We investigate a model system of a chemically reactive binary mixture, where the simple reaction A B between the two constituents of the mixture occurs simultaneously with spinodal decomposition. The competition between the thermodynamic short-range attractive and the reactive long-range repulsive interactions leads to the formation of steady-state patterns. In the case of equal forward and backward reaction rates the steady-state average domain width, R ϱ , scales with the reaction rate, ⌫, as R ϱ ϳ(1/⌫) s , where the exponent s equals approximately 1 3 for low rates and equals exactly 1 4 for high rates. These exponent values and the variation of the maximum amplitude of the order parameter with the reaction rate can be derived by minimizing the free energy in a square wave and a single mode approximation, respectively. The phase segregation dynamics is simulated numerically using the appropriate Langevin equation. ͓S1063-651X͑96͒50509-X͔ PACS number͑s͒: 05.70.Fh, 64.60.Cn, 47.54.ϩr, 61.20.Ja
We consider the pattern dynamics of the lamellar phases observed in Rayleigh-Bénard convection, as described by the Swift-Hohenberg equation, and in the weak segregation regime of diblock copolymers. Both numerical and analytical investigations show that the dynamical growth of the characteristic length scale in both systems is described by the same growth exponents, thus suggesting that both systems are members of the same universality class.
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Very regular beamformer array geometries will have grating lobes in their directivity pattern when applied above a certain frequency. The grating lobes can be suppressed by removing periodicities, typically by the use of random arrays or spiral arrays. Large irregular arrays are, however, difficult to build due to their complicated support structure and cabling. The present paper describes a novel array design, which maintains the low grating lobe level of irregular arrays, but which has a regularity that allows a much simpler support structure and cabling. The performance is compared with that of comparable regular and irregular arrays, and verified through practical measurements. Examples of application to the localization of source of wind noise and high-frequency engine noise will be presented.
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