The systems of conservation laws have been used to model dynamical phase transitions in, for example, the propagating phase boundaries in solids and the van der Waals uid. When integrating such mixed hyperbolic-elliptic systems the Lax-Friedrichs scheme is known to give the correct solutions selected by a viscosity-capillarity criterion except a spike at the phase boundary which does not go awa...

Perceptual constancy-identifying surfaces and objects across large image changes-remains an important challenge for visual neuroscience [1-8]. Liquids are particularly challenging because they respond to external forces in complex, highly variable ways, presenting an enormous range of images to the visual system. To achieve constancy, the brain must perform a causal inference [9-11] that disent...

In this paper we study the effects of variable viscosity and thermal conductivity on the heat transfer in the pressure-driven fully developed flow of a slurry (suspension) between two horizontal flat plates. The fluid is assumed to be described by a constitutive relation for a generalized second grade fluid where the shear viscosity is a function of the shear rate, temperature and concentration...

The effect of thermal radiation on the natural convection flow along a uniformly heated vertical porous plate with variable viscosity and uniform suction velocity was investigated numerically. The fluid considered in this study is of an optically dense viscous incompressible fluid of temperature-dependent viscosity. The laminar boundary layer equations governing the flow are shown to be nonsimi...

We introduce a simplified model for thin-layer flows of granular materials with yield. The model is based on a viscoplastic rheology with Drucker-Prager yield stress and describes the dynamics of the velocity profile as well as the transition between static and flowing material. As opposed to most models developed to describe the static/flowing transition in thin-layer flows, the variable Z in ...

We consider the reconstruction of obstacles inside a bounded domain filled with an incompressible fluid. Our method relies on special complex geometrical optics solutions for the stationary Stokes equation with a variable viscosity.