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American Society for Testing and Materials

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Boundary-layer flow of a nanofluid past a stretching sheet

The flow of homogeneous fluids through porous media: analogies with other physical problems

Natural convective boundary-layer flow of a nanofluid past a vertical plate

Optimal control of the heat storage in a porous slab

By assuming that tau protein can be in seven kinetic states, we developed a model of tau protein transport in the axon and in the axon initial segment (AIS). Two separate sets of kinetic constants were determined, one in the axon and the other in the AIS. This was done by fitting the model predictions in the axon with experimental results and by fitting the model predictions in the AIS with the assumed linear increase of the total tau concentration in the AIS. The calibrated model was used to make predictions about tau transport in the axon and in the AIS. To the best of our knowledge, this is the first paper that presents a mathematical model of tau transport in the AIS. Our modeling results suggest that binding of free tau to microtubules creates a negative gradient of free tau in the AIS. This leads to diffusion-driven tau transport from the soma into the AIS. The model further suggests that slow axonal transport and diffusion-driven transport of tau work together in the AIS, moving tau anterogradely. Our numerical results predict an interplay between these two mechanisms: as the distance from the soma increases, the diffusion-driven transport decreases, while motor-driven transport becomes larger. Thus, the machinery in the AIS works as a pump, moving tau into the axon.

Modeling tau transport in the axon initial segment.

This article presents comparisons between an analytical and a numerical investigation of porosity formation within the mushy zone during the solidification process. For this purpose, a three-phase model (liquid, solid, and gas) of the mushy zone is utilized. This model takes into account the release of the dissolved gas from the alloy as well as the heat transfer and interdendritic fluid flow in the two-phase region. The main difference between the three-phase model and the two-phase model (only liquid and solid), which is usually used to predict the porosity distribution, is the inclusion of a term describing the porosity formation in the continuity equation. The perturbation method is used to obtain an analytical solution describing the porosity formation. Pressure and porosity distributions predicted by these two models are compared for the particular case of aluminum-rich Al-Cu castings.

Andrey V. Kuznetsov

Papers

Optimal control of the heat storage in a porous slab

Modeling tau transport in the axon initial segment.

Comparison between the two- and three-phase models for analysis of porosity formation in aluminum-rich castings

A similarity solution for a falling plume in bioconvention of oxytactic bacteria in a porous medium

An analytical solution describing retrograde viral transport in an axon