arXiv subjects

Harvey Gould

Publications and source records attributed to Harvey Gould.

At least 19 recordsLinked to original sources

arXiv2026

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↗

arXiv2023

Cluster Scaling and Critical Points: A Cautionary Tale

Many systems in nature are conjectured to exist at a critical point, including the brain and earthquake faults. The primary reason for this conjecture is that the distribution of clusters (avalanches of firing neurons in the brain or regions of slip in earthquake faults) can be described by a power law. Because there are other mechanisms such as $1/f$ noise that can produce power laws, other criteria that the cluster critical exponents must satisfy can be used to conclude whether or not the observed power law behavior indicates an underlying critical point rather than an alternate mechanism. We show how a possible misinterpretation of the cluster scaling data can lead to incorrectly conclude that the measured critical exponents do not satisfy these criteria. Examples of the possible misinterpretation of the data for one-dimensional random site percolation and the one-dimensional Ising model are presented. We stress that the interpretation of a power law cluster distribution indicating the presence of a critical point is subtle, and its misinterpretation might lead to the abandonment of a promising area of research.

cond-mat.stat-mech↗

arXiv2021

Simulation of a generalized asset exchange model with economic growth and wealth distribution

The agent-based Yard-Sale model of wealth inequality is generalized to incorporate exponential economic growth and its distribution. The distribution of economic growth is nonuniform and is determined by the wealth of each agent and a parameter $λ$. Our numerical results indicate that the model has a critical point at $λ=1$ between a phase for $λ< 1$ with economic mobility and exponentially growing wealth of all agents and a non-stationary phase for $λ\geq 1$ with wealth condensation and no mobility. We define the energy of the system and show that the system can be considered to be in thermodynamic equilibrium for $λ< 1$. Our estimates of various critical exponents are consistent with a mean-field theory (see following paper). The exponents do not obey the usual scaling laws unless a combination of parameters that we refer to as the Ginzburg parameter is held fixed as the transition is approached. The model illustrates that both poorer and richer agents benefit from economic growth if its distribution does not favor the richer agents too strongly. This work and the accompanying theory paper contribute to understanding whether the methods of equilibrium statistical mechanics can be applied to economic systems.

cond-mat.stat-mech↗

arXiv2021

Mean-field theory of an asset exchange model with economic growth and wealth distribution

We develop a mean-field theory of the growth, exchange and distribution (GED) model introduced by Kang et al. (preceding paper) that accurately describes the phase transition in the limit that the number of agents $N$ approaches infinity. The GED model is a generalization of the Yard-Sale model in which the additional wealth added by economic growth is nonuniformly distributed to the agents according to their wealth in a way determined by the parameter $λ$. The model was shown numerically to have a phase transition at $λ=1$ and be characterized by critical exponents and critical slowing down. Our mean-field treatment of the GED model correctly predicts the existence of the phase transition, critical slowing down, the values of the critical exponents, and introduces an energy whose probability satisfies the Boltzmann distribution for $λ< 1$, implying that the system is in thermodynamic equilibrium in the limit that $N \to \infty$. We show that the values of the critical exponents obtained by varying $λ$ for a fixed value of $N$ do not satisfy the usual scaling laws, but do satisfy scaling if a combination of parameters, which we refer to as the Ginzburg parameter, is much greater than one and is held constant. We discuss possible implications of our results for understanding economic systems and the subtle nature of the mean-field limit in systems with both additive and multiplicative noise.

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↗

arXiv2019

Novel effective ergodicity breaking phase transition in a driven-dissipative system

We show that the Olami-Feder-Christensen model exhibits an effective ergodicity breaking transition as the noise is varied. Above the critical noise, the average stress on each site converges to the global average. Below the critical noise, the stress on individual sites becomes trapped in different limit cycles. We use ideas from the study of dynamical systems and compute recurrence plots and the recurrence rate. We identify the order parameter as the recurrence rate averaged over all sites and find numerical evidence that the transition can be characterized by exponents that are consistent with hyperscaling.

nlin.CD↗

arXiv2019

Prediction in a driven-dissipative system displaying a continuous phase transition

Prediction in complex systems at criticality is believed to be very difficult, if not impossible. Of particular interest is whether earthquakes, whose distribution follows a power law (Gutenberg-Richter) distribution, are in principle unpredictable. We study the predictability of event sizes in the Olmai-Feder-Christensen model at different proximities to criticality using a convolutional neural network. The distribution of event sizes satisfies a power law with a cutoff for large events. We find that prediction decreases as criticality is approached and that prediction is possible only for large, non-scaling events. Our results suggest that earthquake faults that satisfy Gutenberg-Richter scaling are difficult to forecast.

cond-mat.stat-mech↗

arXiv2014

Anomalous mean-field behavior of the fully connected Ising model

Although the fully connected Ising model does not have a length scale, we show that its critical exponents can be found using finite size scaling with the scaling variable equal to N, the number of spins. We find that at the critical temperature of the infinite system the mean value and the most probable value of the magnetization scale differently with N, and the probability distribution of the magnetization is not a Gaussian, even for large N. Similar results inconsistent with the usual understanding of mean-field theory are found at the spinodal. We relate these results to the breakdown of hyperscaling and show how hyperscaling can be restored by increasing N while holding the Ginzburg parameter rather than the temperature fixed.

cond-mat.stat-mech↗

arXiv2013

The Effect of Growth On Equality in Models of the Economy

We investigate the relation between economic growth and equality in a modified version of the agent-based asset exchange model (AEM). The modified model is a driven system that for a range of parameter space is effectively ergodic in the limit of an infinite system. We find that the belief that "a rising tide lifts all boats" does not always apply, but the effect of growth on the wealth distribution depends on the nature of the growth. In particular, we find that the rate of growth, the way the growth is distributed, and the percentage of wealth exchange determine the degree of equality. We find strong numerical evidence that there is a phase transition in the modified model, and for a part of parameter space the modified AEM acts like a geometric random walk.

q-fin.GN↗

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↗

arXiv2007

Teaching statistical physics by thinking about models and algorithms

We discuss several ways of illustrating fundamental concepts in statistical and thermal physics by considering various models and algorithms. We emphasize the importance of replacing students' incomplete mental images by models that are physically accurate. In some cases it is sufficient to discuss the results of an algorithm or the behavior of a model rather than having students write a program.

physics.ed-ph↗

arXiv2007

Approaching equilibrium and the distribution of clusters

We investigate the approach to stable and metastable equilibrium in Ising models using a cluster representation. The distribution of nucleation times is determined using the Metropolis algorithm and the corresponding $ϕ^{4}$ model using Langevin dynamics. We find that the nucleation rate is suppressed at early times even after global variables such as the magnetization and energy have apparently reached their time independent values. The mean number of clusters whose size is comparable to the size of the nucleating droplet becomes time independent at about the same time that the nucleation rate reaches its constant value. We also find subtle structural differences between the nucleating droplets formed before and after apparent metastable equilibrium has been established.

cond-mat.stat-mech↗

arXiv2007

Homogeneous and heterogeneous nucleation of Lennard-Jones liquids

The homogeneous and heterogeneous nucleation of a Lennard-Jones liquid is investigated using the umbrella sampling method. The free energy cost of forming a nucleating droplet is determined as a function of the quench depth, and the saddle point nature of the droplets is verified using an intervention technique. The structure and symmetry of the nucleating droplets is found for a range of temperatures. We find that for deep quenches the nucleating droplets become more anisotropic and diffuse with no well defined core or surface. The environment of the nucleating droplets form randomly stacked hexagonal planes. This behavior is consistent with a spinodal nucleation interpretation. We also find that the free energy barrier for heterogeneous nucleation is a minimum when the lattice spacing of the impurity equals the lattice spacing of the equilibrium crystalline phase. If the lattice spacing of the impurity is different, the crystal grows into the bulk instead of wetting the impurity.

cond-mat.stat-mech↗

arXiv2007

Electron electric dipole moment experiment using electric-field quantized slow cesium atoms

A proof-of-principle electron electric dipole moment (e-EDM) experiment using slow cesium atoms, nulled magnetic fields, and electric field quantization has been performed. With the ambient magnetic fields seen by the atoms reduced to less than 200 pT, an electric field of 6 MV/m lifts the degeneracy between states of unequal mF and, along with the low (approximately 3 m/s) velocity, suppresses the systematic effect from the motional magnetic field. The low velocity and small residual magnetic field have made it possible to induce transitions between states and to perform state preparation, analysis, and detection in regions free of applied static magnetic and electric fields. This experiment demonstrates techniques that may be used to improve the e-EDM limit by two orders of magnitude, but it is not in itself a sensitive e-EDM search, mostly due to limitations of the laser system.

physics.atom-ph↗

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

Focusing a fountain of neutral cesium atoms with an electrostatic lens triplet

An electrostatic lens with three focusing elements in an alternating-gradient configuration is used to focus a fountain of cesium atoms in their ground (strong-field-seeking) state. The lens electrodes are shaped to produce only sextupole plus dipole equipotentials which avoids adding the unnecessary nonlinear forces present in cylindrical lenses. Defocusing between lenses is greatly reduced by having all of the main electric fields point in the same direction and be of nearly equal magnitude. The addition of the third lens gave us better control of the focusing strength in the two transverse planes and allowed focusing of the beam to half the image size in both planes. The beam envelope was calculated for lens voltages selected to produced specific focusing properties. The calculations, starting from first principles, were compared with measured beam sizes and found to be in good agreement. Application to fountain experiments, atomic clocks, and focusing polar molecules in strong-field-seeking states is discussed.

physics.acc-ph↗

arXiv2006

Feasibility of a storage ring for polar molecules in strong-field-seeking states

We show, through modeling and simulation, that it is feasible to construct a storage ring that will store dense bunches of strong-field-seeking polar molecules at 30 m/s (kinetic energy of 2K) and hold them, for several minutes, against losses due to defocusing, oscillations, and diffusion. The ring, 3 m in diameter, has straight sections that afford access to the stored molecules and a lattice structure that may be adapted for evaporative cooling. Simulation is done using a newly-developed code that tracks the particles, in time, through 400 turns; it accounts for longitudinal velocity changes as a function of external electric field, focusing and deflection nonlinearities, and the effects of gravity. An injector, decelerator, and source are included and intensities are calculated.

physics.acc-ph↗

arXiv2006

Demonstration of a Cold Atom Fountain Electron Electric Dipole Moment Experiment

A Cs fountain electron electric dipole moment (EDM) experiment using electric-field quantization is demonstrated. With magnetic fields reduced to 200 pT or less, the electric field lifts the degeneracy between hyperfine levels of different|mF| and, along with the slow beam and fountain geometry, suppresses systematics from motional magnetic fields. Transitions are induced and the atoms polarized and analyzed in field-free regions. The feasibility of reaching a sensitivity to an electron EDM of 2 x 10 exp(-50) C-m [1.3 x 10 exp(-29) e-cm] in a cesium fountain experiment is discussed.

physics.atom-ph↗