Entropy of the Land Parcel Mosaic as a Measure of the Degree of Urbanization.

Quantifying the urbanization level is an essential yet challenging task in urban studies because of the high complexity of this phenomenon. The urbanization degree has been estimated using a variety of social, economic, and spatial measures. Among the spatial characteristics, the Shannon entropy of the landscape pattern has recently been intensively explored as one of the most effective urbanization indexes.

From complex structures to complex processes: percolation theory applied to the formation of a city.

We investigate the morphology of the spatial pattern resulting from the division of land into the parcels that is observed in the centers of the cities, by analyzing the distribution function of the parcel areas. A simple model based on a two-dimensional bond percolation is employed to mimic the process of the formation of the city. The model reproduces the empirical distribution of the parcel areas that is found to exhibit the power law with the exponent tau=2.

Nano- and microscopic surface wrinkles of linearly increasing heights prepared by periodic precipitation.

Arrays of surface wrinkles of linearly increasing heights (from tens of nanometers to tens of micrometers) were prepared via a spontaneous reaction-diffusion process based on periodic precipitation. The slopes, dimensions, and positions of the precipitation bands could be controlled precisely by adjusting the concentrations of the participating chemicals as well as the material properties of patterned substrates. Additional control of periodic precipitation by localized UV irradiation allowed for the preparation of discontinuous and curvilinear structures.

Amplification of changes of a thin film's macromolecular structure into macroscopic reaction-diffusion patterns.

A reaction-diffusion process induced from a micronetwork geometry amplifies changes in the molecular structure of a thin gel film into macroscopic readout patterns. When the gel undergoes a helix-to-coil phase transition, the patterns formed by RD switch from symmetry-broken to symmetric ones. Theoretical analysis explains how the system reconfigures internally in response to mass transfer between the applied network and the probed film.

Wave optics of Liesegang rings.

Liesegang rings refract and reflect at the interface between the regions of the same gel but of different thickness. The incident and the refracted rings obey a refraction law analogous to the Snell's law of classical optics, with a reverse of the spacing coefficient being a counterpart of the refraction index. The wavelike behavior of the rings at the interface is explained by geometrical arguments derived from the Jablczynski's spacing principle, and is reproduced in numerical simulations based on a three-dimensional minimalistic version of the nucleation-growth model.

Multicolour micropatterning of thin films of dry gels.

Micropatterning of surfaces with several chemicals at different spatial locations usually requires multiple stamping and registration steps. Here, we describe an experimental method based on reaction-diffusion phenomena that allows for simultaneous micropatterning of a substrate with several coloured chemicals. In this method, called wet stamping (WETS), aqueous solutions of two or more inorganic salts are delivered onto a film of dry, ionically doped gelatin from an agarose stamp patterned in bas relief.