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We study the gravitational radiation produced by the collisions of bubblewalls or thin fluid shells in cosmological phase transitions. Using theso-called envelope approximation, we obtain analytically the asymptoticbehavior of the gravitational wave spectrum at low and high frequencies for anyphase transition model. The complete spectrum can thus be approximated by asimple interpolation between these asymptotes. We verify this approximationwith specific examples. We use these results to discuss the dependence of thespectrum on the time and size scales of the source.

Model-independent features of gravitational waves from bubble collisions