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Maya Paczuski

Publications and source records attributed to Maya Paczuski.

70 records · Page 4Linked to original sources
arXiv1999

Braided Rivers and Superconducting Vortex Avalanches

Magnetic vortices intermittently flow through preferred channels when they are forced in or out of a superconductor. We study this behavior using a cellular model, and find that the vortex flow can make braided rivers strikingly similar to aerial photographs of braided fluvial rivers, such as the Brahmaputra. By developing an analysis technique suitable for characterizing a self-affine (multi)fractal, the scaling properties of the braided vortex rivers in the model are compared with those of braided fluvial rivers. We suggest that avalanche dynamics leads to braiding in both cases.

cond-mat.stat-mech↗
arXiv1999

Avalanche Merging and Continuous Flow in a Sandpile Model

A dynamical transition separating intermittent and continuous flow is observed in a sandpile model, with scaling functions relating the transport behaviors between both regimes. The width of the active zone diverges with system size in the avalanche regime but becomes very narrow for continuous flow. The change of the mean slope, Delta z, on increasing the driving rate, r, obeys Delta z ~ r^{1/theta}. It has nontrivial scaling behavior in the continuous flow phase with an exponent theta given, paradoxically, only in terms of exponents characterizing the avalanches theta = (1+z-D)/(3-D).

cond-mat.stat-mech↗
arXiv1999

Self-Organization of Complex Systems

The basic laws of physics are simple, so why is the world complex? The theory of self-organized criticality posits that complex behavior in nature emerges from the dynamics of extended, dissipative systems that evolve through a sequence of meta-stable states into a critical state, with long range spatial and temporal correlations. Minor disturbances lead to intermittent events of all sizes. These events organize the system into a complex state that cannot be reduced to a few degrees of freedom. This type of ``punctuated equilibrium'' dynamics has been observed in astrophysical, geophysical, and biological processes, as well as in human social activity.

cond-mat.stat-mech↗
arXiv1998

Simple Model of Large Scale Organization in Evolution

A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age, confirming a general relation between Age and Area proposed by Willis. The ecology exhibits punctuated equilibrium. Analytic and numerical results show that the probability distribution of genera sizes, genera lifetimes, and extinction event sizes are the same power law $P(x) \sim 1/x^2$, consistent with paleontological data.

cond-mat↗
arXiv1998

A Simple Model of Superconducting Vortex Avalanches

We introduce a simple lattice model of superconducting vortices driven by repulsive interactions through a random pinning potential. The model describes the behavior at the scale of the London length lambda or larger. It self-organizes to a critical state, characterized by a constant flux density gradient, where the activity takes place in terms of avalanches spanning all length scales up to the system size. We determine scaling relations as well as four universal critical exponents for avalanche moments and durations: tau = 1.63 +/- 0.02, D = 2.7 +/- 0.1, z = 1.5 +/- 0.1, and tau_t = 2.13 +/- 0.14, for the system driven at the boundary.

cond-mat.stat-mech↗
arXiv1997

Avalanches and Waves in the Abelian Sandpile Model

We numerically study avalanches in the two dimensional Abelian sandpile model in terms of a sequence of waves of toppling events. Priezzhev et al [PRL 76, 2093 (1996)] have recently proposed exact results for the critical exponents in this model based on the existence of a proposed scaling relation for the difference in sizes of subsequent waves, $Δs =s_{k}- s_{k+1}$, where the size of the previous wave $s_{k}$ was considered to be almost always an upper bound for the size of the next wave $s_{k+1}$. Here we show that the significant contribution to $Δs$ comes from waves that violate the bound; the average $<Δs(s_{k})>$ is actually negative and diverges with the system size, contradicting the proposed solution.

cond-mat.stat-mech↗
arXiv1997

Aging in a Model of Self-Organized Criticality

Temporal autocorrelation functions for avalanches in the Bak-Sneppen model display aging behavior similar to glassy systems. Numerical simulations show that they decay as power laws with two distinct regimes separated by a time scale which is the waiting time, or age, of the avalanche. Thus, time-translational invariance is dynamically broken. The critical exponent of the initial decay is that of the familiar stationary dynamics while a new critical exponent for the late-time behavior appears. This new exponent characterizes a non-stationary regime that has not been previously considered in the context of self-organized criticality.

cond-mat↗
arXiv1996

Transport in Sand Piles, Interface Depinning, and Earthquake Models

Recent numerical results for a model describing dispersive transport in rice piles are explained by mapping the model to the depinning transition of an interface that is dragged at one end through a random medium. The average velocity of transport vanishes with system size $L$ as $ \sim L^{2-D}\sim L^{-0.23}$, and the avalanche size distribution exponent $τ= 2 - 1/D \simeq 1.55$, where $D\simeq 2.23$ from interface depinning. We conjecture that the purely deterministic Burridge-Knopoff ``train'' model for earthquakes is in the same universality class.

cond-mat↗
arXiv1996

Continuum Theory with Memory for Avalanches in Self-Organized Criticality

The propagator for the activity in a broad class of self-organized critical models obeys an imaginary-time Schrödinger equation with a nonlocal, history-dependent potential representing memory. Consequently, the probability for an avalanche to spread beyond a distance $r$ in time $t$ has an anomalous tail $\exp{[-C\,x^{1/(D-1)}]}$ for $x=r^D/t \gg 1$ and $D>2$, indicative of glassy dynamics. The theory is verified for an exactly solvable model, where $D=4$ and $C=3/4$, and for the Bak-Sneppen model where it is tested numerically.

cond-mat↗
arXiv1996

Ultrametricity and Memory in a Solvable Model of Self-Organized Criticality

Slowly driven dissipative systems may evolve to a critical state where long periods of apparent equilibrium are punctuated by intermittent avalanches of activity. We present a self-organized critical model of punctuated equilibrium behavior in the context of biological evolution, and solve it in the limit that the number of independent traits for each species diverges. We derive an exact equation of motion for the avalanche dynamics from the microscopic rules. In the continuum limit, avalanches propagate via a diffusion equation with a nonlocal, history-dependent potential representing memory. This nonlocal potential gives rise to a non-Gaussian (fat) tail for the subdiffusive spreading of activity. The probability for the activity to spread beyond a distance $r$ in time $s$ decays as $\sqrt{24\overπ}s^{-3/2}x^{1/3} \exp{[-{3\over 4}x^{1/3}]}$ for $x={r^4\over s} \gg 1$. The potential represents a hierarchy of time scales that is dynamically generated by the ultrametric structure of avalanches, which can be quantified in terms of ``backward'' avalanches. In addition, a number of other correlation functions characterizing the punctuated equilibrium dynamics are determined exactly.

cond-mat↗
arXiv1996

Avalanche Dynamics of Crack Propagation and Contact Line Depinning

A model for crack propagation and contact line depinning is studied. Although the model contains nonlocal interactions, it obeys general scaling relations for depinning via localized bursts or avalanches. Our numerical result for the roughness exponent in one dimension, $χ=0.49 \pm 0.05$, agrees with recent experiments on cracks measuring the in-plane roughness $χ\simeq 0.5 - 0.6$, as well as mean field arguments giving $χ=1/2$, but is significantly higher than the functional renormalization group prediction $χ= 1/3$.

cond-mat↗
arXiv1996

Self-Organized Criticality and $1/f$ Noise in Traffic

Phantom traffic jams may emerge ``out of nowhere'' from small fluctuations rather than being triggered by large, exceptional events. We show how phantom jams arise in a model of single lane highway traffic, which mimics human driving behavior. Surprisingly, the optimal state of highest efficiency, with the largest throughput, is a critical state with traffic jams of all sizes. We demonstrate that open systems self-organize to the most efficient state. In the model we study, this critical state is a percolation transition for the phantom traffic jams. At criticality, the individual jams have a complicated fractal structure where cars follow an intermittent stop and go pattern. We analytically derive the form of the corresponding power spectrum to be $1/f^α$ with $α=1$ exactly. This theoretical prediction agrees with our numerical simulations and with observations of $1/f$ noise in real traffic.

cond-mat↗
arXiv1996

Mass Extinctions vs. Uniformitarianism in Biological Evolution

It is usually believed that Darwin's theory leads to a smooth gradual evolution, so that mass extinctions must be caused by external shocks. However, it has recently been argued that mass extinctions arise from the intrinsic dynamics of Darwinian evolution. Species become extinct when swept by intermittent avalanches propagating through the global ecology. These ideas are made concrete through studies of simple mathematical models of coevolving species. The models exhibit self-organized criticality and describe some general features of the extinction pattern in the fossil record.

cond-mat↗
arXiv1995

Exact Results for Spatio-Temporal Correlations in a Self-Organized Critical Model of Punctuated Equilibrium

We introduce a self-organized critical model of punctuated equilibrium with many internal degrees of freedom ($M$) per site. We find exact solutions for $M\rightarrow \infty$ of cascade equations describing avalanche dynamics in the steady state. This proves the existence of simple power laws with critical exponents that verify general scaling relations for nonequilibrium phenomena. Punctuated equilibrium is described by a Devil's staircase with a characteristic exponent, $τ_{FIRST}=2-d/4$ where $d$ is the spatial dimension.

adap-org↗
arXiv1995

Emergent Traffic Jams

We study a single-lane traffic model that is based on human driving behavior. The outflow from a traffic jam self-organizes to a critical state of maximum throughput. Small perturbations of the outflow far downstream create emergent traffic jams with a power law distribution $P(t) \sim t^{-3/2}$ of lifetimes, $t$. On varying the vehicle density in a closed system, this critical state separates lamellar and jammed regimes, and exhibits $1/f$ noise in the power spectrum. Using random walk arguments, in conjunction with a cascade equation, we develop a phenomenological theory that predicts the critical exponents for this transition and explains the self-organizing behavior. These predictions are consistent with all of our numerical results.

adap-org↗