Introduction. It is known that under many conditions, effective operators will be partial recursive, ([MS], [KLS], [L]). On the other hand, certain pathological examples have been constructed by Friedberg [F] and Pour-El [P] to show that effective operators are not always partial recursive. Pour-El has observed that although it is well known that all partial recursive operators are continuous, ...

In this paper, we consider spatial predator-prey models with diffusion and prey-taxis. We investigate necessary conditions for pattern formation using a variety of non-linear functional responses, linear and non-linear predator death terms, linear and non-linear prey-taxis sensitivities, and logistic growth or growth with an Allee effect for the prey. We identify combinations of the above non-l...

We report on the experimental observation of speckle formation from a transparent crystal formed by a random distribution of nonlinear domains. The angular distribution of second-harmonic light generated by a transparent strontium barium niobate crystal is measured for different diameters of the fundamental beam and crystal thicknesses. Distinct manifestations of speckle pattern formation are f...

The effects of non-equilibrium charge screening in mixtures of oppositely charged interacting molecules on surfaces are analyzed in a closed system. The dynamics of charge screening and the strong deviation from the standard Debye-Hückel theory are demonstrated via a new formalism based on computing radial distribution functions suited for analyzing both short-range and long-range spacial order...

We present an experimental and theoretical investigation of spontaneous pattern formation in the transverse section of a single retroreflected laser beam passing through a cloud of cold rubidium atoms. In contrast to previously investigated systems, the nonlinearity at work here is that of a two-level atom, which realizes the paradigmatic situation considered in many theoretical studies of opti...