arXiv subjects

Frantisek Slanina

Publications and source records attributed to Frantisek Slanina.

At least 19 recordsLinked to original sources

arXiv2025

Random cubic graph embedded in a hypercube: Entanglement spectrum and many-body localization

The schematic model of interacting spins is introduced, which combines the symmetry of hypercube with the simplicity of random regular graph with degree three, i.e. the random cubic graph. We study the localization transition in this model, which shares essential characteristics with the systems exhibiting many-body localization. Namely, we investigate the transition in terms of the entanglement entropy and entanglement spectrum. We also show that the most significant indicator of the localization transition is the failure of eigenstate thermalization hypothesis, when the distribution of matrix elements of local operators changes from Gasussian to bimodal. It also provides good estimate for the critical disorder strength.

cond-mat.stat-mech↗

arXiv2025

Short-range and long-range correlations in driven dense colloidal mixtures in narrow pores

The system of driven dense colloid mixture in a tube with diameter comparable with particle size is modeled by a generalization of asymmetric simple exclusion (ASEP) model. The generalization goes in two directions: relaxing the exclusion constraint by allowing several (but few) particles on a site, and by considering two species of particles, which differ by size and transport coefficients. We calculate the nearest-neighbor correlations using a variant of Kirkwood approximation and show by comparison with numerical simulations that the approximation provides quite accurate results. However, for long-range correlations, we show that the Kirkwood approximation is useless, as it predicts exponential decay of the density-density correlation function with distance, while simulation data indicate that the decay is algebraic. For one-component system, we show that the decay is governed by a power law with universal exponent close to 2. In two-component system, the correlation function behaves in more complicated manner; its sign oscillates but the envelope decays again very slowly and the decay is compatible with power-law with exponent somewhat lower than 2. Therefore, our generalization of ASEP belongs to different universality class than the ensemble of generalized ASEP models which are mappable to zero-range processes.

cond-mat.stat-mech↗

arXiv2025

Hydrodynamic approximations for driven dense colloidal mixtures in narrow pores

The system of driven dense colloid mixtures is studied in one-, two- and three-dimensional geometries. We calculate the diffusion coefficients and mobilities for each particle type, including cross-terms, in a hydrodynamic limit, using a mean-field-type approximation. The set of non-linear diffusion equations are then solved. In one dimension, analytical results are possible. We show that in mixtures, the ``Brazil nut'' phenomenon, or depletion of larger particles by force of smaller ones, appears quite generically. We calculate the ratchet current and quantify the capability of sorting particles according to their size. We also indicate that the ``Brazil nut'' effect lies behind the possibility of perfect separation, where large and big particles travel in strictly opposite direction.

cond-mat.stat-mech↗

arXiv2025

Ratchet effect and jamming in dense mixtures of active and passive colloids in narrow pores

Using the framework of generalized exclusion processes we study mixtures of passive and active particles interacting by steric repulsion. The particles move in a pore with periodically modulated aperture, which is modeled by a quasi-one-dimensional channel with periodic tooth-shaped profile. Internal driving of the active particles induces a ratchet current of these particles. In the current-density diagram, we observe three main regimes: of free flow; of thermally activated processes; of spinodal decomposition. When the density of particles is increased, we observe a transition to jammed state, where the ratchet current is substantially reduced. In time evolution, the transition to jammed state is seen as sudden drop of current at certain time. The probability distribution of these jamming times follows an exponential law. The average jamming time depends itself exponentially on the density of active particles. The coefficient in this exponential is nearly independent of the switching rate of the active particles as well as on the presence or absence of passive particles. Due to the interaction, the current of active particles imposes a drag on the passive particles. In the limit of both large systems and long times, the current of passive particles has always the same direction as the ratchet current of active particles. However, during the evolution of the system we observe very slow (logarithmic in time) approach to the asymptotic value, sometimes accompanied by current reversal, i.e. current of active and passive particles may go in opposite direction.

cond-mat.stat-mech↗

arXiv2017

Inertial hydrodynamic ratchet: Rectification of colloidal flow in tubes of variable diameter

We investigate analytically a microfluidic device consisting of a tube with non-uniform but spatially periodic diameter, where a fluid driven back and forth by a pump carries colloidal particles. Although the net flow of the fluid is zero, the particles move preferentially in one direction due to ratchet mechanism, which occurs by simultaneous effect of inertial hydrodynamics and Brownian motion. We show that the average current is strongly sensitive to particle size, thus facilitating colloidal particle sorting.

cond-mat.soft↗

arXiv2017

Localization in random bipartite graphs: numerical and empirical study

We investigate adjacency matrices of bipartite graphs with power-law degree distribution. Motivation for this study is twofold. First, vibrational states in granular matter and jammed sphere packings; second, graphs encoding social interaction, especially electronic commerce. We establish the position of the mobility edge, and show that it strongly depends on the power in the degree distribution and on the ratio of the sizes of the two parts of the bipartite graph. At the jamming threshold, where the two parts have the same size, localization vanishes. We found that the multifractal spectrum is non-trivial in the delocalized phase, but still near the mobility edge. We also study an empirical bipartite graph, namely the Amazon reviewer-item network. We found that in this specific graph mobility edge disappears and we draw a conclusion from this fact regarding earlier empirical studies of the Amazon network.

physics.soc-ph↗

arXiv2014

Diversity of scales makes an advantage: The case of the Minority Game

We use the Minority Game as a testing frame for the problem of the emergence of diversity in socio-economic systems. For the MG with heterogeneous impacts, we show that the direct generalization of the usual agents' profit does not fit some real-world situations. As a typical example we use the traffic formulation of the MG. Taking into account vehicles of various lengths it can easily happen that one of the roads is crowded by a few long trucks and the other contains more drivers but still is less covered by vehicles. Most drivers are in the shorter queue, so the majority win. To describe such situations, we generalized the formula for agents' profit by explicitly introducing utility function depending on an agent's impact. Then, the overall profit of the system may become positive depending on the actual choice of the utility function. We investigated several choices of the utility function and showed that this variant of the MG may turn into a positive sum game.

q-fin.TR↗

arXiv2014

Dynamical phase transitions in Hegselmann-Krause model of opinion dynamics and consensus

The dynamics of the model of agents with limited confidence introduced by Hegselmann and Krause exhibits multiple well-separated regimes characterised by the number of distinct clusters in the stationary state. We present indications that there are genuine dynamical phase transitions between these regimes. The main indicator is the divergence of the average evolution time required to reach the stationary state. The slowdown close to the transition is connected with the emergence of the groups of mediator agents which are very small but have decisive role in the process of social convergence. More detailed study shows that the histogram of the evolution times is composed of several peaks. These peaks are unambiguously interpreted as corresponding to mediator groups consisting of one, two, three etc. agents. Detailed study reveals that each transition possesses also an internal fine structure.

physics.soc-ph↗

arXiv2014

Complex temporal structure of activity in on-line electronic auctions

We analyze empirical data from the internet auction site Aukro.cz. The time series of activity shows truncated fractal structure on scales from about 1 minute to about 1 day. The distribution of waiting times as well as the distribution of number of auctions within fixed interval is a power law, with exponents $1.5$ and $3$, respectively. Possible implications for the modeling of stock-market fluctuations are briefly discussed.

q-fin.ST↗

arXiv2014

Modules in the metabolic network of E.coli with regulatory interactions

We examine the modular structure of the metabolic network when combined with the regulatory network representing direct regulation of enzymes by small metabolites in E.coli. In order to identify the modular structure we introduce clustering algorithm based on a novel vertex similarity measure for bipartite graphs. We also apply a standard module identification method based on simulated annealing. Both methods identify the same modular core each of them with different resolution. We observe slight but still statistically significant increase of modularity after regulatory interactions addition. Enrichment of the metabolic network with the regulatory information leads to identification of new functional modules, which cannot be detected in the metabolic network only. Regulatory loops in the modules are the source of their self-control, i.e. autonomy, and allow to make hypothesis about module function. This study demonstrates that incorporation of regulatory information is important component in defining functional units of the metabolic network.

q-bio.MN↗

arXiv2014

Localization of eigenvectors in random graphs

Using exact numerical diagonalization, we investigate localization in two classes of random matrices corresponding to random graphs. The first class comprises the adjacency matrices of Erdos-Renyi (ER) random graphs. The second one corresponds to random cubic graphs, with Gaussian random variables on the diagonal. We establish the position of the mobility edge, applying the finite-size analysis of the inverse participation ratio. The fraction of localized states is rather small on the ER graphs and decreases when the average degree increases. On the contrary, on cubic graphs the fraction of localized states is large and tends to $1$ when the strength of the disorder increases, implying that for sufficiently strong disorder all states are localized. The distribution of the inverse participation ratio in localized phase has finite width when the system size tends to infinity and exhibits complicated multi-peak structure. We also confirm that the statistics of level spacings is Poissonian in the localized regime, while for extended states it corresponds to the Gaussian orthogonal ensemble.

cond-mat.stat-mech↗

arXiv2011

Interacting molecular motors: Efficiency and work fluctuations

We investigate the model of "reversible ratchet" with interacting particles, introduced by us earlier [Europhys. Lett. 84, 50009 (2008)]. We further clarify the effect of efficiency enhancement due to interaction and show that it is of energetic origin, rather than a consequence of reduced fluctuations. We also show complicated structures emerging in the interaction and density dependence of the current and response function. The fluctuation properties of the work and input energy indicate in detail the far-from-equilibrium nature of the dynamics.

cond-mat.stat-mech↗

arXiv2011

Equivalence of replica and cavity methods for computing spectra of sparse random matrices

We show by direct calculation that the replica and cavity methods are exactly equivalent for the spectrum of Erdos-Renyi random graph. We introduce a variational formulation based on the cavity method and use it to find approximate solutions for the density of eigenvalues. We also use this variational method for calculating spectra of sparse covariance matrices.

cond-mat.stat-mech↗

arXiv2011

Eigenvector localization as a tool to study small communities in online social networks

We present and discuss a mathematical procedure for identification of small "communities" or segments within large bipartite networks. The procedure is based on spectral analysis of the matrix encoding network structure. The principal tool here is localization of eigenvectors of the matrix, by means of which the relevant network segments become visible. We exemplified our approach by analyzing the data related to product reviewing on Amazon.com. We found several segments, a kind of hybrid communities of densely interlinked reviewers and products, which we were able to meaningfully interpret in terms of the type and thematic categorization of reviewed items. The method provides a complementary approach to other ways of community detection, typically aiming at identification of large network modules.

physics.soc-ph↗

arXiv2010

A contribution to the systematics of stochastic volatility models

We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution has generically a stretched-exponential form, but can assume also an algebraic decay, in the family of models which we call ``GARCH''-type. The intermediate regime is found in the exponential Ornstein-Uhlenbeck process. We calculate also the decay of the autocorrelation function of volatility.

q-fin.ST↗

arXiv2010

Interaction of molecular motors can enhance their efficiency

Particles moving in oscillating potential with broken mirror symmetry are considered. We calculate their energetic efficiency, when acting as molecular motors carrying a load against external force. It is shown that interaction between particles enhances the efficiency in wide range of parameters. Possible consequences for artificial molecular motors are discussed.

cond-mat.stat-mech↗

arXiv2008

Critical comparison of several order-book models for stock-market fluctuations

Far-from-equilibrium models of interacting particles in one dimension are used as a basis for modelling the stock-market fluctuations. Particle types and their positions are interpreted as buy and sell orders placed on a price axis in the order book. We revisit some modifications of well-known models, starting with the Bak-Paczuski-Shubik model. We look at the four decades old Stigler model and investigate its variants. One of them is the simplified version of the Genoa artificial market. The list of studied models is completed by the models of Maslov and Daniels et al. Generically, in all cases we compare the return distribution, absolute return autocorrelation and the value of the Hurst exponent. It turns out that none of the models reproduces satisfactorily all the empirical data, but the most promising candidates for further development are the Genoa artificial market and the Maslov model with moderate order evaporation.

q-fin.TR↗

arXiv2005

Loop expansion around the Bethe-Peierls approximation for lattice models

We develop an effective field theory for lattice models, in which the only non-vanishing diagrams exactly reproduce the topology of the lattice. The Bethe-Peierls approximation appears naturally as the saddle point approximation. The corrections to the saddle-point result can be obtained systematically. We calculate the lowest loop corrections for magnetisation and correlation function.

cond-mat.stat-mech↗