The stability analysis of Marangoni convection in porous media with a deformable upper free surface is investigated. The linear stability theory and the normal mode analysis are applied and the resulting eigenvalue problem is solved exactly. The Darcy law and the Brinkman model are used to describe the flow in the porous medium heated from below. The effect of the Crispation number, Bond number...

A one-sided model of the thermal Marangoni instability owing to evaporation into an inert gas is developed. Two configurations are studied in parallel: a horizontal liquid layer and a spherical droplet. With the dynamic gas properties being admittedly negligible, one-sided approaches typically hinge upon quantifying heat and mass transfer through the gas phase by means of transfer coefficients ...

We present a systematic derivation of the Biot-Savart equation from the nonlinear Schrödinger equation, in the limit when the curvature radius of vortex lines and the intervortex distance are much greater than the vortex healing length, or core radius. We derive the Biot-Savart equations in Hamiltonian form with Hamiltonian expressed in terms of vortex lines,H=κ(2)/8π∫(|s-s'|>ξ(*))(ds·ds')/|s-s...

Understanding the propagation of acoustic waves through a liquid-perfused porous solid framework such as cancellous bone is an important pre-requisite to improve the diagnosis of osteoporosis by ultrasound. In order to elucidate the propagation dependence upon the material and structural properties of cancellous bone, several theoretical models have been considered to date, with Biot-based mode...

A year ago, the author evolved a simulated artificial creature (biot, i.e. biological robot), called LIZZY, which consisted of fully connected neural network modules (called GenNets), whose weights were evolved such that each GenNet performed some desired behavior, such as making the biot walk straight ahead, turn clockwise or anticlockwise, peck, or mate [de Garis 1990, 1991, 1993]. Other such...

Abstract. In this article we obtain rigorously the homogenization limit for a fluid-structurereactive flow system. It consists of cell tissue and intercellular liquid, transporting solutes. The cell tissue is supposed linearly elastic and deforming with a viscous non-stationary flow. The elastic moduli of the tissue change with cumulative concentration value. In the limit, when the scale parame...

The evaluation of current distributions in thick superconductors from field profiles near the sample surface is investigated theoretically. A simple model of a cylindrical sample, in which only circular currents are flowing, reduces the inversion to a linear least squares problem, which is analyzed by singular value decomposition. Without additional assumptions about the current distribution (e...

A frequency independent criterion to determine the limp model validity for highly porous sound absorbing materials is investigated. Although limp model is derived from the Biot theory assuming that the porous frame has no bulk stiffness, it is shown that this model can be used for highly porous materials since the criterion is respected. Abacus giving the criterion limit as function of the poro...

The interaction between a fluid and a poroelastic structure is a complex problem that couples the Navier-Stokes equations for the fluid with the Biot system for the structure. The finite element approximation of this problem is involved due to the fact that both subproblems are indefinite. In this work, we design residual-based stabilization techniques for the Biot system, that have been motiva...