arXiv subjects

George C. M. A. Ehrhardt

Publications and source records attributed to George C. M. A. Ehrhardt.

6 recordsLinked to original sources

arXiv2006

Phenomenological Models of Socio-Economic Network Dynamics

We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is defined by the particular process taking place on the network. The interplay between the two processes produces phase transitions and hysteresis, as seen using numerical simulations for three specific processes. We obtain analytic results using mean field approximations, and for a particular case we derive an exact solution for the network. In common with real-world social networks, we find coexistence of high and low connectivity phases and history dependence.

physics.soc-ph↗

arXiv2005

On the rise and fall of networked societies

We review recent results on the dynamics of social networks which suggest that the interplay between the network formation process and volatility may lead to the occurrence of discontinuous phase transitions and phase coexistence in a large class of models. We then investigate the effects of negative links -- links inhibiting local growth of the network -- and of a geographical distribution of the agents in such models. We show, by extensive numerical simulations, that both effects enhance this phenomenology, i.e. it increases the size of the coexistence region.

physics.soc-ph↗

arXiv2005

Emergence and resilience of social networks: a general theoretical framework

We introduce and study a general model of social network formation and evolution based on the concept of preferential link formation between similar nodes and increased similarity between connected nodes. The model is studied numerically and analytically for three definitions of similarity. In common with real-world social networks, we find coexistence of high and low connectivity phases and history dependence. We suggest that the positive feedback between linking and similarity which is responsible for the model's behaviour is also an important mechanism in real social networks.

physics.soc-ph↗

arXiv2004

Segregation Mechanisms in a Model of an Experimental Binary Granular Mixture

A simple phenomenological model of a binary granular mixture is developed and investigated numerically. We attempt to model the experimental system of [1,2] where a horizontally vibrated binary monolayer was found to exhibit a transition from a mixed to a segregated state as the filling fraction of the mixture was increased. This model is found to reproduce much of the experimentally observed behaviour, most importantly the transition from the mixed to the segregated state. We use the model to investigate granular segregation mechanisms and explain the experimentally observed behaviour.

cond-mat.stat-mech↗

arXiv2001

Persistence of a Continuous Stochastic Process with Discrete-Time Sampling: Non-Markov Processes

We consider the problem of `discrete-time persistence', which deals with the zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T = n(ΔT). For a Gaussian Stationary Process the persistence (no crossing) probability decays as exp(-θ_D T) = [ρ(a)]^n for large n, where a = \exp[-(ΔT)/2], and the discrete persistence exponent, θ_D, is given by θ_D = \ln(ρ)/2\ln(a). Using the `Independent Interval Approximation', we show how θ_D varies with (ΔT) for small (ΔT) and conclude that experimental measurements of persistence for smooth processes, such as diffusion, are less sensitive to the effects of discrete sampling than measurements of a randomly accelerated particle or random walker. We extend the matrix method developed by us previously [Phys. Rev. E 64, 015151(R) (2001)] to determine ρ(a) for a two-dimensional random walk and the one-dimensional random acceleration problem. We also consider `alternating persistence', which corresponds to a < 0, and calculate ρ(a) for this case.

cond-mat.stat-mech↗

arXiv2001

Persistence of a Continuous Stochastic Process with Discrete-Time Sampling

We introduce the concept of `discrete-time persistence', which deals with zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T = n ΔT. For a Gaussian Markov process with relaxation rate μ, we show that the persistence (no crossing) probability decays as ρ(a)^n for large n, where a = \exp(-μΔT), and we compute ρ(a) to high precision. We also define the concept of `alternating persistence', which corresponds to a<0. For a>1, corresponding to motion in an unstable potential (μ<0), there is a nonzero probability of having no zero-crossings in infinite time, and we show how to calculate it.

cond-mat.stat-mech↗