Model, mathematical physicochemical

J. Miodzianowski, Mathematical modeling and physicochemical studies on acid-base equilibria in binary-sol-vent systems (in Polish), Wiadomosci Chemiczne, 54 (2010) 124-154]. 

Mathematical Modeling A function v = g u) (Fig. 4.13, right) is found in the literature that roughly describes the data y = f x) but does not have any physicochemical connection to the problem at hand (Fig. 4.13, left) since the parameter spaces x and y do not coincide with those of u and v, transformations must be introduced ... 

There are two basic classes of mathematical models (see Fig. 5.3-18) (1) purely empirical models, and (2) models based on physicochemical principles. 

Apart from the most widely utilized Snyder and Soczewinski semiempirical model of linear TEC, several other physicochemically grounded approaches to the same question exist as well [12]. Also, a choice of the empirical rules in mathematical... 

Soil compartment chemical fate modeling has been traditionally performed for three distinct subcompartments the land surface (or watershed) the unsaturated soil (or soil) zone and the saturated (or groundwater) zone of a region. In general, the mathematical simulation is structured around two major cycles the hydrologic cycle and the pollutant cycle, each cycle being associated with a number of physicochemical processes. Watershed models account for a third cycle sedimentation. 

The influence of various structural and physicochemical parameters of the stationary and mobile phases on the tailing of a cationic dye in reversed-phase chromatography has been studied in detail. Measurements were performed in a C8 reversed-phase column (80 X 4.6 mm). The isocratic mobile phase was ACN-0.01 M aqueous HC1 (90 10, v/v). Analyses were carried out at 20°C and the flow rate was 1-5 ml/min. The concentration of the cationic dye, l,l -didodecyl-3,3,3, 3 -tetramethylindocarbocyanine perchlorate (Dil) in the model solutions varied between 0.9-309 pM. The dependence of the chromatographic profile of the dye on the injected concentration is illustrated in Fig. 3.112. Calculations and mathematical modelling indicated that the peak tailing of the dye can be... 

Improvements in deterministic (photochemical/diffusion) methods are based largely on accounting for more physicochemical effects in the structure of the model. Specific research subjects for improved models include photochemical aerosol formation and the effects of turbulence on chemical reaction rates. The challenge to the researcher is to incorporate the study of these subjects without needlessly complicating already complex models. How accurate a mathematical simulation is required What, roughly, will be the effect of omitting some particular chemical or physical component What is the sensitivity of model outputs to inaccuracies in the inputs ... 

There are several properties of a chemical that are related to exposure potential or overall reactivity for which structure-based predictive models are available. The relevant properties discussed here are bioaccumulation, oral, dermal, and inhalation bioavailability and reactivity. These prediction methods are based on a combination of in vitro assays and quantitative structure-activity relationships (QSARs) [3]. QSARs are simple, usually linear, mathematical models that use chemical structure descriptors to predict first-order physicochemical properties, such as water solubility. Other, similar models can then be constructed that use the first-order physicochemical properties to predict more complex properties, including those of interest here. Chemical descriptors are properties that can be calculated directly from a chemical structure graph and can include abstract quantities, such as connectivity indices, or more intuitive properties, such as dipole moment or total surface area. QSAR models are parameterized using training data from sets of chemicals for which both structure and chemical properties are known, and are validated against other (independent) sets of chemicals. 

The approach to the quantitative analysis and mathematical modelling of the dipping process is based on the solution of the well-known problem of physicochemical hydrodynamics of the thickness of liquid layers retained on the surface of a body removed from the liquid (see, e.g., u,12>). Upon the assumption that the body (support, prototype, mould) is taken out of the plastisol liquid vertically, the general relationships may be written in the following form 2> 7 11"14> ... 

Thus molecular modeling can be defined as the generation, manipulation, calculation, and prediction of realistic molecular structures and associated physicochemical as well as biochemical properties by the use of a computer. It is primarily a mean of communication between scientist and computer, the imperative interface between human-comprehensive symbolism, and the mathematical description of the molecule. The endeavor is made to perceive and recognize a molecular structure from its symbolic representations with a computer. Thus functions of the molecular modeling include ... 

Transport phenomena modeling. This type of modeling is applicable when the process is well understood and quantification is possible using physical laws such as the heat, momentum, or diffusion transport equations or others. These cases can be analyzed with principles of transport phenomena and the laws governing the physicochemical changes of matter. Transport phenomena models apply to many cases of heat conduction or mass diffusion or to the flow of fluids under laminar flow conditions. Equivalent principles can be used for other problems, such as the mathematical theory of elasticity for the analysis of mechanical, thermal, or pressure stress and strain in beams, plates, or solids. 

Alternative methods include (1) computer-based methods (mathematical models and expert systems) (2) physicochemical methods, in which physical or chemical effects are assessed in systems lacking cells and, most typically, (3) in vitro methods, in which biological effects are observed in cell cultures, tissues, or organs. 

In addition to using PMs, predictions of toxic hazard can also be made by using structure-activity relationships (SARs). A quantitative structure-activity relationship (QSAR) can be defined as any mathematical model for predicting biological activity from the structure or physicochemical properties of a chemical. In this chapter, the premodifer quantitative is used in accordance with the recommendation of Livingstone (1995) to indicate that a quantitative measure of chemical structure is used. In contrast, a SAR is simply a (qualitative) association between a specific molecular (sub)structure and biological activity. 

Structure-activity relationships (SARs) and quantitative structure-activity relationships (QSARs), referred to collectively as QSARs, can be used for the prediction of physicochemical properties, environmental fate parameters (e.g., accumulation and biodegradation), human health effects, and ecotoxicological effects. A SAR is a (qualitative) association between a chemical substructure and the potential of a chemical containing the substructure to exhibit a certain physical or biological effect. A QS AR is a mathematical model that relates a quantitative measure of chemical structure (e.g., a physicochemical property) to a physical property or to a biological effect (e.g., a toxicological endpoint). 

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