Biomedical subjects

J J Lukkien

Publications and source records attributed to J J Lukkien.

4 recordsLinked to original sources

PubMed2003

Infinitely fast diffusion in single-file systems.

We have used dynamic Monte Carlo(DMC) methods and analytical techniques to analyze single-file systems for which diffusion is infinitely fast. We have simplified the master equation removing the fast reactions, and we have introduced a DMC algorithm for infinitely fast diffusion. The DMC method for fast diffusion give similar results as the standard DMC with high diffusion rates. We have investigated the influence of characteristic parameters, such as pipe length, adsorption, desorption, and conversion rate constants on the steady-state properties of single-file systems with a reaction, looking at cases when all the sites are reactive and when only some of them are reactive. We find that the effect of fast diffusion on single-file properties of the system is absent even when diffusion is infinitely fast. Diffusion is not important in these systems. Smaller systems are less reactive and the occupancy profiles for infinitely long systems show an exponential behavior.

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PubMed2003

Analytical results for the reactivity of a single-file system.

We derive analytical expressions for the reactivity of a single-file system with fast diffusion and particles entering and leaving the system at one end. If the conversion reaction is fast, then the reactivity depends only very weakly on the system size, and the conversion is about 100%. If the reaction is slow, then the reactivity becomes proportional to the system size, the loading, and the reaction rate constant. If the system size increases the reactivity goes to the geometric mean of the reaction rate constant and the rate of particles entering and leaving the system. For large systems, the number of unconverted particles decreases exponentially with distance from the open end.

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PubMed2002

Transient behavior in single-file systems.

We have used Monte Carlo methods and analytical techniques to investigate the influence of the characteristics, such as pipe length, diffusion, adsorption, desorption, and reaction rates on the transient properties of single-file systems. The transient or the relaxation regime is the period in which the system is evolving to equilibrium. We have studied the system when all the sites are reactive and also when only some of them are reactive. Comparisons between mean-field predictions, cluster approximation predictions, and Monte Carlo simulations for the relaxation time of the system are shown. We outline the cases where the mean-field analysis gives good results compared to dynamic Monte Carlo results. For some specific cases we can analytically derive the relaxation time. Occupancy profiles for different distributions of the sites both for the mean field and simulations are compared. Different results for slow and fast reaction systems and different distributions of reactive sites are discussed.

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PubMed2002

Steady-state properties of single-file systems with conversion.

We have used Monte Carlo methods and analytical techniques to investigate the influence of the characteristic parameters, such as pipe length, diffusion, adsorption, desorption, and reaction rate constants on the steady-state properties of single-file systems with a reaction. We looked at cases when all the sites are reactive and when only some of them are reactive. Comparisons between mean-field predictions and Monte Carlo simulations for the occupancy profiles and reactivity are made. Substantial differences between mean-field and the simulations are found when rates of diffusion are high. Mean-field results only include single-file behavior by changing the diffusion rate constant, but it effectively allows passing of particles. Reactivity converges to a limit value if more reactive sites are added: sites in the middle of the system have little or no effect on the kinetics. Occupancy profiles show approximately exponential behavior from the ends to the middle of the system.

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