1 Introduction Reasoning About Fluids Via Molecular Collections

CHAPTER 1. INTRODUCTION TO FLUID INCLUSIONS Robert J. BodnarThe Bubble FactoryVirginia TechBlacksburg, VA 24061 USArjb@INTRODUCTIONWhen a crystal grows in the presence of a fluid phase, some of the fluid may be trapped as imperfections in the growing crystal to form fluid inclusions. The trapped fluid may be liquid, vapor, or supercritical fluid, and the composition of the trapped fluid may include essentially pure water, brines of various salinity, gas or gas-bearing liquids, and silicate, sulfide or carbonate melts, among others. As noted by Roedder (1984), some workers use the term fluid inclusion to describe only those inclusions that have trapped a fluid and have remained in the fluid state during cooling to ambient temperatures. With that narrow definition, however, inclusions that originally trapped silicate melt and now contain glass ± crystals (cf. Thomas et al. 2002), or solid carbon dioxide inclusions in diamond that were originally trapped as high density liquid carbon dioxide (Schrauder & Navon 1993), or unusual aqueous inclusions that trapped a calcium chloride-rich brine and now contain crystalline antarcticite without any liquid (Schiffries 1990), would not be considered fluid inclusions. The broader and more modern approach that will be followed here is to use the term "fluid inclusion" to refer to any inclusion that trapped a phase that was a fluid at the temperature and pressure of formation, regardless of the phase state of the inclusion as observed at laboratory conditions. For clarity, terms such as "silicate melt inclusion", "crystallized melt inclusion", "solid carbon dioxide inclusion" and others may be used as necessary to describe inclusions that now contain phases other than liquid or vapor at room temperature, with t h e understanding that all of these are in fact fluid inclusions.Fluid inclusions are a common feature of minerals. In fact, it is much more common to find crystals with optically-resolvable fluid inclusions (= 1 m) than it is to find crystals with no visible fluid inclusions. Even gemstones, which are sought because of their beauty and apparent perfection, often contain large inclusions that are, in some cases, characteristic of the area or mine where they were found (Roedder 1986).Fluid inclusions sufficiently large to study with the heating and freezing stage include those with sizes greater than about 1-2 micrometers. There is no upper limit to the size of natural fluid inclusions, but those with dimensions greater than a few millimeters are uncommon. As noted by Roedder (1984), the number of inclusions in a given sample generally increases with decreasing inclusion size, and some milky quartz and calcite may contain as many as 109 fluid inclusions per cm3. Although it is not possible with present technology to conduct microthermometric analysis of inclusions less than about 1 micrometer in diameter, there is likely a continuum in inclusion size f rom those that are resolvable with the petrographic microscope (˜1 micrometer) down to those that are sub-micrometer size (Fig. 1-1A, B), including those composed of only a few water molecules and have dimensions measured in Angstroms. Using transmission electron microscopy (TEM), Green & Radcliffe (1975) observed 1 nanometer diameter carbon dioxide inclusions in olivine, with a continuum in size from these submicroscopic inclusions to those about 5 micrometers in diameter and easily resolvable with a petrographic microscope. The physical and chemical properties of these nano-inclusions could be significantly different than properties of larger microscopic fluid inclusions. Nevertheless, these sub-microscopic inclusions represent an important reservoir for volatiles in the deeper portions of the earth (Bell & Rossman 1992), and exsolution of volatiles originally dissolved in nominally anhydrous minerals during cooling and uplift might lead to the formation of later fluid inclusions (Spear & Selverstone 1983).The physical and chemical conditions that might lead to the formation of fluid inclusions are many, and some are limited to certain minerals or even specific crystal faces in individual mineralsBodnar RJ (2003) Introduction to fluid inclusions. In I. Samson, A. Anderson, & D. Marshall, eds. Fluid Inclusions: Analysis and Interpretation. Mineral. Assoc. Canada, Short Course 32, 1-8.1F IG. 1-1. (A). Atomic-Force Microscopy image of an 80 nm deep pit with an area ˜500 nm x ˜ 300 nm on an albite cleavage surface. The pit is thought to represent a sub-microscopic fluid inclusion in the albite crystal. (from Hochella et al. 1990). (B). Atomic-Force Microscopy image of a dissolving calcite rhombohedral surface showing numerous small (several tens of nm) pits in the crystal surface. During subsequent crystal growth, each of these pits is likely to become a sub-microscopic fluid inclusion (unpub. image, courtesy of M.F. Hochella, Jr.). (C) Calcite crystal from a vein in the Monterey Formation, California, showing a large, primary petroleum inclusion along a growth surface. The scale bar represents 25 µm (from Bodnar 1990). (D) Orthopyroxene phenocryst in basaltic andesite from White Island, New Zealand, showing numerous growth zones outlined by primary silicate melt inclusions and trapped solid inclusions. The crystal is approximately 2 mm long. (from Rapien 1998). (E) Quartz crystal from the Morro Velho gold mine, Brazil, showing several trails of secondary fluid inclusions cutting the crystal. Width of field of view is approximately 3 mm.2(cf. Watanabe 1987). For a more detailed discussion of these processes, the reader is referred to Goldstein & Reynolds (1994, Chapter 2) and Roedder (1984, Chapter 2). For an interesting historical perspective of ideas concerning the formation and study of fluid inclusions, the reader is referred to Yermakov (1965; sometimes also spelled Ermakov in western translations). Below, I summarize the basics of fluid inclusion origin, classification and selection, and provide one example of the selection criteria one might apply to choose fluid inclusions for study.TEMPORAL CLASSIFICATION OF FLUID INCLUSIONSThere are many ways to classify fluid inclusions (Roedder, 1984; G oldstein, 2003), but one of the most useful classification schemes relates the timing of formation of the inclusion relative to that of the host mineral (Fig 1-2). Accordingly, primary fluid inclusions are formed during, and as a direct result of, growth of the surrounding host crystal. If a crystal fractures after it has been formed, some fluid may enter the fracture and become trapped as secondary fluid inclusions as the fracture heals. Thus, secondary inclusions are trapped after crystal growth is complete. If fracturing occurs during growth of the crystal, pseudosecondary fluid inclusions may be trapped during continued crystal growth. Such inclusions are sometimes referred to as primary-secondary inclusions in the older Soviet literature. Petrographically, the occurrence of pseudo-secondary inclusions is similar to secondary inclusions, but the latter are followed by additional crystal growth. Sometimes the origin of the inclusions relative to formation of the crystal cannot be determined with confidence and the inclusion origin is said to be indeterminable (Goldstein, 2003).Primary inclusions form when fluid is trapped on the active growing surface of a crystal. In mineralogy class, the face of a growing crystal is often portrayed as a perfect surface, with atoms being added to the surface in a very regular fashion. While this is true in the broadest sense, at the atomic scale the growing surface shows considerable topography (Zhang & Nancollas 1990). Recent advances in analytical techniques, such as TEM and atomic-force microscopy (AFM), now permit these surfaces to be viewed at the atomic scale, revealing the many irregularities that occur (Hochella et al. 1990). Growth spirals may develop if the growing crystal contains screw dislocations. In addition, etch pits and etch hillocks may develop on the crystal surface in response to changing degrees of saturation of the fluid - these features provide ideal sites for entrapment of fluid. Other processes, such as precipitation of solids on a growing crystal face, or nucleation of an immiscible fluid phase that adheres to the crystal face (imagine the CO2bubbles that nucleate on the inside surface of F IG. 1-2. Schematic representation showing the formation of primary, secondary and pseudosecondary inclusions during crystal growth.3a beer bottle when it is opened) may "poison" the surface and lead to formation of inclusions as the crystal continues to grow.Determining the temporal classification of any given fluid inclusion is critical to interpreting the origin and evolution of the host mineral, yet this determination is often difficult. Roedder (1984; Table 2-1) lists the various morphological and petrographic criteria that have been used to determine the origin of fluid inclusions. Among the most d iagnostic criteria for a primary origin are inclusions trapped along growth surfaces in crystals (Fig. 1C, D; Fig. 2). Episodic increases in crystal growth rates, resulting from rapid temperature (or pressure) or fluid composition changes, or from deposition of foreign particles on the growing surface (c f. Voigt & Brantley 1991), may lead to trapping of primary inclusions on the growth surface. Watanabe (1987) noted that inclusions were abundant on the fastest growing faces of corundum crystals, but were rare to absent on faces that grew more slowly. Roedder (1984) has also noted that one or a few fluid inclusions distributed randomly within the cores of crystals is good evidence for a primary origin, especially if the inclusions are large relative to the enclosing crystal (cf. Thomas et al. 2002). Note, however, that inclusions that appear to be randomly distributed in three dimensions within a crystal can result from overlapping planes of secondary inclusions (Goldstein, 2003). One property that has been used in the past to indicate a primary origin is the shape of the inclusions. Thus, negative-crystal-shaped inclusions have been interpreted to be primary, regardless of their location and/or distribution within the crystal. Today, based mainly on results of crystal growth and synthetic fluid inclusion studies, it is well known that secondary inclusions with a negative-crystal-shape are common (c f. Sterner & Bodnar 1984), and that inclusion shape alone cannot be used to determine the timing of inclusion fo rmation (relative to the host crystal). Moreover, Bodnar et al. (1985) describe the process of "fluid inclusion maturation", whereby originally large, irregularly shaped inclusions evolve with time to become smaller and more regularly shaped. Note that inclusion shape can be used in some cases to indicate a primary origin, as in the case of fluid inclusions in calcite that taper in the direction of crystal growth (Goldstein, 2003) (Fig. 1.1C).Secondary fluid inclusions are easily identified if they occur along a fracture that crosscuts the entire crystal (Fig. 1E). While it is unlikely that truly secondary inclusions on fractures that crosscut the entire crystal would be mis-interpreted as primary fluid inclusions, it is likely that some primary (or pseudosecondary) inclusions have been interpreted to be secondary.Sisson et al. (1993) observed the formation of fluid inclusions under the microscope during crystallization of KH2PO4 crystals. The inclusions were formed by sealing etch pits and other surface irregularities to form planar arrays that would be interpreted to be secondary based on petrographic characteristics. Johnson (1990) similarly observed primary fluid inclusions in planar arrays in experimentally grown forsterite crystals. These inclusions would likely be interpreted to be secondary because many of the planes are perpendicular to growth faces. In an experimental study of crack-healing in quartz, Brantley (1992) noted the formation of dislocations with hollow cores that trap fluid as inclusions. As the crystals continue to grow, the dislocations propagate along with the growing crystal to produce trails of fluid inclusions that extend to the outer surface of the crystal. Observation of such fluid inclusions along trails that extend from the outer surface of a crystal into the interior would likely be interpreted as secondary (or perhaps pseudosecondary if the trail did not extend completely to the edge of the crystal).To some, the term "secondary inclusion"offers a negative connotation, with the implication that secondary inclusions should be avoided during microthermometric analysis.While this may be true in some instances, whether or not one should study secondary fluid inclusions depends on the geologic problem that is being studied. For example, the quartz grain shown in Figure 1E is from a mineralized vein in the Morro Velho gold deposit, Brazil. In this deposit, gold was introduced into the veins relatively late. If one examines polished sections of these veins under reflected light, bright gold flakes are observed along linear trails in the quartz - these are the same trails that host the secondary inclusions. In this case, the gold was introduced into the veins by the fluids that are now trapped as secondary fluid inclusions in the quartz. Thus, if one is interested in understanding the P-T conditions and fluid composition associated with4gold transport and deposition, it is the secondary inclusions that should be studied, not the primary inclusions in these veins.FLUID INCLUSION ASSEMBLAGEAs noted above, determining the temporal classification of inclusions may be difficult, resulting in a fluid history that is equivocal. To minimize the emphasis on the primary, secondary and pseudosecondary classification of inclusions, Goldstein & Reynolds (1994) introduced the concept of the Fluid Inclusion Assemblage (FIA) to describe a group of fluid inclusions that were all trapped at the same time. An FIA thus defines the most finely discriminated fluid inclusion trapping event that can be identified based on petrography (Goldstein, 2003). This requirement further implies that the inclusions in the FIA were all trapped at approximately the same temperature and pressure, and all trapped a fluid of approximately the same composition. Therefore, the FIA represents a “fluid event” in the history of the system, and the fluid in the inclusions making up the FIA represents the fluid that was present during that event. Note that Goldstein & Reynolds (1994; especially their Fig. 7.1B) describe examples in which the homogenization temperature (and, presumably, the trapping temperature) is not constant within an FIA but, rather, shows systematic increases parallel to the growth direction. In this case, petrographic observations confirm the presence of a relatively thick growth zone that formed during an increasing temperature fluid event.The requirement that the inclusions within an FIA were all trapped “at the same time” is relative and the absolute amount of time of the event will vary according to the environment of formation. In a shallow terrestrial or submarine geothermal system, where temperature and fluid composition might vary significantly over a time scale of days or weeks, fluid inclusions in an FIA might have been trapped over a period of days or less. In a deeper metamorphic environment where pressure-temperature-composition (PTX) conditions may remain reasonably constant for years or tens to hundreds of years, “at the same time” could apply to inclusions trapped over a period of several years to tens or hundreds of years. Brantley et al. (1990) conducted experimental studies of crack healing in quartz at hydrothermal conditions to investigate the time scales involved in inclusionformation. These workers found that cracks ˜100 µm long and 10 µm wide will heal in 4 hours at 600°C and 2 kbars in the presence of pure water.At 200°C, these same cracks can heal in about 40 days to 1,000 years, depending on the activation energy. Brantley (1992) also showed that cracks will heal faster in the presence of H2O-salt solutions, and slower in the presence of H2O-CO2solutions, both compared to rates in pure water.The variation in homogenization temperature that is acceptable within an FIA is thus a function of the actual temperature of formation (which, to a large extent controls how fast crystals can grow), the fluid composition (which controls mineral solubility) and on the geological environment (which generally controls the rate and magnitude of temperature and pressure fluctuations).Determination that all of the inclusions in a group were trapped “at the same time” is based on petrographic analysis of the sample (see Goldstein & Reynolds 1994). A group of inclusions along an easily-recognizable growth zone in t he host mineral may generally be assumed to have all been trapped at the same time and thus representan FIA. Similarly, inclusions along a fracture thatF IG. 1-3. Schematic representation of the variousFIAs that might be observed in a well-cementedsandstone from a hydrocarbon basin. Theoriginal detrital grains are shaded. A descriptionof the various FIAs and information availablefrom those inclusions is shown in Figure 4.(from Bodnar 1994).5F IG. 1-4. Description of the various FIAs shown in Figure 3, along with a summary of information available from each FIA. (from Bodnar 1994).crosscuts a mineral grain were probably all trapped at the same time as the fracture healed. Inclusions that are distributed randomly in three dimensions within the core of a host crystal provide less convincing evidence that a group of inclusions represents an FIA.An Example of the use of FIAsMost samples contain numerous fluid inclusion assemblages, only some of which may be relevant to the problem being considered. Figure 1-3 is a schematic representation of a well- cemented sandstone from a hydrocarbon reservoir, showing several different FIAs. Figure 1-4 describes the various FIAs shown on Figure 3, and briefly summarizes the type of information each FIA might provide. The geological problem that is being investigated will dictate which of the many FIAs should be studied. For example, if the major focus of the study is to understand the tectonic history of the area, then an important question concerns the source(s) of sediments in the basin and the directions of sediment transport. To address this question, one would be interested in the geology of the source region(s). Thus, inherited inclusions in the detrital quartz grains suggest at least two sources for the quartz - a medium-to-high grade metamorphic environment (as evidenced by H2O-CO2 inclusions containing both liquid and vapor CO2) and a shallow granitic6intrusive source (as evidenced by coexisting halite-bearing and vapor-rich fluid inclusions). By determining the relative amounts of the two different types of detrital grains and their variation within a given stratigraphic horizon, it may be possible to determine relative distances to the two different source regions. Variations in the two different detrital FIAs vertically within the sandstone unit may reflect changing tectonic conditions (rates of exhumation?) in the two different source regions with time.A petroleum geologist studying the same sample might not be interested in the source of the sediments, but rather with the timing of hydrocarbon migration relative to cementation and porosity loss or gain. In this case, one would not study FIAs containing inherited inclusions in the detrital grains, but instead would focus on FIAs containing petroleum inclusions and occurring in authigenic quartz near the detrital grain/overgrowth interface. Similarly, analysis of the very latest FIA that contains (secondary) aqueous inclusions and crosscuts all generations of cement as well as the detrital grains might help to determine the thermal history following oil migration. Such information is crucial to (1) understanding the post-migration history of the basin, and (2) whether the original liquid hydrocarbons that filled pore spaces in the rock were subsequently buried beyond the oil window, resulting in degradation of the liquid petroleum into methane and other light gaseous hydrocarbons.Before any FIA can be used to study the thermal and chemical evolution of a geologic system, one must be certain that the i nclusions have trapped a fluid representative of that present at the time of inclusion formation and have not reequilibrated following formation (Bodnar, 2003a). To accomplish this, one must test the inclusions for adherence to “Roedder’s Rules”, which state that:1. the inclusions trapped a single, homogeneousphase.2. the inclusions represent an isochoric (constantvolume) system.3. after trapping, nothing has been added to, orremoved from, the inclusions.That the inclusions do adhere to “Roedder’s Rules” may be confirmed based on petrographic (Bodnar, 2003a; Goldstein, 2003) and microthermometric analysis (Bodnar, 2003b).Finally, it should be emphasized that many of the geological problems one might be trying to resolve using fluid inclusions can be solved without the need for microthermometric or chemical data for the inclusions. For example, if one wants to know if hydrocarbons ever migrated through a given lithologic unit, the simple presence, or absence, of petroleum inclusions in the sample may answer the question. Similarly, if one wishes to know if the fluids in an epithermal precious metal exploration target were boiling, the presence, or absence, of FIAs with coexisting liquid-rich and vapor-rich inclusions may provide the answer, without the need for time-consuming and expensive microthermometric analysis.ACKNOWLEDGEMENTSReviews of an earlier version of this chapter by Harvey Belkin, Guoxiang Chi, Megan Elwood Madden and Jason Reed are greatly appreciated.Funding for work in the Fluids Research Laboratory has been supported over the years by the National Science Foundation, Department of Energy, NASA, and the American Chemical Society. Support during preparation of this manuscript was provided by NSF Grants EAR-0001168 and EAR-0125918.REFERENCESBELL, D.R.& ROSSMAN,G.R. (1992): Water in theEarth's mantle: The role of nominally anhydrousminerals. Science, 255, 1391-1397.B ODNAR, R.J. 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科技英语阅读课后参考答案-Unit1,3Unit 1 MathematicsPart I EST Reading Reading 1Warm-up Questions: Work in pairs and discuss the following questions. 1. Who is Bertrand Russell? Bertrand Arthur William Russell (b.1872 – d.1970) was a British philosopher, logician, essayist and social critic best known for his work in mathematical logic and analytic philosophy. His most influential contributions include his defense of logicism (the view that mathematics is in some important sense reducible to logic), his refining of the predicate calculus introduced by Gottlob Frege (which still forms the basis of most contemporary logic), his defense of neutral monism (the view that the world consists of just one type of substance that is neither exclusively mental nor exclusively physical), and his theories of definite descriptions and logical atomism. Russell is generally recognized as one of the founders of modern analytic philosophy, and is regularly credited with being one of the most important logicians of the twentieth century. 2. What is Russell’s Paradox? Russell discovered the paradox that bears his name in 1901, while working on his Principles of Mathematics (1903). The paradox arises in connection with the set of all sets that are not members of themselves. Such a set, if it exists, will be a member of itself if and only if it is not a member of itself. The paradox is significant since, using classical logic, all sentences are entailed by a contradiction. Russell's discovery thus prompted a large amount of work in logic, set theory, and the philosophy and foundations of mathematics. 3. What effect did Russell’s Paradox have on Gottlob Fregg’s system? At first Frege observed that the consequences of Russell’s paradox are not immediately clear. For example, “Is it always permissible to speak of the extension of a concept, of a class? And if not, how do we recognize the exceptional cases? Can we always infer from the extension of one concept’s coinciding with that of a second, that every object which falls under the first concept also falls under the second? Because of these kinds of worries, Frege eventually felt forced to abandon many of his views. 4. What is Russell’s response to the paradox? Russell's own response to the paradox came with the development of his theory of types in 1903. It was clear to Russell that some restrictions needed to be placed upon the original comprehension (or abstraction) axiom of naive set theory, the axiom that formalizes the intuition that any coherent condition may be used to determine a set (or class). Russell's basic idea was that reference to sets such as the set of all sets that are not members of themselves could be avoided by arranging all sentences into a hierarchy, beginning with sentences about individuals at the lowest level, sentences about sets of individuals at the next lowest level,1sentences about sets of sets of individuals at the next lowest level, and so on Using a vicious circle principle similar to that adopted by the mathematician Henri Poincaré, and his own so-called "no class" theory of classes, Russell was able to explain why the unrestricted comprehension axiom fails: propositional functions, such as the function "x is a set," may not be applied to themselves since self-application would involve a vicious circle. On Russell's view, all objects for which a given condition (or predicate) holds must be at the same level or of the same "type." 5. Have you ever heard of Zermelo-Fraenkel set theory.? Can you give an account of it? Contradictions like Russell’s paradox arose from what was later called the unrestricted comprehension principle: the assumption that, for any property p, there is a set that contains all and only those sets that have p. In Zermelo’s system, the comprehension principle is eliminated in favour of several much more restrictive axioms: a. Axiom of extensionality. If two sets have the same members, then they are identical. b. Axiom of elementary sets. There exists a set with no members: the null, or empty, set. For any two objects a and b, there exists a set (unit set) having as its only member a, as well as a set having as its only members a and b. c. Axiom of separation. For any well-formed property p and any set S, there is a set, S1, containing all and only the members of S that have this property. That is, already existing sets can be partitioned or separated into parts by well-formed properties. d. Power-set axiom. If S is a set, then there exists a set, S1, that contains all and only the subsets of S. e. Union axiom. If S is a set (of sets), then there is a set containing all and only the membersof the sets contained in S. f. Axiom of choice. If S is a nonempty set containing sets no two of which have common members, then there exists a set that contains exactly one member from each member of S. g. Axiom of infinity. There exists at least one set that contains an infinite number of members. With the exception of (b), all these axioms allow new sets to be constructed from already-constructed sets by carefully constrained operations; the method embodies what has come to be known as the “iterative” conception of a set. /doc/a90df7ed551810a6f524860e.html/entries/russell/ Section C Post-reading TaskReading Comprehension1. Directions: Work on your own and fill in the blanks with the main idea. Part 1 (Para. 1): Brief introduction to Russell’s paradox Part 2 (Paras. 2-5): The effect of Russell’s paradox on Gottlob Frege’s system.2Para. 2: Russell’s paradox dealt a heavy blow to Frege’s attempts to develop a foundation for all of mathematics using symbolic logic. Para. 3: An illustration of Russell’s paradox in terms of sets Para. 4: Contradiction found in the set. Para. 5: Frege noticed the devastating effect of Russell’s paradox on his system and inability to solve it. Part 3 (Paras. 6-8): Solutions offered by mathematicians to Russel’s paradox Para. 6: Russell’s own response to the paradox with his "theory of types."Para. 7: Zermelo's solution to Russell's paradox Para. 8: What became of the effort to develop a logical foundation for all of mathematics? Part 4 (Para. 9): Correspondence between Russell and Frege on the paradox 2. Directions: Work in pairs and discuss the following questions. 1) What is the basic idea of Russell’s paradox? 2) How to explain Russell’s paradox in terms of sets? 3) Can you explain the contradiction found in the sets related to Russell’s paradox 4) Is Russell’s own response to the paradox workable? 5) Do you know Zermelo-Fraenkel set theory? (open) 3. Directions: Read the following passage carefully and fill in the blanks with the words you’ve learned in the text. Russell's own response to the paradox came with the development of his theory of types in 1903. It was clear to Russell that some restrictions needed to be placed upon the original comprehension (or abstraction) axiom of naive set theory, the axiom that formalizes the intuition that any coherent condition may be used to determine a set (or class). Russell's basic idea was that reference to sets such as the set of all sets that are not members of themselves could be avoided by arranging all sentences into a hierarchy, beginning with sentences about individuals at the lowest level, sentences about sets of individuals at the next lowest level, sentences about sets of sets of individuals at the next lowest level, and so on. Using a vicious circle principle similar to that adopted by the mathematician Henri Poincaré, and his own so-called "no class" theory of classes, Russell was able to explain why the unrestricted comprehension axiom fails: propositional functions, such as the function "x is a set," may not be applied to themselves since self-application would involve a vicious circle. On Russell's view, all objects for which a given condition (or predicate) holds must be at the same level or of the same "type."Vocabulary and Structure31. Word-building Directions: Give the correct form of the word according to the indication in the brackets. Then complete the sentences using the right form for each word. Use each word once. discover— (suffix) logic— (suffix) correspond—(suffix) describe—(suffix) contradict— (suffix) symbol—(suffix) form—(suffix) develop—(suffix) able—(prefix) equal—(suffix)1) The math may not have been new, but Duchin enjoyed the process of_________, and she got to work collaboratively with half a dozen other math whizzes.( discovery) 2) Packages can be sealed and can contain personal _________if it relates to the contents of the package.( correspondence) 3) New research indicates that the brain region may prefer_________ notation to other numeric representations .( symbolic) 4) To do this, an ideal model based on the _________ paradigm was constructed and then compared with a neutral model reflecting the further education system as it existed before the Act took effect.( equality) 5) Is this not in flagrant _________to Einstein's rule that signals do not travel faster than the velocity of light?( contradiction) 6) Sequential organization has the major advantage that the records are stored in a _________ order, presumably that sequence to which the records are normally required for printing and for soft copy reports.( logical) 7) The mathematical _________ of a zero-sum two-person game is not difficult to construct, and determining the optimal strategies and the value of the game is computationally straightforward.( description) 8) The proof we now know required the_________ unknown in Fermat's time.( development) of an entire field of mathematics that was9) Williams adds that many courses in geometry, “the one high school class that demands _________ reasoning,” have already been “gutted” and are no longer proof-based.( formal) 10) The concept of total aircraft ownership will become increasingly important should the traditional trade structure be _________to cover the expanse of technologies economically.( unable) 2. Directions: Complete the sentences with the words given in the brackets. Change the form if necessary. 1) The key to unraveling such apparent paradoxes is to characterize the initial set of possibilities ("initial" meaning before you receive any extra information) and then to eliminate possibilities based on that extra information. (base) 42) Indeed, this separation of meaning is reflected by the definition of "weak" in the OALD, with a distinct sense reserved for its use when pertaining to that of solutions (definition) 3) The resulting radical pollution control programme outlined by Nixon, calling for a 90 per cent reduction in vehicle emissions by 1980, not only led to him being credited (albeit briefly) as policy initiator of an environmental clean-up but also provided him with the chance to deal a blow to one of his most important opponents in the 1972 elections, Edmund Muskie (blow) 4) Singapore's continuing investments in education and training has brought a tenfold increase in our pool of Information Technology professionals and the Singapore worker has been consistently rated by BERI as the world's best in terms of technical skills, attitude and productivity. (term) 5) In this work he was led to topology, a still new kind of mathematics related to geometry, and to the study of shapes (compact manifolds) of all dimensions. (lead) 6) If there is no allowable string which spans the whole graph, then we can search in the same way as described above, but wherever the required path does not exist in the tree, check if that position in the tree is flagged for end-of-word (way) 7) During the past century, steps forward in physics have often come in the form of newly found particles; in engineering, more complex devices; in astronomy, farther planets and stars; in biology, rarer genes; and in chemistry, more useful materials and medications. (form) 8) A second reason for measurements is the more theoretical, put by Love as " the discovery of numerical relations between the quantities that can be measured to serve as a basis for the inductive determination of the form of the intrinsic energy function. " (serve) 9) Thus the optimum conditions for coastal terrace development would seem to be areas with small tidal ranges. Finally, tidal range is an important factor in the generation of tidal currents which may locally become of geomorphological importance (become) 10) The original double entrance doors to the booking hall had been replaced by an utterly incongruous picture window as had adjacent booking hall and waiting room windows. (replace) 3. Directions: Reorder the disordered parts of a sentence to make a complete sentence. 1) A simpleway to describe topology is as a 'rubber sheet geometry' — topologists study those properties of shapes that remain the same when the shapes are stretched or compressed. 2) Since the mid-1990s scientists have floated the idea that representations of numeric quantities, whether expressed as digits or as written words, are codified by the parietal cortex, a higher-processing region in the brain located just above the forehead. 3) As activity was monitored, located just above the forehead ,researchers noted changes under the assumption that the brain reduces activity as it becomes accustomed to a stimulus and then reactivates when a novel stimulus is presented. 4) That has not stopped physicists from devising new algorithms for the devices, which can calculate a lot faster than ordinary computers—in fact, exponentially faster, in quite a literal5sense. 5) Such a device would be made of metamaterial, a thicket of metal rings or other shapes that bends light in funny ways. 4. Directions: Change the following sentences into nominalized ones. 1) The passage of night could be marked by the appearance of 18 of these stars. 2) The full proof of Fermat's Last Theorem is contained in these two papers. 3) The concept of fixed-length hours, however, did not originate until the Hellenistic period. 4) There is a probability that my first sock is red because only one of the remaining three socks is red. 5) The importance of accurate data in quantitative modeling is central to using Bayes's theorem to calculate the probability of the existence of God.Discourse Understanding1. C. A "3 percent margin of error" means that there is a 95 percent chance that the survey result will be within 3 percent of the population value.2. E. How is it that a survey of only 1,000 people can reach this level of accuracy?3. G. The margin of error depends inversely on the square root of the sample size.4. A. The margin of error is a mathematical abstraction, and there are a number of reasons why actual errors in surveys are larger.5. F. Finally, the 3 percent margin of error is an understatement because opinions change.Reading 2 (/doc/a90df7ed551810a6f524860e.html/article.cfm?id=mandelbrot-set-1990-hor gan) Section A Pre-reading TaskWarm-up Questions /doc/a90df7ed551810a6f524860e.html/article.cfm?id=mandelbrot-set-1990 1. Who discovered the Mandelbrot set? This is not a trick question, not easy to answer. Many people including Mandelbrot have laid claim to the discovery. 2. Why was the set named after Benoit B. Mandelbrot? The set is named after Benoit B. Mandelbrot, a mathematician at the IBM Thomas J. Watson Research Center because he coined the term fractal to describe phenomena (such as coastlines, snowflakes, mountains and trees) whose patterns repeat themselves at smaller and smaller scales. 3. Why has there been so much controversy about who discovered the Mandelbrot set?6Mandelbrot claims that he and he alone discovered the Mandelbrot set, but there are other mathematicians who have challenged his claim. 4. What did the challengers say about Mandelbrot’s claim of discovery? Two mathematicians said that they independently discovered and described the set at about the same time as Mandelbrot did. And another mathematician also asserted that his work on the set not only predated Mandelbrot's efforts but also helped to guide them 5. Why did some professors support Mandelbrot’s claim? Mandelbrot deserves to have the set named after him, because his efforts brought the set to the attention of both the public and of the pure-mathematics community.Section C Post-reading TaskReading and Understanding1. Choose the best summary of the passage. C A B D2. Complete the sentences based on the text. 1) The term Mandelbrot set is used to refer both to a general class of_________________ and to a particular instance of such a set. （fractal sets） 2) 2.In general, a Mandelbrot set marks the set of points in the _________________ such that the corresponding Julia set is connected and not computable. （complex plane） 3) "The" Mandelbrot set is the set obtained from the _________________ z_(n+1)==z_n︿2+c with z_0==c, where points in the complex plane for which the orbit of z_n tend to infinity are in the set. （quadratic recurrence equation） does not4) Setting z_0 equal to any point in the set that is not a _________________ gives the same result. （periodic point） 5) The Mandelbrot set was originally called a _________________ by Mandelbrot. J. Hubbard and A. Douady proved that the Mandelbrot set is connected（ molecule） /doc/a90df7ed551810a6f524860e.html/11901033_d.html Language in Use1. Match the Chinese in the left column with the English in the right column. 迭代函数 iterative function 优先权之争 priority battle 分形特征 fractal properties7有意义 make sense 以越来越⼩的规模重复同⼀模式 patterns repeat themselves at smaller and smaller scales 混沌理论chaos theory 季刊 a quarterly journal 数学界 the mathematics community 波纹线 crisp lines 会议公报 proceedings of a conference 2. Join the following short sentences into longer ones. e.g. a. A fractal is generally a rough or fragmented geometric shape . b. The shape can be subdivided in parts. c. each part is (at least approximately) a reduced-size copy of the whole, a property called d. each part has a property of self-similarity. e.g. A fractal is generally "a rough or fragmentedgeometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole", a property called self-similarity. 1) In addition to coining the term "fractal" to describe objects and surfaces which are irregular at various dimensions of scale, he also introduced such concepts as "fractal dimensions" and the particular fractal known as the Mandelbrot set, frequently represented with the mathematical formula z → z2 + c. 2) It appeared that things were settling into a pleasant and fruitful routine, with his school lessons supplemented by long talks with his uncle about classical analysis, the iterative work of Pierre Fatou and the equally fascinating Julia Sets generated by Gaston Julia 3) Just as the youthful Mandelbrot had passed his college entrance exams by translating algebraic problems into geometrical problems, and solving them by intuitively deducing the "perfected" shape, he here realized there was something deeper, something mathematical, behind these strange patterns. 4) But the beauty in Mandelbrot's models was not that they generated a deceitful randomness, but that they could generate graphed data whose visual pattern accurately mimicked the visual patterns created by real phenomena。

根据最早期的科学研究调查，石油的形成被归结为两种起源：有机的和无机的。

一些化学家和天文学家认为石油是无机起源的，有的是火成岩成因，有的是宇宙成因，或者是两者的结合体。

大部分石油地质学家认为石油是由埋藏的有机物质经成岩作用形成的，并且指出石油形成于沉积岩而不是火成岩。

经济而精确的化学分析技术的出现使得生油岩的研究成为可能。

现在，可以把石油和生成它的页岩进行对比，用来确定潜在的生油岩、它们生油或生气的倾向，以及它们的热成熟度水平。

要形成商业性油气藏，必须满足5个条件：1．必须有富含有机质的源岩以产生石油和或天然气；2．源岩必须经受足够的热演化以生成石油；3．必须有能够容纳排出的油气的储集层。

该储集层必须具有孔隙度来存储油和或气，以及渗透性而让流体流动；4．储集层必须被非渗透性的盖层所封闭，以防止油气向上逸散到地表；5．源岩、储集层和盖层必须合理地分布来圈闭石油。

From the earliest days of scientific investigation the formation of petroleum had been attributed to two origins: inorganic and organic. Some chemists and astronomers argued for an inorganic origin --- ometimes igneous, sometimes extraterrestrial, or a mixture of both. Most petroleum geologists believe that petroleum forms from the diagenesis of buried organic matter and note that it is indigenous to sedimentary rocks rather than igneous ones. The advent of cheap and accurate chemical analytical techniques allowed petroleum source rocks to be studied. It is now possible to match petroleum with its parent shale and to identify potential source rocks, their tendency to generate oil or gas, and their level of thermal maturation.For a commercial oil accumulation to occur, five conditions must be fulfilled:1. There must be an organic-rich source rock to generate the oil and/or gas.2. The source rock must have been heated sufficiently to yield its petroleum.3. There must be a reservoir to contain the expelled hydrocarbons. This reservoir must have porosity, to contain the oil and/or gas, and permeability, to permit fluid flow.4. The reservoir must be sealed by an impermeable cap rock to prevent the upward escape of petroleum to the earth's surface.5. Source, reservoir, and seal must be arranged in such a way as to trap the petroleum.原油储量是指从已知油田的油井中将来可望产出原油的估计数量。