1,721,008 research outputs found
Mathematical Expression of a Global Environmental Catastrophe
No full textTwo hundred and fifty-two million years ago, life on Earth nearly vanished. So many marine animal species disappeared—more than 90 percent—that the event, known as the end-Permian extinction, qualifies as the most severe mass extinction in the geologic record. Unlike the later demise of the dinosaurs, the end-Permian extinction is not linked to a meteor impact. Yet it is unquestionably associated with major environmental change, including a strong perturbation of Earth’s carbon cycle. Recently, an additional piece of the puzzle fell into place. Massive Siberian volcanism, long thought to
coincide roughly with the extinction, is now known to have preceded it and continued beyond it.United States. National Aeronautics and Space Administration (Astrobiology Grant NNA13AA90A
Earth’s carbon cycle: A mathematical perspective
Full text linkThe carbon cycle represents metabolism at a global scale. When viewed through a mathematical lens, observational data suggest that the cycle exhibits an underlying mathematical structure. This review focuses on two types of emerging results: evidence of global dynamical coupling between life and the environment, and an understanding of the ways in which smaller-scale processes determine the strength of that coupling. Such insights are relevant not only to predicting future climate but also to understanding the long-term co-evolution of life and the environment.NASA Astrobiology Institute (NNA08CN84A)NASA Astrobiology Institute (NNA13AA90A)National Science Foundation (U.S.) (OCE-0930866)National Science Foundation (U.S.) (EAR-1338810
Impact of structured heterogeneities on reactive two-phase porous flow
No full textTwo-phase flow through heterogeneous media leads to scale-free distributions of irregularly shaped pockets of one fluid trapped within the other. Although reactions within these fluids are often modeled at the homogeneous continuum scale, there exists no current framework for upscaling from the pore scale that accounts for the complex and scale-free geometry of the bubbles. In this paper, we apply a linear-kinetics reaction-diffusion model to characterize the steady-state chemical environment inside the irregular pockets. Using a combination of theory and invasion-percolation simulations, we derive scaling laws describing the distribution of diffusion times within bubbles. We show that chemical concentrations within the bubbles are determined by the Laplace transform of the entire distribution of diffusion times from each location. This serves as a means to compute average concentrations of reactant within a bubble of unique geometry and size. Furthermore, the overall system size imposes upper bounds on the distribution of bubble sizes, thereby imposing a system-size dependence on the statistics and average concentrations. These conclusions have profound implications for continuum models of porous reactive flow, where kinetic and equilibrium parameters are often chosen from laboratory measurements made at centimeter scales.United States. Dept. of Energy. Office of Basic Energy Sciences (Award DE-AC02-05CH11231
Thresholds of catastrophe in the Earth system
No full textThe history of the Earth system is a story of change. Some changes are gradual and benign, but others, especially those associated with catastrophic mass extinction, are relatively abrupt and destructive. What sets one group apart from the other? Here, I hypothesize that perturbations of Earth's carbon cycle lead to mass extinction if they exceed either a critical rate at long time scales or a critical size at short time scales. By analyzing 31 carbon isotopic events during the past 542 million years, I identify the critical rate with a limit imposed by mass conservation. Identification of the crossover time scale separating fast from slow events then yields the critical size. The modern critical size for the marine carbon cycle is roughly similar to the mass of carbon that human activities will likely have added to the oceans by the year 2100.National Science Foundation (U.S.) (Grant EAR-1338810)United States. National Aeronautics and Space Administration (Astrobiology Grant NNA13AA90A
Random channel kinetics for reaction–diffusion systems
No full textA random channel approach is developed for reaction–diffusion processes in disordered systems. Although the starting point of our research is the kinetic study of the decay and preservation of marine organic carbon, our approach can be used for describing other disordered kinetic catalytic processes with random pathways. We consider a generic catalytic mechanism with two species: (a) a catalyst, which is continuously produced by a variable number of independent sources randomly distributed in space; this catalyst diffuses from the sources and is degrading according to a first order kinetic law; the generation, the degradation and the diffusion of the catalyst balance each other out and a stationary concentration field is generated; (b) an active species, which decays according to a second order kinetic law; the decay rate is proportional to the product of the concentrations of the catalyst and the concentration of the active species. We show that the catalyst concentration field can be represented by the sum of a random number of Yukawa-like potentials. The average value of the survival function of the active species can be expressed as a grand canonical average of a nonlinear functional of the catalyst field and can be evaluated exactly. We show that a good approximation is given by a nearest neighbor approach, where only the contribution of the closest source is taken into account for the computation of the random concentration field of the catalyst. We discuss the application of the model to the problem of decay and preservation of marine organic carbon. With minor adaptation the model can be applied to other problems of disordered kinetics, such as spatially distributed heterogeneous catalytic processes.National Science Foundation (U.S.) (Grant EAR-0420592)National Science Foundation (U.S.) (Grant CHE-0847073)NASA Astrobiology InstituteRomanian Ministry of Research and Education (CEEX Grant M1-C2-3004/2006
Path Selection in a Poisson field
No full textA criterion for path selection for channels growing in a Poisson field is presented. We invoke a generalization of the principle of local symmetry. We then use this criterion to grow channels in a confined geometry. The channel trajectories reveal a self-similar shape as they reach steady state. Analyzing their paths, we identify a cause for branching that may result in a ramified structure in which the golden ratio appears.United States. Dept. of Energy. Office of Basic Energy Sciences. Chemical Sciences, Geosciences, & Biosciences Division (Award Number FG02-99ER15004
Exact solution for the Poisson field in a semi-infinite strip
No full textThe Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips
Mechanisms for mechanical trapping of geologically sequestered carbon dioxide
Full text linkCarbon dioxide (CO[subscript 2]) sequestration in subsurface reservoirs is important for limiting atmospheric CO[subscript 2] concentrations. However, a complete physical picture able to predict the structure developing within the porous medium is lacking. We investigate theoretically reactive transport in the long-time evolution of carbon in the brine–rock environment. As CO[subscript 2] is injected into a brine–rock environment, a carbonate-rich region is created amid brine. Within the carbonate-rich region minerals dissolve and migrate from regions of high-to-low concentration, along with other dissolved carbonate species. This causes mineral precipitation at the interface between the two regions. We argue that precipitation in a small layer reduces diffusivity, and eventually causes mechanical trapping of the CO[subscript 2]. Consequently, only a small fraction of the CO[subscript 2] is converted to solid mineral; the remainder either dissolves in water or is trapped in its original form. We also study the case of a pure CO[subscript 2] bubble surrounded by brine and suggest a mechanism that may lead to a carbonate-encrusted bubble owing to structural diffusion.United States. Dept. of Energy. Office of Science (Contract DE-AC02-05CH11231 Subcontract 6896518
Carbon transit through degradation networks
Full text linkThe decay of organic matter in natural ecosystems is controlled by a network of biologically, physically, and chemically driven processes. Decomposing organic matter is often described as a continuum that transforms and degrades over a wide range of rates, but it is difficult to quantify this heterogeneity in models. Most models of carbon degradation consider a network of only a few organic matter states that transform homogeneously at a single rate. These models may fail to capture the range of residence times of carbon in the soil organic matter continuum. Here we assume that organic matter is distributed among a continuous network of states that transform with stochastic, heterogeneous kinetics. We pose and solve an inverse problem in order to identify the rates of carbon exiting the underlying degradation network (exit rates) and apply this approach to plant matter decay throughout North America. This approach provides estimates of carbon retention in the network without knowing the details of underlying state transformations. We find that the exit rates are approximately lognormal, suggesting that carbon flow through a complex degradation network can be described with just a few parameters. These results indicate that the serial and feedback processes in natural degradation networks can be well approximated by a continuum of parallel decay rates.National Science Foundation (U.S.) (Grant EAR-0420592)United States. National Aeronautics and Space Administration (Grant NNA08CN84A
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