János Török

Criterion for phase separation in one-dimensional driven systems.

A general criterion for the existence of phase separation in driven density-conserving one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steady-state currents of domains in the system. A quantitative criterion for the existence of phase separation is conjectured using a correspondence made between driven diffusive models and zero-range processes. The criterion is verified in all cases where analytical results are available, and predictions for other models are provided.

Opinions, conflicts, and consensus: modeling social dynamics in a collaborative environment.

Information-communication technology promotes collaborative environments like Wikipedia where, however, controversy and conflicts can appear. To describe the rise, persistence, and resolution of such conflicts, we devise an extended opinion dynamics model where agents with different opinions perform a single task to make a consensual product. As a function of the convergence parameter describing the influence of the product on the agents, the model shows spontaneous symmetry breaking of the final consensus opinion represented by the medium. In the case when agents are replaced with new ones at a certain rate, a transition from mainly consensus to a perpetual conflict occurs, which is in qualitative agreement with the scenarios observed in Wikipedia.

The green wave model of two-dimensional traffic: Transitions in the flow properties and in the geometry of the traffic jam

We carried out computer simulations to study the green wave model (GWM), the parallel updating version of the two-dimensional traffic model of Biham et al. The better convergence properties of the GWM together with a multi-spin coding technique enabled us to extrapolate to the infinite system size which indicates a nonzero density transition from the free flow to the congested state (jamming transition). In spite of the sudden change in the symmetry of the correlation function at the transition point, finite size scaling and temporal scaling seems to hold, at least above the threshold density. There is a second transition point at a density deep in the congested phase where the geometry of the cluster of jammed cars changes from linear to branched: Just at this transition point this cluster has fractal geometry with dimension 1.58. The jamming transition is also described within the mean field approach.

Shear band formation in granular media as a variational problem

Strain in sheared dense granular material is often localized in a narrow region called the shear band. Recent experiments in a modified Couette cell provided localized shear flow in the bulk away from the confining walls. The nontrivial shape of the shear band was measured as the function of the cell geometry. First, we present a geometric argument for narrow shear bands that connects the function of their surface position with the shape in the bulk. Assuming a simple dissipation mechanism, we show that the principle of minimum dissipation of energy provides a good description of the shape function. Furthermore, we discuss the possibility and behavior of shear bands that are detached from the free surface and are entirely covered in the bulk.

Modeling social dynamics in a collaborative environment

Wikipedia is a prime example of today’s value production in a collaborative environment. Using this example, we model the emergence, persistence and resolution of severe conflicts during collaboration by coupling opinion formation with article editing in a bounded confidence dynamics. The complex social behavior involved in editing articles is implemented as a minimal model with two basic elements; (i) individuals interact directly to share information and convince each other, and (ii) they edit a common medium to establish their own opinions. Opinions of the editors and that represented by the article are characterised by a scalar variable. When the pool of editors is fixed, three regimes can be distinguished: (a) a stable mainstream article opinion is continuously contested by editors with extremist views and there is slow convergence towards consensus, (b) the article oscillates between editors with extremist views, reaching consensus relatively fast at one of the extremes, and (c) the extremist editors are converted very fast to the mainstream opinion and the article has an erratic evolution. When editors are renewed with a certain rate, a dynamical transition occurs between different kinds of edit wars, which qualitatively reflect the dynamics of conflicts as observed in real Wikipedia data.

Self-organization, localization of shear bands, and aging in loose granular materials

We introduce a mesoscopic model for the formation and evolution of shear bands in loose granular media. Numerical simulations reveal that the system undergoes a nontrivial self-organization process which is governed by the motion of the shear band and the consequent restructuring of the material along it. High density regions are built up, progressively confining the shear bands in localized regions. This results in an inhomogeneous aging of the material with a very slow increase in the mean density, displaying an unusual glassylike system-size dependence.

Sharp crossover and anomalously large correlation length in driven systems

Models of one-dimensional driven diffusive systems sometimes exhibit an abrupt increase in the correlation length to an anomalously large but finite value as the parameters of the model are varied. This behaviour may be misinterpreted as a genuine phase transition. A simple mechanism for this sharp increase is presented. The mechanism is introduced within the framework of a recently suggested correspondence between driven diffusive systems and zero-range processes. It is shown that when the dynamics of the model is such that small domains are suppressed in the steady-state distribution, anomalously large correlation lengths may build up. The mechanism is examined in detail in two models.

Multilayer weighted social network model

Recent empirical studies using large-scale data sets have validated the Granovetter hypothesis on the structure of the society in that there are strongly wired communities connected by weak ties. However, as interaction between individuals takes place in diverse contexts, these communities turn out to be overlapping. This implies that the society has a multilayered structure, where the layers represent the different contexts. To model this structure we begin with a single-layer weighted social network (WSN) model showing the Granovetterian structure. We find that when merging such WSN models, a sufficient amount of interlayer correlation is needed to maintain the relationship between topology and link weights, while these correlations destroy the enhancement in the community overlap due to multiple layers. To resolve this, we devise a geographic multilayer WSN model, where the indirect interlayer correlations due to the geographic constraints of individuals enhance the overlaps between the communities and, at the same time, the Granovetterian structure is preserved.

Morphologies of three-dimensional shear bands in granular media

We present numerical results on spontaneous symmetry breaking strain localization in axisymmetric triaxial shear tests of granular materials. We simulated shear band formation using the three-dimensional distinct element method with spherical particles. We demonstrate that the local shear intensity, the angular velocity of the grains, the coordination number, and the local void ratio are correlated and any of them can be used to identify shear bands; however, the latter two are less sensitive. The calculated shear band morphologies are in good agreement with those found experimentally. We show that boundary conditions play an important role. We discuss the formation mechanism of shear bands in the light of our observations and compare the results with experiments. At large strains, with enforced symmetry, we found strain hardening.

Analytic study of clustering in shaken granular material using zero-range processes

We show that models used to described granular clustering due to vertical shaking belong to the class of zero-range processes. This correspondence allows us to derive exactly in a very easy and straightforward manner a number of properties of the models like particle distribution functions, phase diagram, and characteristic time of clusterization.