Fault-fracture patterns have been studied in slabs of clay during extensional deformations. Fractures nucleate and grow on many scales. A new scaling relation is proposed for the length l of a fracture as a function of the area l ϳ A b , with the same exponent b 0.68 6 0.03 for many deformation types. A consequence of this scaling relation is that the width of a fracture scales with the length as w ϳ l ͑12b͒͞b . A spring network model is shown to reproduce the pattern, both visually and statistically, with the same scaling exponents. [S0031-9007(96)

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A new method combining optical and electrical impedance measurements is described that enables submicroscopic cell movements to be monitored. The cells are grown on small gold electrodes that are transparent to light. This modified electrical cell-substrate impedance sensor (ECIS) allows simultaneous microscopic recording of both growth and motility, thus enabling cell confluence on the electrodes to be systematically correlated to the impedance in regular time intervals of seconds and for extended periods of time. Furthermore, the technique provides an independent measure of monolayer cell densities that we compare to calculated values from a theoretical model. We have followed the attachment and spreading behavior of epithelial Madin-Darby canine kidney strain I (MDCK-I) cell cultures on microelectrodes for up to 40 h. The studies reveal a high degree of correlation between the measured resistance at 4 kHz and the corresponding cell confluence in 4- to 6-h intervals with typical linear cross-correlation factors of r equaling approximately 0.9. In summary, the impedance measured with the ECIS technique provides a good quantitative measure of cell confluence.

In this paper we present results of structural studies of compacting experimental systems of ductile grains in two and three dimensions. The high precision of our two-dimensional experiments enables a detailed study of the evolution of coordination numbers and local crystalline arrangements as a function of the packing fraction. The structure in both dimensions deviates considerably from that of hard disks and spheres, although geometrically, crystalline arrangements dominate on a local scale ͑in two dimensions͒. In three dimensions, the evolution of the coordination number is compared to experimental packings of hard and ductile grains from the literature. This comparison shows that the evolution of coordination number with packing fraction is not unique for ductile systems in general, but must depend on rheology and grain size.

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