arXiv subjects

Maya Paczuski

Publications and source records attributed to Maya Paczuski.

At least 55 records · Page 3Linked to original sources

arXiv2004

Correlated dynamics in human printing behavior

Arrival times of requests to print in a student laboratory were analyzed. Inter-arrival times between subsequent requests follow a universal scaling law relating time intervals and the size of the request, indicating a scale invariant dynamics with respect to the size. The cumulative distribution of file sizes is well-described by a modified power law often seen in non-equilibrium critical systems. For each user, waiting times between their individual requests show long range dependence and are broadly distributed from seconds to weeks. All results are incompatible with Poisson models, and may provide evidence of critical dynamics associated with voluntary thought processes in the brain.

cs.PF↗

arXiv2004

How far away is the next earthquake?

Spatial distances between subsequent earthquakes in southern California exhibit scale-free statistics, with a critical exponent $δ\approx 0.6$, as well as finite size scaling. The statistics are independent of the threshold magnitude as long as the catalog is complete, but depend strongly on the temporal ordering of events, rather than the geometry of the spatial epicenter distribution. Nevertheless, the spatial distance and waiting time between subsequent earthquakes are uncorrelated with each other. These observations contradict the theory of aftershock zone scaling with main shock magnitude.

cond-mat.other↗

arXiv2004

A dynamical model of a GRID market

We discuss potential market mechanisms for the GRID. A complete dynamical model of a GRID market is defined with three types of agents. Providers, middlemen and users exchange universal GRID computing units (GCUs) at varying prices. Providers and middlemen have strategies aimed at maximizing profit while users are 'satisficing' agents, and only change their behavior if the service they receive is sufficiently poor or overpriced. Preliminary results from a multi-agent numerical simulation of the market model shows that the distribution of price changes has a power law tail.

cs.MA↗

arXiv2004

Scaling law for seismic hazard after a main shock

After a large earthquake, the likelihood of successive strong aftershocks needs to be estimated. Exploiting similarities with critical phenomena, we introduce a scaling law for the decay in time following a main shock of the expected number of aftershocks greater than a certain magnitude. Empirical results that support our scaling hypothesis are obtained from analyzing the record of earthquakes in California. The proposed form unifies the well-known Omori and Gutenberg-Richter laws of seismicity, together with other phenomenological observations. Our results substantially modify presently employed estimates and may lead to an improved assessment of seismic hazard after a large earthquake.}

cond-mat.other↗

arXiv2003

A Heavenly Example of Scale Free Networks and Self-Organized Criticality

The sun provides an explosive, heavenly example of self-organized criticality. Sudden bursts of intense radiation emanate from rapid rearrangements of the magnetic field network in the corona. Avalanches are triggered by loops of flux that reconnect or snap into lower energy configurations when they are overly stressed. Our recent analysis of observational data reveals that the loops (links) and footpoints (nodes), where they attach on the photosphere, embody a scale free network. The statistics of the avalanches and of the network structure are unified through a simple dynamical model where the avalanches and network co-generate each other into a complex, critical state. This particular example points toward a general dynamical mechanism for self-generation of complex networks.

cond-mat.stat-mech↗

arXiv2003

Scale free networks of earthquakes and aftershocks

We propose a new metric to quantify the correlation between any two earthquakes. The metric consists of a product involving the time interval and spatial distance between two events, as well as the magnitude of the first one. According to this metric, events typically are strongly correlated to only one or a few preceding ones. Thus a classification of events as foreshocks, main shocks or aftershocks emerges automatically without imposing predefined space-time windows. To construct a network, each earthquake receives an incoming link from its most correlated predecessor. The number of aftershocks for any event, identified by its outgoing links, is found to be scale free with exponent $γ= 2.0(1)$. The original Omori law with $p=1$ emerges as a robust feature of seismicity, holding up to years even for aftershock sequences initiated by intermediate magnitude events. The measured fat-tailed distribution of distances between earthquakes and their aftershocks suggests that aftershock collection with fixed space windows is not appropriate.

cond-mat.stat-mech↗

arXiv2003

Scale-Free Magnetic Networks: Comparing Observational Data with a Self-Organizing Model of the Coronal Field

We propose that the coronal magnetic field, linking concentrations on the photosphere through an interwoven web of flux, embodies a scale-free network. It arises from a self-organized critical dynamics including flux emergence, the diffusion and merging of magnetic concentrations, as well as avalanches of reconnecting flux tubes. Magnetic concentrations such as fragments, pores and sunspots, are `nodes' joined by flux tubes or `links'. The number of links emanating from a node is scale-free. We reanalyze the quiet-Sun data of Close et al and show that the distribution of magnetic concentration strengths is a power law with an index $γ= 1.7 \pm 0.3$, over the entire range of the measurement, about $(2-500)\times 10^{17}$ Mx. This distribution is compatible with that for the sizes of active regions reported by Harvey and Schwaan. Thus magnetic concentrations may be scale-free from the smallest measurable fragments to the large active regions. Numerical simulations of a self-organized critical model give the same index $γ$, within statistical uncertainty. The exponential distribution of flux tube lengths also agrees quantitatively with results from the model. Calibration with the measured diffusion constant of magnetic concentrations allows us to calculate a flux turnover time in the model to be of order 10 hours and the total solar flux to be of order $10^{23}$Mx, agreeing with observations. We introduce two other statistical quantities to characterize scale-free networks. The probability distribution for the amount of flux connecting a pair of concentrations, and the number of distinct concentrations linked to a given one are predicted to be scale-free, with different indices. Our approach unifies the observation of scale free flare energies with the coronal magnetic field structure.

astro-ph↗

arXiv2002

A Nonconservative Earthquake Model of Self-Organized Criticality on a Random Graph

We numerically investigate the Olami-Feder-Christensen model on a quenched random graph. Contrary to the case of annealed random neighbors, we find that the quenched model exhibits self-organized criticality deep within the nonconservative regime. The probability distribution for avalanche size obeys finite size scaling, with universal critical exponents. In addition, a power law relation between the size and the duration of an avalanche exists. We propose that this may represent the correct mean-field limit of the model rather than the annealed random neighbor version.

cond-mat.stat-mech↗

arXiv2002

Luminous matter may arise from a turbulent plasma state of the early universe

The almost perfect uniformity of the cosmic microwave background (CMB) radiation, discovered by Penzias and Wilson in 1965 appears to present clearcut evidence that the universe was uniform and in equilibrium at the decoupling transition when a plasma of protons and electrons condensed into a gas of Hydrogen. COBE indicates that only very small ripples of order 10^{-5} existed at decoupling. Gravity then caused hydrogen to cluster and possibly reheat parts of the universe to form the luminous matter that we observe today. We suggest an alternative scenario, where a spatially intermittent structure of extremely hot matter already existed in an otherwise uniform plasma state at the decoupling transition. The plasma was not in equilibrium but in a very high Reynolds number turbulent state. The sparse bursts would not affect the uniformity of the CMB radiation. Luminous matter originates from localized hot bursts already present in the plasma state prior to decoupling. No reheating, and no exotic matter is needed to get luminous matter.

astro-ph↗

arXiv2001

Flux flow noise and braided rivers of superconducting vortices

Current-voltage measurements of type-II superconductors are described by a coarse-grained model of superconducting vortex dynamics. We find that the power spectra of the voltage fluctuations, and the noise power, are related to the large scale morphology of the plastic flux flow. At currents corresponding to the peak in differential resistance, the flux flow forms a braided river, the noise power is maximal, and the power spectra has a 1/f^α form with α\approx 1.8 over a wide frequency range. This agrees with recent experiments on NbSe_2. The observed variation of αwith applied current is a crossover phenomenon.

cond-mat.stat-mech↗

arXiv2001

Scaling in a Nonconservative Earthquake Model of Self-Organised Criticality

We numerically investigate the Olami-Feder-Christensen model for earthquakes in order to characterise its scaling behaviour. We show that ordinary finite size scaling in the model is violated due to global, system wide events. Nevertheless we find that subsystems of linear dimension small compared to the overall system size obey finite (subsystem) size scaling, with universal critical coefficients, for the earthquake events localised within the subsystem. We provide evidence, moreover, that large earthquakes responsible for breaking finite size scaling are initiated predominantly near the boundary.

cond-mat.stat-mech↗

arXiv2001

Large Scale Structures, Symmetry, and Universality in Sandpiles

We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the avalanches in the self-organized critical state. It does, however, introduce long-range spatial correlations within the metastable states. We find large scale networks of occupied sites whose density vanishes in the thermodynamic limit, for d>1.

cond-mat.stat-mech↗

arXiv2001

A Simple Model for Plastic Dynamics of a Disordered Flux Line Lattice

We use a coarse-grained model of superconducting vortices driven through a random pinning potential to study the nonlinear current-voltage (IV) characteristics of flux flow in type II superconductors with pinning. In experiments, the IV relation measures flux flow down a flux density gradient. The work presented here treats this key feature explicitly. As the vortex repulsion weakens, the vortex pile maintains a globally steeper slope, corresponding to a larger critical current, for the same pinning potential. In addition, the magnitude of the peak in the differential resistance falls as the resistance peak shifts to higher currents. The model also exhibits so-called "IV fingerprints", and crossover to Ohmic (linear) behavior at high currents. Thus, many of the varieties of plastic behavior observed experimentally for soft flux line systems in the ``peak regime'' are reproduced in numerical simulations of the zero temperature model. The nonlinear transport behaviors are related to the self-organized, large scale morphologies of the vortex river flow down the slope of the vortex pile. These morphologies include isolated filamentary channels, braided rivers, and flooded rivers. We propose that these self-organized morphologies of flux flow down a flux gradient govern the various plastic flow behaviors, including nonlinear IV characteristics, observed in type II superconductors.

cond-mat.supr-con↗

arXiv2000

Solitons in the one-dimensional forest fire model

Fires in the one-dimensional Bak-Chen-Tang forest fire model propagate as solitons, resembling shocks in Burgers turbulence. The branching of solitons, creating new fires, is balanced by the pair-wise annihilation of oppositely moving solitons. Two distinct, diverging length scales appear in the limit where the growth rate of trees, $p$, vanishes. The width of the solitons, $w$, diverges as a power law, $1/p$, while the average distance between solitons diverges much faster as $ d \sim \exp(π^2/12p)$.

cond-mat.stat-mech↗

arXiv2000

Theoretical Results for Sandpile Models of SOC with Multiple Topplings

We study a directed stochastic sandpile model of Self-Organized Criticality, which exhibits recurrent, multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the steady-state all stable states are equally likely. Then we explicitly derive a discrete dynamical equation for avalanches on the lattice. By coarse-graining we arrive at a continuous Langevin equation for the propagation of avalanches and calculate all the critical exponents characterizing them. The avalanche equation is similar to the Edwards-Wilkinson equation, but with a noise amplitude that is a threshold function of the local avalanche activity, or interface height, leading to a stable absorbing state when the avalanche dies. It represents a new type of absorbing state phase transition.

cond-mat.stat-mech↗

arXiv2000

Self-Organized Criticality and Universality in a Nonconservative Earthquake Model

We make an extensive numerical study of a two dimensional nonconservative model proposed by Olami-Feder-Christensen to describe earthquake behavior. By analyzing the distribution of earthquake sizes using a multiscaling method, we find evidence that the model is critical, with no characteristic length scale other than the system size, in agreement with previous results. However, in contrast to previous claims, we find convergence to universal behaviour as the system size increases, over a range of values of the dissipation parameter, $α$. We also find that both ``free'' and ``open'' boundary conditions tend to the same result. Our analysis indicates that, as $L$ increases, the behaviour slowly converges toward a power law distribution of earthquake sizes $P(s) \sim s^{-τ}$ with exponent $τ\simeq 1.8$. The universal value of $τ$ we find numerically agrees quantitatively with the empirical value ($τ=B+1$) associated with the Gutenberg-Richter law.

cond-mat.stat-mech↗

arXiv2000

Spatial competition and price formation

We look at price formation in a retail setting, that is, companies set prices, and consumers either accept prices or go someplace else. In contrast to most other models in this context, we use a two-dimensional spatial structure for information transmission, that is, consumers can only learn from nearest neighbors. Many aspects of this can be understood in terms of generalized evolutionary dynamics. In consequence, we first look at spatial competition and cluster formation without price. This leads to establishement size distributions, which we compare to reality. After some theoretical considerations, which at least heuristically explain our simulation results, we finally return to price formation, where we demonstrate that our simple model with nearly no organized planning or rationality on the part of any of the agents indeed leads to an economically plausible price.

nlin.AO↗

arXiv2000

Self-organized Networks of Competing Boolean Agents

A model of Boolean agents competing in a market is presented where each agent bases his action on information obtained from a small group of other agents. The agents play a competitive game that rewards those in the minority. After a long time interval, the poorest player's strategy is changed randomly, and the process is repeated. Eventually the network evolves to a stationary but intermittent state where random mutation of the worst strategy can change the behavior of the entire network, often causing a switch in the dynamics between attractors of vastly different lengths.

cond-mat.stat-mech↗