Interpreting Natural Systems

In a response to Menuge, theoretical chemist Walter Thorson calls for maintaining a clear distinction between science and theology. He writes. 

But even with the attempt to keep science and theology separate, it seems likely that such theological musings will also influence aspects of an ongoing scientific approach. For those pursuing advances in both science and theology, the two fields are often found to be quite compatible, leading to many fruitful interactions. 

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Another approach to assess the partitioning of metals among the phases comprising natural particulate matter is to sequentially and selectively extract or dissolve portions of natural particulate matter. Based on the release of trace metals accompanying each step, associations between the trace metal and the extracted phase are inferred. Both of the above approaches have drawbacks, and at this time it is impossible to predict in advance how and to what extent metals and particulate matter will bond to one another in a natural system. Despite the uncertainties, empirical results can often be interpreted using the framework provided here. 

Tables I and II present the results of the Work Group discussions for the screening and site-specific level models, respectively. The assessment in these tables is based on a ranking scale between 0 and 100 0 indicates situations where no testing has been attempted and 100 identifies areas where extensive testing has been completed with sufficient post-audits to validate the predictive capability of relevant models. The scores can also be interpreted to mean the extent to which additional field testing would improve our understanding of how well the models represent natural systems. It is important to note that the scores do not indicate model accuracy per se they show the degree to which current field testing has been able to identify or estimate model accuracy.

Figure 3. The modeling relation, as adapted from J. L. Casti [90] The encoding operation provides the link between a natural system (real world) and its formal representation (mathematical world). A set of rules and computational methods allows to infer properties (theorems) of the formal system. Using a decoding relation, we can interpret those theorems in terms of the behavior of the natural system. In this sense, the inferred properties of the formal system become predictions about the natural system, allowing us to verify the consistency of the encoding. The modeling process needs to provide the appropriate encoding/decoding relations that translate back and forth between thereal world and the mathematical world.

Many of the same factors which complicate the interpretation of laboratory kinetic studies are among the most important limitations on the application of laboratory dissolution rate data to natural systems. These include uncertainty about 1) the effective surface area in natural systems (56,57) 2) the extent to which surface area and surface roughness change with reaction progress ( 18) and 3) the magnitude of solution composition effects on rates in natural systems. 

The sensitivity analysis of a system of chemical reactions consist of the problem of determining the effect of uncertainties in parameters and initial conditions on the solution of a set of ordinary differential equations [22, 23], Sensitivity analysis procedures may be classified as deterministic or stochastic in nature. The interpretation of system sensitivities in terms of first-order elementary sensitivity coefficients is called a local sensitivity analysis and typifies the deterministic approach to sensitivity analysis. Here, the first-order elementary sensitivity coefficient is defined as the gradient... 

The interpretation of Eh-pH diagrams implies assumption of complete equilibrium among the various solutes and condensed forms. Although this assumption is plausible in a compositionally simple system such as that represented in figure 8.20, it cannot safely be extended to more complex natural systems, where the various redox couples are often in apparent disequilibrium. It is therefore necessary to be cautious when dealing with the concept of the system Eh and the various redox parameters. 

An industrial ecologist s tasks are to interpret and adapt an understanding of the natural system and apply it to the design of man-made systems, in order to achieve a pattern of industrialization that is not only more efficient, but also intrinsically adjusted to the tolerances and characteristics of the natural system. In this way, it will have a built-in insurance against further environmental surprises, because their essential causes will have been designed out [29]. 

A clear understanding of processes in natural systems, which is critical to the interpretation of many such disturbance studies, can be difficult to achieve. Although radioisotopes facilitate the nonintrusive study of biogeo-chemical processes in undisturbed ecosystems (22-25), radioisotope applications may be impossible for a variety of operational and political reasons. 

Land (e.g., 198S) has stressed the chemical and structural variations associated with natural dolomites, and has gone so far as to suggest that the name "dolomite" be used in the same way that the mineral name "feldspar" is used. The fact that dolomite is relatively unreactive compared to most other sedimentary carbonate minerals has severely limited experimental studies under temperature and pressure conditions that exist during shallow burial. Consequently, most information on the chemical behavior of dolomite must be obtained from observations of complex natural systems. Such observations are all too often open to multiple interpretations. 

Observations of natural systems have been subject to substantially different interpretations owing to the inherent complexity of these systems. There has been an unfortunate tendency to interpret observations using the popular hypothesis at a particular time in attempting to explain all such diagenesis. It should be kept in mind that just as there are many roads to heaven (or hell ), there are many pathways to thermodynamic stability. 

In the second half of the 20th century it is precisely the classical equilibrium thermodynamics that became a basis for the creation of numerous computing systems for analysis of irreversible processes in complex open technical and natural systems as applied to the solution of theoretical and applied problems in various fields. The methods of MP, i.e., the mathematical discipline that emerged from the Lagrange interpretation of the equilibrium state, were a main computational tool employed for the studies. 

Carbonate Complexes. Of the many ligands which are known to complex plutonium, only those of primary environmental concern, that is, carbonate, sulfate, fluoride, chloride, nitrate, phosphate, citrate, tributyl phosphate (TBP), and ethylenediaminetet-raacetic acid (EDTA), will be discussed. Of these, none is more important in natural systems than carbonate, but data on its reactions with plutonium are meager, primarily because of competitive hydrolysis at the low acidities that must be used. No stability constants have been published on the carbonate complexes of plutonium(III) and plutonyl(V), and the data for the plutoni-um(IV) species are not credible. Results from studies on the solubility of plutonium(IV) oxalate in K2CO3 solutions of various concentrations have been interpreted to indicate the existence of complexes as high as Pu(C03) , a species that is most unlikely from both electrostatic and steric considerations. From the influence of K2CO3 concentration on the solubility of PuCOH) at an ionic strength of 10 M, the stability constant of the complex Pu(C03) was calculated (10) to be 9.1 X 10 at 20°. This value... 

One of the earliest successful applications of EXAFS to probe a me-talloenzyme was the study of the molybdenum site of nitrogenase. Studies were made on both the C. pasteurianum and A. vinelandii MoFe-proteins and on isolated FeMoco (116). These studies showed definitively that molybdenum is present as part of a polynuclear cluster containing sulfur and iron, with Mo—S and Mo—Fe distances of —2.36 and —2.72 A, respectively. This work inspired the successful development of many chemical systems containing Mo—Fe—S clusters, and XAS studies of these systems strengthened the basis for the interpretation of corresponding data for the natural system. The most accurate picture of the molybdenum site of FeMoco currently available involves a coordination of about three oxygen (or nitrogen), sulfur, and iron atoms at —2.10, —2.37, and —2.70 A, respectively (117). 

Many researchers have employed log([M" J/[H i") versus log[H4Si04 j and similar diagrams to explain and interpret natural water systems, where M denotes a cation and n its charge (cf. Helge-sonetal. 1969 Lippmann 1979 Faust andAly 1981 Bowers et al. 1984 Drever 1988 Nesbitt and Wilson 1992 Anderson and Crerar 1993 Nordstrom and Munoz 1994 Cramer and Smellie 1994). Of necessity, simplified clay compositions have been assumed in order to show them on such diagrams. Assumptions and limitations comparable to those that were inherent in the construction and use of Figs. 9.8 and 9.9 apply to all such diagrams. 

What follows is a discussion of some of the carbon and sulphur mechanisms and ideas contained within the diagenetic literature. It is intended to give the reader both a general background against which to interpret observations and also to emphasise the importance of microstructure in understanding natural systems. 

The control over the uptake experiment in a chromatographic column and interpretation of results is even more difficult than with static experiments. For example the pH in dynamic experiments varies not only as a function of time but also spatially (as a function of the position in a column). On the other hand, chromatography is an efficient method to entirely remove certain solutes from solution, it is also used to simulate migration of pollutants in natural systems. 

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