7 problems

Let $L_c$ be the macroscale characteristic length and let $alpha_\text{max}$ denote the maximum Brinkman penalization value. The numerical study considers their relation through a…

Dissipation-minimization conjecture. The parameters $(V,A_s,A_f)$ are chosen in such a way that the dissipation $R$ is minimal. The claim concerns the selection of parameters for a…

The actively deforming porous medium is described by the coupled solid–fluid evolution equations, with the muscle action prescribed as a traveling force and the momenta defined fro…

The model considers a horizontal cross-section through a fiber and vessel in maple sapwood, with gas, liquid, and ice arranged as distinct concentric annular layers. During previou…

Robinson's conjecture. There are three types of solutions: type $I$, type $II$, and type $III$.

Persistence conjecture. We conjecture that the saturation overshoots in the BVE-model persist as $\beta_x$, $\beta_z$, $psilon_x$, and $psilon_z$ tend to zero.

Couple-stress pumping conjecture. When the pressure rise $\Delta p$ is negative, the couple stress effect creates resistance to flow and reduces the velocity; however, in the free-…