... Corresponding author. Email: z-bazant@northwestern.edu 18 06 2023 17 07 2023 19 07 2023 07 08 2023 osmotic pressures ion concentration in pores diffusion permeability tests critical time of water outflow porous rocks shale basalt peridotite mafic rocks hydraulic...

...Kees Wapenaar; Jacob Fokkema We thank Stefan Stijlen for bringing the singularity of matrix C to our attention. 07 07 2010 17 08 2010 differential equations diffusion flow matrix algebra vectors waves Matrix C defined in Appendices C and D is singular...

... approaches complement approximate analytical methods in the determination of moment Lyapunov exponents and provides criteria on assessing the accuracy of approximate analytical results. For stochastic dynamical systems described by Itô stochastic differential equations, the solutions are diffusion processes...

... that magnetic stabilization is obtained because the two-phase magnetic body force enhances the diffusion effect of the void waves. It is experimentally clarified that the two-phase flow state can be stabilized and homogenized by magnetization of the fluid and that vapor bubbles can be minutely produced...

... the results are obtained without requiring explicit solution of the PDE. The development is presented via case studies of the linear diffusion equation and the non-linear Kortweg de-Vries equation which indicate strategies for exploiting the various properties of correlation moments developed in the text...

..., manifests itself, resulting in all stress components, pore pressure, and temperature being z independent. Naturally, both heat and fluid flux components in the z direction vanish and all diffusion phenomena occur in the x - y plane which is isotropic. It would therefore be useful to derive...

...Kees Wapenaar and; Jacob Fokkema Diffusion, flow, and wave phenomena can each be captured by a unified differential equation in matrix-vector form. This equation forms the basis for the derivation of unified reciprocity theorems for diffusion, flow and wave phenomena. Contributed...

...S. Roy, Assistant Professor, Mem. ASME; W. X. Xu, Graduate Research Assistant; S. J. Park, Graduate Research Assistant; K. M. Liechti, Professor It is now well known that Fick’s Law is frequently inadequate for describing moisture diffusion in polymers or polymer composites. Non-Fickian...