bluuebunny/crossref_metadata_2025 huggingface dataset:
Complexity
Authors: Greenlaw Raymond , Hoover H. James , Ruzzo Walter L.
Published: November 2020

The goal of this chapter is to provide the formal basis for many key concepts that are used throughout the book. These include the notions of problem, definitions of important complexity classes, reducibility, and completeness, among others. Thus far, we have used the term "problem" somewhat vaguely. In order to compare the difficulty of various problems we need to make this concept precise. Problems typically come in two flavors: search problems and decision problems. Consider the following search problem, to find the value of the maximum flow in a network. Example 3.1.1 Maximum Flow Value (MaxFlow-V) Given: A directed graph G = (V,E) with each edge e labeled by an integer capacity c(e) ≥ 0, and two distinguished vertices, s and t. Problem: Compute the value of the maximum flow from source s to sink t in G. The problem requires us to compute a number — the value of the maximum flow. Note, in this case we are actually computing a function. Now consider a variant of this problem. Example 3.1.2 Maximum Flow Bit (MaxFlow-B) Given: A directed graph G = (V, E) with each edge e labeled by an integer capacity c(e)≥ 0, and two distinguished vertices, s and t, and an integer i. Problem: Is the ith bit of the value of the maximum flow from source s to sink t in G a 1? This is a decision problem version of the flow problem. Rather than asking for the computation of some value, the problem is asking for a "yes" or "no" answer to a specific question. Yet the decision problem MaxFlow-B is equivalent to the search problem MaxFlow-V in the sense that if one can be solved efficiently in parallel, so can the other. Why is this? First consider how solving an instance of MaxFlow-B can be reduced to solving an instance of MaxFlow-V. Suppose that you are asked a question for MaxFlow-B, that is, "Is bit i of the maximum flow a 1?" It is easy to answer this question by solving MaxFlow-V and then looking at bit i of the flow.
The Circuit Value Problem
Authors: Greenlaw Raymond , Hoover H. James , Ruzzo Walter L.
Published: November 2020

In this chapter we return to the Circuit Value Problem, introduced in Section 4.2. First, we will give the formal proof of Theorem 4.2.2 that CVP is P-complete, which we only sketched previously. Then we will show that a number of useful variants and restricted versions of CVP are also P-complete. Recall the definition of the Circuit Value Problem (Definition 4.2.1) in which given an encoding ᾱ of a Boolean circuit α, a designated output y , and values for the inputs x1,..., xn, we ask if output y of α is TRUE. To show CVP is P-complete under ≤mNC1 reducibility requires showing CVP is in P, and that each language L in P is ≤mNC1 reducible to CVP. It is easy to see that given the encoding ᾱ of a circuit and the values of its inputs, one can compute the value of each gate in a number of steps that is polynomial in the size of α. On a random access machine this can be done in linear time by considering the gates in topological order (which also can be computed in linear time; see Gormen, Leiserson, and Rivest [70], for example). On a deterministic Turing machine the process is a bit more clumsy but can still be done in polynomial time. Pippenger shows that even time O(nlogn) suffices, where n is the length of the encoding of α [284]. Thus, we have the following lemma. Lemma 6.1.1 The Circuit Value Problem is in P. The more difficult step in proving that CVP is P-complete under ≤mNC1 reducibility is showing there is a ≤mNC1 reduction from each language in P to CVP. Ladner proved this by simulating Turing machines with circuits. The idea is as follows. First, recall that for each language L in P, there is a 1-tape Turing machine M that on input x = x1,..., xn halts in time t(n) = nO(1) with output equal to 1 if and only if x is in L. Note that, for each n, the machine M uses at most t(n) space on its tape.
Introduction
Authors: Nēmec Václav
Published: November 2020

Friends and associates of Daniel F. Merriam have prepared this volume in Dan's honor to commemorate his 65th birthday and mark the 25th anniversary of the International Association for Mathematical Geology. This compendium is in the tradition of the Festschriften issued by European universities and scholarly organizations to honor an individual who has bequeathed an exceptional legacy to his students, associates, and his discipline. Certainly Dan has made such an impact on geology, and particularly mathematical geology. It is a great privilege for rne to write the introduction to this Festschrift. The editors are to be congratulated for their idea to collect and to publish so many representative scientific articles written by famous authors of several generations. Dan Merriam is the most famous mathematical geologist, in the world. This statement will probably provoke some criticism against an over-glorification of Dan. Some readers will have their own candidates (including themselves) for such a top position. I would like to bring a testimony that the statement is correct and far from an ad hoc judgment only for this solemn occasion. It may be of interest to describe how I became acquainted with Dan. In my opinion this will show how thin and delicate was the original tissue of invisible ties which helped to build up the first contacts among Western and Eastern colleagues in the completely new discipline of mathematical geology. The role of Dan Merriam in opening and increasing these contacts has been very active indeed. In the Fall 1964 I was on a family visit in the United States. This was— after the coup of Prague in 1948—my first travel to the free Western world. With some experience in computerized evaluation of ore deposits, I was curious to see the application of computers in geology and to meet colleagues who had experience with introducing statistical methods into regular estimation of ore reserves. I had very useful contacts in Colorado and in Arizona. In Tucson I visited the real birthplace of the APCOM symposia.
Gold Prospecting With Factorial Cokriging In The Limousin, France
Authors: Wackernagel Hans , Sanguinetti Henri
Published: November 2020

In geochemical prospecting for gold a major difficulty is that many values are below the chemical detection limit. Tracers for gold thus play an important role in the evaluation of multivariate geochemical data. In this case study we apply geostatistical methods presented in Wackernagel (1988) to multielement exploration data from a prospect near Limoges, France. The analysis relies upon a metallogenetic model by Bonnemaison and Marcoux (1987, 1990) describing auriferous mineralization in shear zones of the Limousin. The aim of geochemical exploration is to find deposits of raw materials. What is a deposit? It is a geological anomaly which has a significant average content of a given raw material and enough spatial extension to have economic value. The geological body denned by an anomaly is generally buried at a specific depth and may be detectable at the surface through indices. These indices, which we shall call superficial anomalies, are disposed in three manners: at isolated locations, along faults, and as dispersion halos. These two definitions of the word "anomaly" correspond to a vision of the geological phenomenon in its full continuity. Yet in exploration geochemistry only a discrete perception of the phenomenon is possible through samples taken along a regularly meshed grid. A superficial anomaly thus can be apprehended by one or several samples or it can escape the grip of the geochemist when it is located between the nodes of the mesh. A geochemical anomaly, in the strict sense, only exists at the nodes of the sampling grid and we shall distinguish between: a pointwise anomaly defined on a single sample, and a groupwise anomaly defined on several neighboring samples. This distinction is important both upstream, for the geological interpretation of geochemical measurements, and downstream, at the level of geostatistical manipulation of the data. It will condition an exploration strategy on the basis of the data representations used in this case study. A pointwise anomaly, i.e., a high, isolated value of the material being sought, will correspond either to a geological phenomenon of limited extent or to a well hidden deposit.
Can The Ginsburg Model Generate Cycles?
Authors: Schwarzacher W.
Published: November 2020

The Ginsburg model of carbonate accumulation is an often-quoted mechanism for generating so-called autocycles. It is shown that the model does not represent a self-oscillating system; oscillations can only be generated if at least two critical parameters controlling sedimentation are introduced. The Ginsburg model is a conceptual model which tries to explain the behavior of some carbonate shelves that undergo continuous tectonic subsidence and that carry on their surface a very active carbonate factory. Unfortunately the original model has only been published in abstract form—the relevant part of which is quoted here in full (Ginsburg, 1971, p. 340): . . . "The Florida Bay lagoon and the tidal flats of the Bahamas and Persian Gulf are traps for line sediment produced on the large adjacent open platforms or shelves. The extensive source areas produce carbonate mud by precipitation and by the disintegration of organic skeletons. The carbonate mud moves shoreward by wind-driven, tidal or estuarinelike circulation, and deposition is accelerated and stabilized by marine plants and animals. Because the open marine source areas are many times larger than the nearshore traps, seaward progradation of the wedge of sediments is inevitable. This seaward progradation gives a regressive cycle from open marine shelf or platform to supratidal flat. As the shoreline progrades seaward the size of the open marine source area decreases; eventually reduced production of mud no longer exceeds slow continuous subsidence and a new transgression begins. When the source area expands so that production again exceeds subsidence a new regressive cycle starts.". . . The author is very grateful to Dr. Ginsburg for supplying some additional information that is not obvious from the abstract. The subsidence must be differential and a broad, open shelf that gradually tilts seaward is visualized. All of the sediment produced on the shelf is transported shoreward, where it accumulates as a wedge-shaped deposit that builds into a tidal bank. A further analysis of the model is interesting for two reasons. First, the model has been and still is seriously suggested as a possible mechanism to explain cyclicity on carbonate platforms (see Goldhammer et al, 1987, for references).
Fractals In Geosciences— Challenges And Concerns
Authors: Herzfeld UteChristina
Published: November 2020

"Fractals" and "chaos" have become increasingly popular in geology; however, the use of "fractal" methods is mostly limited to simple cases of selfsimilarity, often taken as the prototype of a scaling property if not mistaken as equivalent to a fractal as such. Here; a few principles of fractal and chaos theory are clarified, an overview of geoscience applications is given, and possible pitfalls are discussed. An example from seafloor topography relates fractal dimension, self-similarity, and multifractal cascade scaling to traditional geostatistical and statistical concepts. While the seafloor has neither self-similar nor cascade scaling behavior, methods developed in the course of "fractal analysis" provide ways to quantitatively describe variability in spatial structures across scales arid yield geologically meaningful results. Upon hearing the slogan "the appleman reigns between order and chaos" in the early 1980's and seeing colorful computer-generated pictures, one was simply fascinated by the strangely beautiful figure of the "appleman" that, when viewed through a magnifying glass, has lots of parts that, are smaller, and smaller, and smaller applemen. The "appleman" is the recurrent feature of the Mandelbrot set, a self-similar fractal, and in a certain sense, the universal fractal (e.g., see Peitgen and Saupe, 1988, p. 195 ff.). Soon the realm of the appleman expanded, made possible by increasing availability of fast, cheap computer power and increasingly sophisticated computer graphics. In its first phase of popularity, when the Bremen working group traveled with their computer graphics display seeking public recognition through exhibits in the foyers of savings banks, the fractal was generally considered to be a contribution to modern art (Peitgen and Richter, The Beauty of Fractals, 1986). While the very title of Mandelbrot's famous book, The Fractal Geometry of Nature (1983), proclaims the discovery of the proper geometry to describe nature, long hidden by principals of Euclidean geometry, the "fractal" did not appeal to Earth scientists for well over two decades after its rediscovery by Mandelbrot (1964, 1965, 1967, 1974, 1975).
Model documentation
Authors: Schenck Douglas , Wilson Peter
Published: November 2020

As is noted throughout this book, an information model does not merely consist of the formal model but also includes supporting editorial and technical material. Reading an uncommented EXPRESS model is like trying to decipher undocumented program code — possible, but error prone. Further, there are many things that cannot be expressed in EXPRESS — diagrams, for example, or references to the general literature, and so on. Two forms of documentation appear to be prevelant: the embedded and the partitioned style. We discuss both of these, although we prefer the former of the two. The model developer, though, should decide on a style that suits the purposes at hand. We also indicate how versions of a document could be produced in either style. This is based on the fact that an information model can be stored electronically (i.e., as computer files), and printed versions produced via a wordprocessor or other kind of desktop publishing system. The document style for an information model is typically much more detailed than is found for computer programs. On the other hand, it is usually less complex in its ordering than in the program documentation style known as literate programming. In addition to documenting the overall scope and purpose of the model, the content and relationship of the schemas in the model should be described in broad terms. A diagrammatic sketch of the major elements and relationships in the model is also useful. This overview material should also contain the definitions of terms that are used in the model. A section could also be included on the usage of the model, as seen by the authors. Each aspect of a model (i.e., schema, entity, attribute, function, rule, etc.) should have a related description. Each schema requires a description of its scope and its relationship, if any, to other schemas in the model. This sets the context for the entities and other constructs that form the schema content. The semantics of each type should be described. In particular, the meanings of enuneration items require a description — the meaning of a name may be obvious to the author, but not necessarily to the reader.
Basic elements
Authors: Schenck Douglas , Wilson Peter
Published: November 2020

We start with the basic stuff used to build EXPRESS: the characters you use to build ‘words’ and the different kinds of words that may appear in the source. Computer languages call these words tokens. You compose characters according to syntax rules to form different kinds of tokens. In turn, tokens are composed into statements and statements are composed into blocks (we will get to statements and blocks directly). The syntax alone does not define the language however — we also need to be concerned with semantics. Semantics deals with the meaning of well formed syntax. As an example, EXPRESS has tokens for identifiers and reserved words. Although they both look like ‘words’ they are different; an identifier cannot be the same as a keyword. EXPRESS expects to see identifiers and reserved words in specific places within statements. It is an error to put an identifier where a reserved word is expected and vice versa. EXPRESS is correctly written only when both the syntactic and semantical rules are observed. EXPRESS source is composed as a stream of characters. The source stream is decoded into tokens, statements and blocks according to the syntax rules. The source is typically broken into a number of physical lines, which is any number (including zero) of characters ended by a ‘newline.’ The source will be more attractive and easier to read when statements are broken into lines and whitespace is used to set off different constructs. The following declarations are the same to an EXPRESS parser, but give different impressions to human readers. The EXPRESS character set is easy to explain —just look at your computer keyboard. Most of the characters you see there are used to write EXPRESS. However, there is a more complicated explanation which follows: the EXPRESS character set is denned as cells 00-7F of plane 00 of group 00 of ISO 10646. Of those characters, cells 20-7E as shown in Table 9.1 are actually used to write EXPRESS. Any other character (cells 00-1F, 7F) is called a ‘rogue’ character, and if used is treated as a space unless it appears within a string literal or a remark.
Symbols
Authors: Schenck Douglas , Wilson Peter
Published: November 2020

EXPRESS-G has three basic kinds of symbol; defintion, relation, and composition. Definition and relation symbols are used to define the contents and structure of an information model. Composition symbols enable the diagrams to be spread across many physical pages. A definition symbol is a rectangle enclosing the name of the thing being defined. The type of the definition is denoted by the style of the box. Symbols are provided for EXPRESS simple types, defined types, entity types and schemas. The EXPRESS language offers a number of predefined simple types, namely Binary, Boolean, Integer, Logical, Number, Real and String. These are the terminal types of the language. The symbol for them is a solid rectangle with a double vertical line at its right end. The name of the type is enclosed within the box, as shown in Figure 18.1. The EXPRESS Generic pseudotype is not represented in EXPRESS-G as it is only used as a formal parameter to a function or procedure, and EXPRESS-G does not have these. The symbols for the select, enumeration and defined data type are dashed boxes as shown in Figure 18.2. • The symbol for a defined data type is a dashed box enclosing the name of the type. • The symbol for a select type is a dashed box with a double vertical line at the left end, enclosing the name of the select. • The symbol for an enumeration type is a dashed box with a double vertical line at the right end, enclosing the name of the enumeration. Although an enumeration is not a terminal of the EXPRESS language (because its definition includes the enumerated things), it is a terminal of the EXPRESS-G language. Figure 18.3 shows the symbol for an entity, which is a solid rectangle enclosing the name of the entity. The symbol for a schema is shown in Figure 18.3. It is a solid rectangle divided in half by a horizontal line. The name of the schema is written in the upper half of the rectangle. The lower half of the symbol is empty. EXPRESS-G does not support any notation for either function or procedure definitions.
Sample Models
Authors: Schenck Douglas , Wilson Peter
Published: November 2020

This Chapter contains a sampler of EXPRESS models, each of which has been used as the basis for the earlier EXPRESS-G model illustrations. No claim is made that the models are either realistic or good — the models have been constructed to show certain aspects of EXPRESS-G rather than to illustrate information modeling in general. Here is a summary of what the model in Example 20.1 says: a person must be either a male or a female. Every person has some defining characteristics, such as first and last names, date of birth, type of hair, and may also have zero or more children (which are, of course, also people). A male may be married to a female, and vice-versa. The partners in a marriage must be unique — this model is only appropriate for monogamous societies. There is one particular piece of information about females that does not apply to males; a female may have a maiden name. The Age of a person is a derived attribute that is calculated through the function years, which determines the number of years between the date input as a parameter and the current date. A Person has an inverse attribute which relates people who are children to their parents.
Knowledge, Values, and Technological Decisions: A Decision Theoretic Approach
Authors: Giere Ronald N.
Published: November 2020

Before World War II, most decisions involving the introduction of new technologies were made primarily by individuals or corporations, with only minimal interference from government, usually in the form of regulations. Since the war, however, the increased complexity of modern technologies and their impact on society as a whole have tended to force the focus of decision making toward the federal government, although this power is still usually exercised in the form of regulation rather than outright control. Given the huge social consequences of many such decisions, it seems proper that the decision-making process be moved further into the public arena. Yet one may wonder whether the society has the resources and mechanisms for dealing with these issues. Thus, the nature of such controversies, and the possible means for their resolution, has itself become an object of intense interest. One may approach this subject from at least as many directions as there are academic specialties. Many approaches are primarily empirical in that they attempt to determine the social and political mechanisms that are currently operative in the generation and resolution of controversies over new technologies (Nelkin 1979). Such studies usually do not attempt to determine whether the social mechanisms actually operating are effective mechanisms in the sense that they tend to produce decisions that in fact result in the originally desired out comes. The approach of this chapter is much more theoretical. It begins with a standard model of decision making and then analyzes the nature of technological decisions in terms of the postulated model. The advantage of such an approach is that it provides a clear and simple framework for both analyzing a controversy and judging its outcome. The disadvantage is that it tells us little about the actual social and political processes in the decision. Eventually we would like an account that incorporates both theoretical and empirical viewpoints. Regarding the proposed model, there are several ingredients in any decision. This chapter concentrates on one of these ingredients: scientific knowledge, particularly statistical knowledge of the type associated with studies of low-level environmental hazards. There is no presumption, however, that statistical knowledge, or scientific knowledge generally, is the most important ingredient in any decision.
Reductionist Approaches to Risk
Authors: Shrader-Frechette Kristin
Published: November 2020

Many Americans, sensitized by the media to the dangers of cigarette smoking, have been appalled to discover on their visits to the Far East that most adult Chinese smoke. The Chinese, on the other hand, consume little alcohol and have expressed bewilderment about the hazardous and excessive drinking in the West. Differences in risk acceptance, however, are not merely cross cultural. Within a given country, some persons are scuba divers, hang gliders, or motorcyclists, and some are not; there are obvious discrepancies in attitudes toward individual risk. At the level of societal risk—for example, from nuclear power, toxic dumps, and liquefied natural gas facilities—different persons also exhibit analogous disparities in their hazard evaluations. In this chapter I shall argue that two of the major accounts of societal risk acceptance are highly questionable. Both err because of fundamental flaws in their conception of knowledge. This means that to understand the contemporary controversy over societal risk, we need to accomplish a philosophical task, that is, to uncover the epistemologies assumed by various participants in the conflict. Proponents of both positions err, in part, because they are reductionistic and because they view as irrational the judgments of citizens who are risk averse. After showing why both views are built on highly doubtful philosophical presuppositions, I shall argue in favor of a middle position that I call scientific proceduralism. An outgrowth of Karl Popper's views, this account is based on the notion that objectivity in hazard assessment requires that risk judgments be able to withstand criticism by scientists and lay people affected by the risks. Hence the position is sympathetic to many populist attitudes toward involuntary and public hazards. Although scientific proceduralism is not the only reasonable view that one might take regarding risk, I argue that it is at least a rational one. And if so, then rational behavior should not be defined purely in terms of the assessments of either the cultural relativists or the naive positivists. Most importantly, risk experts should not "write off" the common person. Because hazard assessment is dominated by these two questionable positions, it is reasonable to ask whether criticizing them threatens the value of quantified risk analysis (QRA). Indeed, many of those allegedly speaking "for the people," as I claim to be doing, are opposed to scientific and analytic methods of assessing environmental dangers.
Introduction
Authors: Schmickler Wolfgang
Published: November 2020

Electrochemistry is an old science: There is good archaeological evidence that an electrolytic cell was used by the Parthans (250 B.C. to 250 A.D.), probably for electroplating, though a proper scientific investigation of electrochemical phenomena did not start before the experiments of Volta and Galvani. The meaning and scope of electrochemical science has varied throughout the ages: For a long time it was little more than a special branch of thermodynamics; later attention turned to electrochemical kinetics. During recent decades, with the application of various surface-sensitive techniques to electrochemical systems, it has become a science of interfaces, and this, we think, is where its future lies. So in this book we use as a working definition: . . . Electrochemistry is the study of structures and processes at the interface between an electronic conductor (the electrode) and an ionic conductor (the electrolyte) or at the interface between two electrolytes. . . This definition requires some explanation. (1) By interface we denote those regions of the two adjoining phases whose properties differ significantly from those of the bulk. These interfacial regions can be quite extended, particularly in those cases where a metal or semiconducting electrode is covered by a thin film. Sometimes the term interphase is used to indicate the spatial extention. (2) It would have been more natural to restrict the definition to the interface between an electronic and an ionic conductor only, and, indeed, this is generally what we mean by the term electrochemical interface. However, the study of the interface between two immiscible electrolyte solutions is so similar that it is natural to include it under the scope of electrochemistry. Metals and semiconductors are common examples of electronic conductors, and under certain circumstances even insulators can be made electronically conducting, for example by photoexcitation. Electrolyte solutions, molten salts, and solid electrolytes are ionic conductors. Some materials have appreciable electronic and ionic conductivities, and depending on the circumstances one or the other or both may be important.
The metal-solution interface
Authors: Schmickler Wolfgang
Published: November 2020

The interface between a metal and an electrolyte solution is the most important electrochemical system, and we begin by looking at the simplest case, in which no electrochemical reactions take place. The system we have in mind consists of a metal electrode in contact with a solution containing inert, nonreacting cations and anions. A typical example would be the interface between a silver electrode and an aqueous solution of KF. We further suppose that the electrode potential is kept in a range in which no or only negligible decomposition of the solvent takes place - in the case of an aqueous solution, this means that the electrode potential must be below the oxygen evolution and above the hydrogen evolution region. Such an interface is said to be ideally polarizable, a terminology based on thermodynamic thinking. The potential range over which the system is ideally polarizable is known as the potential window, since in this range electrochemical processes can be studied without interference by solvent decomposition. As we pointed out in the introduction, a double layer of equal and opposite charges exists at the interface. In the solution this excess charge is concentrated in a space-charge region, whose extension is the greater the lower the ionic concentration. The presence of this spacecharge region entails an excess (positive or negative) of ions in the interfacial region. In this chapter we consider the case in which this excess is solely due to electrostatic interactions; in other words, we assume that there is no specific adsorption. This case is often difficult to realize in practice, but is of principal importance for understanding more complicated situations. A simple but surprisingly good model for the metal-solution interface was developed by Gouy and Chapman as early as 1910. The basic ideas are the following: The solution is modeled as point ions embedded in a dielectric continuum representing the solvent; the metal electrode is considered as a perfect conductor. The distribution of the ions near the interface is calculated from electrostatics and statistical mechanics.
The semiconductor-electrolyte interface
Authors: Schmickler Wolfgang
Published: November 2020

Many naturally occurring substances, in particular the oxide films that form spontaneously on some metals, are semiconductors. Also, electrochemical reactions are used in the production of semiconductor chips, and recently semiconductors have been used in the construction of electrochemical photocells. So there are good technological reasons to study the interface between a semiconductor and an electrolyte. Our main interest, however, lies in more fundamental questions: How does the electronic structure of the electrode influence the properties of the electrochemical interface, and how does it affect electrochemical reactions? What new processes can occur at semiconductors that are not known from metals? We begin by recapitulating a few facts about semiconductors. Electronic states in a perfect semiconductor are delocalized just as in metals, and there are bands of allowed electronic energies. According to a well-known theorem, bands that are either completely filled or completely empty do not contribute to the conductivity. In semiconductors the current-carrying bands do not overlap as they do in metals; they are separated by the band gap, and the Fermi level lies right in this gap. The band below the Fermi level, which at T = 0 is completely filled, is known as the valence band; the band above, which is empty at T = 0, is the conduction band. In a pure or intrinsic semiconductor, the Fermi level is close to the center of the band gap. At room temperature a few electrons are excited from the valence into the conduction band, leaving behind electron vacancies or holes (denoted by h+). The electric current is carried by electrons in the conduction band and holes in the valence band. The concentrations nc of the conduction electrons and pv of the holes are determined from Fermi statistics.
Proton- and ion-transfer reactions
Authors: Schmickler Wolfgang
Published: November 2020

We consider the transfer of an ion or proton from the solution to the surface of a metal electrode; often this is accompanied by a simultaneous discharge of the transferring particle, such as by a fast electron transfer. The particle on the surface may be an adsorbate as in the reaction: . . .Cl - (sol) ⇋ Clad + e- (metal) . . . (9.1) In this case the discharge can be partial; that is, the adsorbate can carry a partial charge, as discussed in Chapter 4. Alternatively the particle can be incorporated into the electrode as in the deposition of a metal ion on an electrode of the same composition, or in the formation of an alloy. An example of the latter is the formation of an amalgam such as: . . . Zn2++2e- ⇋ Zn(Hg) . . . (9.2) The reverse process is the transfer of a particle from the electrode surface to the solution; often the particle on the surface is uncharged or partially charged, and is ionized during the transfer. Ion- and proton-transfer reactions are almost always preceded or followed by other reaction steps. We first consider only the chargetransfer step itself. Ions and protons are much heavier than electrons. While electrons can easily tunnel through layers of solution 5 to 10 Å thick, protons can tunnel only over short distances, up to about 0.5 Å, and ions do not tunnel at all at room temperature. The transfer of an ion from the solution to a metal surface can be viewed as the breaking up of the solvation cage and subsequent deposition, the reverse process as the jumping of an ion from the surface into a preformed favorable solvent configuration. In simple cases the transfer of an ion obeys a slightly modified form of the Butler-Volmer equation. Consider the transfer of an ion from the solution to the electrode. As the ion approaches the electrode surface, it loses a part of its solvation sphere, and it displaces solvent molecules from the surface; consequently its Gibbs energy increases at first.
Thermodynamics of ideal polarizable interfaces
Authors: Schmickler Wolfgang
Published: November 2020

For liquid electrodes thermodynamics offers a precise way to determine the surface charge and the surface excesses of a species. This is one of the reasons why much of the early work in electrochemistry was performed on liquid electrodes, particularly on mercury - another reason is that it is easier to generate clean liquid surfaces than clean solid surfaces. With some caveats and modifications, thermodynamic relations can also be applied to solid surfaces. We will first consider the interface between a liquid electrode and an electrolyte solution, and turn to solid electrodes later.
The double layer in the absence of specific adsorption
Authors: Schmickler Wolfgang
Published: November 2020

One of the fundamental problems in electrochemistry is the distribution of the potential and of the particles at the interface. Here we will expand on the subject of Chapter 3, and consider the interface between a metal and an electrolyte solution in the absence of specific adsorption. Until about 1980 a simple model of this interface prevailed, which was based on a particular interpretation of the interfacial capacity. The metal was assumed to be a perfect conductor in the classical sense, and hence a region of constant potential right up to the metal surface. As was pointed out in Chapter 3, the inverse capacity can be split into two terms, a Gouy-Chapman and a Helmholtz term: l/C = l/CGc + 1/CH. It was argued that these two terms pertain to two different regions in the solution: the space charge or diffuse double layer, which is already familiar to us, and the Stern or outer Helmholtz layer giving rise to the Helmholtz capacity. Since the latter does not depend on the concentration of the ions, the Stern layer was supposed to consist of a monolayer of solvent molecules adsorbed on the metal surface. The plane passing through the centers of these molecules was called the outer Helmholtz plane. Rather elaborate models were developed for the dielectric properties of this layer in order to explain Helmholtz capacity curves such as those shown in Fig. 3.3. This Gouy-Chapman-Stern model, as it was named after its main contributors, is a highly simplified model of the interface, too simple for quantitative purposes. It has been superseded by more realistic models, which account for the electronic structure of the metal, and the existence of an extended boundary layer in the solution. It is, however, still used even in current publications, and therefore every electrochemist should be familiar with it. In the remainder of this chapter we will present elements of modern double-layer theory. Two phases meet at this interface: the metal and the solution. We will consider each phase in turn.
Quantum theory of electron-transfer reactions
Authors: Schmickler Wolfgang
Published: November 2020

The theory of electron-transfer reactions presented in Chapter 6 was mainly based on classical statistical mechanics. While this treatment is reasonable for the reorganization of the outer sphere, the inner-sphere modes must strictly be treated by quantum mechanics. It is well known from infrared spectroscopy that molecular vibrational modes possess a discrete energy spectrum, and that at room temperature the spacing of these levels is usually larger than the thermal energy kT. Therefore we will reconsider electron-transfer reactions from a quantum-mechanical viewpoint that was first advanced by Levich and Dogonadze. In this course we will rederive several of, the results of Chapter 6, show under which conditions they are valid, and obtain generalizations that account for the quantum nature of the inner-sphere modes. By necessity this chapter contains more mathematics than the others, but the calculations are not particularly difficult. Readers who are not interested in the mathematical details can turn to the summary presented in Section 6. To be specific we consider electron transfer from a reactant in a solution, such as [Fe(H2O)6]2+, to an acceptor, which may be a metal or semiconductor electrode, or another molecule. To obtain wavefunctions for the reactant in its reduced and oxidized state, we rely on the Born-Oppenheimer approximation, which is commonly used for the calculation of molecular properties. This approximation is based on the fact that the masses of the nuclei in a molecule are much larger than the electronic mass. Hence the motion of the nuclei is slow, while the electrons are fast and follow the nuclei almost instantaneously. The mathematical consequences will be described in the following. Let us denote by R the coordinates of all the nuclei involved, those of the central ion, its ligarids, and the surrounding solvation sphere, and by r the coordinates of all electrons.
The Northern Rio Grande Basin
Authors: Graf William L.
Published: November 2020

In northern New Mexico, the environmental plutonium bound to sedimentary particles is the most mobile in river systems, particularly the Rio Grande. This chapter describes the physical characteristics of the drainage basin into which Los Alamos National Laboratory has released plutonium. I review those characteristics of the basin that most strongly influence the movement of sediment and its associated plutonium: landforms, geology and soils, climate, vegetation, and precipitation. Precipitation and elevation provide the energy that is the primary driving force behind river processes in the Northern Rio Grande Basin. The geographic variation in stream flow and the temporal characteristics of its magnitude and frequency explain how water, sediment, and contaminants such as plutonium move through the system. An accurate accounting of stream flow is therefore essential to the development of a basinwide budget for water, sediment, and contaminants. Calculations for the mechanics of sediment transport (and the transport of associated contaminants) thus depend on measurements of stream flow from a variety of places within the system. In this chapter I examine the basic data for stream flow in the basin and then define and explain the temporal and geographical variation in the system’s river flows. The result is a regional stream-flow budget. The portion of the Northern Rio Grande emphasized in this book consists of the watershed upstream from the U.S. Geological Survey stream gage on the Rio Grande at San Marcial, at the headwaters of Elephant Butte Reservoir. The drainage network in this 71,700-sq-km area is the principal mechanism for the surface transport and storage of plutonium. The Rio Grande begins as a trickle of meltwater from a semipermenant snowbank at Stoney Pass in the San Juan Mountains in southwestern Colorado. Steep mountain tributaries are the primary sources of water, joining the main stem as it trends southeastward to the San Luis Valley and the Alamosa, Colorado, area. Additional mountain waters from the Rio Conejos, which drains the southern San Juan Mountains in southern Colorado, join the main stream as it flows southward into New Mexico. The northern Sangre de Cristo Mountains in Colorado generate surface runoff, but relatively little reaches the main river.
Reparian Vegetation
Authors: Graf William L.
Published: November 2020

The interaction among water, sediment, landforms, and human environmental manipulation on the Northern Rio Grande has produced a distinctive assemblage of plants in the riparian (or near-channel) community. The fluvial landforms and the sediment of which they are composed are often not immediately visible in field investigations because of the dense cover of riparian vegetation. In aerial photography—the primary source of data for historical river-channel change and sedimentation- riparian vegetation is often the only aspect of the near-channel environment that is amenable to interpretation and mapping. Vegetation also provides information about the date of emplacement of the sediments on which it grows, information useful in tracking contaminants introduced into the system during known time periods. Vegetation communities therefore provide useful keys to identifying the distribution of near-channel sediments and the contaminants they contain. This chapter briefly reviews the origin and changes in riparian vegetation in the study area, including its connections with geomorphic systems. Almost all major rivers in the American Southwest have undergone considerable geomorphic and vegetation change since the early nineteenth century when channel margins were the sites of bogs, lakes, abandoned meanders (sloughs), and marshes. Most major rivers had broad, sandy channels with braided configurations and meandering low-flow channels. Even small tributaries had marshy areas created by beavers. The riparian vegetation originally evolved in association with frequent extensive flooding. Removal of the beavers, the development of gullies and arroyos, land-management schemes, changes in climate, and the construction of dams changed the streams into single-thread or compound channels that flooded less often. The Rio Grande’s recent history is typical of the larger region except for the extensive recent engineering works that restrict the active channel and flood plains. There are few detailed descriptions of the channel and riparian vegetation before major human intervention, but generally, most firsthand observers indicate that the Northern Rio Grande was broad and shallow, with meandering subchannels frequently altered by flooding. After channel migration, cottonwood, willow, and cattail colonized the newly exposed alluvial surfaces. Early in the twentieth century, the cottonwood groves near the river rarely developed trees more than about 10 m high before more changes in the channel destroyed them.
Sediment and Plutonium Storage Upstream from Cochiti
Authors: Graf William L.
Published: November 2020

The foregoing chapters demonstrated that large amounts of sediment and much of the plutonium entering the Northern Rio Grande have been stored along the river channel. A composite budget analysis gives the quantities of materials involved annually, but except in very broad terms it does not describe where the materials are stored. It is a matter of scale: The budget indicates the overall quantities of sediment and plutonium stored in the system but does not reveal on a local scale where one might search for the materials. The next chapters show that the storage process has particular geographic characteristics and that in representative reaches it is possible to map those sediments that were deposited during the years of maximum input of plutonium into the system. These critical deposits are likely to contain more plutonium than are similar deposits of other years. In this way, the evidence of environmental change along the river provides a guide for determining the fate of plutonium in the system. A sampling program for assessing the storage of plutonium along the Northern Rio Grande depends on the development of the connections among vegetation communities, fluvial landforms, sedimentary deposits, and plutonium contents. Although it is not possible here to map and interpret completely the entire 313 km of river from Espanola to San Marcial, limited reaches can serve as representatives of larger portions of the whole. Eleven representative reaches, each about 3 to 6 km long, provide information on the entire study area because each representative reach exemplifies the conditions that obtain over a much larger portion of the total length of the river. My selection of the representative reaches began by reviewing the entire river by aerial photography and then directly in the field. The river divides itself into sections based on the geomorphologic conditions as modified by engineering works. Each representative reach illustrates the conditions within one larger section. For example, the Frijoles representative reach is similar to other relatively short reaches throughout White Rock Canyon.
General Lessons and Conclusions
Authors: Graf William L.
Published: November 2020

The initial investigations reported here offer some broad lessons from the analysis of a specific example. Application of the techniques and results in the Los Alamos case to other areas or cases would require modifications, and even the conclusions about plutonium in the Northern Rio Grande are more first approximations than final answers. After reviewing the lessons of the Los Alamos work, this chapter summarizes some of the natural scientific lessons, with particular reference to the changing Northern Rio Grande and some observations about the interactions between natural science for plutonium and the associated public policy and politics surrounding the issue. Because this work is a beginning rather than an ending, this chapter concludes with some speculations on the future of plutonium in the Northern Rio Grande. The lessons from the particular case of Los Alamos and the Rio Grande extend far beyond northern New Mexico. As a “test bed,” the laboratory, its plutonium releases, and the data-rich Rio Grande provide generalizations useful to researchers, monitors, regulators, decision makers, and managers of other systems and locations. This chapter reviews these lessons as two distinct groups: general guidelines and specific sediment-sampling procedures. First are several general guidelines that should direct any effort at assessing the plutonium system of a river affected by industrial-waste disposal, an accidental release during transportation, or distribution from a nuclear detonation involving surface materials or from atmospheric fallout. Second, because of the overriding importance of sediment in the transport and storage of plutonium, several specific procedures should be followed when sampling soils and sediment, to ensure accurate interpretations of the results. A refined sampling and monitoring program for plutonium in sediment should be driven by a philosophy that has the following general principles. 1. Obtain an accurate inventory of sediment-bound plutonium at the source location. If the source of contaminated sediments in a river system is a known mass, such as a well-defined waste-disposal site, a tailings accumulation, or another readily measured mass of material, a reasonable estimate of the total inventory of plutonium in the source is possible.