saccharomyces cerevisiae (baker’s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. because of heterogeneous nature of cell populations, the cell population balance equation (pbe) can be used to capture the dynamic behavior of such cultures. in this work, an unstructured-segregated model is used for d...

1 OVERVIEW This guide describes a collection of programs for (1) creating and reening tri-angulations on surfaces, and (2) solving integral equations using collocation methods over these triangulations. The main purpose of this package is to allow for experimentation with numerical methods for solving boundary integral equations that are deened on piecewise smooth surfaces in R 3. General surve...

This guide describes a collection of programs for creating and re ning triangulations on surfaces and solving integral equations using collocation methods over these tri angulations The main purpose of this package is to allow for experimentation with numerical methods for solving boundary integral equations that are de ned on piecewise smooth surfaces in R For a general survey of the numerical...

A new approach to the numerical solution of systems of first-order ordinary differential equations is given by finding local Galerkin approximations on each subinterval of a given mesh of size h. One step at a time, a piecewise polynomial, of degree n and class C°, is constructed, which yields an approximation of order 0(A*") at the mesh points and 0(A"+1) between mesh points. In addition, the ...

This guide describes a collection of programs for (1) creating and re ning triangulations on surfaces, and (2) solving integral equations using collocation methods over these triangulations. The main purpose of this package is to allow for experimentation with numerical methods for solving boundary integral equations that are de ned on piecewise smooth surfaces in R. General surveys of the nume...

We consider a piecewise continuous, piecewise monotone interval map and a weight of bounded variation, constant on homtervals and continuous at periodic points of the map. With these data we associate a sequence of weighted Milnor-Thurston kneading matrices, converging to a countable matrix with coeecients analytic functions. We show that the determinants of these matrices converge to the inver...

We derive a posteriori error estimates, which exhibit optimal global order, for a class of time stepping methods of any order that include Runge–Kutta Collocation (RK-C) methods and the continuous Galerkin (cG) method for linear and nonlinear stiff ODEs and parabolic PDEs. The key ingredients in deriving these bounds are appropriate one-degree higher continuous reconstructions of the approximat...

We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case, our methods require only C3 regularity of the maps in the IFS. The key idea, which has been known in varying degrees of generality for many years, is to associate to the IFS a parametrized family of positive, linear, Perron-Frobenius op...