A Stefan problem for a protocell model
نویسندگان
چکیده
The paper considers a simple model of radially symmetric cell which undergoes growth due to a continuous supply of nutrient, and disintegration as a result from the various tasks the cell performs. The boundary of the cell is a \free boundary", unknown in advance, which evolves by responding to both the growth and disintegration processes. If the nutrient concentration (at in nity) exceeds a certain critical number, then two stationary solutions exist. It is established, by rigorous mathematical proofs, that the stationary solution with the smaller radius is unstable, whereas the stationary solution with the larger radius is stable.
منابع مشابه
UNIQUENESS OF SOLUTION FOR A CLASS OF STEFAN PROBLEMS
This paper deals with a theoretical mathematical analysis of one-dimensional solidification problem, in which kinetic undercooling is incorporated into the This temperature condition at the interface. A model problem with nonlinear kinetic law is considered. We prove a local result intimate for the uniqueness of solution of the corresponding free boundary problem.
متن کاملA study of a Stefan problem governed with space–time fractional derivatives
This paper presents a fractional mathematical model of a one-dimensional phase-change problem (Stefan problem) with a variable latent-heat (a power function of position). This model includes space–time fractional derivatives in the Caputo sense and time-dependent surface-heat flux. An approximate solution of this model is obtained by using the optimal homotopy asymptotic method to find the solu...
متن کاملTHE STEFAN PROBLEM WITH KINETIC FUNCTIONS AT THE FREE BOUNDARY
This paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. A model problem with nonlinear kinetic law is considered. The main result is an existence theorem. The mathematical effects of the kinetic term are discussed
متن کاملNewton-Product Integration for a Stefan Problem with Kinetics
Stefan problem with kinetics is reduced to a system of nonlinear Volterra integral equations of second kind and Newton's method is applied to linearize it. Product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. An example is provided to illustrated the applicability of the method.
متن کاملDevelopment of a phase change model for volume-of-fluid method in OpenFOAM
In this present study, volume of fluid method in OpenFOAM open source CFD package will be extended to consider phase change phenomena with modified model due to condensation and boiling processes. This model is suitable for the case in which both unsaturated phase and saturated phase are present and for beginning boiling and condensation process needn't initial interface. Both phases (liquid-va...
متن کامل