arXiv subjects

Adam Lipowski

Publications and source records attributed to Adam Lipowski.

At least 55 records · Page 3Linked to original sources

arXiv2005

A model of student's dilemma

Each year perhaps millions of young people face the following dilemma: should I continue my education or rather start working with already acquired skills. Right decision must take into account somebody's own abilities, accessibility to education institutions, competition, and potential benefits. A multi-agent, evolutionary model of this dilemma predicts a transition between stratified and homogeneous phases, evolution that diminishes fitness, fewer applicants per seat for decreased capacity of the university, and presence of poor students at élite universities.

cond-mat.other↗

arXiv2005

Periodicity of mass extinctions without an extraterrestrial cause

We study a lattice model of a multi-species prey-predator system. Numerical results show that for a small mutation rate the model develops irregular long-period oscillatory behavior with sizeable changes in a number of species. The periodicity of extinctions on Earth was suggested by Raup and Sepkoski but so far is lacking a satisfactory explanation. Our model indicates that this is a natural consequence of the ecosystem dynamics, not the result of any extraterrestrial cause.

cond-mat.other↗

arXiv2004

Extinction dynamics of Lotka-Volterra ecosystems on evolving networks

We study a model of a multi-species ecosystem described by Lotka-Volterra-like equations. Interactions among species form a network whose evolution is determined by the dynamics of the model. Numerical simulations show power-law distribution of intervals between extinctions, but only for ecosystems with sufficient variability of species and with networks of connectivity above certain threshold that is very close to the percolation threshold of the network. Effect of slow environmental changes on extinction dynamics, degree distribution of the network of interspecies interactions, and some emergent properties of our model are also examined.

q-bio.PE↗

arXiv2003

Synchronization and partial synchronization of linear maps

We study synchronization of low-dimensional ($d=2,3,4$) chaotic piecewise linear maps. For Bernoulli maps we find Lyapunov exponents and locate the synchronization transition, that numerically is found to be discontinuous (despite continuously vanishing Lyapunov exponent(s)). For tent maps, a limit of stability of the synchronized state is used to locate the synchronization transition that numerically is found to be continuous. For nonidentical tent maps at the partial synchronization transition, the probability distribution of the synchronization error is shown to develop highly singular behavior. We suggest that for nonidentical Bernoulli maps (and perhaps some other discontinuous maps) partial synchronization is merely a smooth crossover rather than a well defined transition. More subtle analysis in the $d=4$ case locates the point where the synchronized state becomes stable. In some cases, however, a riddled basin attractor appears, and synchronized and chaotic behaviors coexist. We also suggest that similar riddling of a basin of attractor might take place in some extended systems where it is known as stable chaos.

cond-mat.stat-mech↗

arXiv2003

Yang-Lee zeroes for an urn model for the separation of sand

We apply the Yang-Lee theory of phase transitions to an urn model of separation of sand. The effective partition function of this nonequilibrium system can be expressed as a polynomial of the size-dependent effective fugacity $z$. Numerical calculations show that in the thermodynamic limit, the zeros of the effective partition function are located on the unit circle in the complex $z$-plane. In the complex plane of the actual control parameter certain roots converge to the transition point of the model. Thus the Yang-Lee theory can be applied to a wider class of nonequilibrium systems than those considered previously.

cond-mat.stat-mech↗

arXiv2003

Synchronization in coupled map lattices as an interface depinning

We study an SOS model whose dynamics is inspired by recent studies of the synchronization transition in coupled map lattices (CML). The synchronization of CML is thus related with a depinning of interface from a binding wall. Critical behaviour of our SOS model depends on a specific form of binding (i.e., transition rates of the dynamics). For an exponentially decaying binding the depinning belongs to the directed percolation universality class. Other types of depinning, including the one with a line of critical points, are observed for a power-law binding.

cond-mat.stat-mech↗

arXiv2003

Some recent developments in models with absorbing states

We describe some of the recent results obtained for models with absorbing states. First, we present the nonequilibrium absorbing-state Potts model and discuss some of the factors that might affect the critical behaviour of such models. In particular we show that in two dimensions the further neighbour interactions might split the voter critical point into two critical points. We also describe some of the results obtained in the context of synchronization of chaotic dynamical systems. Moreover, we discuss the relation of the synchronization transition with some interfacial models.

cond-mat.stat-mech↗

arXiv2003

Synchronization of Random Linear Maps

We study synchronization of random one-dimensional linear maps for which the Lyapunov exponent can be calculated exactly. Certain aspects of the dynamics of these maps are explained using their relation with a random walk. We confirm that the Lyapunov exponent changes sign at the complete synchronization transition. We also consider partial synchronization of nonidentical systems. It turns out that the way partial synchronization manifests depends on the type of differences (in Lyapunov exponent or in contraction points) between the systems. The crossover from partial synchronization to complete synchronization is also examined.

nlin.CD↗

arXiv2003

Splitting the voter criticality

Recently some two-dimensional models with double symmetric absorbing states were shown to share the same critical behaviour that was called the voter universality class. We show, that for an absorbing-states Potts model with finite but further than nearest neighbour range of interactions the critical point is splitted into two critical points: one of the Ising type, and the other of the directed percolation universality class. Similar splitting takes place in the three-dimensional nearest-neighbour model.

cond-mat.stat-mech↗

arXiv2002

Oscillations and dynamics in a two-dimensional prey-predator system

Using Monte Carlo simulations we study two-dimensional prey-predator systems. Measuring the variance of densities of prey and predators on the triangular lattice and on the lattice with eight neighbours, we conclude that temporal oscillations of these densities vanish in the thermodynamic limit. This result suggests that such oscillations do not exist in two-dimensional models, at least when driven by local dynamics. Depending on the control parameter, the model could be either in an active or in an absorbing phase, which are separated by the critical point. The critical behaviour of this model is studied using the dynamical Monte Carlo method. This model has two dynamically nonsymmetric absorbing states. In principle both absorbing states can be used for the analysis of the critical point. However, dynamical simulations which start from the unstable absorbing state suffer from metastable-like effects, which sometimes renders the method inefficient.

cond-mat.stat-mech↗

arXiv2002

Dynamical properties of the synchronization transition

We study the dynamics of the synchronization transition (ST) of one-dimensional coupled map lattices. For the Bernoulli map it was recently found by Ahlers and Pikovsky (Phys. Rev. Lett. {\bf 88}, 254101 (2002)) that the ST belongs to the directed percolation (DP) universality class. Spreading dynamics confirms such an identification, only for a certain class of synchronized configurations. For homogeneous configurations spreading exponents $η$ and $δ$ are different than DP exponents but their sum equals to the corresponding sum of DP exponents. Such a relation is typical to some models with infinitely many absorbing states. Moreover, we calculate the spreading exponents for the tent map for which the ST belongs to the bounded Kardar-Parisi-Zheng (BKPZ) universality class. Our estimation of spreading exponents are consistent with the hyperscaling relation. Finally, we examine the asymmetric tent map. For small asymmetry the ST remains of the BKPZ type. However, for large asymmetry a different critical behaviour appears with exponents being relatively close to the ones of DP.

cond-mat.stat-mech↗

arXiv2002

Exponential velocity tails in a driven inelastic Maxwell model

The problem of the steady-state velocity distribution in a driven inelastic Maxwell model of shaken granular material is revisited. Numerical solution of the master equation and analytical arguments show that the model has bilateral exponential velocity tails ($P(v)\sim e^{-|v|/\sqrt D}$), where $D$ is the amplitude of the noise. Previous study of this model predicted Gaussian tails ($P(v)\sim e^{-av^2}$).

cond-mat.stat-mech↗

arXiv2002

Dynamics of the breakdown of granular clusters

Recently van der Meer et al. studied the breakdown of a granular cluster (Phys. Rev. Lett. {\bf 88}, 174302 (2002)). We reexamine this problem using an urn model, which takes into account fluctuations and finite-size effects. General arguments are given for the absence of a continuous transition when the number of urns (compartments) is greater than two. Monte Carlo simulations show that the lifetime of a cluster $τ$ diverges at the limits of stability as $τ\sim N^{1/3}$, where $N$ is the number of balls. After the breakdown, depending on the dynamical rules of our urn model, either normal or anomalous diffusion of the cluster takes place.

cond-mat.stat-mech↗

arXiv2001

Urn model of separation of sand

We introduce an urn model which describes spatial separation of sand. In this dynamical model, in a certain range of parameters spontaneous symmetry breaking takes place and equipartitioning of sand into two compartments is broken. The steady-state equation for an order parameter, a critical line, and the tricritical point on the phase diagram are found exactly. Master equation and the first-passage problem for the model are solved numerically and the results are used to locate first-order transitions. Exponential divergence of a certain characteristic time shows that the model can also exhibit very strong metastability. In certain cases characteristic time diverges as N^{z}, where N is the number of balls and z=1/2 (critical line), 2/3 (tricritical point), or 1/3 (limits of stability).

cond-mat.stat-mech↗

arXiv2001

On the critical behavior of a lattice prey-predator model

The critical properties of a simple prey-predator model are revisited. For some values of the control parameters, the model exhibits a line of directed percolation like transitions to a single absorbing state. For other values of the control parameters one finds a second line of continuous transitions toward infinite number of absorbing states, and the corresponding steady-state exponents are mean-field like. The critical behavior of the special point T (bicritical point), where the two transition lines meet, belongs to a different universality class. The use of dynamical Monte-Carlo method shows that a particular strategy for preparing the initial state should be devised to correctly describe the physics of the system near the second transition line. Relationships with a forest fire model with immunization are also discussed.

cond-mat.stat-mech↗

arXiv2000

Novel criticality in a model with absorbing states

We study a one-dimensional model which undergoes a transition between an active and an absorbing phase. Monte Carlo simulations supported by some additional arguments prompted as to predict the exact location of the critical point and critical exponents in this model. The exponents $δ=0.5$ and $z=2$ follows from random-walk-type arguments. The exponents $β= ν_{\perp}$ are found to be non-universal and encoded in the singular part of reactivation probability, as recently discussed by H. Hinrichsen (cond-mat/0008179). A related model with quenched randomness is also studied.

cond-mat.stat-mech↗

arXiv2000

Generic Criticality in a Model of Evolution

Using Monte Carlo simulations, we show that for a certain model of biological evolution, which is driven by non-extremal dynamics, active and absorbing phases are separated by a critical phase. In this phase both the density of active sites $ρ(t)$ and the survival probability of spreading $P(t)$ decay as $t^{-δ}$, where $δ\sim 0.5$. At the critical point, which separates the active and critical phases, $δ\sim 0.29$, which suggests that this point belongs to the so-called parity-conserving universality class. The model has infinitely many absorbing states and, except for a single point, has no conservation law.

cond-mat.stat-mech↗

arXiv1999

Oscillatory behaviour in a lattice prey-predator system

Using Monte Carlo simulations we study a lattice model of a prey-predator system. We show that in the three-dimensional model populations of preys and predators exhibit coherent periodic oscillations but such a behaviour is absent in lower-dimensional models. Finite-size analysis indicate that amplitude of these oscillations is finite even in the thermodynamic limit. In our opinion, this is the first example of a microscopic model with stochastic dynamics which exhibits oscillatory behaviour without any external driving force. We suggest that oscillations in our model are induced by some kind of stochastic resonance.

cond-mat.stat-mech↗