doi:10.5194/adgeo-37-47-2014 © Author(s) 2014. CC Attribution 3.0 License. Advances in (original) (raw)
Transport capacity and saturation mechanism in a real-space cellular automaton dune model
Advances in Geosciences, 2014
In a real-space cellular automaton dune model, individual physical processes such as erosion, deposition and transport are implemented by nearest neighbor interactions and a time-dependent stochastic process. Hence, the transport capacity, the saturation mechanism and the characteristic wavelength for the formation of dunes are emergent properties that can only be determined a posteriori from the output of the numerical simulations. Here we propose a simplified version of the model to establish asymptotic relations between the microscopic erosion-deposition-transport rate parameters and the characteristic length and time scales of the flux saturation mechanism. In particular, we show that, in the cellular automaton, the saturation length is a mean transport distance controlled by the deposition of mobile sedimentary cells. Then, we discuss how these results can be used to determine the sediment flux within dune fields and the rate parameters of a new class of discrete models that concentrate on the effect of heterogeneities in grain-size on dune morphodynamics.
Journal of Geophysical Research, 2009
1] We present a new 3-D cellular automaton model for bed form dynamics in which individual physical processes such as erosion, deposition, and transport are implemented by nearest neighbor interactions and a time-dependent stochastic process. Simultaneously, a lattice gas cellular automaton model is used to compute the flow and quantify the bed shear stress on the topography. Local erosion rates are assumed to be proportional to the shear stress in such a way that there is a complete feedback mechanism between flow and bed form dynamics. In the numerical simulations of dune fields, we observe the formation and the evolution of superimposed bed forms on barchan and transverse dunes. Using the same model under different initial conditions, we perform the linear stability analysis of a flat sand bed disturbed by a small sinusoidal perturbation. Comparing the most unstable wavelength in the model with the characteristic size of secondary bed forms in nature, we determine the length and time scales of our cellular automaton model. Thus, we establish a link between discrete and continuous approaches and open new perspectives for modeling and quantification of complex patterns in dune fields.
Simulating the Curti–Sarno debris flow through cellular automata: the model SCIDDICA (release S2)
Physics and Chemistry of the Earth, Parts A/B/C, 2002
Cellular automata (CA) are based on a regular division of the space in cells. Each cell embeds an identical finite automaton, whose input is given by the states of neighbouring cells. The transition function r of the CA is made of a set of rules, simultaneously applied, step by step, to each cell of the cellular space. Rules are derived by subdividing, in computational terms, the physical phenomenon into a set of independent, elementary processes. By properly combining each elementary result, the behaviour of the phenomenon can be simulated.
Cellular Automata as Microscopic Models of Cell Migration in Heterogeneous Environments
Current Topics in Developmental Biology, 2008
A.1. States in Lattice-Gas Cellular Automata A.2. Dynamics in Lattice-Gas Cellular Automata Appendix B Appendix C Appendix D References Understanding the precise interplay of moving cells with their typically heterogeneous environment is crucial for central biological processes as embryonic morphogenesis, wound healing, immune reactions or tumor growth. Mathematical models allow for the analysis of cell migration strategies involving complex feedback mechanisms between the cells and their microenvironment. Here, we introduce a cellular automaton (especially lattice-gas cellular automaton-LGCA) as a microscopic model of cell migration together with a (mathematical) tensor characterization of different biological environments. Furthermore, we show how mathematical analysis of the LGCA model can yield an estimate for the cell dispersion speed within a given environment. Novel imaging techniques like diffusion tensor imaging (DTI) may provide tensor data of biological microenvironments. As an application, we present LGCA simulations of a proliferating cell population moving in an external field defined by clinical DTI data. This system can serve as a model of in vivo glioma cell invasion.
A congestion model for cell migration
Communications on Pure and Applied Analysis, 2011
This paper deals with a class of macroscopic models for cell migration in a saturated medium for two-species mixtures. Those species tend to achieve some motion according to a desired velocity, and congestion forces them to adapt their velocity. This adaptation is modelled by a correction velocity which is chosen minimal in a least-square sense. We are especially interested in two situations: a single active species moves in a passive matrix (cell migration) with a given desired velocity, and a closed-loop Keller-Segel type model, where the desired velocity is the gradient of a self-emitted chemoattractant.
Incorporating Active Transport of Cellular Cargo in Stochastic Mesoscopic Models of Living Cells
Multiscale Modeling & Simulation, 2010
We propose a new multiscale method to incorporate active transport of cargo particles in biological cells in stochastic, mesoscopic models of reaction-transport processes. Given a discretization of the computational domain, we find stochastic, convective mesoscopic molecular fluxes over the edges or facets of the subvolumes and relate the process to a corresponding first order finite volume discretization of the linear convection equation. We give an example of how this can be used to model active transport of cargo particles on a microtubule network by the motor proteins kinesin and dynein. In this way we extend mesoscopic reaction-diffusion models of biochemical reaction networks to more general models of molecular transport within the living cell. * Financial support has been obtained from the Swedish Graduate School of Mathematics and Computing.
Biased global random walk, a cellular automaton for diffusion
2005
The new cellular automaton for diffusion presented in this paper is self-averaging and free of overshooting errors. These properties make it appropriate for the evaluation of the numerical methods which allow overshooting to optimize the efficiency. The perspective of parallelization and the possible extension to reaction-diffusion make the algorithm attractive as a tool for modelling complex transport processes.
A cellular-automata model of flow in ant-trails: non-monotonic variation of speed with density
Generically, in models of driven interacting particles the average speed of the particles decreases monotonically with increasing density. We propose a counter-example, motivated by the motion of ants in a trail, where the average speed of the particles varies non-monotonically with their density because of the coupling of their dynamics with another dynamical variable. These results, in principle, can be tested experimentally. ‡
Cellular automaton models for time-correlated random walks: derivation and analysis
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This means that the corresponding dynamics is characterized by memory effects that slowly decay in time. Motivated by this we construct non-Markovian lattice-gas cellular automata models for moving agents with memory. For this purpose the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect our approach is " data-driven ". Particular examples we consider are velocity correlations that decay exponentially or as power laws, where the latter functions generate anomalous diffusion. The computational efficiency of cellular automata combined with our analytical results paves the way to explore the relevance of memory and anomalous diffusion for the dynamics of interacting cell populations, like confluent cell monolayers and cell clustering.
Particles and Patterns in Cellular Automata
1999
Los Alamos National LaboratoW, an affirmative actiotiequal opportunity employer, is operated by the University of California for the U.S. Department of Energy under contract W-7405-ENG-36. By acceptance of this article, the publisher recognizes that the U.S. Government retains a nonexclusive, royaltyfree license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes. Los Alamos National Laboratory requests that the publisher identify this article as work performed under the auspices of the U.S. Department of Energy. Los Alamos National Laboratory strongly supports academic freedom and a researcher's right to publisk as an institution, however, the Laboratory does not endorse the vlewpolnt of a publication or guarantee its technical correctness.
Bulletin of mathematical biology, 2015
Collective dynamics of migrating cell populations drive key processes in tissue formation and maintenance under normal and diseased conditions. Collective cell behavior at the tissue level is typically characterized by considering cell density patterns such as clusters and moving cell fronts. However, there are also important observables of collective dynamics related to individual cell behavior. In particular, individual cell trajectories are footprints of emergent behavior in populations of migrating cells. Lattice-gas cellular automata (LGCA) have proven successful to model and analyze collective behavior arising from interactions of migrating cells. There are well-established methods to analyze cell density patterns in LGCA models. Although LGCA dynamics are defined by cell-based rules, individual cells are not distinguished. Therefore, individual cell trajectories cannot be analyzed in LGCA so far. Here, we extend the classical LGCA framework to allow labeling and tracking of i...
Diffusion in a lattice-automaton model of bioturbation by small deposit feeders
Journal of Marine Research, 2001
The mixing of 2 1 0 Pb and tagged particles is examined in a lattice-automaton model for bioturbation containing small deposit feeders. The values of the biodiffusioncoef cient, D B , calculated using typical biological parameter values, i.e., size, abundance, feeding and locomotion rates, are similar to those expected from marine sediments of a given sedimentation rate. Most biological parameters appear to exert primarily linear effects on D B values, while most nonlinearities seem to be model artifacts or failures of the assumptions in the basic D B model. The model highlights the importance of ingestion-egestion, over simple particle displacement, as an agent of bioturbation. The tagged particles are used to calculate root-mean-squareddisplacement plots, which are linear over long time spans, indicating diffusive behavior. However, initial trends on such plots are not usually linear, indicating that the calculated D B is time dependent for surprisingly long periods after the beginning of such experiments. The latter constitutes a warning to the interpretationof short-term tracer experiments where tagged-particlesare salted onto the sediment-water interface and mixing is dominated by small deposit feeders.
Stability analysis of a hybrid cellular automaton model of cell colony growth
Physical review. E, Statistical, nonlinear, and soft matter physics, 2007
Cell colonies of bacteria, tumour cells and fungi, under nutrient limited growth conditions, exhibit complex branched growth patterns. In order to investigate this phenomenon we present a simple hybrid cellular automaton model of cell colony growth. In the model the growth of the colony is limited by a nutrient that is consumed by the cells and which inhibits cell division if it falls below a certain threshold. Using this model we have investigated how the nutrient consumption rate of the cells affects the growth dynamics of the colony. We found that for low consumption rates the colony takes on a Eden-like morphology, while for higher consumption rates the morphology of the colony is branched with a fractal geometry. These findings are in agreement with previous results, but the simplicity of the model presented here allows for a linear stability analysis of the system. By observing that the local growth of the colony is proportional to the flux of the nutrient we derive an approximate dispersion relation for the growth of the colony interface. This dispersion relation shows that the stability of the growth depends on how far the nutrient penetrates into the colony. For low nutrient consumption rates the penetration distance is large, which stabilises the growth, while for high consumption rates the penetration distance is small, which leads to unstable branched growth. When the penetration distance vanishes the dispersion relation is reduced to the one describing Laplacian growth without ultra-violet regularisation. The dispersion relation was verified by measuring how the average branch width depends on the consumption rate of the cells and shows good agreement between theory and simulations.
Cellular Automata Approach to Reaction-Diffusion Systems
Springer proceedings in physics, 1989
We propose a cellular automaton model for a simple reactiondiffusion system: a three-molecular autocatalytic scheme known as the Schlagl model. Cellular automata simulations show qualitative behavior in agreement with Schagl's phenomenological description: bistability and front propagation. Quantitatively, significant discrepancies are observed between the phenomenological predictions and the results of the simulations, which can be interpreted in terms of reactive recorrelations. These discrepancies are directly related to the ratio of reactive collisions versus elastic collisions and can be eliminated by efficient "stirring". Correspondingly we observe mesoscopic effects like the formation of unsteady domains which cannot be predicted by the phenomenological theory.