We introduce a lattice Boltzmann model for simulating immiscible binary fluids in two dimensions. The model, based on the Boltzmann equation of lattice-gas hydrodynamics, incorporates features of a previously introduced discrete immiscible lattice-gas model. A theoretical value of the surface-tension coefficient is derived and found to be in excellent agreement with values obtained from simulations. The model serves as a numerical method for the simulation of immiscible twophase flow; a preliminary application illustrates a simulation of flow in a two-dimensional microscopic model of a porous medium. Extension of the model to three dimensions appears straightforward.

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The end-Permian mass extinction was the most severe biodiversity crisis in Earth history. To better constrain the timing, and ultimately the causes of this event, we collected a suite of geochronologic, isotopic, and biostratigraphic data on several well-preserved sedimentary sections in South China. High-precision U-Pb dating reveals that the extinction peak occurred just before 252.28 ± 0.08 million years ago, after a decline of 2 per mil (‰) in δ(13)C over 90,000 years, and coincided with a δ(13)C excursion of -5‰ that is estimated to have lasted ≤20,000 years. The extinction interval was less than 200,000 years and synchronous in marine and terrestrial realms; associated charcoal-rich and soot-bearing layers indicate widespread wildfires on land. A massive release of thermogenic carbon dioxide and/or methane may have caused the catastrophic extinction.

The existence of unusually large fluctuations in the Neoproterozoic (1,000 -543 million years ago) carbon-isotopic record implies strong perturbations to the Earth's carbon cycle. To analyze these fluctuations, we examine records of both the isotopic content of carbonate carbon and the fractionation between carbonate and marine organic carbon. Together, these are inconsistent with conventional, steady-state models of the carbon cycle. The records can be well understood, however, as deriving from the nonsteady dynamics of two reactive pools of carbon. The lack of a steady state is traced to an unusually large oceanic reservoir of organic carbon. We suggest that the most significant of the Neoproterozoic negative carbon-isotopic excursions resulted from increased remineralization of this reservoir. The terminal event, at the ProterozoicCambrian boundary, signals the final diminution of the reservoir, a process that was likely initiated by evolutionary innovations that increased export of organic matter to the deep sea.T he coevolution of the biosphere and geosphere is reflected in large part by changes in the long-term carbon cycle (1). Past changes within the cycle are recorded in the isotopic content of carbonate and organic carbon buried in ancient sediments (2). Extraordinarily large fluctuations occur in the Neoproterozoic [1,000-543 million years ago (Ma)] carbon-isotopic record both immediately preceding the Cambrian diversification of complex animal life (3-5) and in the Ϸ200 million years before it (6). There is much interest in determining not only the cause of these isotopic events (3-9) but how, if at all, they are related to early animal evolution (10).Here we analyze a significant portion of the Neoproterozoic isotopic record by portraying it as a dynamical trajectory in a two-dimensional space indexed by the isotopic content of carbonate carbon and the fractionation between carbonate and marine organic carbon. This depiction, analogous to the construction of phase portraits in dynamical systems theory (11), provides specific predictions for a carbon cycle evolving quasistatically in a succession of steady states. We find that the Cenozoic portion (0-65 Ma) of the carbon-isotopic record satisfies these predictions; however, the Neoproterozoic record does not.The dynamics of a system with two sizeable and isotopically distinct pools of reactive carbon suffice to explain the Neoproterozoic records. Then as now one pool was oceanic and atmospheric CO 2 . Here we show that the other was probably oceanic organic carbon. The isotopic data indicate that this reservoir was large and that its average properties changed slowly. However, fluctuations in its size would have led to major variations in the isotopic record. Moreover, even if the size of the organic reservoir had been perfectly constant, changes in the fractionation associated with organic production would have led to isotopic fluctuations much greater than those predicted by steady-state theory.The fluctuations of greatest interest are those associ...

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Theories of scaling apply wherever similarity exists across many scales. This similarity may be found in geometry and in dynamical processes. Universality arises when the qualitative character of a system is sufficient to quantitatively predict its essential features, such as the exponents that characterize scaling laws. Within geomorphology, two areas where the concepts of scaling and universality have found application are the geometry of river networks and the statistical structure of topography. We begin this review with a pedagogical presentation of scaling and universality. We then describe recent progress made in applying these ideas to networks and topography. This overview leads to a synthesis that attempts a classification of surface and network properties based on generic mechanisms and geometric constraints. We also briefly review how scaling and universality have been applied to related problems in sedimentology—specifically, the origin of stromatolites and the relation of the statistical properties of submarine-canyon topography to the size distribution of turbidite deposits. Throughout the review, our intention is to elucidate not only the problems that can be solved using these concepts, but also those that cannot.

The balance between photosynthetic organic carbon production and respiration controls atmospheric composition and climate 1,2. The majority of organic carbon is respired back to carbon dioxide in the biosphere, but a small fraction escapes remineralization and is preserved over geologic timescales 3. By removing reduced carbon from Earth's surface, this sequestration process promotes atmospheric oxygen accumulation 2 and carbon dioxide removal 1. Two major mechanisms have been proposed to explain organic carbon preservation: selective preservation of biochemically unreactive compounds 4,5 and protection resulting from interactions with a mineral matrix 6,7. While both mechanisms can play a role across a range of environments and timescales, their global relative importance on 10 3-to 10 5-year timescales remains uncertain 4. Here we present a global dataset of the distributions of organic carbon activation energy and corresponding radiocarbon ages in soils, sediments, and dissolved organic carbon; we find that activation energy distributions broaden over time in all mineral-containing samples. This result requires increasing bondstrength diversity, consistent with the formation of organo-mineral bonds 8 but inconsistent with selective preservation. Radiocarbon ages further reveal that high-energy, mineralbound organic carbon persists for millennia relative to low-energy, unbound organic carbon. Our results provide globally coherent evidence for the proposed 7 importance of mineral protection in promoting organic carbon preservation. We suggest that similar studies of bond-strength diversity in ancient sediments may elucidate how and why organic carbon preservation-and thus atmospheric composition and climate-has varied over geologic time. Two classes of mechanisms-selectivity and protection-have been proposed to explain why some organic carbon (OC) escapes remineralization in soils and sediments 4-7. Biochemical selectivity hypotheses state that intrinsically bioavailable compounds such as sugars and amino acids are rapidly respired, whereas "recalcitrant" (macro)molecules such as lignin are selectively preserved due to their low energy yield, large size, and/or a lack of enzymes that can decompose them 4,5. Selective preservation has been extensively documented in dissolved OC (DOC) 9 , decaying woody tissue 10 , and sapropel sediments containing almost exclusively organic matter 5. In contrast, protection hypotheses state that particles shield OC from respiration regardless of intrinsic recalcitrance, potentially due to occlusion within pore spaces that are inaccessible to microbes and their extracellular enzymes 4,8,11-14. Specifically, protection often involves inspiration was always invaluable. We thank the National Ocean Sciences Accelerator Mass Spectrometer staff, especially A

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