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The matter before a Big Bang was presumed to be with a power law thermal absorptivity and it was confined in an annular domain. We study the possible hot-spot occurring of this exotic matter by adopting the boundary perturbation approach and selecting specific critical parameters after intensive (numerically) searching. We found the small wavy roughness may delay a possible Big-Bang explosion and shift the critical location.

Discrete kinetic theory approach has been used to study dilute, monatomic gas¯ow between two walls in microdomains. A four-velocity coplanar model has been adopted, where the microscopic velocity-orientation angle is a function of the Knudsen number. Diffusive re¯ection boundary condition has been incorporated to obtain the solution. Subsequently, the macroscopic velocity slip at the wall, the velocity pro®le across the walls and the volume¯ow rate are calculated for the transition¯ow regime, where the Knudsen number varies between 0.1 and 10. Furthermore, the`kinetic' temperature for this non-equilibrium system has been calculated based on the velocity pro®les. The temperature jump at the wall and the Nusselt number are estimated and compared with the continuum-limit approximations.