Biomedical subjects

Adam Lipowski

Publications and source records attributed to Adam Lipowski.

14 recordsLinked to original sources

PubMed2006

Molecular dynamics simulations of ballistic annihilation.

Using event-driven molecular dynamics we study one- and two-dimensional ballistic annihilation. We estimate exponents xi and gamma, which describe the long-time decay of the number of particles [n(t) approximately t-xi] and of their typical velocity [v(t) approximately t-gamma]. To a good accuracy our results confirm the scaling relation xi+gamma=1. In the two-dimensional case our results are in good agreement with those obtained from Boltzmann kinetic theory.

Journal Article↗

PubMed2006

Long-term evolution of an ecosystem with spontaneous periodicity of mass extinctions.

Twenty years ago, after analysing palaeontological data, Raup and Sepkoski suggested that mass extinctions on Earth appear cyclically in time with a period of approximately 26 million years (My). To explain the 26My period, a number of proposals were made involving, e.g., astronomical effects, increased volcanic activity, or the Earth's magnetic field reversal, none of which, however, has been confirmed. Here we study a spatially extended discrete model of an ecosystem and show that the periodicity of mass extinctions might be a natural feature of the ecosystem's dynamics and not the result of a periodic external perturbation. In our model, periodic changes of the diversity of an ecosystem and some of its other characteristics are induced by the coevolution of species. In agreement with some palaeontological data, our results show that the longevity of a species depends on the evolutionary stage at which the species is created. Possible further tests of our model are also discussed.

Animals↗

PubMed2005

Traveling salesman problem with a center.

We study a traveling salesman problem where the path is optimized with a cost function that includes its length L as well as a certain measure C of its distance from the geometrical center of the graph. Using simulated annealing (SA) we show that such a problem has a transition point that separates two phases differing in the scaling behavior of L and C, in efficiency of SA, and in the shape of minimal paths.

Journal Article↗

PubMed2005

Periodicity of mass extinctions without an extraterrestrial cause.

We study a lattice model of a multispecies 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 [Proc. Natl. Acad. Sci. 81, 801 (1984)], but thus far is lacking a satisfactory explanation. Our model indicates that this might be a natural consequence of the ecosystem dynamics and not the result of any extraterrestrial cause.

Animals↗

PubMed2003

Synchronization in coupled map lattices as an interface depinning.

We study a solid-on-solid (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 behavior 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.

Journal Article↗

PubMed2003

Splitting the voter Potts model critical point.

Recently some two-dimensional models with double symmetric absorbing states were shown to share the same critical behavior that was called the voter universality class. We show that, for an absorbing-states Potts model with finite but further than nearest-neighbor range of interactions, the critical point is split 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-neighbor model.

Journal Article↗

PubMed2003

Dynamical properties of the synchronization transition.

We use spreading dynamics to study the synchronization transition (ST) of one-dimensional coupled map lattices (CML's). Recently, Baroni et al. [Phys. Rev. E 63, 036226 (2001)] have shown that the ST belongs to the directed percolation (DP) universality class for discontinuous CML's. This was confirmed by accurate numerical simulations for the Bernoulli map by Ahlers and Pikovsky [Phys. Rev. Lett. 88, 254101 (2002)]. Spreading dynamics confirms such an identification only for random synchronized states. For homogeneous synchronized states the spreading exponents eta and delta are different from the DP exponents but their sum equals the corresponding sum of the DP exponents. Such a relation is typical of 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-Zhang (BKPZ) universality class. The estimation of spreading exponents for random synchronized states is consistent with the hyperscaling relation, while it is inconsistent for the homogeneous ones. Finally, we examine the asymmetric tent map. For small asymmetry the ST remains of the BKPZ type. However, for large asymmetry a different critical behavior appears, with exponents being relatively close to those for DP.

Journal Article↗

PubMed2002

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) approximately e(-|v|/sqrt[D])], where D is the amplitude of the noise. Previous study of this model predicted Gaussian tails [P(v) approximately e(-av(2))].

Journal Article↗

PubMed2002

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 neighbors, 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 behavior 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 metastablelike effects, which sometimes renders the method inefficient.

Journal Article↗

PubMed2002

Dynamics of the breakdown of granular clusters.

Recently van der Meer et al. studied the breakdown of a granular cluster [Phys. Rev. Lett. 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 tau diverges at the limits of stability as tau approximately 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.

Journal Article↗

PubMed2002

Moment ratios for an urn model of sand compartmentalization.

Numerically solving a master equation for a recently introduced nonequilibrium urn model of sand compartmentalization, we show that the order-parameter moment ratios of the fourth and sixth order remain constant along an exactly located line of critical points. Obtained values are in very good agreement with values predicted by Brézin and Zinn-Justin for the equilibrium Ising model above the critical dimension. At the tricritical point, these ratios acquire values that also agree with a suitably extended Brézin and Zinn-Justin approach.

Journal Article↗

PubMed2002

Dynamics-dependent criticality in models with q absorbing states.

We study a one-dimensional, nonequilibrium Potts-like model that has q symmetric absorbing states. For q=2, as expected, the model belongs to the parity-conserving universality class. For q=3 the critical behavior depends on the dynamics of the model. Under a certain dynamics it remains generically in the active phase, which is also the feature of some other models with three absorbing states. However, a modified dynamics induces a parity-conserving phase transition. Relations with branching-annihilating random walk models are discussed in order to explain such a behavior.

Journal Article↗

PubMed2002

Phase transitions in nonequilibrium d-dimensional models with q absorbing states.

A nonequilibrium Potts-like model with q absorbing states is studied using Monte Carlo simulations. In two dimensions and q=3 the model exhibits a discontinuous transition. For the three-dimensional case and q=2 the model exhibits a continuous transition with beta=1 (mean field). Simulations are inconclusive, however, in the two-dimensional case for q=2. We suggest that in this case the model is close to or at the crossing point of lines separating three different types of phase transitions. The proposed phase diagram in the (q,d) plane is very similar to that of the equilibrium Potts model. In addition, our simulations confirm the field-theory prediction that in two dimensions a branching-annihilating random walk model without parity conservation belongs to the directed percolation universality class.

Journal Article↗

PubMed2002

Urn model of separation of sand.

We introduce an urn model that 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. The 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).

Journal Article↗