E. M. de Jager

Computer implementation of simulation models for non-linear, non-ideal chromatography: Part 1. Fundamental mathematical considerations

Abstract A proper mathematical model is essential for understanding processes in chromatographic columns. In this paper two models are developed, a discrete and a continuous model, both describing the behaviour of mass transport in chromatographic columns, with linear or non-linear distribution isotherms and with or without longitudinal dispersion. The discrete model is used for computer simulations of chromatographic problems. The mathematical expressions are derived from physical fundamentals in such a way that computer implementation is feasible without great problems. To check the correctness of the numerical solutions, exact solutions of parts of the continuous model are derived. The influence of the choice of explicit difference schemes on the numerical solution is discussed.

The role of the theoretical plate concept and gamma density functions in studies on mass transport and mass loadability of chromatographic columns

SummaryThe validity of the use of the plate theory in transport processes with non-Gaussian peak shapes is discussed. It is shown that the application of the plate theory implies the assumption of a peak with a gamma density shape which, however, converges rapidly to symmetrical Gaussian shape for large plate numbers. A proposal for an extension of the plate theory, based on a gamma density function is given. This approach results in an extra parameter which characterizes the asymmetry of a peak. Use of the suggested fitting function permits an estimate of the moments of the peak, even without the use of a computer. The proposed model can be used to determine a transfer function for the chromatographic system, allowing a system theoretical approach to determine the influence of, for example, amplifiers, filters and detectors on the peak shape. The exponentially modified Gauss (EMG) is one of the possible peak shapes included in the model.

Computer implementation of simulation models for non-linear, non-ideal chromatography: Part 2. Numerical Experiments and Results [l]

Abstract The more practical aspects of simulation of discrete mathematical models are described. Particular attention is given to the model describing the behaviour of mass transport m Chromatographic columns with a non-linear isotherm and with or without longitudinal dispersion. Rules for building general usable simulation software are explained. An outline of the program, without extensive treatment of program listings and flow diagrams, is given and experimental conditions and results are discussed.

Prolongation structures and Backlund transformations for the matrix Korteweg-de Vries and the Boomeron equation

Prolongation structures are determined for the matrix Korteweg-de Vries and the Boomeron equation by using the integrability condition for a linear system of first-order equations. Symmetries of these prolongation structures are used to derive Backlund transformations and to construct solutions for both equations.

Reflection and transmission of plane waves by layered periodic media

The reflection and transmission coefficients (at normal incidence) for plane parallel slabs consisting of N inhomogeneous and exactly identical parallel layers are expressed in terms of the corresponding coefficients for a single layer. The analysis is effected by two different methods, one of which stems from the so called invariant imbedding viewpoint while the other relies on a more conventional matrix argument.

Continuous Dynamical Systems

Dynamics is a time-evolutionary process. It may be deterministic or stochastic. Long-term predictions of some systems often become impossible. Even their trajectories cannot be represented by usual geometry.

Concentrated force acting in an inviscid and incompressible parallel flow

The paper discusses the steady disturbance velocity field induced by a concentrated force acting at a fixed point of space in a parallel flow of an inviscid and incompressible fluid. Force and parallel flow have the same direction. The induced velocity field, its pressure field and its acceleration held are described by means of generalized functions (distributions). Copyright (C) 2000 John Wiley & Sons, Ltd.

Hyperbolic Singular Perturbations of Non Linear First Order Differential Equations

Publisher Summary This chapter discusses the hyperbolic singular perturbations of nonlinear first order differential equations. The nonlinear Cauchy problem is considered. A modification of a fixed-point theorem of Van Harten is discussed in the chapter. A priori estimate for the solution of a linear singular perturbation problem of hyperbolic type is described. Formal approximation of the Cauchy problem is analyzed. Estimation of the remainder term R is also explained in this chapter.

On the Solution of an Integral Equation of Convolution Type

The solution

On Functions Holomorfic in Tube Domains Irn+ iC

Q_\lambda ^\mu