Percolation and Burgers' dynamics in a model of capillary formation.

[Article] Percolation and Burgers’ dynamics in a model of capillary formation

Ergodic Theory of the Burgers Equation

The ultimate goal of these lectures is to present the ergodic theory of the Burgers equation with random force in noncompact setting. Developing such a theory has been considered a hard problem since the first publication on the randomly forced inviscid Burgers [EKMS00]. It was solved in a recent work [BCK] for the forcing of Poissonian type. The Burgers equation is a basic fluid dynamic model,...

Percolation, morphogenesis, and burgers dynamics in blood vessels formation.

Experiments of in vitro formation of blood vessels show that cells randomly spread on a gel matrix autonomously organize to form a connected vascular network. We propose a simple model which reproduces many features of the biological system. We show that both the model and the real system exhibit a fractal behavior at small scales, due to the process of migration and dynamical aggregation, foll...

Invasion Percolation in Presence of Gravity

Simultaneous capillary dominated displacement of the wetting and non-wetting phases are processes of interest in many disciplines including modeling of the penetration of polluting liquids in hydrology or the secondary migration in petroleum reservoir engineering. Percolation models and in particular invasion percolation is well suited to characterize the slow immiscible displaceme...

Modeling and investigating the effect of ultrasound waves pressure on the microbubble oscillation dynamics in microvessels containing an incompressible fluid (Research Article)

Understanding the dynamics of microbubble oscillation in an elastic microvessel is important for the safe and effective applications of ultrasound contrast agents in imaging and therapy. Numerical simulations based on 2D finite element model are performed to investigate the effect of acoustic parameters such as pressure and frequency on the dynamic interaction of the fluid-blood-vessel system. ...