Biomedical subjects

B C Grandi

Publications and source records attributed to B C Grandi.

3 recordsLinked to original sources

PubMed1999

Monte Carlo simulation of an antiferromagnetic Ising model at two competing temperatures.

We consider a two-dimensional antiferromagnet Ising system interacting with a heat bath at temperature T. The dynamics of the system is simulated by two competing stochastic processes: the two-spin-exchange Kawasaki kinetics at temperature T>0 and the one-spin-flip Glauber dynamics at T(G)-->0(-), which mimics the increase of the energy of the system. These two processes have probabilities 1-p and p, respectively. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model and the corresponding critical exponents. Contrary to the ferromagnetic case, the phase diagram obtained does not exhibit the phenomenon of self-organization: for any nonzero value of the competing parameter p, and for any value of T, the only stationary phase which remains is the ferromagnetic one. At the phase transition between the antiferromagnetic and paramagnetic phases, at p=0, the values found for the critical exponents agree with those of the corresponding equilibrium Ising model.

Journal Article↗

PubMed1999

Theory of the NO+CO surface-reaction model.

We derive a pair approximation (PA) for the NO+CO model with instantaneous reactions. For both the triangular and square lattices, the PA, derived here using a simpler approach, yields a phase diagram with an active state for CO-fractions y in the interval y(1)<y<y(2), with a continuous (discontinuous) phase transition to a poisoned state at y(1) (y(2)). This is in qualitative agreement with simulation for the triangular lattice, where our theory gives a rather accurate prediction for y(2). To obtain the correct phase diagram for the square lattice, i.e., no active stationary state, we reformulate the PA using sublattices. The (formerly) active regime is then replaced by a poisoned state with broken symmetry (unequal sublattice coverages), as observed recently by Kortlüke et al. [Chem. Phys. Lett. 275, 85 (1997)]. In contrast with their approach, in which the active state persists, although reduced in extent, we report here the qualitatively correct theory of the NO+CO model on the square lattice. Surface diffusion of nitrogen can lead to an active state in this case. In one dimension, the PA predicts that diffusion is required for the existence of an active state.

Journal Article↗

PubMed1999

Competitive dynamics in a three-dimensional Ising model.

We consider a three-dimensional ferromagnetic Ising model on a cubic lattice in contact with a heat bath at temperature T. The states of the system evolve in time according to two stochastic processes: the one-spin-flip Glauber dynamics where the order parameter is not conserved, and the two-spin-exchange Kawasaki kinetics, which conserves the order parameter. The former process mimics an input of energy into the system. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model, and the corresponding critical exponents. Similarly to the observed for the related two-dimensional ferromagnetic Ising model, the phase diagram obtained exhibits the phenomenon of self-organization. Although the stationary states are mainly ferromagnetic at low temperatures, an antiferromagnetic phase appears for extremely high values of the flux of energy. Unlike the ferromagnetic case, the region of the phase diagram occupied by the antiferromagnetic phase is now larger. The determined critical exponents for this nonequilibrium model are in agreement with the well-known accepted values for the three-dimensional equilibrium Ising model.

Journal Article↗