arXiv subjects

W. Klein

Publications and source records attributed to W. Klein.

33 records · Page 2Linked to original sources

arXiv2007

Transient Nucleation near the Mean-Field Spinodal

Nucleation is considered near the pseudospinodal in a one-dimensional $ϕ^4$ model with a non-conserved order parameter and long-range interactions. For a sufficiently large system or a system with slow relaxation to metastable equilibrium, there is a non-negligible probability of nucleation occurring before reaching metastable equilibrium. This process is referred to as transient nucleation. The critical droplet is defined to be the configuration of maximum likelihood that is dynamically balanced between the metastable and stable wells. Time-dependent droplet profiles and nucleation rates are derived, and theoretical results are compared to computer simulation. The analysis reveals a distribution of nucleation times with a distinct peak characteristic of a nonstationary nucleation rate. Under the quench conditions employed, transient critical droplets are more compact than the droplets found in metastable equilibrium simulations and theoretical predictions.

cond-mat.stat-mech↗

arXiv2007

The structure of fluctuations near mean-field critical points and spinodals and its implication for physical processes

We analyze the structure of fluctuations near critical points and spinodals in mean-field and near-mean-field systems. Unlike systems that are non-mean-field, for which a fluctuation can be represented by a single cluster in a properly chosen percolation model, a fluctuation in mean-field and near-mean-field systems consists of a large number of clusters, which we term fundamental clusters. The structure of the latter and the way that they form fluctuations has important physical consequences for phenomena as diverse as nucleation in supercooled liquids, spinodal decomposition and continuous ordering, and the statistical distribution of earthquakes. The effects due to the fundamental clusters implies that they are physical objects and not only mathematical constructs.

cond-mat.stat-mech↗

arXiv2006

Ergodicity in Natural Earthquake Fault Networks

Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C.D. Ferguson, W. Klein, and J.B. Rundle, Phys. Rev. E 60, 1359 (1999); D. Egolf, Science 287, 101 (2000)]. These driven mean-field threshold systems feature long-range interactions and can be treated as equilibrium-like systems with dynamics that are statistically stationary over long time intervals. Recently the equilibrium property of ergodicity was identified in an earthquake fault system, a natural driven threshold system, by means of the Thirumalai-Mountain (TM) fluctuation metric developed in the study of diffusive systems [K.F. Tiampo, J.B. Rundle, W. Klein, J.S. Sa Martins, and C. D. Ferguson, Phys. Rev. Lett. 91, 238501 (2003)]. In this work we analyze the seismicity of three naturally-occurring earthquake faults networks from a variety of tectonic settings in an attempt to investigate the range of applicability of effective ergodicity, using the TM metric and other, related statistics. Results suggest that, once variations in the catalog data resulting from technical and network issues are accounted for, all of these natural earthquake systems display stationary periods of metastable equilibrium and effective ergodicity that are disrupted by large events. We conclude that a constant rate of events is an important prerequisite for these periods of punctuated ergodicity, and that while the level of temporal variability in the spatial statistics is the controlling factor in the ergodic behavior of seismic networks, no single statistic is sufficient to ensure quantification of ergodicity. Specifically, we demonstrate that stationarity, while a necessary condition, is not sufficient to ensure ergodicity in fault systems.

physics.geo-ph↗

arXiv2006

Simulation of the Burridge-Knopoff Model of Earthquakes with Variable Range Stress Transfer

Simple models of earthquake faults are important for understanding the mechanisms for their observed behavior, such as Gutenberg-Richter scaling and the relation between large and small events, which is the basis for various forecasting methods. Although cellular automaton models have been studied extensively in the long-range stress transfer limit, this limit has not been studied for the Burridge-Knopoff model, which includes more realistic friction forces and inertia. We find that the latter model with long-range stress transfer exhibits qualitatively different behavior than both the long-range cellular automaton models and the usual Burridge-Knopoff model with nearest neighbor springs, depending on the nature of the velocity-weakening friction force. This result has important implications for our understanding of earthquakes and other driven dissipative systems.

cond-mat.stat-mech↗

arXiv2004

Simulations of Spinodal Nucleation in Systems with Elastic Interactions

Systems with long-range interactions quenched into a metastable state near the pseudospinodal exhibit nucleation that is qualitatively different than the classical nucleation observed near the coexistence curve. We have observed nucleation droplets in our Langevin simulations of a two-dimensional model of martensitic transformations and have determined that the structure of the nucleating droplet differs from the stable martensite structure. Our results, together with experimental measurements of the phonon dispersion curve, allow us to predict the nature of the droplet. These results have implications for nucleation in many solid-solid transitions and the structure of the final state.

cond-mat.stat-mech↗

arXiv2004

Heterogeneity in Classical and Non-Classical Nucleation

We investigate heterogeneous and homogeneous nucleation in nearest-neighbor and long-range Ising models for various quench depths. We find that the system has a true crossover from heterogeneous to homogeneous nucleation for increasing quench depth only if the interaction is sufficiently long-range. The survival curves, defined as the fraction of systems that remain in the metastable state after a given time, have qualitatively different shapes as a function of quench depth for heterogeneous and homogeneous nucleation when the interaction is short-range, but have identical shapes within the accuracy of our data for long-range interactions.

cond-mat.stat-mech↗

arXiv2003

Zeros of the Partition Function and Pseudospinodals in Long-Range Ising Models

The relation between the zeros of the partition function and spinodal critical points in Ising models with long-range interactions is investigated. We find the spinodal is associated with the zeros of the partition function in four-dimensional complex temperature/magnetic field space. The zeros approach the real temperature/magnetic field plane as the range of interaction increases.

cond-mat↗

arXiv2003

Non-clasical Nucleation in Supercooled Nickel

The dynamics of homogeneous nucleation and growth of crystalline nickel from the super-cooled melt is examined during rapid quenching using molecular dynamics and a modified embedded atom method potential. The character of the critical nuclei of the crystallization transition is examined using common neighbor analysis and visualization. At nucleation the saddle point droplet consists of randomly stacked planar structures with an in plane triangular order. These results are consistent with previous theoretical results that predict that the nucleation process in some metals is non-classical due to the presence of long-range forces and a spinodal.

cond-mat.mtrl-sci↗

arXiv2002

Precursory dynamics in threshold systems

A precursory dynamics, motivated by the analysis of recent experiments on solid-on-solid friction, is introduced in a continuous cellular automaton that mimics the essential physical contents of earthquake source processes. The resulting system of equations for the inter-event cycle can be decoupled and yields an analytical solution in the mean-field limit, exhibiting a smoothing effect of the dynamics on the stress field. Simulation results show the resulting departure from scaling at the large-event end of the frequency distribution, and support claims that the field leakage may parametrize the superposition of scaling and characteristic regimes observed in real earthquake faults.

cond-mat.stat-mech↗

arXiv2001

Nucleation in Systems with Elastic Forces

Systems with long-range interactions when quenced into a metastable state near the pseudo-spinodal exhibit nucleation processes that are quite different from the classical nucleation seen near the coexistence curve. In systems with long-range elastic forces the description of the nucleation process can be quite subtle due to the presence of bulk/interface elastic compatibility constraints. We analyze the nucleation process in a simple 2d model with elastic forces and show that the nucleation process generates critical droplets with a different structure than the stable phase. This has implications for nucleation in many crystal-crystal transitions and the structure of the final state.

cond-mat.mtrl-sci↗

arXiv2001

The instability of Alexander-McTague crystals and its implication for nucleation

We show that the argument of Alexander and McTague, that the bcc crystalline structure is favored in those crystallization processes where the first order character is not too pronounced, is not correct. We find that any solution that satisfies the Alexander-McTague condition is not stable. We investigate the implication of this result for nucleation near the pseudo- spinodal in near-meanfield systems.

cond-mat.stat-mech↗

arXiv2001

Nonlinear Network Dynamics on Earthquake Fault Systems

Earthquake faults occur in networks that have dynamical modes not displayed by single isolated faults. Using simulations of the network of strike-slip faults in southern California, we find that the physics depends critically on both the interactions among the faults, which are determined by the geometry of the fault network, as well as on the stress dissipation properties of the nonlinear frictional physics, similar to the dynamics of integrate-and-fire neural networks.

cond-mat.stat-mech↗

arXiv2000

Clusters and Fluctuations at Mean-Field Critical Points and Spinodals

We show that the structure of the fluctuations close to spinodals and mean-field critical points is qualitatively different than the structure close to non-mean-field critical points. This difference has important implications for many areas including the formation of glasses in supercooled liquids. In particular, the divergence of the measured static structure function in near-mean-field systems close to the glass transition is suppressed relative to the mean-field prediction in systems for which a spatial symmetry is broken.

cond-mat.stat-mech↗

arXiv2000

Scaling in a cellular automaton model of earthquake faults

We present theoretical arguments and simulation data indicating that the scaling of earthquake events in models of faults with long-range stress transfer is composed of at least three distinct regions. These regions correspond to three classes of earthquakes with different underlying physical mechanisms. In addition to the events that exhibit scaling, there are larger ``breakout'' events that are not on the scaling plot. We discuss the interpretation of these events as fluctuations in the vicinity of a spinodal critical point.

cond-mat.stat-mech↗

arXiv1998

Molecular Dynamics Study of Long-Lived Structures in a Fragile Glass Forming Liquid

We present molecular dynamics results for a two component, two-dimensional Lennard-Jones supercooled liquid near the glass transition. We find that the supercooled liquid is spatially heterogeneous and that there are long-lived clusters whose size distribution satisfies a scaling relation up to a cutoff. The similarity of several properties of the supercooled liquid to those of a mean-field glass-forming fluid near the spinodal suggests that the glass transition in the supercooled liquid is associated with an underlying thermodynamic instability.

cond-mat.dis-nn↗