Tree size distribution as the stationary limit of an evolutionary master equation.

The diameter distribution of a given species of deciduous trees is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data in mature semi-natural forest and ancient, traditionally managed wood-pasture from Central Europe. These distribution functions collapse on a universal shape if the tree sizes are normalized to the mean value in the considered sample.

Transient Dynamics in the Random Growth and Reset Model.

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches.

Gintropy: Gini Index Based Generalization of Entropy.

Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index, on the other hand, is an established measure for social and economical inequalities in a society. In this paper, we explore the mathematical similarities and connections in these two quantities and introduce a new measure that is capable of connecting these two at an interesting analogy level.

Flickering candle flames and their collective behavior.

Oscillation and collective behavior of diffusion flames is a fascinating phenomena. Considering candle bundles with different sizes in variable oxygen concentration, the flickering dynamics of the flames are experimentally and theoretically investigated. Trends for the flickering frequency as a function of the candle number in the bundle and oxygen concentration is revealed for various topologies of the candles packing.

Scaling in the space-time of the Internet.

The Internet on the router level, is a complex network embedded in a geographical space. We provide experimental evidences suggesting that the average travel time for a message, with fixed length, increases roughly as the square root of the geographical distance. To understand this scaling law and other measurable topological properties of the Internet as a graph, we introduce and study a simple network model.

Cell-size distribution and scaling in a one-dimensional Kolmogorov-Johnson-Mehl-Avrami lattice model with continuous nucleation.

The Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth model is considered on a one-dimensional (1D) lattice. Cells can grow with constant speed and continuously nucleate on the empty sites. We offer an alternative mean-field-like approach for describing theoretically the dynamics and derive an analytical cell-size distribution function.

Science and Facebook: The same popularity law!

The distribution of scientific citations for publications selected with different rules (author, topic, institution, country, journal, etc…) collapse on a single curve if one plots the citations relative to their mean value. We find that the distribution of "shares" for the Facebook posts rescale in the same manner to the very same curve with scientific citations. This finding suggests that citations are subjected to the same growth mechanism with Facebook popularity measures, being influenced by a statistically similar social environment and selection mechanism.

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.

Time-scale effects on the gain-loss asymmetry in stock indices.

The gain-loss asymmetry, observed in the inverse statistics of stock indices is present for logarithmic return levels that are over 2%, and it is the result of the non-Pearson-type autocorrelations in the index. These non-Pearson-type correlations can be viewed also as functionally dependent daily volatilities, extending for a finite time interval. A generalized time-window shuffling method is used to show the existence of such autocorrelations.

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.

Kinetic roughening of a soft dewetting line under quenched disorder: A numerical study.

An elegant simulation method, suitable for investigating the dewetting dynamics of thin and viscous liquid layers, is discussed. The efficiency of the method is exemplified by studying a two-parameter depinninglike model defined on inhomogeneous solid surfaces. The morphology and the statistical properties of the contact line are mapped in the relevant parameter space, and as a result critical behavior in the vicinity of the depinning transition is revealed.

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 belt's surface, modeled as noise.

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.

Spring-block model reveals region-like structures.

A mechanical spring-block model is used for realizing an objective space partition of settlements from a geographic territory in region-like structures. The method is based on the relaxation-dynamics of the spring-block system and reveals in a hierarchical manner region-like entities at different spatial scales. It takes into account in an elegant manner both the spatiality of the elements and the connectivity relations among them.

Persistent collective trend in stock markets.

Empirical evidence is given for a significant difference in the collective trend of the share prices during the stock index rising and falling periods. Data on the Dow Jones Industrial Average and its stock components are studied between 1991 and 2008. Pearson-type correlations are computed between the stocks and averaged over stock pairs and time.

Criticality and pattern formation in fracture by residual stresses.

We address the slow generation of crack networks as a problem of pattern formation. Issues of pattern selection and the associated statistical properties were considered by means of a detailed theoretical analysis and simulations of a discrete spring-block model. Developed after observations in desiccation experiments, the model describes the nucleation and propagation of cracks in a layer in contact with a frictional substrate.

A spatially explicit model for tropical tree diversity patterns.

A simple two-parameter model resembling the classical voter model is introduced to describe macroecological properties of tropical tree communities. The parameters of the model characterize the speciation- and global-dispersion rates. Monte Carlo type computer simulations are performed on the model, investigating species abundances and the spatial distribution of individuals and species.

Nontrivial spontaneous synchronization.

The collective behavior of an ensemble of multimode stochastic oscillators is investigated. The oscillators are pulse coupled; they are able to emit pulses and to detect the pulses emitted by the others. As a function of the output intensity in the system they can operate in different modes having different pulsing periods.

Shake-induced order in nanosphere systems.

Self-assembled patterns obtained from a drying nanosphere suspension are investigated by computer simulations and simple experiments. Motivated by the earlier experimental results of Sasaki and Hane and Schöpe, we confirm that more ordered triangular lattice structures can be obtained whenever a moderate intensity random shaking is applied on the drying system. Computer simulations are realized on an improved version of a recently elaborated Burridge-Knopoff-type model.

Spatial stochastic resonance in one-dimensional Ising systems.

The one-dimensional Ising model is analytically studied in a spatially periodic and oscillatory external magnetic field using the transfer-matrix method. For low enough magnetic field intensities the correlation between the external magnetic field and the response in magnetization presents a maximum for a given temperature. The phenomenon can be interpreted as a resonance phenomenon induced by the stochastic heat bath.

Spiral cracks in drying precipitates.

We investigate the formation of spiral crack patterns during the desiccation of thin layers of precipitates in contact with a substrate. This symmetry-breaking fracturing mode is found to arise naturally not from torsion forces but from a propagating stress front induced by the foldup of the fragments. We model their formation mechanism using a coarse-grain model for fragmentation and successfully reproduce the spiral cracks.

Physics of the rhythmic applause.

We report on a series of measurements aimed to characterize the development and the dynamics of the rhythmic applause in concert halls. Our results demonstrate that while this process shares many characteristics of other systems that are known to synchronize, it also has features that are unexpected and unaccounted for in many other systems. In particular, we find that the mechanism lying at the heart of the synchronization process is the period doubling of the clapping rhythm.