Solving Differential Equations in R

Soetaert, Karline; Meysman, Filip J. R.; Petzoldt, Thomas

doi:10.1063/1.3498463

Cited by 223 publications

(248 citation statements)

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“…We implemented this model in R, along with the height growth and crown-rise models suggested by Valentine and Mäkelä (2005). The set of differential equations was solved with package deSolve (see Soetaert et al 2010). The solution comprises time courses of basal area, height, and crown height, as well as time-courses of cross-sectional areas at annual nodes between breast height and the tip height.…”

Section: Discussionmentioning

confidence: 99%

Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce

Valentine

Mäkelä

Green

et al. 2011

Trees

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We derive and analyze a model that relates the growth rate of cross-sectional area ('csa') at any height on the central stem of a tree to crown-length dynamics. The derivation is based, in part, on assumptions that (a) active csa on the central stem relates allometrically to the length of crown above the cross section, and (b) inactive csa is proportional to active csa within the crown. We also assume that the deactivation rate of csa beneath the crown is determined, in part, by the rate of crown rise. Integration of the growth-rate model under an additional assumptionthat total crown length is constant after stand closureprovides a simple model of annual or periodic growth of total csa that can be fit to standard growth data. Three implications of the assumptions and integration are notable: (1) total csa within the crown scales allometrically with stem length above the cross section; (2) for a special case, total csa beneath the crown scales with stem length above the cross section; more generally, csa scales with a linear combination of the stem and crown lengths; and (3) the stem beneath the crown forms to approximate a frustum of a quadratic paraboloid. Basal area data from a loblolly pine (Pinus taeda L.) spacing trial show good agreement with (1) and (2), and with an empirical model developed from the special case of (2). Data from the plots of a Norway spruce (Picea abies (L.) Karst.) thinning trial, where crown length remained approximately constant, show good agreement with (2) and the empirical model. Prediction (3) is demonstrated by simulation.

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Section: Discussionmentioning

confidence: 99%

Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce

Valentine

Mäkelä

Green

et al. 2011

Trees

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“…Meishan (Chen et al, 1991) Meishan (Hoffman et al, 1998) Meishan (Xu & Yan 1993) Meishan (Zuo et al, 2006) Meishan A (Kaiho et al, 2006) Meishan B Meishan B (Jin et al, 2000) Meishan B (Xie et al, 2007) Meishan D (Baud et al, 1989) Meishan D (Cao et al, 2002) Meishan D (Gruszczynski et al, 2003) Meishan D (Riccardi et al, 2007) Meishan Z (Gruszczynski et al, 2003) (b where D 0 is a function of temperature and salinity and has been calculated with the R package marelac (Soetaert et al, 2016). Bioturbation is implemented as two separate processes: bio-mixing and bio-irrigation (Kristensen et al, 2012) following conventional descriptions (Boudreau, 1984;Meysman et al, 2010).…”

Section: Biozonesmentioning

confidence: 99%

Latest Permian carbonate carbon isotope variability traces heterogeneous organic carbon accumulation and authigenic carbonate formation

et al. 2017

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Abstract. Bulk-carbonate carbon isotope ratios are a widely applied proxy for investigating the ancient biogeochemical carbon cycle. Temporal carbon isotope trends serve as a prime stratigraphic tool, with the inherent assumption that bulk micritic carbonate rock is a faithful geochemical recorder of the isotopic composition of seawater dissolved inorganic carbon. However, bulk-carbonate rock is also prone to incorporate diagenetic signals. The aim of the present study is to disentangle primary trends from diagenetic signals in carbon isotope records which traverse the Permian-Triassic boundary in the marine carbonate-bearing sequences of Iran and South China. By pooling newly produced and published carbon isotope data, we confirm that a global first-order trend towards depleted values exists. However, a large amount of scatter is superimposed on this geochemical record. In addition, we observe a temporal trend in the amplitude of this residual δ 13 C variability, which is reproducible for the two studied regions. We suggest that (sub-)sea-floor microbial communities and their control on calcite nucleation and ambient porewater dissolved inorganic carbon δ 13 C pose a viable mechanism to induce bulk-rock δ 13 C variability. Numerical model calculations highlight that early diagenetic carbonate rock stabilization and linked carbon isotope alteration can be controlled by organic matter supply and subsequent microbial remineralization. A major biotic decline among Late Permian bottom-dwelling organisms facilitated a spatial increase in heterogeneous organic carbon accumulation. Combined with low marine sulfate, this resulted in varying degrees of carbon isotope overprinting. A simulated time series suggests that a 50 % increase in the spatial scatter of organic carbon relative to the average, in addition to an imposed increase in the likelihood of sampling cements formed by microbial calcite nucleation to 1 out of 10 samples, is sufficient to induce the observed signal of carbon isotope variability. These findings put constraints on the application of Permian-Triassic carbon isotope chemostratigraphy based on whole-rock samples, which appears less refined than classical biozonation dating schemes. On the other hand, this signal of increased carbon isotope variability concurrent with the largest mass extinction of the Phanerozoic may proPublished by Copernicus Publications on behalf of the European Geosciences Union.

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“…Whatman cellulose sheets, which serve as biofilm support and the only source of carbon, are cut to the nearest 0.2 mm into chads of 55 mm length and 60 mm width for a total footprint area of 6600 mm 2 . Experiments are run in triplicate for all paper types: Group I (Whatman #1: CPC 13, 34, 35); Group II (Whatman #598: CPC 19,21,23); Group III (Whatman #3: CPC 17,24,25). Substrate packing inside the reactors is done such that both sides of the paper are fully exposed to the medium and to the inoculum.…”

Section: Continuous-flow Reactors and Substrate Preparationsmentioning

confidence: 99%

Mathematical modeling to validate on-line CO2 measurements as a metric for cellulolytic biofilm activity in continuous-flow bioreactors

Dumitrache

Eberl

Allen

et al. 2015

Biochemical Engineering Journal

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Solving Differential Equations in R

Cited by 223 publications

References 1 publication

Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce

Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce

Latest Permian carbonate carbon isotope variability traces heterogeneous organic carbon accumulation and authigenic carbonate formation

Mathematical modeling to validate on-line CO2 measurements as a metric for cellulolytic biofilm activity in continuous-flow bioreactors

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