn this paper we study the properties of the Barabási model of queuing under the hypothesis that the number of tasks is steadily growing in time. We map this model exactly onto an invasion percolation dynamics on a Cayley tree. This allows us to recover the correct waiting time distribution PW(τ)~τ−3/2 at the stationary state (as observed in different realistic data) and also to characterize it as a sequence of causally and geometrically connected bursts of activity. We also find that the approach to stationarity is very slow
Fixed scale transformation approach for born model of fractures
No full textWe use the Fixed Scale Transformation theoretical approach to study the problem of fractal growth in fractures generated by using the Born Model. In this case the application of the method is more complex because of the vectorial nature of the model considered. In particular, one needs a careful choice of the lattice path integral for the fracture evolution and the identification of the appropriate way to take effectively into account screening effects. The good agreement of our results with computer simulations shows the validity and flexibility of the FST method in the study of fractal patterns evolution
The corporate boards networks
No full textIn this work we apply network theory to detect in a quantitative fashion some of the characters of the system composed by companies and their boards of directors. Modelling this as a bipartite graph, we can derive two networks (one for the companies and one for the directors) and apply to them the standard graph analysis instruments. The emerging picture shows an environment where the exchange of information and mutual influences, conveyed by interlocks between boards, is predominant. Such a result should be taken into account when modelling this system
Invasion percolation and critical transient in the Barabási Model of human dynamics
Full text linkWe introduce an exact probabilistic description for L=2 of the Barabási model for the dynamics of a list of L tasks. This permits us to study the problem out of the stationary state and to solve explicitly the extremal limit case where a critical behavior for the waiting time distribution is observed. This behavior deviates at any finite time from that of the stationary state. We study also the characteristic relaxation time for finite time deviations from stationarity in all cases showing that it diverges in the extremal limit, confirming that these deviations are important at all time
Self-affine properties of fractures in brittle materials
No full textWe present the result of numerical simulations for a fracturing process in a three-dimensional solid subjected to a mode-I load in a quasi-static regime. The solid is described using the Born model on an FCC lattice with a starting notch. We obtain a value of the roughness exponent ζ≈0.5 in agreement with the value measured in microfracturing experiments. Our result supports the idea that at small length scales the fracturing process can be considered as quasi-static, which is the basic of the possible application of the model of line depinning to the case of fractures
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