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The diffraction of a diffusion front by concave and convex wedges is studied for Nagumo and Fisher's equations on the limit of fast reaction and small diffusion, using both the asymptotic theory and full numerical solutions. For the case of a convex corner, the full numerical solution confirms that the front evolves according to the asymptotic theories. On the other hand, for the concave corner, it is shown numerically that the diffraction produces at the corner a region of low values of the solution for both the Nagumo and Fisher's equations. Moreover, in both cases, the front eventually evolves, leaving behind a cavity. In the case of the Nagumo equation, it is shown that the long-term behavior of the diffraction front is just a traveling front, bent at the sloping wall. The bent region maintains its size as the front travels. This behavior is predicted by an exact traveling wave solution of the asymptotic equation for the front propagation. Good agreement is found between the numerical and the asymptotic solutions. On the other hand, behavior of the diffracted front for Fisher's equation is different. In this case, the front is bent at the sloping wall, but, as time passes, the bend becomes smaller and moves toward the sloping wall. This behavior is, again, predicted by the asymptotic solution. The numerics strongly suggest that the final state for the concave corner is a steady cavity-like solution with low values at the corner and high

A radiation resonance effect observed in the reflection spectra from overdense plasmas illuminated by femtosecond laser pulses at normal incidence is reported from particle-in-cell simulations. Harmonic emission at multiple orders of the fundamental is found to exhibit resonance phenomena, with the number of resonances and power emitted depending on the electron plasma density. For relatively low laser intensities the reflected light at the laser frequency shows prominent resonant emission around specific values of the plasma density, mainly at 4, 16, and 36 times critical. For increasing laser intensities, strong harmonic emission around 4 and 16 times critical dominates the reflection spectra. In the case of the third laser harmonic, the emission is found to be resonant about those densities and presents, additionally, a distinctive resonant region around nine times critical. A simple radiation model for the power of the third harmonic was proposed confirming a resonant effect dependent on the electron plasma density. For higher harmonic numbers, weak radiation resonances persist in the emission spectra, with their number increasing with order. The resonance effect reported in this paper is found to occur at densities that approximately satisfy n(e)/n(c)=4n(2), where n(e) and n(c) are the plasma and the critical density, respectively, and n is an integer. For the third harmonic, the second resonance corresponds to n=1.5.

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