Tamás Vicsek | Eötvös Loránd University Budapest (original) (raw)

Papers by Tamás Vicsek

Bacterial colonies can develop chiral morphology in which the colony consists of twisted branches... more Bacterial colonies can develop chiral morphology in which the colony consists of twisted branches, all with the same handedness. Microscopic observations of the chiral growth are presented. We propose that the observed (macroscopic) chirality results from the microscopic chirality of the flagella (via handedness in tumbling) together with orientation interaction between the bacteria. The above assumptions are tested using a generalized version of the communicating walkers model.

chapter in Fractal Growth Phenomena

A simple model with a novel type of dynamics is introduced in order to investigate the emergence ... more A simple model with a novel type of dynamics is introduced in order to investigate the emergence
of self-ordered motion in systems of particles with biologically motivated interaction. In our model
particles are driven with a constant absolute velocity and at each time step assume the average direction
of motion of the particles in their neighborhood with some random perturbation (g) added. We present
numerical evidence that this model results in a kinetic phase transition from no transport (zero average
velocity, ~v, ( = 0) to finite net transport through spontaneous symmetry breaking of the rotational
symmetry. The transition is continuous, since ~v, ~ is found to scale as (71, —g)t with p = 0.45.

Wereview the observations and the basic laws describing the essential aspects of collective motio... more Wereview the observations and the basic laws describing the essential aspects of collective
motion — being one of the most common and spectacular manifestation of coordinated
behavior. Our aim is to provide a balanced discussion of the various facets of this highly
multidisciplinary field, including experiments, mathematical methods and models for
simulations, so that readers with a variety of background could get both the basics and
a broader, more detailed picture of the field. The observations we report on include
systems consisting of units ranging from macromolecules through metallic rods and
robots to groups of animals and people. Some emphasis is put on models that are simple
and realistic enough to reproduce the numerous related observations and are useful for
developing concepts for a better understanding of the complexity of systems consisting
of many simultaneously moving entities. As such, these models allow the establishing of
a few fundamental principles of flocking. In particular, it is demonstrated, that in spite of
considerable differences, a number of deep analogies exist between equilibrium statistical
physics systems and those made of self-propelled (in most cases living) units. In both cases
only a few well defined macroscopic/collective states occur and the transitions between

Contents Preface ... more Contents
Preface
5
Introduction
7
1 Basic concepts (T. Vicsek)
11
1.1 Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.1.1 Noise versus ﬂuctuations . . . . . . . . . . . . . . . . . . . . . 13
1.1.2 Molecular motors driven by noise and ﬂuctuations . . . . . . . 14
1.2 Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2.1 Critical behaviour . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2.2 Scaling of event sizes: Avalanches . . . . . . . . . . . . . . . . 17
1.2.3 Scaling of patterns and sequences: Fractals . . . . . . . . . . . 19
1.2.4 Scaling in group motion: Flocks . . . . . . . . . . . . . . . . . 22
2 Introduction to complex patterns, ﬂuctuations and scaling 25
2.1 Fractal geometry (T. Vicsek) . . . . . . . . . . . . . . . . . . . . . .
. 26
2.1.1 Fractals as mathematical and biological objects . . . . . . . . 27
2.1.2 Deﬁnitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.3 Useful rules . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 31
2.1.4 Self-similar and self-aﬃne fractals . . . . . . . . . . . . . . . . 33
2.1.5 Multifractals . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.1.6 Methods for determining fractal dimensions . . . . . . . . . . 36
2.2 Stochastic processes (I. Der´´enyi) . . . . . . . . . . . . . . . . . . . . 39
2.2.1 The physics of microscopic objects . . . . . . . . . . . . . . . 39
2.2.2 Kramers formula and Arrhenius law . . . . . . . . . . . . . . 41
2.3 Continuous phase transitions (Z. Csah´´ok) . . . . . . . . . . . . . . . . 43
2.3.1 The Potts model . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.3.2 Mean-ﬁeld approximation . . . . . . . . . . . . . . . . . . . . 46
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
1

2
CONTENTS
3 Self-organised criticality (SOC) (Z. Csah´ok) 53
3.1 SOC model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 54
3.2 Applications in biology . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.1 SOC model of evolution . . . . . . . . . . . . . . . . . . . . . 56
3.2.2 SOC in lung inﬂation . . . . . . . . . . . . . . . . . . . . . . . 62
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4 Patterns and correlations
67
4.1 Bacterial colonies (A. Czir´ok) . . . . . . . . . . . . . . . . . . . . . . 67
4.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1.2 Bacteria in colonies . . . . . . . . . . . . . . . . . . . . . . . .
68
4.1.3 Compact morphology . . . . . . . . . . . . . . . . . . . . . . . 75
4.1.4 Branching morphology . . . . . . . . . . . . . . . . . . . . . . 86
4.1.5 Chiral and rotating colonies . . . . . . . . . . . . . . . . . . . 104
4.2 Statistical analysis of DNA sequences (T. Vicsek) . . . . . . . . . . . 112
4.2.1 DNA walk . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 113
4.2.2 Word frequency analysis . . . . . . . . . . . . . . . . . . . . . 117
4.2.3 Vector space techniques . . . . . . . . . . . . . . . . . . . . . 117
4.3 Analysis of brain electrical activity: the dimensional complexity of the electroencephalogram
(M. Moln´ar) . . . . . . . . . . . . . . . . . . . 120
4.3.1 Neurophysiological basis of the electroencephalogram and event- related potentials . . .
. . . . . . . . . . . . . . . . . . . . . . 120
4.3.2 Linear and non-linear methods for the analysis of the EEG . . 122
4.3.3 Examples for the application of PD2 to EEG and ERP analysis 125
4.3.4 Dimensional analysis of ERPs . . . . . . . . . . . . . . . . . . 128
4.3.5 Clinical applications . . . . . . . . . . . . . . . . . . . . . . . 132
4.3.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . 135
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5 Microscopic mechanisms of biological motion (I. Der´enyi, T. Vicsek) 147
5.1 Characterisation of motor proteins . . . . . . . . . . . . . . . . . . . 147
5.1.1 Cytoskeleton . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.1.2 Muscle contraction . . . . . . . . . . . . . . . . . . . . . . . . 151
5.1.3 Rotary motors . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.1.4 Motility assay . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5.2 Fluctuation driven transport . . . . . . . . . . . . . . . . . . . . . . . 160
5.2.1 Basic ratchet models . . . . . . . . . . . . . . . . . . . . . . . 162
5.2.2 Brief overview of the models . . . . . . . . . . . . . . . . . . . 163
5.2.3 Illustration of the second law of thermodynamics . . . . . . . 164

CONTENTS
3
5.3 Realistic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
5.3.1 Kinesin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
5.3.2 Myosin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
5.3.3 ATP synthase . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
5.4 Collective eﬀects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
5.4.1 Finite sized particles in a “rocking ratchet” . . . . . . . . . . . 192
5.4.2 Finite sized particles in a “ﬂashing ratchet” . . . . . . . . . . 199
5.4.3 Collective behaviour of rigidly attached particles . . . . . . . . 205
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
6 Collective motion
217
6.1 Flocking: collective motion of self-propelled particles (A. Czir´ok, T. Vicsek) . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 217
6.1.1 Models and simulations . . . . . . . . . . . . . . . . . . . . . . 218
6.1.2 Scaling properties . . . . . . . . . . . . . . . . . . . . . . . . . 219
6.1.3 Further variants of SPP models . . . . . . . . . . . . . . . . . 228
6.1.4 Mean-ﬁeld theory for lattice models . . . . . . . . . . . . . . . 234
6.1.5 Continuum equations for the 1d system . . . . . . . . . . . . . 240
6.1.6 Hydrodynamic formulation for 2D . . . . . . . . . . . . . . . . 247
6.1.7 The existence of long-range order . . . . . . . . . . . . . . . . 251
6.2 Correlated Motion of Pedestrians (D. Helbing, P. Molna´r) . . . . . . 254
6.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
6.2.2 Pedestrian Dynamics . . . . . . . . . . . . . . . . . . . . . . . 255
6.2.3 Trail Formation . . . . . . . . . . . . . . . . . . . . . . . . . . 275
6.2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

Complex Adaptive Systems Modeling, 2013

Recently developed,concepts,and,techniques,of analyzing,complex,systems,provide new,insight into ... more Recently developed,concepts,and,techniques,of analyzing,complex,systems,provide new,insight into the structure of social networks. Uncovering,recurrent preferences,and,organizational,principles in such networks,is a key issue to characterize them. We investigate school friendship networks from the Add Health database. Applying threshold analysis, we find that the friendship networks,do not form a single connected,component,through,mutual,strong nominations,within a school, while under weaker conditions such interconnectedness is present. We extract the

Journal of Statistical Physics, 2014

ABSTRACT Gregarious animals need to make collective decisions in order to keep their cohesiveness... more ABSTRACT Gregarious animals need to make collective decisions in order to keep their cohesiveness. Several species of them live in multilevel societies, and form herds composed of smaller communities. We present a model for the development of a leadership hierarchy in a herd consisting of loosely connected sub-groups (e.g. harems) by combining self organization and social dynamics. It starts from unfamiliar individuals without relationships and reproduces the emergence of a hierarchical and modular leadership network that promotes an effective spreading of the decisions from more capable individuals to the others, and thus gives rise to a beneficial collective decision. Our results stemming from the model are in a good agreement with our observations of a Przewalski horse herd (Hortob\'agy, Hungary). We find that the harem-leader to harem-member ratio observed in Przewalski horses corresponds to an optimal network in this approach regarding common success, and that the observed and modeled harem size distributions are close to a lognormal.

2008 Second IEEE International Conference on Self-Adaptive and Self-Organizing Systems, 2008

Topics in Modern Statistical Physics, 1992

Physical Review Letters, 2001

New Journal of Physics, 2015

A number of novel experimental and theoretical results have recently been obtained on active soft... more A number of novel experimental and theoretical results have recently been obtained on active soft matter, demonstrating the various interesting universal and anomalous features of this kind of driven systems. Here we consider the adhesion difference-driven segregation of actively moving units, a fundamental but still poorly explored aspect of collective motility. In particular, we propose a model in which particles have a tendency to adhere through a mechanism which makes them both stay in touch and synchronize their direction of motion - but the interaction is limited to particles of the same kind. The calculations corresponding to the related differential equations can be made in parallel, thus a powerful GPU card allows large scale simulations. We find that in a very large system of particles, interacting without explicit alignment rule, three basic segregation regimes seem to exist as a function of time: i) at the beginning the time dependence of the correlation length is analogous to that predicted by the Cahn-Hillard theory, ii) next rapid segregation occurs characterized with a separation of the different kinds of units being faster than any previously suggested speed, finally, iii) the growth of the characteristic sizes in the system slows down due to a new regime in which self-confined, rotating, splitting and re-joining clusters appear. Our results can explain recent observations of segregating tissue cells in vitro.

Fractal Growth Phenomena, 1989

Understanding Complex Systems, 2009

Physica A: Statistical Mechanics and its Applications, 2002