In certain experimental conditions, bacteria form complex spatial-temporal patterns. A striking example of such kind was reported by Budrene and Berg (1991), who observed a wide variety of different colony structures ranging from arrays of spots to radially oriented stripes or arrangements of more complex elongated spots, formed by Escherichia coli. We discuss the relevant mechanisms of intercellular regulation in bacterial colony which may cause pattern formation, and formulate the corresponding mathematical model. In numerical experiments a variety of patterns, observed in real systems, is reproduced. The dynamics of their formation is investigated.

This paper introduces a novel method of modelling acoustic and elastic wave propagation in inhomogeneous media with sharp variations of physical properties based on the recently developed grid‐characteristic method which considers different types of waves generated in inhomogeneous linear‐elastic media (e.g., longitudinal, transverse, Stoneley, Rayleigh, scattered PP‐, SS‐waves, and converted PS‐ and SP‐waves). In the framework of this method, the problem of solving acoustic or elastic wave equations is reduced to the interpolation of the solutions, determined at earlier time, thus avoiding a direct solution of the large systems of linear equations required by the FD or FE methods. We apply the grid‐characteristic method to compare wave phenomena computed using the acoustic and elastic wave equations in geological medium containing a hydrocarbon reservoir or a fracture zone. The results of this study demonstrate that the developed algorithm can be used as an effective technique for modelling wave phenomena in the models containing hydrocarbon reservoir and/or the fracture zones, which are important targets of seismic exploration.

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