A new fractional derivative involving the normalized sinc function without singular kernel

In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative results between classical and fractional-order operators are presented. The results are significant in the analysis of one-dimensional anomalous heat-transfer problems.Comment: Keywords: Fractional derivative, anomalous heat diffusion, integral transform, analytical solutio

Caustic graphene plasmons with Kelvin angle

A century-long argument made by Lord Kelvin that all swimming objects have an effective Mach number of 3, corresponding to the Kelvin angle of 19.5 degree for ship waves, has been recently challenged with the conclusion that the Kelvin angle should gradually transit to the Mach angle as the ship velocity increases. Here we show that a similar phenomenon can happen for graphene plasmons. By analyzing the caustic wave pattern of graphene plasmons stimulated by a swift charged particle moving uniformly above graphene, we show that at low velocities of the charged particle, the caustics of graphene plasmons form the Kelvin angle. At large velocities of the particle, the caustics disappear and the effective semi-angle of the wave pattern approaches the Mach angle. Our study introduces caustic wave theory to the field of graphene plasmonics, and reveals a novel physical picture of graphene plasmon excitation during electron energy-loss spectroscopy measurement.Comment: 15 pages, 4 figure