Zoltán Néda

Human Mobility in a Continuum Approach

Human mobility is investigated using a continuum approach that allows to calculate the probability to observe a trip to any arbitrary region, and the fluxes between any two regions. The considered description offers a general and unified framework, in which previously proposed mobility models like the gravity model, the intervening opportunities model, and the recently introduced radiation model are naturally resulting as special cases. A new form of radiation model is derived and its validity is investigated using observational data offered by commuting trips obtained from the United States census data set, and the mobility fluxes extracted from mobile phone data collected in a western European country. The new modeling paradigm offered by this description suggests that the complex topological features observed in large mobility and transportation networks may be the result of a simple stochastic process taking place on an inhomogeneous landscape.

Viscous potential flow analysis of peripheral heavy ion collisions

The conditions for the development of a Kelvin-Helmholtz Instability (KHI) for the Quark-gluon Plasma (QGP) flow in a peripheral heavy-ion collision is investigated. The projectile and target side particles are separated by an energetically motivated hypothetical surface, characterized with a phenomenological surface tension. In such a view, a classical potential flow approximation is considered and the onset of the KHI is studied. The growth rate of the instability is computed as function of phenomenological parameters characteristic for the QGP fluid: viscosity, surface tension and flow layer thickness.

Kuramoto-type phase transition with metronomes

Metronomes placed on the perimeter of a disc-shaped platform, which can freely rotate in a horizontal plane, are used for a simple classroom illustration of the Kuramoto-type phase transition. The rotating platform induces a global coupling between the metronomes, and the strength of this coupling can be varied by tilting the metronomes’ swinging plane relative to the radial direction on the disc. As a function of the tilting angle, a transition from spontaneously synchronized to unsynchronized states is observable. By varying the number of metronomes on the disc, finite-size effects are also exemplified. A realistic theoretical model is introduced and used to reproduce the observed results. Computer simulations of this model allow a detailed investigation of the emerging collective behaviour in this system.

Dynamical Stationarity as a Result of Sustained Random Growth

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast-growing complex systems. In order to model such phenomena we apply both a discrete and a continuous master equation. The derivation of elementary rates from known stationary distributions is a generalization of the fluctuation-dissipation theorem. Entropic distance evolution is given for such systems. We reconstruct distributions obtained for growing networks, particle production, scientific citations, and income distribution.

Chaos on the conveyor belt.

The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by a spring to an external static point and, due to the dragging effect of the belt, the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can be achieved only by taking into account the spatial inhomogeneity of the friction force on the belts surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic, dynamics and phase transition-like behavior. Noise-induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks (around five).

The rhythm of coupled metronomes

AbstractnSpontaneous synchronization of an ensemble of metronomes placed on a freely rotatingnplatform is studied experimentally and by computer simulations. A striking in-phasensynchronization is observed when the metronomes’ beat frequencies are fixed above ancritical limit. Increasing the number of metronomes placed on the disk leads to annobservable decrease in the level of the emerging synchronization. A realistic model withnexperimentally determined parameters is considered in order to understand the observednresults. The conditions favoring the emergence of synchronization are investigated. It isnshown that the experimentally observed trends can be reproduced by assuming a finitenspread in the metronomes’ natural frequencies. In the limit of large numbers ofnmetronomes, we show that synchronization emerges only above a critical beat frequencynvalue.

A spring-block analogy for the dynamics of stock indexes

A spring-block chain placed on a running conveyor belt is considered for modeling stylized facts observed in the dynamics of stock indexes. Individual stocks are modeled by the blocks, while the stock-stock correlations are introduced via simple elastic forces acting in the springs. The dragging effect of the moving belt corresponds to the expected economic growth. The spring-block system produces collective behavior and avalanche like phenomena, similar to the ones observed in stock markets. An artificial index is defined for the spring-block chain, and its dynamics is compared with the one measured for the Dow Jones Industrial Average. For certain parameter regions the model reproduces qualitatively well the dynamics of the logarithmic index, the logarithmic returns, the distribution of the logarithmic returns, the avalanche-size distribution and the distribution of the investment horizons. A noticeable success of the model is that it is able to account for the gain-loss asymmetry observed in the inverse statistics. Our approach has mainly a pedagogical value, bridging between a complex socio-economic phenomena and a basic (mechanical) model in physics.

Further We Travel the Faster We Go.

The average travelling speed increases in a nontrivial manner with the travel distance. This leads to scaling-like relations on quite extended spatial scales, for all mobility modes taken together and also for a given mobility mode in part. We offer a wide range of experimental results, investigating and quantifying this universal effect and its measurable causes. The increasing travelling speed with the travel distance arises from the combined effects of: choosing the most appropriate travelling mode; the structure of the travel networks; the travel times lost in the main hubs, starting or target cities; and the speed limit of roads and vehicles.

Fragmentation of drying paint layers

Fragmentation of thin layers of drying granular materials on a frictional surface are studied both by experiments and computer simulations. Besides a qualitative description of the fragmentation phenomenon, the dependence of the average fragment size as a function of the layer thickness is thoroughly investigated. Experiments are done using a special nail polish, which forms characteristic crack structures during drying. In order to control the layer thickness, we diluted the nail polish in acetone and evaporated in a controlled manner different volumes of this solution on glass surfaces. During the evaporation process we managed to get an instable paint layer, which formed cracks as it dried out. In order to understand the obtained structures a previously developed spring-block model was implemented in a three-dimensional version. The experimental and simulation results proved to be in excellent qualitative and quantitative agreement. An earlier suggested scaling relation between the average fragment siz...

Equilibrium distributions in entropy driven balanced processes

For entropy driven balanced processes we obtain final states with Poisson, Bernoulli, negative binomial and Polya distributions. We apply this both for complex networks and particle production. For random networks we follow the evolution of the degree distribution, Pn, in a system where a node can activate k fixed connections from K possible partnerships among all nodes. The total number of connections, N, is also fixed. For particle physics problems Pn is the probability of having n particles (or other quanta) distributed among k states (phase space cells) while altogether a fixed number of N particles reside on K states.