849 research outputs found
Long-time evolution of sequestered CO in porous media
CO sequestration in subsurface reservoirs is important for limiting
atmospheric CO 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 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
concentration 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. Consequently, only a small
fraction of the CO 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 bubble surrounded by brine and suggest a mechanism that may
lead to a carbonate-encrusted bubble due to structural diffusion
Scaling of a slope: the erosion of tilted landscapes
We formulate a stochastic equation to model the erosion of a surface with
fixed inclination. Because the inclination imposes a preferred direction for
material transport, the problem is intrinsically anisotropic. At zeroth order,
the anisotropy manifests itself in a linear equation that predicts that the
prefactor of the surface height-height correlations depends on direction. The
first higher-order nonlinear contribution from the anisotropy is studied by
applying the dynamic renormalization group. Assuming an inhomogeneous
distribution of soil substrate that is modeled by a source of static noise, we
estimate the scaling exponents at first order in \ep-expansion. These
exponents also depend on direction. We compare these predictions with empirical
measurements made from real landscapes and find good agreement. We propose that
our anisotropic theory applies principally to small scales and that a
previously proposed isotropic theory applies principally to larger scales.
Lastly, by considering our model as a transport equation for a driven diffusive
system, we construct scaling arguments for the size distribution of erosion
``events'' or ``avalanches.'' We derive a relationship between the exponents
characterizing the surface anisotropy and the avalanche size distribution, and
indicate how this result may be used to interpret previous findings of
power-law size distributions in real submarine avalanches.Comment: 19 pages, includes 10 PS figures. J. Stat. Phys. (in press
Earth’s carbon cycle: A mathematical perspective
The 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
Stochastic equation for the erosion of inclined topography
We present a stochastic equation to model the erosion of topography with fixed inclination. The inclination causes the erosion to be anisotropic. A zero-order consequence of the anisotropy is the dependence of the prefactor of the surface height-height correlations on direction. The lowest higher-order contribution from the anisotropy is studied by applying the dynamic renormalization group. In this case, assuming an inhomogenous distribution of soil material, we find a one-loop estimate of the roughness exponents. The predicted exponents are in good agreement with new measurements made from seafloor topography.Postprint (published version
Carbon transit through degradation networks
The 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
Inverse method for estimating respiration rates from decay time series
Long-term organic matter decomposition experiments typically measure the mass lost from decaying organic matter as a function of time. These experiments can provide information about the dynamics of carbon dioxide input to the atmosphere and controls on natural respiration processes. Decay slows down with time, suggesting that organic matter is composed of components (pools) with varied lability. Yet it is unclear how the appropriate rates, sizes, and number of pools vary with organic matter type, climate, and ecosystem. To better understand these relations, it is necessary to properly extract the decay rates from decomposition data. Here we present a regularized inverse method to identify an optimally-fitting distribution of decay rates associated with a decay time series. We motivate our study by first evaluating a standard, direct inversion of the data. The direct inversion identifies a discrete distribution of decay rates, where mass is concentrated in just a small number of discrete pools. It is consistent with identifying the best fitting "multi-pool" model, without prior assumption of the number of pools. However we find these multi-pool solutions are not robust to noise and are over-parametrized. We therefore introduce a method of regularized inversion, which identifies the solution which best fits the data but not the noise. This method shows that the data are described by a continuous distribution of rates, which we find is well approximated by a lognormal distribution, and consistent with the idea that decomposition results from a continuum of processes at different rates. The ubiquity of the lognormal distribution suggest that decay may be simply described by just two parameters: a mean and a variance of log rates. We conclude by describing a procedure that estimates these two lognormal parameters from decay data. Matlab codes for all numerical methods and procedures are provided
Geometry of Valley Growth
Although amphitheater-shaped valley heads can be cut by groundwater flows
emerging from springs, recent geological evidence suggests that other processes
may also produce similar features, thus confounding the interpretations of such
valley heads on Earth and Mars. To better understand the origin of this
topographic form we combine field observations, laboratory experiments,
analysis of a high-resolution topographic map, and mathematical theory to
quantitatively characterize a class of physical phenomena that produce
amphitheater-shaped heads. The resulting geometric growth equation accurately
predicts the shape of decimeter-wide channels in laboratory experiments,
100-meter wide valleys in Florida and Idaho, and kilometer wide valleys on
Mars. We find that whenever the processes shaping a landscape favor the growth
of sharply protruding features, channels develop amphitheater-shaped heads with
an aspect ratio of pi
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