Biomedical subjects

H van Beijeren

Publications and source records attributed to H van Beijeren.

3 recordsLinked to original sources

PubMed2001

Diffusion with random distribution of static traps.

The survival probability P(c,t) of a random walk of t steps with static traps at concentration c is studied in two and three dimensions by an efficient Monte Carlo method based on a mapping onto a polymer model. On the basis of the theoretical work of Donsker and Varadhan [Commun. Pure Appl. Math. 28, 525 (1975); 32, 721 (1979)] and of Rosenstock [J. Math. Phys. (N.Y.) 11, 487 (1970)] one expects a data collapse for -ln[P(c,t)]/ln(t) plotted vs square root of [lambda t]/ln(t) [with lambda = -ln(1-c)], in two dimensions, and for -t(-1/3)ln[P(c,t)] vs t(2/3)lambda in three dimensions. These predictions are well supported by the Monte Carlo results.

Journal Article↗

PubMed2001

Equilibrium crystal shapes in the Potts model.

The three-dimensional q-state Potts model, forced into coexistence by fixing the density of one state, is studied for q=2, 3, 4, and 6. As a function of temperature and number of states, we studied the resulting equilibrium droplet shapes. A theoretical discussion is given of the interface properties at large values of q. We found a roughening transition for each of the numbers of states we studied, at temperatures that decrease with increasing q, but increase when measured as a fraction of the melting temperature. We also found equilibrium shapes closely approaching a sphere near the melting point, even though the three-dimensional Potts model with three or more states does not have a phase transition with a diverging length scale at the melting point.

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PubMed2000

Chaotic properties of dilute two- and three-dimensional random Lorentz gases. II. Open systems.

We calculate the spectrum of Lyapunov exponents for a point particle moving in a random array of fixed hard disk or hard sphere scatterers, i.e., the disordered Lorentz gas, in a generic nonequilibrium situation. In a large system which is finite in at least some directions, and with absorbing boundary conditions, the moving particle escapes the system with probability one. However, there is a set of zero Lebesgue measure of initial phase points for the moving particle, such that escape never occurs. Typically, this set of points forms a fractal repeller, and the Lyapunov spectrum is calculated here for trajectories on this repeller. For this calculation, we need the solution of the recently introduced extended Boltzmann equation for the nonequilibrium distribution of the radius of curvature matrix and the solution of the standard Boltzmann equation. The escape-rate formalism then gives an explicit result for the Kolmogorov Sinai entropy on the repeller.

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