When posed on a periodic domain in one space variable, linear dispersive evolution equations with integral polynomial dispersion relations exhibit strikingly different behaviors depending upon whether the time is rational or irrational relative to the length of the interval, thus producing the Talbot effect of dispersive quantization and fractalization. The goal here is to show that these remarkable phenomena extend to nonlinear dispersive evolution equations. We will present numerical simulations, based on operator splitting methods, of the nonlinear Schrödinger and Korteweg--deVries equations with step function initial data and periodic boundary conditions. For the integrable nonlinear Schrödinger equation, our observations have been rigorously confirmed in a recent paper of Erdoǧan and Tzirakis, [10].

With the rapid development of electronics, thermal management has become one of the most crucial issues. Intense research has focused on surface modifications used to enhance heat transfer. In this study, multilayer copper micromeshes (MCMs) are developed for commercial compact electronic cooling. Boiling heat transfer performance, including critical heat flux (CHF), heat transfer coefficients (HTCs), and the onset of nucleate boiling (ONB), are investigated. The effect of micromesh layers on the boiling performance is studied, and the bubbling characteristics are analyzed. In the study, MCM-5 shows the highest critical heat flux (CHF) of 207.5 W/cm² and an HTC of 16.5 W(cm²·K) because of its abundant micropores serving as nucleate sites, and outstanding capillary wicking capability. In addition, MCMs are compared with other surface structures in the literature and perform with high competitiveness and potential in commercial applications for high-power cooling.