A lattice Boltzmann model is proposed to asses the impact of variable molecular transport effects on the heat and mass transfer in a horizontal shallow cavity due to natural convection. The formulation includes a generalized form of the Soret and Dufour mass and heat diffusion (cross diffusion) vectors derived from non-equilibrium thermodynamics and fluctuation theory. Both the individual cross...

For a specific choice of the diffusion, the parabolic-elliptic PatlakKeller-Segel system with non-linear diffusion (also referred to as the quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold phenomenon: there is a critical mass Mc > 0 such that all the solutions with initial data of mass smaller or equal to Mc exist globally while the solution blows up in finite time ...

1. Review the concept of heat and the processes of diffusion and osmosis. Learn the factors that affect the rate of diffusion. 2. Observe Brownian motion and relate this observation to the concept of heat energy. 3. Measure the speed of diffusion of dyes in a gel, and the speed of diffusion of gases in air. Relate the speed of diffusion to molecular mass and medium. 4. Investigate the process o...

Water diffusion within the structure of a brain extracellular space is analyzed numerically for various diffusion parameters of brain tissue namely extracellular space porosity and tortuosity. An algorithm for predicting diffusion pattern of water molecules within human brain considering the mechanics of water diffusion within porous media is developed. The extracellular space is modeled as a h...

We investigate the question of whether ambipolar diffusion (ion-neutral drift) determines the smallest length and mass scale on which structure forms in a turbulent molecular cloud. We simulate magnetized turbulence in a mostly neutral, uniformly driven, turbulent medium, using a three-dimensional, two-fluid, magnetohydrodynamics (MHD) code modified from Zeus-MP. We find that substantial struct...

Analysis of diffusion in a complex environment shows that the conventional diffusion equation based on Fick’s law fails to model the anomalous character of the diffusive mass transport observed in the field and laboratory experiments. New mathematical models of diffusive transport, different from Fick’s law, were proposed and validated in literature. In the present paper the examples of the equ...