Does reactive surface area depend on grain size? Results from pH 3, 25 circle C far-from-equilibrium flow-through dissolution experiments on anorthite and biotite

Laboratory determined mineral weathering rates need to be normalised to allow their extrapolation to natural systems. The principle normalisation terms used in the literature are mass, and geometric- and BET specific surface area (SSA). The purpose of this study was to determine how dissolution rates normalised to these terms vary with grain size. Different size fractions of anorthite and biotite ranging from 180-150 to 20-10 mu m were dissolved in pH 3, HCl at 25 degrees C in flow through reactors under far from equilibrium conditions. Steady state dissolution rates after 5376 h (anorthite) and 4992 h (biotite) were calculated from Si concentrations and were normalised to initial- and final- mass and geometric-, geometric edge- (biotite), and BET SSA. For anorthite, rates normalised to initial- and final-BET SSA ranged from 0.33 to 2.77 X 10(-10) mol(feldspar) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 5.74 to 8.88 X 10(-10) mol(feldspar) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.11 to 1.65 mol(feldspar) g(-1) s(-1). For biotite, rates normalised to initial- and final-BET SSA ranged from 1.02 to 2.03 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric SSA ranged from 3.26 to 16.21 X 10(-12) mol(biotite) m(-2) s(-1), rates normalised to initial- and final-geometric edge SSA ranged from 59.46 to 111.32 x 10(-12) mol(biotite) m(-2) s(-1) and rates normalised to initial- and final-mass ranged from 0.81 to 6.93 X 10(-12) mol(biotite) g(-1) s(-1). For all normalising terms rates varied significantly (p <= 0.05) with grain size. The normalising terms which gave least variation in dissolution rate between grain sizes for anorthite were initial BET SSA and initial- and final-geometric SSA. This is consistent with: (1) dissolution being dominated by the slower dissolving but area dominant non-etched surfaces of the grains and, (2) the walls of etch pits and other dissolution features being relatively unreactive. These steady state normalised dissolution rates are likely to be constant with time. Normalisation to final BET SSA did not give constant ratios across grain size due to a non-uniform distribution of dissolution features. After dissolution coarser grains had a greater density of dissolution features with BET-measurable but unreactive wall surface area than the finer grains. The normalising term which gave the least variation in dissolution rates between grain sizes for biotite was initial BET SSA. Initial- and final-geometric edge SSA and final BET SSA gave the next least varied rates. The basal surfaces dissolved sufficiently rapidly to influence bulk dissolution rate and prevent geometric edge SSA normalised dissolution rates showing the least variation. Simple modelling indicated that biotite grain edges dissolved 71-132 times faster than basal surfaces. In this experiment, initial BET SSA best integrated the different areas and reactivities of the edge and basal surfaces of biotite. Steady state dissolution rates are likely to vary with time as dissolution alters the ratio of edge to basal surface area. Therefore they would be more properly termed pseudo-steady state rates, only appearing constant because the time period over which they were measured (1512 h) was less than the time period over wich they would change significantly. (c) 2006 Elsevier Inc. All rights reserved.

‘The Making of the Book’: Roy Fisher, the Circle Press and the poetics of book art

Between 1972 and 2001, the English late-modernist poet Roy Fisher provided the text for nine separate artist's books produced by Ron King at the Circle Press. Taken together, as Andrew Lambirth has written, the Fisher-King collaborations represent a sustained investigation of the various ways in which text and image can be integrated, breaking the mould of the codex or folio edition, and turning the book into a sculptural object. From the three-dimensional pop-up designs of Bluebeard's Castle (1973), each representing a part of the edifice (the portcullis, the armoury and so on), to ‘alphabet books’ such as The Half-Year Letters (1983), held in an ingenious french-folded concertina which can be stretched to over a metre long or compacted to a pocketbook, the project of these art books is to complicate their own bibliographic codes, and rethink what a book can be. Their folds and reduplications give a material form to the processes by which meanings are produced: from the discovery, in Top Down, Bottom Up (1990), of how to draw on both sides of the page at the same time, to the developments of The Left-Handed Punch (1987) and Anansi Company (1992), where the book becomes first a four-dimensional theatre space, in which a new version of Punch and Judy is played out by twelve articulated puppets, and then a location for characters that are self-contained and removable, in the form of thirteen hand-made wire and card rod-puppets. Finally, in Tabernacle (2001), a seven-drawer black wooden cabinet that stands foursquare like a sculpture (and sells to galleries and collectors for over three thousand pounds), the conception of the book and the material history of print are fully undone and reconstituted. This paper analyses how the King-Fisher art books work out their radically material poetics of the book; how their emphasis on collaboration, between artist and poet, image and text, and also book and reader – the construction of meaning becoming a co-implicated process – continuously challenges hierarchies and fixities in our conception of authorship; and how they re-think the status of poetic text and the construction of the book as material object.

Open cluster survival within the solar circle: Teutsch 145 and Teutsch 146 star

Teutsch 145 and Teutsch 146 are shown to be open clusters (OCs) orbiting well inside the solar circle, a region where several dynamical processes combine to disrupt most OCs on a time-scale of a few 108 yr. BVI photometry from the GALILEO telescope is used to investigate the nature and derive the fundamental and structural parameters of the optically faint and poorly known OCs Teutsch 145 and 146. These parameters are computed by means of field-star-decontaminated colour-magnitude diagrams and stellar radial density profiles (RDPs). Cluster mass estimates are made based on the intrinsic mass functions (MFs). We derive the ages 200+100(-50) and 400 +/- 100 Myr, and the distances from the Sun d(circle dot) = 2.7 +/- 0.3 and 3.8 +/- 0.2 kpc, respectively, for Teutsch 145 and 146. Their integrated apparent and absolute magnitudes are m(V) approximate to 12.4 and 13.3 and M(V) approximate to -5.6 and -5.3. The MFs (detected for stars with m greater than or similar to 1 M(circle dot)) have slopes similar to Salpeter`s initial mass function. Extrapolated to the H-burning limit, the MFs would produce total stellar masses of similar to 1400 M(circle dot), typical of relatively massive OCs. Both OCs are located deep into the inner Galaxy and close to the Crux-Scutum arm. Since cluster-disruption processes are important, their primordial masses must have been higher than the present-day values. The conspicuous stellar density excess observed in the innermost bin of both RDPs might reflect the dynamical effects induced by a few 108 yr of external tidal stress.

TRANSITIVE CIRCLE EXCHANGE TRANSFORMATIONS WITH FLIPS

We study the existence of transit we exchange transformations with flips defined on the unit circle S(1). We provide a complete answer to the question of whether there exists a transitive exchange transformation of S(1) defined on a subintervals and having f flips.

PARALLEL ALGORITHMS FOR MAXIMAL CLIQUES IN CIRCLE GRAPHS AND UNRESTRICTED DEPTH SEARCH

We present parallel algorithms on the BSP/CGM model, with p processors, to count and generate all the maximal cliques of a circle graph with n vertices and m edges. To count the number of all the maximal cliques, without actually generating them, our algorithm requires O(log p) communication rounds with O(nm/p) local computation time. We also present an algorithm to generate the first maximal clique in O(log p) communication rounds with O(nm/p) local computation, and to generate each one of the subsequent maximal cliques this algorithm requires O(log p) communication rounds with O(m/p) local computation. The maximal cliques generation algorithm is based on generating all maximal paths in a directed acyclic graph, and we present an algorithm for this problem that uses O(log p) communication rounds with O(m/p) local computation for each maximal path. We also show that the presented algorithms can be extended to the CREW PRAM model.

Minimizing the object dimensions in circle and sphere packing problems

Given a fixed set of identical or different-sized circular items, the problem we deal with consists on finding the smallest object within which the items can be packed. Circular, triangular, squared, rectangular and also strip objects are considered. Moreover, 2D and 3D problems are treated. Twice-differentiable models for all these problems are presented. A strategy to reduce the complexity of evaluating the models is employed and, as a consequence, instances with a large number of items can be considered. Numerical experiments show the flexibility and reliability of the new unified approach. (C) 2007 Elsevier Ltd. All rights reserved.

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

Maximizing measures for endomorphisms of the circle

We study a given fixed continuous function phi : S(1) -> R and an endomorphism f : S(1)-> S(1), whose f-invariant probability measures maximize integral phi d mu. We prove that the set of endomorphisms having a f maximizing invariant measure supported on a periodic orbit is C(0) dense.

On isomorphism classes of C(2(m) circle plus [0, alpha]) spaces

We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces 2(m) circle plus [0, alpha], the topological sums of Cantor cubes 2(m), with m smaller than the first sequential cardinal, and intervals of ordinal numbers [0, alpha]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of C(2(m) circle plus [0, alpha]) spaces with m >= N(0) and alpha >= omega(1) are the trivial ones. This result leads to some elementary questions on large cardinals.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

A full family of multimodal maps on the circle

We exhibit a family of trigonometric polynomials inducing a family of 2m-multimodal maps on the circle which contains all relevant dynamical behavior.

Spaces of compact operators on C(2(m) circle plus [0, alpha]) spaces

We classify up to isomorphism the spaces of compact operators K(E, F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2(m) circle plus [0, alpha], the topological sum of Cantor cubes 2(m) and the intervals of ordinal numbers [0, alpha]. More precisely, we prove that if 2(m) and aleph(gamma) are not real-valued measurable cardinals and n >= aleph(0) is not sequential cardinal, then for every ordinals xi, eta, lambda and mu with xi >= omega(1), eta >= omega(1), lambda = mu < omega or lambda, mu is an element of [omega(gamma), omega(gamma+1)[, the following statements are equivalent: (a) K(C(2(m) circle plus [0, lambda]), C(2(n) circle plus [0, xi])) and K(C(2(m) circle plus [0, mu]), C(2(n) circle plus [0, eta]) are isomorphic. (b) Either C([0, xi]) is isomorphic to C([0, eta] or C([0, xi]) is isomorphic to C([0, alpha p]) and C([0, eta]) is isomorphic to C([0,alpha q]) for some regular cardinal alpha and finite ordinals p not equal q. Thus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators. (C) 2010 Elsevier Inc. All rights reserved.