A hybrid differential-discrete mathematical model has been used to simulate biofilm structures (surface shape, roughness, porosity) as a result of microbial growth in different environmental conditions. In this study, quantitative two- and three-dimensional models were evaluated by introducing statistical measures to characterize the complete biofilm structure, both the surface structure and volume structure. The surface enlargement, coefficient of roughness, fractal dimension of surface, biofilm compactness, and solids hold-up were found to be good measures of biofilm structure complexity. Among many possible factors affecting the biofilm structure, the influence of biomass growth in relation to the diffusive substrate transport was investigated. Porous biofilms, with many channels and voids between the "finger-like" or "mushroom" outgrowth, were obtained in a substrate-transport-limited regime. Conversely, compact and dense biofilms occurred in systems limited by the biomass growth rate and not by the substrate transfer rate. The surface complexity measures (enlargement, roughness, fractal dimension) all increased with increased transport limitation, whereas the volume measures (compactness, solid hold-up) decreased, showing the change from a compact and dense to a highly porous and open biofilm.

/pdf/mathematical-modeling-of-biofilm-structure-with-a-hybrid-3m7k50x6cn.pdf

Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach.

We consider a new cellular automata rule for a synchronous random walk on a two-dimensional square lattice, subject to an exclusion principle. It is found that the macroscopic behavior of our model obeys the telegraphists's equation, with an adjustable diffusion constant. By construction, the dynamics of our model is exactly described by a linear discrete Boltzmann equation which is solved analytically for some boundary conditions. Consequently, the connection between the microscopic and the macroscopic descriptions is obtained exactly and the continuous limit studied rigorously. The typical system size for which a true diffusive behavior is observed may be deduced as a function of the parameters entering into the rule. It is shown that a suitable choice of these parameters allows us to consider quite small systems. In particular, our cellular automata model can simulate the Laplace equation to a precision of the order (λ/L)6, whereL is the size of the system andλ the lattice spacing. Implementation of this algorithm on special-purpose machines leads to the fastest way to simulate diffusion on a lattice.

Cellular Automata Model for the Diffusion Equation

Cellular automata simulations for enzymatic reaction networks differ from other models for reaction-diffusion systems, since enzymes and metabolites have very different properties. This paper presents a model where each lattice site can can contain at most one enzyme molecule, but many metabolite molecules. The rules are constructed to conform to the Michaelis-Menten kinetics by modeling the underlying mechanism of enzymatic conversion. Different possible approaches to rule construction are presented and analyzed, and simulations are shown for single reactions and simple enzyme networks.

/pdf/cellular-automata-approaches-to-enzymatic-reaction-networks-1gl9ldl8rh.pdf

Cellular Automata Approaches to Enzymatic Reaction Networks

Two-dimensional numerical analysis of local hemodynamics on flow-reduction mechanism by stent implantation in cerebral aneurysms is presented to understand these interesting hydrodynamic phenomena and improve this promising minimally invasive treatment. Recently in the cerebral aneurysm treatment, this new endovascular occlusion technique using a porous tubular shaped stent or coils sometimes replaces invasive open surgeries. It is thought that the flow reduction by the stent implantation prevents the aneurysm rupture, however its mechanism is not well understood. We reveal the fundamental flow reduction mechanism by the stent implantation in dependence of the aneurysm size using the lattice Boltzmann approach.

/pdf/lattice-boltzmann-analysis-of-the-flow-reduction-mechanism-1hhk9r2lo2.pdf

Lattice Boltzmann analysis of the flow reduction mechanism in stented cerebral aneurysms for the endovascular treatment

This paper describes a new simulation technique for diffusion phenomena over the sea surface using cellular automata, which is capable of making prediction of oil dispersion from tankers come into collision or stranded on rocks. Cellular automata is applied to solve a diffusion equation, in which the simulation results are compared with the analytical solution, and the applicability is shown in predicting the oil dispersion in the accident of a tanker occurred in Japan Sea in January, 1997. The simulation results by cellular automata show good agreement with analytical solution of diffusion equation and that the prediction of oil dispersion in Japan Sea can be made in a short time by a personal computer with high accuracy.

Coastal oil pollution prediction by a tanker using cellular automata

Diffusion is a general phenomenon playing an important role in many physical or chemical problems. As a result, one often observes the formation of diffusion fronts having complex properties. An analytical analysis of these problems is often not possible and thus, one uses numerical simulation. However, actual diffusion of particles is a time-consuming process. Accordingly deterministic cellular automata algorithms can be very useful. In this paper, we review several situations in which diffusion plays an important role. We then define a class of cellular automaton algorithms for diffusion. We do the explicit derivation of the macroscopic diffusion equations from the microscopic rules and discuss the possible difficulties. The algorithms are then tested in the framework of nonequilibrium diffusion and gradient percolation. It is shown that this cellular automaton approach reproduces very well the expected results both for the solutions of the diffusion equation and for the detailed properties of the diffusion front (fractal dimension). Finally, a novel class of algorithms, avoiding some difficulties previously met, is defined and the corresponding macroscopic properties are given.

Cellular Automata Approach to Diffusion Problems

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Cellular Automata Approach to Diffusion Problems