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Register a new userConvergence dynamics of 2-dimensional isotropic and anisotropic Bak-Sneppen models
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The conventional Hamming distance measurement captures only the short-time dynamics of the displacement between the uncorrelated random configurations. The minimum difference technique introduced by Tirnakli and Lyra [Int. J. Mod. Phys. C 14, 805 (2003)] is used to study the short-time and long-time dynamics of the two distinct random configurations of the isotropic and anisotropic Bak-Sneppen models on a square lattice. Similar to 1-dimensional case, the time evolution of the displacement is intermittent. The scaling behavior of the jump activity rate and waiting time distribution reveal the absence of typical spatial-temporal scales in the mechanism of displacement jumps used to quantify the convergence dynamics.
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We implement the damage spreading technique on 2-dimensional isotropic and anisotropic Bak-Sneppen models. Our extensive numerical simulations show that there exists a power-law sensitivity to the initial conditions at the statistically stationary state (self-organized critical state). Corresponding growth exponent $alpha$ for the Hamming distance and the dynamical exponent $z$ are calculated. These values allow us to observe a clear data collapse of the finite size scaling for bo
The short-time and long-time dynamics of the Bak-Sneppen model of biological evolution are investigated using the damage spreading technique. By defining a proper Hamming distance measure, we are able to make it exhibits an initial power-law growth which, for finite size systems, is followed by a decay towards equilibrium. In this sense, the dynamics of self-organized critical states is shown to be similar to the one observed at the usual critical point of continuous phase-transitions and at the onset of chaos of non-linear low-dimensional dynamical maps. The transient, pre-asymptotic and asymptotic exponential relaxation of the Hamming distance between two initially uncorrelated equilibrium configurations is also shown to be fitted within a single mathematical framework. A connection with nonextensive statistical mechanics is exhibited.
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The dynamics of entanglement in the one-dimensional spin-1/2 anisotropic XXZ model is studied using the quantum renormalization-group method. We obtain the analytical expression of the concurrence, for two different quenching methods, it is found that initial state plays a key role in the evolution of system entanglement, i.e., the system returns completely to the initial state every other period. Our computations and analysis indicate that the first derivative of the characteristic time at which the concurrence reaches its maximum or minimum with respect to the anisotropic parameter occurs nonanalytic behaviors at the quantum critical point. Interestingly, the minimum value of the first derivative of the characteristic time versus the size of the system exhibits the scaling behavior which is the same as the scaling behavior of the system ground-state entanglement in equilibrium. In particular, the scaling behavior near the critical point is independent of the initial state.
We propose a 2-dimensional cellular automaton model to simulate pedestrian traffic. It is a vmax=1 model with exclusion statistics and parallel dynamics. Long-range interactions between the pedestrians are mediated by a so called floor field which modifies the transition rates to neighbouring cells. This field, which can be discrete or continuous, is subject to diffusion and decay. Furthermore it can be modified by the motion of the pedestrians. Therefore the model uses an idea similar to chemotaxis, but with pedestrians following a virtual rather than a chemical trace. Our main goal is to show that the introduction of such a floor field is sufficient to model collective effects and self-organization encountered in pedestrian dynamics, e.g. lane formation in counterflow through a large corridor. As an application we also present simulations of the evacuation of a large room with reduced visibility, e.g. due to failure of lights or smoke.
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