A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multicompartment partial differential equation models, interconnected with interface conditions, is presented and analyzed. The study of interface problems is motivated by models of mass transfer of solutes through semipermeable membranes. More specifically, a model problem consisting of a system of semili...

Transplantation of islet or beta cells is seen as the cure for type 1 diabetes since it allows physiological regulation of blood glucose levels without requiring any compliance from the patients. In order to circumvent the use of immunosuppressive drugs (and their side effects), semipermeable membranes have been developed to encapsulate and immunoprotect transplanted cells. This review presents...

In power generating terms, a pressure retarded osmosis (PRO) energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is p...

In thermodynamically characterizing a mixture comprising finite number of molecules, we consider two kinds protocol for producing from pure substance. The first is single alchemical operation, whereas the second series processes with feedback control in information thermodynamics and conventional mixing semipermeable membranes. A comparison numerically determined free-energy changes provides co...

We propose a family of Interior Penalty Discontinuous Galerkin (IP-DG) finite element methods for the solution of semilinear convection-reaction-diffusion systems on partitioned subdomains arising in the modelling of mass transfer through semipermeable membranes. Non-linear interface conditions are imposed at the sub-domain interfaces. The problem considered is relevant to the modelling of chem...

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...

The destabilizing effect of four different types of multivalued conditions describing the influence of semipermeable membranes or of unilateral inner sources to the reaction-diffusion system is investigated. The validity of the assumptions sufficient for the destabilization which were stated in the first part is verified for these cases. Thus the existence of points at which the spatial pattern...