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Tamas Vicsek

Publications and source records attributed to Tamas Vicsek.

At least 55 records · Page 3Linked to original sources
arXiv2004

Reverse engineering of linking preferences from network restructuring

We provide a method to deduce the preferences governing the restructuring dynamics of a network from the observed rewiring of the edges. Our approach is applicable for systems in which the preferences can be formulated in terms of a single-vertex energy function with f(k) being the contribution of a node of degree k to the total energy, and the dynamics obeys the detailed balance. The method is first tested by Monte-Carlo simulations of restructuring graphs with known energies, then it is used to study variations of real network systems ranging from the co-authorship network of scientific publications to the asset graphs of the New York Stock Exchange. The empirical energies obtained from the restructuring can be described by a universal function f(k) -k ln(k), which is consistent with and justifies the validity of the preferential attachment rule proposed for growing networks.

cond-mat.stat-mech↗
arXiv2004

Statistical mechanics of topological phase transitions in networks

We provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to the level of noise during the rewiring of the edges. The associated microscopic dynamics satisfies the detailed balance condition and is equivalent to a lattice gas model on the edge-dual graph of a fully connected network. In our studies -- based on an exact enumeration method, Monte-Carlo simulations, and theoretical considerations -- we find a rich variety of topological phase transitions when the temperature is varied. These transitions signal singular changes in the essential features of the global structure of the network. Depending on the energy function chosen, the observed transitions can be best monitored using the order parameters Phi_s=s_{max}/M, i.e., the size of the largest connected component divided by the number of edges, or Phi_k=k_{max}/M, the largest degree in the network divided by the number of edges. If, for example the energy is chosen to be E=-s_{max}, the observed transition is analogous to the percolation phase transition of random graphs. For this choice of the energy, the phase-diagram in the [ ,T] plane is constructed. Single vertex energies of the form E=sum_i f(k_i), where k_i is the degree of vertex i, are also studied. Depending on the form of f(k_i), first order and continuous phase transitions can be observed. In case of f(k_i)=-(k_i+c)ln(k_i), the transition is continuous, and at the critical temperature scale-free graphs can be recovered.

cond-mat.stat-mech↗
arXiv2003

Topological phase transitions of random networks

To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables us to establish an equivalence between the equilibrium rewiring problem we consider and the dynamics of a lattice gas on the edge-dual graph of a fully connected network. By assigning energies to the different network topologies and defining the appropriate order parameters, we find a rich variety of topological phase transitions, defined as singular changes in the essential feature(s) of the global connectivity as a function of a parameter playing the role of the temperature. In the ``critical point'' scale-free networks can be recovered.

cond-mat.stat-mech↗
arXiv2003

Protein induced morphological transitions in KCl crystal growth

We investigated the formation of KCl crystals on glass surface by phase contrast, fluorescent, and atomic force microscopy on the micrometer scale, and observed interesting morphological transitions as a function of the experimental conditions. The presence of proteins in the solution from which the salt crystals grow during the drying up leads to complex microscopic patterns of crystals some of which are analogous to those commonly observed on the macroscopic scale. We tested the effect of tubulin, FITC-labeled albumin and IgG on the morphology of crystals grown either slowly or fast. A rich variety of protein specific and concentration dependent morphologies was found and described by a morphological diagram. We give a phenomenological interpretation, which can explain the growth of complex patterns. Fluorescent images prove that a protein layer covers the surface of the KCl structures. We propose that this layer reduces the anisotropy of the effective surface tension during growth. The tip splitting fractal regime is attributed to the decrease of anisotropy. Other possible mechanisms, which can cause morphological transition, are also discussed. We found elongated saw-toothed crystals induced by proteins, especially IgG and identified their structure.

physics.bio-ph↗
arXiv2002

DNA uptake into nuclei: Numerical and analytical results

The dynamics of polymer translocation through a pore has been the subject of recent theoretical and experimental works. We have considered theoretical estimates and performed computer simulations to understand the mechanism of DNA uptake into the cell nucleus, a phenomenon experimentally investigated by attaching a small bead to the free end of the double helix and pulling this bead with the help of an optical trap. The experiments show that the uptake is monotonous and slows down when the remaining DNA segment becomes very short. Numerical and analytical studies of the entropic repulsion between the DNA filament and the membrane wall suggest a new interpretation of the experimental observations. Our results indicate that the repulsion monotonically decreases as the uptake progresses. Thus, the DNA is pulled in (i) either by a small force of unknown origin, and then the slowing down can be interpreted only statistically; (ii) or by a strong but slow ratchet mechanism, which would naturally explain the observed monotonicity, but then the slowing down requires additional explanations. Only further experiments can unambiguously distinguish between these two mechanisms.

cond-mat.soft↗
arXiv2002

Crowd behaves as excitable media during Mexican wave

Mexican wave, or La Ola, first widely broadcasted during the 1986 World Cup held in Mexico, is a human wave moving along the stands of stadiums as one section of spectators stands up, arms lifting, then sits down as the next section does the same. Here we use variants of models originally developed for the description of excitable media to demonstrate that this collective human behaviour can be quantitatively interpreted by methods of statistical physics. Adequate modelling of reactions to triggering attempts provides a deeper insight into the mechanisms by which a crowd can be stimulated to execute a particular pattern of behaviour and represents a possible tool of control during events involving excited groups of people.

cond-mat.stat-mech↗
arXiv2002

Deterministic Scale-Free Networks

Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are stochastic, that is they create networks in which the nodes appear to be randomly connected to each other. Here we propose a simple model that generates scale-free networks in a deterministic fashion. We solve exactly the model, showing that the tail of the degree distribution follows a power law.

cond-mat.stat-mech↗
arXiv2001

Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law

Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to describe the spectral density of uncorrelated random graphs, much less is known about the eigenvalues of real-world graphs, describing such complex systems as the Internet, metabolic pathways, networks of power stations, scientific collaborations or movie actors, which are inherently correlated and usually very sparse. An important limitation in addressing the spectra of these systems is that the numerical determination of the spectra for systems with more than a few thousand nodes is prohibitively time and memory consuming. Making use of recent advances in algorithms for spectral characterization, here we develop new methods to determine the eigenvalues of networks comparable in size to real systems, obtaining several surprising results on the spectra of adjacency matrices corresponding to models of real-world graphs. We find that when the number of links grows as the number of nodes, the spectral density of uncorrelated random graphs does not converge to the semi-circle law. Furthermore, the spectral densities of real-world graphs have specific features depending on the details of the corresponding models. In particular, scale-free graphs develop a triangle-like spectral density with a power law tail, while small-world graphs have a complex spectral density function consisting of several sharp peaks. These and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks.

cond-mat.stat-mech↗
arXiv2001

Segregation of granular binary mixtures by a ratchet mechanism

We report on a segregation scheme for granular binary mixtures, where the segregation is performed by a ratchet mechanism realized by a vertically shaken asymmetric sawtooth-shaped base in a quasi-two-dimensional box. We have studied this system by computer simulations and found that most binary mixtures can be segregated using an appropriately chosen ratchet, even when the particles in the two components have the same size, and differ only in their normal restitution coefficient or friction coefficient. These results suggest that the components of otherwise non-segregating granular mixtures may be separated using our method.

cond-mat.stat-mech↗
arXiv2000

Simulating Dynamical Features of Escape Panic

One of the most disastrous forms of collective human behaviour is the kind of crowd stampede induced by panic, often leading to fatalities as people are crushed or trampled. Sometimes this behaviour is triggered in life-threatening situations such as fires in crowded buildings; at other times, stampedes can arise from the rush for seats or seemingly without causes. Tragic examples within recent months include the panics in Harare, Zimbabwe, and at the Roskilde rock concert in Denmark. Although engineers are finding ways to alleviate the scale of such disasters, their frequency seems to be increasing with the number and size of mass events. Yet, systematic studies of panic behaviour, and quantitative theories capable of predicting such crowd dynamics, are rare. Here we show that simulations based on a model of pedestrian behaviour can provide valuable insights into the mechanisms of and preconditions for panic and jamming by incoordination. Our results suggest practical ways of minimising the harmful consequences of such events and the existence of an optimal escape strategy, corresponding to a suitable mixture of individualistic and collective behaviour.

cond-mat.stat-mech↗
arXiv2000

Theory of periodic swarming of bacteria: application to Proteus mirabilis

The periodic swarming of bacteria is one of the simplest examples for pattern formation produced by the self-organized collective behavior of a large number of organisms. In the spectacular colonies of Proteus mirabilis (the most common species exhibiting this type of growth) a series of concentric rings are developed as the bacteria multiply and swarm following a scenario periodically repeating itself. We have developed a theoretical description for this process in order to get a deeper insight into some of the typical processes governing the phenomena in systems of many interacting living units. All of our theoretical results are in excellent quantitative agreement with the complete set of available observations.

physics.bio-ph↗
arXiv2000

Freezing by Heating in a Driven Mesoscopic System

We investigate a simple model corresponding to particles driven in opposite directions and interacting via a repulsive potential. The particles move off-lattice on a periodic strip and are subject to random forces as well. We show that this model - which can be considered as a continuum version of some driven diffusive systems - exhibits a paradoxial, new kind of transition called here ``freezing by heating''. One interesting feature of this transition is that a crystallized state with a higher total energy is obtained from a fluid state by increasing the amount of fluctuations.

cond-mat.stat-mech↗
arXiv1999

Optimal Self-Organization

We present computational and analytical results indicating that systems of driven entities with repulsive interactions tend to reach an optimal state associated with minimal interaction and minimal dissipation. Using concepts from non-equilibrium thermodynamics and game theoretical ideas, we generalize this finding to an even wider class of self-organizing systems which have the ability to reach a state of maximal overall ``success''. This principle is expected to be relevant for driven systems in physics like sheared granular media, but it is also applicable to biological, social, and economic systems, for which only a limited number of quantitative principles are available yet.

cond-mat.stat-mech↗
arXiv1999

Self-Organised Optimality in Driven Systems with Symmetrical Interactions

Extremal principles are fundamental in our interpretation of phenomena in nature. One of the best known examples is the second law of thermodynamics, governing most physical and chemical systems and stating the continuous increase of entropy in closed systems. Biological and social systems, however, are usually open and characterised by self-organised structures. Being results of an evolutionary optimisation process, one may conjecture that such systems use resources like energy very efficiently, but there is no proof for this. Recent results on driven systems indicate that systems composed of competing entities tend to reach a state of self-organised optimality associated with minimal interaction or minimal dissipation, respectively. Using concepts from non-equilibrium thermodynamics and game theoretical ideas, we will show that this is universal to an even wider class of systems which, generally speaking, have the ability to reach a state of maximal overall ``success''. This principle is expected to be relevant for driven systems in physics, but its main significance concerns biological and social systems, for which only a limited number of quantitative principles are available yet.

cond-mat.stat-mech↗
arXiv1998

Realistic Models of Biological Motion

The origin of biological motion can be traced back to the function of molecular motor proteins. Cytoplasmic dynein and kinesin transport organelles within our cells moving along a polymeric filament, the microtubule. The motion of the myosin molecules along the actin filaments is responsible for the contraction of our muscles. Recent experiments have been able to reveal some important features of the motion of individual motor proteins, and a new statistical physical description - often referred to as ``thermal ratchets'' - has been developed for the description of motion of these molecules. In this approach the motors are considered as Brownian particles moving along one-dimensional periodic structures due to the effect of nonequilibrium fluctuations. Assuming specific types of interaction between the particles the models can be made more realistic. We have been able to give analytic solutions for our model of kinesin with elastically coupled Brownian heads and for the motion of the myosin filament where the motors are connected through a rigid backbone. Our theoretical predictions are in a very good agreement with the various experimental results. In addition, we have considered the effects arising as a result of interaction among a large number of molecular motors, leading to a number of novel cooperative transport phenomena.

cond-mat.stat-mech↗
arXiv1998

Lattice-gas model for collective biological motion

A simple self-driven lattice-gas model for collective biological motion is introduced. We find weakly first order phase transition from individual random walks to collective migration. A mean-field theory is presented to support the numerical results.

cond-mat.stat-mech↗
arXiv1998

Cooperative Transport of Brownian Particles

We consider the collective motion of finite-sized, overdamped Brownian particles (e.g., motor proteins) in a periodic potential. Simulations of our model have revealed a number of novel cooperative transport phenomena, including (i) the reversal of direction of the net current as the particle density is increased and (ii) a very strong and complex dependence of the average velocity on both the size and the average distance of the particles.

cond-mat.stat-mech↗