Waves are superoscillatory where their local phase gradient exceeds the maximum wavenumber in their Fourier spectrum. We consider the superoscillatory area fraction of random optical speckle patterns. This follows from the joint probability density function of intensity and phase gradient for isotropic Gaussian random wave superpositions. Strikingly, this fraction is 1/3 when all the waves in t...

In this paper we present a simple and robust random projection method for underresolved numerical simulation of stiff detonation waves in chemically reacting flows. This method is based on the random projection method proposed by the authors for general hyperbolic systems with stiff reaction terms [W. Bao and S. Jin, J. Comput. Phys., 163 (2000), pp. 216–248], where the ignition temperature is ...

We present an approach for subwavelength focusing of microwaves using both a time-reversal mirror placed in the far field and a random distribution of scatterers placed in the near field of the focusing point. The far-field time-reversal mirror is used to build the time-reversed wave field, which interacts with the random medium to regenerate not only the propagating waves but also the evanesce...

Density gradients aligned at an angle to pressure result in baroclinic torque fluid flows, generating vorticity. In this work, we study the vorticity generated by exerted interaction of jumps across random two-dimensional shock waves with density gradients. A field has acoustic spectral energy scaling as {\epsilon}^{2/3}{\ell}^{-1/3}k^{-2} where k is wavenumber, {\epsilon} dissipation, and \ell...

We construct deterministic solutions to the Helmholtz equation in $\mathbb{R}^m$ which behave accordingly Random Wave Model. then find number of their nodal domains, volume and topologies nesting trees set growing balls around origin. The proof pseudo-random behaviour functions under consideration hinges on a de-randomisation technique pioneered by Bourgain proceeds via computing $L^p$-norms. s...