Oscillations and collective behavior in convection-driven fluid columns are investigated and discussed in analogy with similar phenomenon observed for the flickering flames of candle bundles. Experimentally, it is shown that an ascending circular helium gas column performs an oscillation which is similar in several aspects to the oscillation of diffusion flames. Increasing the nozzle diameter leads to a decrease in the oscillation frequency, while increasing the flow rate results in an increase in this frequency. For helium columns oscillating at nearby frequency and placed close to each other, anti-phase synchronization and beating phenomena are observed. A toy-model based on elementary fluid dynamics describes the observed oscillations and leads to frequencies with the proper trend and values in the right order of magnitude.

"The two-body cross-correlation for the diffusive motion of colloidal nano-spheres is experimentally investigated. Polystyrene nano-spheres were used in a very low concentration suspension in order to minimize the three- or more body collective effects. Beside the generally used longitudinal and transverse component correlations we investigate also the Pearson correlation in the magnitude of the displacements. In agreement with previous studies we find that the longitudinal and transverse component correlations decay as a function of the inter-particle distance following a power-law trend with an exponent around -2. The Pearson correlation in the magnitude of the displacements decay also as a power-law with an exponent around -1. Keywords: colloidal particles, Brownian motion, cross-correlation. "

Systems of locally coupled identical Kuramoto rotators in a 1D ring-like topology are considered. We investigate the emergent stationary collective modes in such systems. These spatio-temporal patterns are interpreted as generalized synchronization modes of the system, or can be viewed as self-closing rotating waves on a circle with a well defined winding number. Our study investigates the predictability of the final stable state when the phases of the rotators are randomly initialized. First we summarize the known results regarding this type of collective behavior in circular oscillator ensembles using a novel theoretical framework. Interpreting the system as a gradient system we identify all possible stationary states including a new class of unstable asymptotic solutions. The linear stability of the emergent patterns is also determined and it is linked to the winding number, which labels the stationary states, in agreement with the results in [1, 2, 3]. Computer experiments were considered, confirming that the distribution of the probability of appearance for the stable collective modes is well approximated by a Gaussian envelope curve. We also show that variance of the distributions scales linearly with the system size [1]. New results are obtained by numerically studying the dynamics of the system. Using multidimensional geometry we interpret the phase space of the system as various distinct planes confined in a hypercube. We show that the motion of the characteristic point of the system is only possible on the surface of these planes. Unfortunately for the general d > 3 case the actual trajectories cannot be directly visualized, so we present different attempts to picture the time-evolution of the system. We show that the complexity of the dynamics is rapidly increasing with the system size. This feature indicates that predictions on the final state of the system made solely from the random initial conditions become more and more difficult as we consider bigger systems. We argue however, that the final stationary mode is always predictable after a certain time-moment of the dynamics. A simple method is proposed for identifying this time-moment, ts. We study numerically the scaling of the average time for the selection process as a function of the system parameters.

We review and classify stochastic processes without detailed balance condition. We obtain stationary distributions and investigate their stability in terms of generalized entropic divergences beyond the Kullback-Leibler formula. A simple stochastic model with local growth rates and direct resetting to the ground state is investigated and applied to various networks, scientific citations and Facebook popularity, hadronic yields in high energy particle reactions, income and wealth distributions, biodiversity and settlement size distribution.

Identical Kuramoto oscillators with nearest neighbor coupling are considered in a 1D ring-like topology. In agreement with previous results obtained for such systems [1-3], we find that the system exhibits nontrivial collective behavior patterns. We interpret these emergent structures as different synchronization modes. One can also consider these dynamically stationary states as rotating waves with a well defined winding number or phase shift between the oscillators. As a first task we have reproduced all the results known for such systems. By performing a standard linear stability analysis we link the stability of the stationary states to the winding numbers. Our results are in agreement with the stability conditions given in [3]. Starting the dynamics from random initial conditions the probability of appearance for the stable collective modes was computationally studied. We found that these probabilities are well approximated by a Gaussian envelope curve. We also show that variance of the distributions scales linearly with the system size. These results are in agreement with the ones communicated in [2]. Novel and interesting results are also obtained. Using multidimensional geometry we investigate the dynamics of the system and the basin of attractions for different stationary states. The used image for the phase space enables us to take a deeper look on the processes governing the dynamics. In such manner we attempt a theoretical explanation for the observed normal distribution of the stable states and the scaling properties for its variance. We show that the motion of the characteristic point is limited only to a restricted subspace of N-1 dimensional hyperplanes confined in the N dimensional phase space of the system. A series of two dimensional cross sections of the attraction basins suggest that the structure of the attractor domains are complicated, and hence the time-evolution of the system is simple only in the vicinity of the stable states. Empirically we find an interesting restriction for the dynamics of the characteristic point in the used N dimensional hyperspace. Generalizing the Kuramoto order-parameter for the rotating wave-like states we give an empirical estimate for the time-length of the state-selection process.

Spontaneous synchronization of interacting pendulum clocks offers a fascinating and pedagogical demonstration for order-disorder type phase transitions. A minimal model consisting of self-sustained harmonic oscillators placed on a common platform is used to model such systems. Varying the frequency of the oscillators, the mass of the platform and the friction coefficient of the platform we illustrate transitions from partially synchronized to unsynchronized states. Finite size effects are studied and the results are discussed in view of recent experiments performed with metronomes. We find a highly non-trivial trend for the synchrony level as a function of the number of oscillators placed on the platform: there is a an optimal number of oscillators for which the maximum synchrony level is reached.

Metronomes placed on a smoothly rotating disk are used for exemplifying order-disorder type phase-transitions. The ordered phase corresponds to spontaneously synchronized beats, while the disordered state is when the metronomes swing in unsynchronized manner. Using a given metronome ensemble, we propose several methods for switching between ordered and disordered states. The system is studied by controlled experiments and a realistic model. The model reproduces the experimental results, and allows to study large ensembles with good statistics. Finite-size effects and the increased fluctuation in the vicinity of the phase-transition point are also successfully reproduced.

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.

Spontaneous synchronization of an ensemble of metronomes placed on a freely rotating platform is studied experimentally and by computer simulations. A striking in-phase synchronization is observed when the metronomes’ beat frequencies are fixed above a critical limit. Increasing the number of metronomes placed on the disk leads to an observable decrease in the level of the emerging synchronization. A realistic model with experimentally determined parameters is considered in order to understand the observed results. The conditions favoring the emergence of synchronization are investigated. It is shown that the experimentally observed trends can be reproduced by assuming a finite spread in the metronomes’ natural frequencies. In the limit of large numbers of metronomes, we show that synchronization emerges only above a critical beat frequency value.

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.

Evaporation of a small glass of ethylic alcohol is studied both experimentally and through an elementary thermal physics approach. For a cylindrical beaker and no air flow in the room, a simple quadratic relation is found between the evaporation time and the mass of evaporated liquid. This problem and the obtained results offer excellent possibilities for simple student experiments and for testing basic principles of thermal physics. As an example, we use the obtained results for estimating the value of the Boltzmann constant from evaporation experiments.

Diversity patterns of tree species in a tropical forest community are approached by a simple lattice model and investigated by Monte Carlo simulations using a backtracking method. Our spatially explicit neutral model is based on a simple statistical physics process, namely the diffusion of seeds. The model has three parameters: the speciation rate, the size of the meta-community in which the studied tree-community is embedded, and the average surviving time of the seeds. By extensive computer simulations we aim the reproduction of relevant statistical measures derived from the experimental data of the Barro Colorado Island tree census in year 1995. The first two parameters of the model are fixed to known values, characteristic of the studied community, thus obtaining a model with only one freely adjustable parameter. As a result of this, the average number of species in the considered territory, the relative species abundance distribution, the species-area relationship and the spatial auto-correlation function of the individuals in abundant species are simultaneously fitted with only one parameter which is the average surviving time of the seeds.

We analyze the income distribution of employees for 9 consecutive years (2001-2009) using a complete social security database for an economically important district of Romania. The database contains detailed information on more than half million taxpayers, including their monthly salaries from all employers where they worked. Besides studying the characteristic distribution functions in the high and low/medium income limits, the database allows us a detailed dynamical study by following the time-evolution of the taxpayers income. To our knowledge, this is the first extensive study of this kind (a previous japanese taxpayers survey was limited to two years). In the high income limit we prove once again the validity of Pareto's law, obtaining a perfect scaling on four orders of magnitude in the rank for all the studied years. The obtained Pareto exponents are quite stable with values around $\alpha \approx 2.5$, in spite of the fact that during this period the economy developed rapidly and also a financial-economic crisis hit Romania in 2007-2008. For the low and medium income category we confirmed the exponential-type income distribution. Following the income of employees in time, we have found that the top limit of the income distribution is a highly dynamical region with strong fluctuations in the rank. In this region, the observed dynamics is consistent with a multiplicative random growth hypothesis. Contrarily with previous results obtained for the japanese employees, we find that the logarithmic growth-rate is not independent of the income.

The dynamical development of the cooling and hadronizing quark-gluon Plasma (QGP) is studied in a simple model assuming critical fluctuations in the QGP to Hadronic Matter (HM) and a first order transition in a small finite system. We consider an earlier determined free-energy density curve in the neighbourhood of the critical point, with two local minima corresponding to the equilibrium hadronic and QGP configurations. In this approach the divergence at e = 0 eliminates fluctuations with negative or zero energy. The barrier between the equilibrium states is obtained from an estimated value of the surface tension between the two phases. We obtain a characteristic behavior for the skewness and the kurtosis of energy density fluctuations, which can be studied via a beam energy scan program.

A lattice Kinetic Monte Carlo (KMC) approach is considered to study the statistical properties of the diffusion of Pt atom clusters on a Pt(111) surface. The interatomic potential experienced by the diffusing atoms is calculated by the embedded atom method and the hopping barrier for the allowed atomic movements are calculated using the Nudged Elastic Band method. The diffusion coefficient is computed for various cluster sizes and system temperatures. The obtained results are in agreement with the ones obtained in previous experimental and theoretical works. A simple scaling argument is proposed for the size dependence of the diffusion coefficient's pre-factor. A detailed statistical analysis of the event by event KMC dynamics reveals two important and co-existing mechanisms for the diffusion of the cluster's center of mass. At low temperatures (below T = 400K) the dominating mechanism responsible for the displacement of the cluster's center of mass is the periphery (or edge) diffusion of the atoms. At high temperatures (above T = 800K) the dissociation and recombination of the clusters becomes more and more important.

The collaboration network generated by the Erasmus student mobilities in the year 2003 is analyzed and modeled. Nodes of this bipartite network are European universities and links are the Erasmus mobilities between these universities. This network is a complex directed and weighted graph. The non-directed and non-weighted projection of this network does not exhibit a scale-free nature, but proves to be a small-word type random network with a giant component. The connectivity data indicates an exponential degree distribution, a relatively high clustering coefficient and a small radius. It can be easily modeled by using a simple configuration model and arguing the exponential degree distribution. The weighted and directed version of the network can also be described by means of simple random network models.

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. Simulation results are critically compared with the experimental data obtained from a tree census on a 50 hectare area of the Barro Colorado Island (BCI), Panama. Fitting to only two observable quantities from the BCI data (total species number and the slope of the log-log species-area curve at the maximal area), it is possible to reproduce the full species-area curve, the relative species abundance distribution, and a more realistic spatial distribution of species.

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. The system is designed to optimize the output intensity around a fixed f(*) output threshold. In order to do so a simple dynamics is considered. Whenever the total output intensity in the system is lower than f(*), a mode with a higher interpulse period is chosen. If the light intensity in the system is higher than f(*), a mode with a lower interpulse period is selected. As a side effect of this simple optimization rule, for a given f(*) interval a nontrivial synchronization of the oscillators is observed. The synchronization level is studied by computer simulations, investigating the influence of model parameters (number of modes, stochasticity of the oscillators, the f(*) threshold value, and interaction topology). An experimental realization of this system is also considered; an ensemble of electronic oscillators communicating with light pulses was constructed and studied. The experimental system behaves in many ways similar to the theoretically considered multimode stochastic oscillator ensemble.

Random networks with co-existing positive and negative links are studied from the viewpoint of the NP hard correlation clustering problem. The task is to produce a clustering of the vertices which maximizes the number of positive edges within clusters and the number of negative edges between clusters. Simulated annealing, Monte Carlo renormalization and molecular dynamics optimization are used to find the optimal cluster structure. Recently, this problem was studied for globally coupled systems and an interesting phase-transition-like phenomenon was predicted: in the thermodynamic limit the relative size of the largest cluster, r, exhibits a step-like behavior as a function of the density of positive links q (r = 0 if q < 1/2 and r = 1 if q > 1/2). Here we prove that when considering random networks with a constant bond density, the same phase transition is expected. A totally different result emerges however, when networks with a fixed average number of connections per node are considered. In such cases a nontrivial spin-glass-type behavior is found, where the location of the critical point shifts toward q > 1/2 values. The results also suggest that instead of the simple step-like behavior, the r(q) curve has a more complex shape, which depends on the specific topology of the considered network.

Nowadays, Cellular Neural/Nonlinear Networks (CNN) are practically implemented in parallel, analog computers, showing a fast developing trend. It is important also for physicists to be aware that such computers are appropriate for implementing in an elegant manner practically important algorithms, which are extremely slow on the classical digital architecture. Here, CNN is used for optimization of spin-glass systems. We prove, that a CNN in which the parameters of all cells can be separately controlled, is the analog correspondent of a two-dimensional Ising type spin-glass system. Using the properties of CNN we show that one single operation on the CNN chip would yield a local minimum of the spin-glass energy function. By using this property a fast optimization method, similar to simulated annealing, can be built. After estimating the simulation time needed for this algorithm on CNN based computers, and comparing it with the time needed on normal digital computers using the classical simulated annealing algorithm, the results look promising: a speed-up of the order 1012 is expected already at 50×50 lattice sizes. Hardwares realized nowadays are of 128×128 size. Also, there seem to be no technical difficulties adapting CNN chips for such problems and the needed local control of the parameters could be fully developed in the near future.