We investigate an intermittent process obtained from the combination of a nonlinear diffusion equation and pauses. We consider the porous media equation with reaction terms related to the rate of switching the particles from the diffusive mode to the resting mode or switching them from the resting to the movement. The results show that in the asymptotic limit of small and long times, the spread...

Driven diffusive systems have been a paradigm for modelling many physical, chemical, and biological transport processes. In the systems, spatial correlation plays an important role in the emergence of a variety of nonequilibrium phenomena and exhibits rich features such as pronounced oscillations. However, the lack of analytical results of spatial correlation precludes us from fully understandi...

The diffusive-ballistic heat conduction of finite-length single-walled carbon nanotubes has been studied by means of nonequilibrium molecular dynamics simulations. The length dependence of thermal conductivity [1] is quantified for a range of nanotube lengths up to 1.6 μm at room temperature. A gradual transition from nearly pure ballistic to diffusive-ballistic heat conduction was identified f...

In this paper we derive diffusive relaxation schemes for the linear semiconductor Boltzmann equation that work in both the kinetic and diffusive regimes. Similar to our earlier approach for multiscale transport equations, we use the evenand oddparity formulation of the kinetic equation, and then reformulate it into the diffusive relaxation system (DRS). In order to handle the implicit anisotrop...

The thermal conductivities of empty and water-filled single-walled carbon nanotubes CNTs with diameters between 0.83 and 1.36 nm and lengths ranging from 200 to 1400 nm are predicted using molecular dynamics simulation. Using a direct application of the Fourier law, we explore the transition to fully diffusive phonon transport with increasing CNT length. For empty CNTs, we find that the CNT len...

To date, it has not been possible to measure microscopic diffusive water movements in epithelia and in the interstitial space of complex tissues and organs. Diffusive water movements are essential for life because they convey physiologically important small molecules, e.g. nutrients and signaling ligands throughout the extracellular space of complex tissues. Here we report the development of a ...

Applying diffusive models for simulating the spatiotemporal change of concentration of tumour cells is a modern application of predictive oncology. Diffusive models are used for modelling glioblastoma, the most aggressive type of glioma. This paper presents the results of applying a linear quadratic model for simulating the effects of radiotherapy on an advanced diffusive glioma model. This dif...