arXiv subjects

Miroslav Kotrla

Publications and source records attributed to Miroslav Kotrla.

18 recordsLinked to original sources

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↗

arXiv2012

The first-principles study of thermodynamical properties of random magnetic overlayers on fcc-Cu(001) substrate

We present the theoretical study of thermodynamical properties of fcc-Cu(001) substrate covered by iron-cobalt monolayer as well as by incomplete iron layer. The effective two-dimensional Heisenberg Hamiltonian is constructed from first principles and properties of exchange interactions are investigated. The Curie temperatures are estimated using the Monte-Carlo (MC) simulations and compared with a simplified approach using the random-phase approximation (RPA) in connection with the virtual-crystal approach (VCA) to treat randomness in exchange integrals. Calculations indicate a weak maximum of the Curie temperature as a function of composition of the iron-cobalt overlayer. While a good quantitative agreement between RPA-VCA and MC was found for iron-cobalt monolayer, the RPA-VCA approach fails quantitatively for low coverage due to the magnetic percolation effect. We also present the study of the effect of alloy disorder on the shape of magnon spectra of random overlayers.

cond-mat.mtrl-sci↗

arXiv2008

Heterogeneous nucleation and adatom detachment at 1-D growth of Indium on Si(100)-2x1

Growth of atomic indium chains - 1D islands - on the Si(100)-2x1 surface was observed by scanning tunneling microscopy (STM) at room temperature and simulated by means of a kinetic Monte Carlo method. Density of indium islands and island size distribution were obtained for various deposition rates and coverage. STM observation of growth during deposition of indium provided information on growth kinetics and relaxation of grown layers. Important role of C-type defects at adsorption of metal atoms was observed. Measured growth characteristics were simulated using a microscopic model with anisotropic surface diffusion and forbidden zones along the metal chains. An analysis of experimental and simulation data shows that detachment of indium adatoms from the chains substantially influences a growth scenario and results in monotonously decreasing chain length distribution function at low coverage. Diffusion barriers determined from the simulations correspond to almost isotropic diffusion of indium adatoms on the surface. The results are discussed with respect to data reported in earlier papers for other metals.

cond-mat.mtrl-sci↗

arXiv2008

Study of the island morphology at the early stages of Fe/Mo(110) MBE growth

We present theoretical study of morphology of Fe islands grown at Mo(110) surface in sub-monolayer MBE mode. We utilize atomistic SOS model with bond counting, and interactions of Fe adatom up to third nearest neighbors. We performed KMC simulations for different values of adatom interactions and varying temperatures. We have found that, while for the low temperature islands are fat fractals, for the temperature 500K islands have faceted rhombic-like shape. For the higher temperature, islands acquire a rounded shape. In order to evaluated qualitatively morphological changes, we measured averaged aspect ration of islands. We calculated dependence of the average aspect ratio on the temperature, and on the strength of interactions of an adatom with neighbors.

cond-mat.mtrl-sci↗

arXiv2004

Kinetics of step bunching during growth: A minimal model

We study a minimal stochastic model of step bunching during growth on a one-dimensional vicinal surface. The formation of bunches is controlled by the preferential attachment of atoms to descending steps (inverse Ehrlich-Schwoebel effect) and the ratio $d$ of the attachment rate to the terrace diffusion coefficient. For generic parameters ($d > 0$) the model exhibits a very slow crossover to a nontrivial asymptotic coarsening exponent $β\simeq 0.38$. In the limit of infinitely fast terrace diffusion ($d=0$) linear coarsening ($β$ = 1) is observed instead. The different coarsening behaviors are related to the fact that bunches attain a finite speed in the limit of large size when $d=0$, whereas the speed vanishes with increasing size when $d > 0$. For $d=0$ an analytic description of the speed and profile of stationary bunches is developed.

cond-mat.stat-mech↗

arXiv2002

Dynamic scaling and universality in evolution of fluctuating random networks

We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys. Rev. Lett. 83, 5587 (1999)]. The averaged size and connectivity of the network increase as power-laws in early times but later saturate. Saturated values and times of saturation change with paramaters controlling the local evolution of the network topology. Both saturated values and times of saturation obey also power-law dependences on controlling parameters. Scaling exponents are calculated and universal features are discussed.

cond-mat.stat-mech↗

arXiv2002

Competing mechanisms for step meandering in unstable growth

The meander instability of a vicinal surface growing under step flow conditions is studied within a solid-on-solid model. In the absence of edge diffusion the selected meander wavelength agrees quantitatively with the continuum linear stability analysis of Bales and Zangwill [Phys. Rev. B {\bf 41}, 4400 (1990)]. In the presence of edge diffusion a local instability mechanism related to kink rounding barriers dominates, and the meander wavelength is set by one-dimensional nucleation. The long-time behavior of the meander amplitude differs in the two cases, and disagrees with the predictions of a nonlinear step evolution equation [O. Pierre-Louis et al., Phys. Rev. Lett. {\bf 80}, 4221 (1998)]. The variation of the meander wavelength with the deposition flux and with the activation barriers for step adatom detachment and step crossing (the Ehrlich-Schwoebel barrier) is studied in detail. The interpretation of recent experiments on surfaces vicinal to Cu(100) [T. Maroutian et al., Phys. Rev. B {\bf 64}, 165401 (2001)] in the light of our results yields an estimate for the kink barrier at the close packed steps.

cond-mat.stat-mech↗

arXiv2001

Effects of atomic interactions in two component submonolayer growth

We discuss effects of the different chemical bondings on the island morphology and on the island density scaling in two-component submonolayer growth. Different regimes depending on the strength of the mutual interactions and on the relative mobility of species are described and studied by kinetic Monte Carlo simulations using a two-component solid-on-solid growth model. Results for the temperature and flux dependence of the island density as well as examples of the surface morphologies are presented.

cond-mat.mtrl-sci↗

arXiv2001

Effects of adsorbates on submonolayer growth

The effects of adsorbates on nucleation and growth of two-dimensional islands is investigated by kinetic Monte Carlo simulations and rate equation theory. The variation of island morphology with adsorbate parameters is discussed and the temperature-dependence of island density in the case of immobile adsorbates is studied in detail. A set of rate equations for the description of nucleation in the presence of predeposited mobile and immobile adsorbates is developed.

cond-mat.mtrl-sci↗

arXiv2000

Random networks created by biological evolution

We investigate a model of evolving random network, introduced by us previously {[}{\it Phys. Rev. Lett.} {\bf 83}, 5587 (1999){]} . The model is a generalization of the Bak-Sneppen model of biological evolution, with the modification that the underlying network can evolve by adding and removing sites. The behavior and the averaged properties of the network depend on the parameter $p$, the probability to establish link to the newly introduced site. For $p=1$ the system is self-organized critical, with two distinct power-law regimes with forward-avalanche exponents $τ=1.98\pm 0.04$ and $τ^\prime = 1.65\pm 0.05$. The average size of the network diverge as power-law when $p\to 1$. We study various geometrical properties of the network: probability distribution of sizes and connectivities, size and number of disconnected clusters and the dependence of mean distance between two sites on the cluster size. The connection with models of growing networks with preferential attachment is discussed.

cond-mat.stat-mech↗

arXiv2000

Submonolayer epitaxy with impurities

The effect of impurities on epitaxial growth in the submonolayer regime is studied using kinetic Monte Carlo simulations of a two-species solid-on-solid growth model. Both species are mobile, and attractive interactions among adatoms and between adatoms and impurities are incorporated. Impurities can be codeposited with the growing material or predeposited prior to growth. The activated exchange of impurities and adatoms is identified as the key kinetic process in the formation of a growth morphology in which the impurities decorate the island edges. The dependence of the island density on flux and coverage is studied in detail. The impurities strongly increase the island density without appreciably changing its power-law dependence on flux, apart from a saturation of the flux dependence at high fluxes and low coverages. A simple analytic theory taking into account only the dependence of the adatom diffusion constant on impurity coverage is shown to provide semi-quantitative agreement with many features observed in the simulations.

cond-mat.mtrl-sci↗

arXiv1999

Submonolayer growth with decorated island edges

We study the dynamics of island nucleation in the presence of adsorbates using kinetic Monte Carlo simulations of a two-species growth model. Adatoms (A-atoms) and impurities (B-atoms) are codeposited, diffuse and aggregate subject to attractive AA- and AB-interactions. Activated exchange of adatoms with impurities is identified as the key process to maintain decoration of island edges by impurities during growth. While the presence of impurities strongly increases the island density, a change in the scaling of island density with flux, predicted by a rate equation theory for attachment-limited growth [D. Kandel, Phys. Rev. Lett. 78, 499 (1997)], is not observed. We argue that, within the present model, even completely covered island edges do not provide efficient barriers to attachment.

cond-mat.mtrl-sci↗

arXiv1999

Extremal dynamics model on evolving networks

We investigate an extremal dynamics model of evolution with a variable number of units. Due to addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly concentrated in the largest cluster. The time dependence of the number of units exhibits intermittent structure. The self-organized criticality is manifested by a power-law distribution of forward avalanches, but two regimes with distinct exponents tau = 1.98 +- 0.04 and tau^prime = 1.65 +- 0.05 are found. The distribution of extinction sizes obeys a power law with exponent 2.32 +- 0.05.

cond-mat.stat-mech↗

arXiv1998

Scaling in the two-component surface growth

We studied scaling in kinetic roughening and phase ordering during growth of binary systems using 1+1 dimensional single-step solid-on-solid model with two components interacting via Ising-like interaction with the strength K. We found that the model exhibits crossover from the intermediate regime, with effective scaling exponents for kinetic roughening significantly larger than for the ordinary single-step growth model, to asymptotic regime with exponents of the Kardar-Parisi-Zhang class. Crossover time and length are exponentially increasing with K. For a given large K, scaling with enhanced exponents is valid over many decades. The effective scaling exponents are continuously increasing with K. Surface ordering proceeds up to crossover. Average size of surface domains increases during growth with the exponent close to 1/2, the spin-spin correlation function and the distribution of domains obey scaling with the same exponent.

cond-mat.stat-mech↗

arXiv1997

Interplay between kinetic roughening and phase ordering

We studied interplay between kinetic roughening and phase ordering in 1+1 dimensional single-step solid-on-solid growth model with two kinds of particles and Ising-like interaction. Evolution of both geometrical and compositional properties was investigated by Monte Carlo simulations for various strengths of coupling. We found that the initial growth is strongly affected by interaction between species, scaling exponents are enhanced and the ordering on the surface is observed. However, after certain time, ordering along the surface stops and the scaling exponents cross over to exponents of the Kardar-Parisi-Zhang universality class. For sufficiently strong strength of coupling, ordering in vertical direction is present and leads to columnar structure persisting for a long time.

cond-mat.stat-mech↗

arXiv1994

Crossover effects in the Wolf-Villain model of epitaxial growth in 1+1 and 2+1 dimensions

A simple model of epitaxial growth proposed by Wolf and Villain is investigated using extensive computer simulations. We find an unexpectedly complex crossover behavior of the original model in both 1+1 and 2+1 dimensions. A crossover from the effective growth exponent $β_{\rm eff}\!\approx\!0.37$ to $β_{\rm eff}\!\approx\!0.33$ is observed in 1+1 dimensions, whereas additional crossovers, which we believe are to the scaling behavior of an Edwards--Wilkinson type, are observed in both 1+1 and 2+1 dimensions. Anomalous scaling due to power--law growth of the average step height is found in 1+1 D, and also at short time and length scales in 2+1~D. The roughness exponents $ζ_{\rm eff}^{\rm c}$ obtained from the height--height correlation functions in 1+1~D ($\approx\!3/4$) and 2+1~D ($\approx\!2/3$) cannot be simultaneously explained by any of the continuum equations proposed so far to describe epitaxial growth.

cond-mat↗