Integration of different models in the design of chemical processes: Application to the design of a power plant

With advances in the synthesis and design of chemical processes there is an increasing need for more complex mathematical models with which to screen the alternatives that constitute accurate and reliable process models. Despite the wide availability of sophisticated tools for simulation, optimization and synthesis of chemical processes, the user is frequently interested in using the ‘best available model’. However, in practice, these models are usually little more than a black box with a rigid input–output structure. In this paper we propose to tackle all these models using generalized disjunctive programming to capture the numerical characteristics of each model (in equation form, modular, noisy, etc.) and to deal with each of them according to their individual characteristics. The result is a hybrid modular–equation based approach that allows synthesizing complex processes using different models in a robust and reliable way. The capabilities of the proposed approach are discussed with a case study: the design of a utility system power plant that has been decomposed into its constitutive elements, each treated differently numerically. And finally, numerical results and conclusions are presented.

Saint Mathew Law and Bonini Paradox in Textual Theory of Complex Models

The mathematical models of the complex reality are texts belonging to a certain literature that is written in a semi-formal language, denominated L(MT) by the authors whose laws linguistic mathematics have been previously defined. This text possesses linguistic entropy that is the reflection of the physical entropy of the processes of real world that said text describes. Through the temperature of information defined by Mandelbrot, the authors begin a text-reality thermodynamic theory that drives to the existence of information attractors, or highly structured point, settling down a heterogeneity of the space text, the same one that of ontologic space, completing the well-known law of Saint Mathew, of the General Theory of Systems and formulated by Margalef saying: “To the one that has more he will be given, and to the one that doesn't have he will even be removed it little that it possesses.

Comparisons of models predicting ambient lake phosphorus concentrations /

Mode of access: Internet.

Comparison of numerical and physical hydraulic models, Masonboro Inlet, North Carolina /

"June 1977."

Mathematical instruction in France.

Appendices C and D "for later publication."

Models to illustrate the foundations of mathematics /

Mode of access: Internet.

Modelling of froth transportation in industrial flotation cells: Part I. Development of froth transportation models for attached particles

Modelling of froth transportation, as part of modelling of froth recovery, provides a scale-up procedure for flotation cell design. It can also assist in improving control of flotation operation. Mathematical models of froth velocity on the surface and froth residence time distribution in a cylindrical tank flotation cell are proposed, based on mass balance principle of the air entering the froth. The models take into account factors such as cell size, concentrate launder configuration, use of a froth crowder, cell operating conditions including froth height and air rate, and bubble bursting on the surface. (C) 2004 Elsevier Ltd. All rights reserved.

Using the canonical modelling approach to simplify the simulation of function in functional-structural plant models

Functional-structural plant models that include detailed mechanistic representation of underlying physiological processes can be expensive to construct and the resulting models can also be extremely complicated. On the other hand, purely empirical models are not able to simulate plant adaptability and response to different conditions. In this paper, we present an intermediate approach to modelling plant function that can simulate plant response without requiring detailed knowledge of underlying physiology. Plant function is modelled using a 'canonical' modelling approach, which uses compartment models with flux functions of a standard mathematical form, while plant structure is modelled using L-systems. Two modelling examples are used to demonstrate that canonical modelling can be used in conjunction with L-systems to create functional-structural plant models where function is represented either in an accurate and descriptive way, or in a more mechanistic and explanatory way. We conclude that canonical modelling provides a useful, flexible and relatively simple approach to modelling plant function at an intermediate level of abstraction.

Inter- and intralaboratory variation of in vitro diffusion cell measurements: An international multicenter study using quasi-standardized methods and materials

In vitro measurements of skin absorption are an increasingly important aspect of regulatory studies, product support claims, and formulation screening. However, such measurements are significantly affected by skin variability. The purpose of this study was to determine inter- and intralaboratory variation in diffusion cell measurements caused by factors other than skin. This was attained through the use of an artificial (silicone rubber) rate-limiting membrane and the provision of materials including a standard penetrant, methyl paraben (MP), and a minimally prescriptive protocol to each of the 18 participating laboratories. Standardized calculations of MP flux were determined from the data submitted by each laboratory by applying a predefined mathematical model. This was deemed necessary to eliminate any interlaboratory variation caused by different methods of flux calculations. Average fluxes of MP calculated and reported by each laboratory (60 +/- 27 mug cm(-2) h(-1), n = 25, range 27-101) were in agreement with the standardized calculations of MP flux (60 +/- 21 mug cm(-2) h(-1), range 19-120). The coefficient of variation between laboratories was approximately 35% and was manifest as a fourfold difference between the lowest and highest average flux values and a sixfold difference between the lowest and highest individual flux values. Intra-laboratory variation was lower, averaging 10% for five individuals using the same equipment within a single laboratory. Further studies should be performed to clarify the exact components responsible for nonskin-related variability in diffusion cell measurements. It is clear that further developments of in vitro methodologies for measuring skin absorption are required. (C) 2005 Wiley-Liss, Inc.

A mathematical model of integrin-mediated haptotactic cell migration

Haptotactic cell migration, a directed response to gradients of cell—extracellular matrix adhesion, is an important process in a number of biological phenomena such as wound healing and tumour cell invasion. Previously, mathematical models of haptotaxis have been developed on the premise that cells migrate in response to gradients in the density of the extracellular matrix. In this paper, we develop a novel mathematical model of haptotaxis which includes the adhesion receptors known as integrins and a description of their functional activation, local recruitment and protrusion as part of lamellipodia. Through the inclusion of integrins, the modelled cell matter is able to respond to a true gradient of cell–matrix adhesion, represented by functionally active integrins. We also show that previous matrix-mediated models are in fact a subset of the novel integrin-mediated models, characterised by specific choices of diffusion and haptotaxis coefficients in their model equations. Numerical solutions suggest the existence of travelling waves of cell migration that are confirmed via a phase plane analysis of a simplified model.