Charles D. Holland

Hormesis: A Highly Generalizable and Reproducible Phenomenon With Important Implications for Risk Assessment

From a comprehensive search of the literature, the hormesis phenomenon was found to occur over a wide range of chemicals, taxonomic groups, and endpoints. By use of computer searches and extensive cross-referencing, nearly 3000 potentially relevant articles were identified. Evidence of chemical and radiation hormesis was judged to have occurred in approximately 1000 of these by use of a priori criteria. These criteria included study design features (e.g., number of doses, dose range), dose-response relationship, statistical analysis, and reproducibility of results. Numerous biological endpoints were assessed, with growth responses the most prevalent, followed by metabolic effects, reproductive responses, longevity, and cancer. Hormetic responses were generally observed to be of limited magnitude with an average maximum stimulation of 30 to 60 percent over that of the controls. This maximum usually occurred 4- to 5-fold below the NOAEL for a particular endpoint. The present analysis suggests that hormesis is a reproducible and generalizable biological phenomenon and is a fundamental component of many, if not most, dose-response relationships. The relatively infrequent observation of hormesis in the literature is believed to be due primarily to experimental design considerations, especially with respect to the number and range of doses and endpoint selection. Because of regulatory considerations, most toxicologic studies have been carried out at high doses above the low-dose region where the hormesis phenomenon occurs.

Gear's procedure for the simultaneous solution of differential and algebraic equations with application to unsteady state distillation problems

Abstract The dynamic equations modeling a sieve plate at unsteady state are developed. Gears procedure for the simultaneous solution of systems of stiff differential and algebraic equations is presented and demonstrated for the solution of unsteady state distillation problems. It is shown that the basic stage model can be modified by the addition of one variable and one equation such that Gears procedures are readily applied. The proposed model and solution procedure is contrasted to recently published procedures. Numerical results are given for the solution of a problem involving an extractive distillation column at unsteady state.

Development and comparison of a generalized semi-implicit Runge-Kutta method with Gear's method for systems of coupled differential and algebraic equations

Abstract A generalized form of the semi-implicit Runge-Kutta method proposed by Michelsen[1, 2] is developed and its performance is compared with Michelsens method and Gears method[3, 4] in the solution of a dynamic model for an absorber. The necessity for the definition of new variables in the application of Michelsens method in order to place the set of differential equations in state variable form [equations of the form ẏ = f(y)] is removed by the generalized semi-implicit Runge-Kutta method.

Analysis and evaluation of the relative gains for nonlinear systems

Abstract By beginning with the most general implicit relationships between the controlled variables and the manipulated variables of a control system, formulas for computing the relative gain are developed. This approach leads to a more comprehensive analysis and consequently a better understanding of the conditions responsible for infinite relative gains. Also, the use of the Jacobian method of determinants to minimize the number of computer solutions required to evaluate the elements of the relative gain matrix is demonstrated by use of a numerical example.

A modification of broyden's method for the solution of sparse systems—with application to distillation problems described by nonideal thermodynamic functions

Abstract An algorithm that permits Broydens method to be used for the solution of large systems of algebraic equations with sparse Jacobians is presented. The new procedure is compared to Schuberts modification of Broydens method and to the Newton-Raphson method by solving an extractive distillation problem. It is demonstrated that the new procedure is competitive with Schuberts method when it is necessary to evaluate Jacobian matrices numerically.

Use of multipoint algorithms and continuation methods in the solution of distillation problems

Abstract The use of multipoint algorithms combined with continuation methods for the solution of difficult steady-state distillation problems is illustrated. The characteristics of the different combinations of methods are presented and compared by solving a variety of distillation problems. The associated problem of multiple solutions is presented and a method for solving problems of this type is proposed and demonstrated.

Solution of difficult distillation problems by use of a combination of the Newton—Raphson and functional transformation methods

Abstract By use of a combination of the functional transformation and the Newton—Raphson methods, it is possible to solve most problems which are either difficult or impossible to solve by use of the Newton—Raphson method alone. In this note, the functional transformation method introduced by Vazquez-Esparragoza et al. (1987) for solving small systems of one or two nonlinear equations is applied to large systems of nonlinear equations.

Solution of systems of columns with energy exchange between recycle streams

Abstract A column modular method which makes use of the capital Θ method of convergence is presented for solving problems involving systems of distillation columns containing both mass and energy recycle streams. Three types of energy exchange are considered: (1) the use of one stream to condense another, (2) the transfer of energy from one recycle stream to another through the use of a heat exchanger, and (3) the use of a trim heat exchanger to adjust the heat content or temperature of a given stream.

The Jacobi Eigenvalue Criterion: A Dynamic Extension and Stability Theorem

Abstract The Jacobi Eigenvalue criterion is a recently developed, steady state, scaling independent tool for the selection of variable pairing for multiloop control systems (Mijares et al., 1986). This criterion is based on the Jacobi Iteration method for solving sets of linear equations or obtaining the inverse of a matrix. A dynamic extension of the Jacobi Eigenvalue criterion which consists in evaluating the spectral radius of the Jacobi Iteration matrix in the frequency range of interest is presented. The Jacobi Eigenvalue criterion is inherently a diagonal dominance measure, and as such, is readily applied to develop an extension of Rosenbrocks Nyquist stability theorem. The extended Jacobi Eigenvalue criterion is then compared to different interaction and weak coupling measures used for design of decentralized control structures which are based on conditions for generalized diagonal dominance and H-matrices. Two examples are used to illustrate the use of the Jacobi Eigenvalue criterion and its relationship with the other weak coupling measures.

An Analysis of Robust Stability Conditions for Multivariable Systems with Unstructured Uncertainties by Use of IMC

In this paper it is demonstrated how conditions for guaranteeing robust stability for multivariable systems with unstructured uncertainties represented as single perturbations may be derived through the use of an Internal Model Control (IMC) scheme. The presented development provides a methodology for obtaining robust stability conditions for systems with unstructured uncertainties, and gives further insight into the relations between the stability conditions for the different uncertainty representations.