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Data were taken from the results obtained from 13-μm-thick samples in a 10% sucrose experiments under 1540-nm irradiation (14 W/cm 2). ( C) The hole radius decreased at a rate that increased as the radius became smaller. The asterisk in the magnified view indicates the starting point for the calculation of the rate at which the radius decreased. The letters a to j indicate the images at (A). The hole became slightly larger and then gradually decreased. The radius decreased slightly, and then, a hole opening event was observed as a morphology jump. Each opening had an initial radius of 3.3 ± 0.2 μm, and the boundaries gradually became clearer. The blue rectangle in the top graph indicates a magnified view. This hole opened four times and then merged with an adjacent hole. ( B) The radius of the hole described in (A) versus the time.
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Additional visualizations are provided in movie S2. Right images show schematic diagrams of the system states. Left images show the experimental results. This distance indicated repulsion between the holes, probably due to reduced photon absorption at the hole site, which reduced the temperature around the hole. The typical distance between the centers of adjacent holes was 22.4 ± 0.3 μm (fig. 3A, e) in a channel of thinner ice could merge with adjacent holes and create an open solution channel ( Fig. The holes either remained closed or repeated the opening and closing cycle ( Fig. Thereafter, the radius decreased at a rate that increased from 0.021 ± 0.003 μm/s to 0.040 ± 0.004 μm/s ( Fig. 3A, d), the ice melted rapidly to form a hole ( Fig. 3A, a to c), and once the thin layer breached ( Fig. We described the hole formation process as follows: The ice became thinner, while a circular boundary emerged ( Fig. The holes dynamically emerged and disappeared periodically as the system was subjected to irradiation ( Fig. The ice crystals expanded at the expense of the hole areas. Circular holes with a radius of 3.3 ± 0.2 μm formed in the ice crystals. An example of the pattern evolution is shown in movie S1. Irradiating the sample while maintaining the stage at this temperature resulted in the spontaneous development of a spatial pattern ( Fig. Warming the frozen sample to a temperature of −2☌ resulted in the formation of isolated 10- to 100-μm-diameter ice crystals. This process moved the partially frozen system toward global equilibrium. Ice growth and melting changed the solution concentration, which influenced the melting temperature. The presence of sucrose slowed the pattern formation dynamics, as discussed below, although the sucrose did not change the water absorption spectrum compared to that of pure water at 1540 nm (fig. We prepared a two-phase system by cooling a 13-μm-thick sample of a 10% sucrose solution to −25☌ using a custom-made temperature-controlled stage ( Fig. At this wavelength, the absorption coefficient of ice is three times than that of water ( Fig. We irradiated a thin layer of ice crystals in a sucrose solution using 1540-nm laser illumination at an intensity of 14 W/cm 2.
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Further examples are observed in vegetation patterns in dry environments ( 4, 5), the skin color of animals ( 6, 7), wrinkle formation in ferrofluid mixtures under a magnetic field ( 8), drying paint films ( 9), the formation of brine channels in sea ice ( 10– 12), and the dendritic growth of crystals ( 13). This model may be modified to address other pattern formation phenomena. One of these classes involves the formation of stationary patterns. Solving the partial differential equations of such a system, he found six possible solution classes.
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He defined two chemicals, an activator and an inhibitor, that react with each other and diffuse differently through a cell tissue. Turing developed a theory, called the reaction-diffusion (RD) model, by which some systems can spontaneously develop a spatial pattern. One such example is the division of cells in a developing embryo, as described by Turing ( 1– 3). Spontaneous self-organization in a system can lead to pattern formation.