arXiv subjects

Petr Seba

Publications and source records attributed to Petr Seba.

At least 19 recordsLinked to original sources

arXiv2010

Built-up structure criticality

The built-up land represents an important type of overall landscape. In this paper the built-up land structure in the largest cities in the Czech Republic and selected cities in the U.S.A. is analysed using the framework of statistical physics. We calculate the variance of the built-up area and the number variance of built-up landed plots in discs. In both cases the variance as a function of a disc radius follows a power law. The obtained values of power law exponents are comparable through different cities. The study is based on cadastral data from the Czech Republic and building footprints from GIS data in the U.S.A.

physics.soc-ph↗

arXiv2009

Walkers on the circle

We experimentally demonstrate that the statistical properties of distances between pedestrians which are hindered from avoiding each other are described by the Gaussian Unitary Ensemble of random matrices. The same result has recently been obtained for an $n$-tuple of non-intersecting (one-dimensional, unidirectional) random walks. Thus, the observed behavior of autonomous walkers conditioned not to cross their trajectories (or, in other words, to stay in strict order at any time) resembles non-intersecting random walks.

physics.soc-ph↗

arXiv2009

Departure of some parameter-dependent spectral statistics of irregular quantum graphs from Random Matrix Theory predictions

Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities c(x) and c(w,x) as well as the distributions of level curvatures and avoided crossing gaps are calculated. The numerical results are compared with the predictions of Random Matrix Theory (RMT) for Gaussian Orthogonal Ensemble (GOE) and for coupled GOE matrices. The application of coupled GOE matrices was justified by studying localization phenomena in graphs' wave functions Psi(x) using the Inverse Participation Ratio (IPR) and the amplitude distribution P(Psi(x)).

nlin.CD↗

arXiv2009

Parking and the visual perception of space

Using measured data we demonstrate that there is an amazing correspondence among the statistical properties of spacings between parked cars and the distances between birds perching on a power line. We show that this observation is easily explained by the fact that birds and human use the same mechanism of distance estimation. We give a simple mathematical model of this phenomenon and prove its validity using measured data.

physics.soc-ph↗

arXiv2009

Traffic and the visual perception of space

During the attempt to line up into a dense traffic people have necessarily to share a limited space under turbulent conditions. From the statistical point view it generally leads to a probability distribution of the distances between the traffic objects (cars or pedestrians). But the problem is not restricted on humans. It comes up again when we try to describe the statistics of distances between perching birds or moving sheep herd. Our aim is to demonstrate that the spacing distribution is generic and independent on the nature of the object considered. We show that this fact is based on the unconscious perception of space that people share with the animals. We give a simple mathematical model of this phenomenon and prove its validity on the real data that include the clearance distribution between: parked cars, perching birds, pedestrians, cars moving in a dense traffic and the distances inside a sheep herd.

physics.soc-ph↗

arXiv2009

Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption

We present the results of experimental and numerical study of the distribution of the reflection coefficient P(R) and the distributions of the imaginary P(v) and the real P(u) parts of the Wigner's reaction K matrix for irregular fully connected hexagon networks (graphs) in the presence of strong absorption. In the experiment we used microwave networks, which were built of coaxial cables and attenuators connected by joints. In the numerical calculations experimental networks were described by quantum fully connected hexagon graphs. The presence of absorption introduced by attenuators was modelled by optical potentials. The distribution of the reflection coefficient P(R) and the distributions of the reaction K matrix were obtained from the measurements and numerical calculations of the scattering matrix S of the networks and graphs, respectively. We show that the experimental and numerical results are in good agreement with the exact analytic ones obtained within the framework of random matrix theory (RMT).

nlin.CD↗

arXiv2008

Spectral rigidity of vehicular streams (Random Matrix Theory approach)

Using the methods originally developed for Random Matrix Theory we derive an exact mathematical formula for number variance (introduced in [4]) describing a rigidity of particle ensembles with power-law repulsion. The resulting relation is consequently compared with the relevant statistics of the single-vehicle data measured on the Dutch freeway A9. The detected value of an inverse temperature, which can be identified as a coefficient of a mental strain of car drivers, is then discussed in detail with the respect to the traffic density and flow.

math-ph↗

arXiv2008

Chaos in a one-dimensional integrable quantum system

We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties are nontrivial. The level spacing distribution between its neighboring odd and even levels displays a surprising agreement with the prediction obtained for the Gaussian Orthogonal Ensemble of random matrices.

quant-ph↗

arXiv2008

Spectral Density of Sample Covariance Matrices of Colored Noise

We study the dependence of the spectral density of the covariance matrix ensemble on the power spectrum of the underlying multivariate signal. The white noise signal leads to the celebrated Marchenko-Pastur formula. We demonstrate results for some colored noise signals.

physics.data-an↗

arXiv2008

Parking in the city: an example of limited resource sharing

During the attempt to park a car in the city the drivers have to share limited resources (the available roadside). We show that this fact leads to a predictable distribution of the distances between the cars that depends on the length of the street segment used for the collective parking. We demonstrate in addition that the individual parking maneuver is guided by generic psychophysical perceptual correlates. Both predictions are compared with the actual parking data collected in the city of Hradec Kralove (Czech Republic).

physics.soc-ph↗

arXiv2007

Parking in the city

We show that the spacing distribution between parked cars can be obtained as a solution of certain linear distributional fixed point equation. The results are compared with the data measured on the streets of Hradec Kralove. We also discuss a relation of this results to the random matrix theory.

nlin.AO↗

arXiv2007

Statistical variances in traffic data

We perform statistical analysis of the single-vehicle data measured on the Dutch freeway A9 and discussed in Ref. [2]. Using tools originating from the Random Matrix Theory we show that the significant changes in the statistics of the traffic data can be explained applying equilibrium statistical physics of interacting particles.

physics.data-an↗

arXiv2005

Metastable Congested States in Multisegment Traffic Cellular Automaton

We investigate a simple multisegment cellular automaton model of traffic flow. With the introduction of segment-dependent deceleration probability, metastable congested states in the intermediate density region emerge, and the initial state dependence of the flow is observed. The essential feature of three-phased structure empirically found in real-world traffic flow is reproduced without elaborate assumptions.

physics.soc-ph↗

arXiv2005

Approximations by graphs and emergence of global structures

We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wavefunctions approximate solutions of the Schroedinger equation with energy rescaled by the billiard dimension. As an example, we analyze a Sinai billiard with attached leads. The results illustrate emergence of global structures in large quantum graphs and offer interesting comparisons with patterns observed in complex networks of a different nature.

quant-ph↗

arXiv2004

Physics, Stability and Dynamics of Supply Networks

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the non-linear behaviour is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting new features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed "bull-whip effect" in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.

cond-mat.stat-mech↗

arXiv2002

Extended Standard Map with Spatio-Temporal Asymmetry

We analyze the transport properties of a set of symmetry-breaking extensions %, both spatial and temporal, of the Chirikov--Taylor Map. The spatial and temporal asymmetries result in the loss of periodicity in momentum direction in the phase space dynamics, enabling the asymmetric diffusion which is the origin of the unidirectional motion. The simplicity of the model makes the calculation of the global dynamical properties of the system feasible both in phase space and in controlling-parameter space. We present the results of numerical experiments which show the intricate dependence of the asymmetric diffusion to the controlling parameters.

cond-mat.stat-mech↗

arXiv2001

Resonances of the Frobenius-Perron Operator for a Hamiltonian Map with a Mixed Phase Space

Resonances of the (Frobenius-Perron) evolution operator P for phase-space densities have recently attracted considerable attention, in the context of interrelations between classical and quantum dynamics. We determine these resonances as well as eigenvalues of P for Hamiltonian systems with a mixed phase space, by truncating P to finite size in a Hilbert space of phase-space functions and then diagonalizing. The corresponding eigenfunctions are localized on unstable manifolds of hyperbolic periodic orbits for resonances and on islands of regular motion for eigenvalues. Using information drawn from the eigenfunctions we reproduce the resonances found by diagonalization through a variant of the cycle expansion of periodic-orbit theory and as rates of correlation decay.

nlin.CD↗

arXiv2001

Frobenius-Perron Resonances for Maps with a Mixed Phase Space

Resonances of the time evolution (Frobenius-Perron) operator P for phase space densities have recently been shown to play a key role for the interrelations of classical, semiclassical and quantum dynamics. Efficient methods to determine resonances are thus in demand, in particular for Hamiltonian systems displaying a mix of chaotic and regular behavior. We present a powerful method based on truncating P to a finite matrix which not only allows to identify resonances but also the associated phase space structures. It is demonstrated to work well for a prototypical dynamical system.

nlin.CD↗