arXiv subjects

William Klein

Publications and source records attributed to William Klein.

10 recordsLinked to original sources

arXiv2025

Simulation of a generalized asset exchange model with investment and income mechanisms

An agent-based model of the economy is generalized to incorporate investment and guaranteed income mechanisms in addition to the exchange and distribution mechanisms considered in earlier models. We find realistic wealth distributions and realistic values of the Gini coefficients and the Pareto index. We also show that although the system reaches a steady state, the system is not in thermal equilibrium. The nonequilibrium behavior is associated with the multiplicative noise generated by the investment mechanism.

cond-mat.stat-mech↗

arXiv2020

Predicting nucleation near the spinodal in the Ising model using machine learning

We use a Convolutional Neural Network (CNN) and two logistic regression models to predict the probability of nucleation in the two-dimensional Ising model. The three models successfully predict the probability for the Nearest Neighbor Ising model for which classical nucleation is observed. The CNN outperforms the logistic regression models near the spinodal of the Long Range Ising model, but the accuracy of its predictions decreases as the quenches approach the spinodal. Occlusion analysis suggests that this decrease is due to the vanishing difference between the density of the nucleating droplet and the background. Our results are consistent with the general conclusion that predictability decreases near a critical point.

physics.comp-ph↗

arXiv2013

Spatial heterogeneity in earthquake fault-like systems

The inhomogeneity of the materials with different physical properties in the Earth is responsible for a wide variety of spatial and temporal behaviors. In this work, we study an earthquake fault model based on Olami-Feder-Christensen (OFC) and Rundle-Jackson-Brown (RJB) cellular automata models with particular aspects of spatial heterogeneities and long-range stress interactions. In our model some localized stress accumulators are added into the system by converting a percentage of randomly selected sites into stronger sites which are called asperity cells. These asperity cells support much higher failure stresses than the surrounding regular lattice sites but eventually rupture when the applied stress reaches their threshold stress. We find that changing the spatial configuration of those stronger sites generally increases capability of the fault system to generate larger events, but that the total percentage of asperities is important as well. We also observe an increasing number of larger events associated with the total number of asperities in the lattice.

physics.geo-ph↗

arXiv2013

Kinetic Pathways of the DNA Melting Transition

We investigate kinetic pathways of the DNA melting transition using variable-range versions of the Poland-Scheraga (PS) and Peyrard-Dauxois-Bishop (PDB) models of DNA. In the PS model, we construct a phi^4-field theory to calculate the critical droplet profile, the initial growth modes, and the exponent characterizing the divergence of the susceptibility near the spinodal. In the PDB model, we use a mean field analysis to calculate susceptibility exponent. We compare these theoretical results with Monte Carlo and Brownian dynamic simulations on the PS and PDB models, respectively. We find that by increasing the range of interaction, the system can be brought close to a pseudospinodal, and that in this region the nucleating droplet is diffuse in contrast to the compact droplets predicted by classical nucleation theory.

physics.bio-ph↗

arXiv2013

Ergodicity breaking in geometric Brownian motion

Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time-average. A common tactic for bringing time averages closer to ensemble averages is diversification. In this letter we study the effects of diversification using the concept of ergodicity breaking.

math-ph↗

arXiv2010

A damage model based on failure threshold weakening

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular-automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size $L$ is increased for fixed $R$. We also examine the effect of the weakening parameter on the frequency-magnitude scaling relationship and the ergodic behavior of the model.

physics.geo-ph↗

arXiv2008

Near mean-field behavior in the generalized Burridge-Knopoff earthquake model with variable range stress transfer

Simple models of earthquake faults are important for understanding the mechanisms for their observed behavior in nature, such as Gutenberg-Richter scaling. Because of the importance of long-range interactions in an elastic medium, we generalize the Burridge-Knopoff slider-block model to include variable range stress transfer. We find that the Burridge-Knopoff model with long-range stress transfer exhibits qualitatively different behavior than the corresponding long-range cellular automata models and the usual Burridge-Knopoff model with nearest-neighbor stress transfer, depending on how quickly the friction force weakens with increasing velocity. Extensive simulations of quasiperiodic characteristic events, mode-switching phenomena, ergodicity, and waiting-time distributions are also discussed. Our results are consistent with the existence of a mean-field critical point and have important implications for our understanding of earthquakes and other driven dissipative systems.

cond-mat.soft↗

arXiv2006

Kinetics of the Melting Transition in DNA

We investigate the kinetics of the DNA melting transition using modified versions of the Peyrard-Dauxois-Bishop and Poland-Scheraga models that include long and short range interactions. Using Brownian dynamics and Monte Carlo simulations, we observe metastable states prior to nucleation and demonstrate that the profile and growth modes of the critical droplet can have both classical and spinodal characteristics depending on the interaction range and the temperature quench depth.

cond-mat.other↗

arXiv2006

Space-Time Clustering and Correlations of Major Earthquakes

Earthquake occurrence in nature is thought to result from correlated elastic stresses, leading to clustering in space and time. We show that occurrence of major earthquakes in California correlates with time intervals when fluctuations in small earthquakes are suppressed relative to the long term average. We estimate a probability of less than 1% that this coincidence is due to random clustering.

physics.data-an↗

arXiv2001

The Phase Dynamics of Earthquakes: Implications for Forecasting in Southern California

We analyze the space-time patterns of earthquake occurrence in southern California using a new method that treats earthquakes as a phase dynamical system. The system state vector is used to obtain a probability measure for current and future earthquake occurrence. Thousands of statistical tests indicate the method has considerable forecast skill. We emphasize that the method is not a model, and there are no unconstrained or free parameters to be determined by fits to training data sets.

cond-mat.stat-mech↗