In this work, we always assume that the drift and diffusion functions satisfy globally Lipschitz conditions (cf. (3.1)), which excludes many important model equations in applications.
KCM/TPNM is computationally fast and it allows a study of the diffusion synchronously and globally in the network, avoiding thus its fractionation in single pores and the use of just one geometric model to describe the porous spaces.
The purpose of the operator splitting is to separate the nonlinear but local reaction computations from the linear but globally coupled diffusion computations.
Comparing across imaging modalities, the present data suggest that CBF may be a more sensitive marker as the changes are detected globally whereas diffusion and functional connectivity measures only showed regional effects.
It has been demonstrated that post-mortem interval globally reduces diffusion-weighted MRI metrics in controlled rodent (D'Arceuil and de Crespigny, 2007), porcine (Widjaja et al., 2009) and donated human tissue (Kim et al., 2009), although scan interval does not have the same effect (Yong-Hing et al., 2005; Dyrby et al., 2010).
The thermal diffusion, or Soret effect, is analyzed globally with a separation ratio and locally with the distributions of ethanol mole fraction on the horizontal and vertical lines in the center of the porous cavity.
This shows that a large enough diffusion coefficient may always make the system globally exponentially synchronous.
It is well known that the diffusion coefficient of equation (1.1) is not globally Lipschitz.
Recently, there have been some papers in being able to reveal the dynamics of the systems with Gaussian diffusion, such as stationary patterns [1 4], globally asymptotic stability [2, 5] and so on.
On the contrary, if the wettability of gold for the substrate is improved (chemical modification of the surface), the interactions between the two materials are globally stronger, and both the diffusion and coalescence of the metal clusters are disfavored [21].
