Diffusive Wave Model and Its Applications to Biology and Physics

This study presents the diffusive wave model, relevant dispersion law and the applications to the signal transduction of live cells, phason dynamics of quasicrystals, Brownian movement, electro-magnetic field and fluid dynamics fluctuation, respectively. The common features of these diffusive waves are summarized, which present diffusion as well as wave behaviour, or exactly speaking, they present a duality of diffusion and wave or the duality of wave and diffusion. Furthermore, the general nature of the motion is discussed from the point of view of Landau elementary excitation of condensed matter, this may lead to a concept of generalized elementary excitation (or generalized quasiparticle) corresponding to the diffusive wave.