Point-connected rigid bodies in a topological tree

Identical equations of motion are shown to emerge for a system ofn+1 rigid bodies all interconnected byn points, each of which is common to two bodies, by means of each of the following derivation procedures, all of which employ a kinematical identity developed by Hooker and Margulies: The Hooker-Margulies/Hooker equations; Kane's quasicoordinate formulation of D'Alembert's principle; the combination of Lagrange's generalized coordinate equations and Lagrange's quasicoordinate equations; and the combination of Lagrange's generalized coordinate equations and the vector rotational equationM=H applied to the total system and resolved into a vector basis fixed in a reference body of the system. Thus the previously published Hooker-Margulies/Hooker equations are shown to be the natural result of several derivation procedures other than the Newton-Euler method originally used, provided that the central kinematical identity of the original derivation of Hooker and Margulies is employed.     

Incorporating solid solutions in reactive transport equations using a kinetic discrete-composition approach

A new approach is proposed for incorporating solid solution reactions into mass conservation equations describing reaction paths in both closed and open systems. The method is applicable to problems involving advective, dispersive, and diffusive transport in a porous medium. By representing the continuously variable solid solution composition with a discrete set of stoichiometric solids that span composition space, combined with a kinetic formulation of their rates of reaction, a self-determining spatial and temporal evolution of the solid solution concentration and composition is obtained. It is demonstrated that equilibrium of an aqueous solution with a stoichiometric solid derived from a solid solution corresponds to equilibrium of the solid solution itself if and only if equilibrium of the stoichiometric solid is stable. One advantage of this approach is that it is unnecessary to introduce any additional compositional variables to represent the solid solution. Discretization may be over the entire range of composition space, or over some subset depending on the system. A major consequence of the kinetic discrete-composition solid solution representation is that modeling solid solutions is similar to modeling pure mineral phases with the exception of a weighting factor applied to reaction rates of stoichiometric solids corresponding to a common solid solution. With this approach, precipitation leads to a discrete zonation of the solid solution that approximates the continuous variation in composition expected for the actual solid solution. The approach is demonstrated for a hypothetical ideal and non-ideal binary solid solution A_xB_1−xC for a reaction path formulation and reactive transport involving advection and diffusion.     

Semi-analytical solutions of a contaminant transport equation with nonlinear sorption in 1D

A new method to determine semi-analytical solutions of one-dimensional contaminant transport problem with nonlinear sorption is described. This method is based on operator splitting approach where the convective transport is solved exactly and the diffusive transport by finite volume method. The exact solutions for all sorption isotherms of Freundlich and Langmuir type are presented for the case of piecewise constant initial profile and zero diffusion. Very precise numerical results for transport with small diffusion can be obtained even for larger time steps (e.g., when the Courant-Friedrichs-Lewy (CFL) condition failed).     

Kinetics of Mn(II) oxidation by Leptothrix discophora SS1

The kinetics of Mn(II) oxidation by the bacterium Leptothrix discophora SS1 was investigated in this research. Cells were grown in a minimal mineral salts medium in which chemical speciation was well defined. Mn(II) oxidation was observed in a bioreactor under controlled conditions with pH, O₂, and temperature regulation. Mn(II) oxidation experiments were performed at cell concentrations between 24 mg/L and 35 mg/L, over a pH range from 6 to 8.5, between temperatures of 10°C and 40°C, over a dissolved oxygen range of 0 to 8.05 mg/L, and with L. discophora SS1 cells that were grown in the presence of Cu concentrations ranging from zero to 0.1 μM. Mn(II) oxidation rates were determined when the cultures grew to stationary phase and were found to be directly proportional to O₂ and cell concentrations over the ranges investigated. The optimum pH for Mn(II) oxidation was approximately 7.5, and the optimum temperature was 30°C. A Cu level as low as 0.02 μM was found to inhibit the growth rate and yield of L. discophora SS1 observed in shake flasks, while Cu levels between 0.02 and 0.1 μM stimulated the Mn(II) oxidation rate observed in bioreactors. An overall rate law for Mn(II) oxidation by L. discophora as a function of pH, temperature, dissolved oxygen concentration (D.O.), and Cu concentration is proposed. At circumneutral pH, the rate of biologically mediated Mn(II) oxidation is likely to exceed homogeneous abiotic Mn(II) oxidation at relatively low (≈μg/L) concentrations of Mn oxidizing bacteria.     

A decade of change in the Skidaway River estuary I. Hydrography and nutrients

The Skidaway River estuary is a tidally-dominated subtropical estuary in the southeastern USA surrounded by extensiveSpartina salt marshes. Weekly smapling at high and low tide began in 1986 for hydrography, nutrients, chlorophylla, particulate matter, and microbial and plankton biomass and composition; hydrographic and nutrient data during 1986–1996 are reported here. Salinity varied inversely with river discharge and exhibited variability at all time scales but with no long-term trend. Water temperature typically ranged over 25°C and was without apparent long-term frend. Seasonal cycles in concentrations of NO₃, NH₄, PO₄, Si(OH)₄, and DON were observed, with annual maxima generally occurring in late summer. Superimposed on seasonal cycles, all five nutrients exhibited steady increases in minimum, mean, and maximum concentrations; mean concentrations increased c. 50–150% during the decade. Nutrient concentrations were highly correlated with water temperature over the ten-year period, but weakly related to salinity and discharge. Nutrients were strongly correlated with one another, and the relative ratios among inorganic nutrients showed little long-term trend. Correlations among temperature and nutrient concentrations exhibited considerable inter-annual variability. Major spikes in organic and inorganic nutrient concentrations coincided with significant rainfall events; concentrations increased hyperbolically with rainfall. Although pristine compared to more heavily impacted waterways primarily outside the region, residential development and population density have been increasing rapidly during the past 15–20 years. Land use is apparently altering nutrient loading over the long-term (months-years), and superimposed on this are stochastic meteorological events that accelerate these changes over the short term (days-weeks).     

Probing mid-mantle heterogeneity using PKP coda waves

We investigate the utility of PKP coda waves for studying weak scattering from small-scale heterogeneity in the mid-mantle. Coda waves are potentially a useful probe of heterogeneity in the mid-mantle because they are not preferentially scattered near the CMB, as PKP precursors are, but are sensitive to scattering at all depths. PKP coda waves have not been used for this purpose historically because of interference with other late-arriving energy due to near-surface resonance and scattering. Any study of deep mantle scattering using coda waves requires the removal of near-surface effects from the data. We have analyzed 3624 recordings of PKP precursors and coda made by stations in the Incorporated Research Institutions for Seismology (IRIS) Global Seismographic Network (GSN). To study the range and time dependence of the scattered waves, we binned and stacked envelopes of the recordings. We have considered precursors that arrive within a 20 s window before PKP and coda waves in a 60 s window after PKP. The PKP scattered waves increase in amplitude rapidly with range as predicted by scattering theory. At ranges below 125°, we predict and observe essentially no scattered energy preceding PKP. Coda amplitudes at these ranges are independent of range and provide an estimate of energy due to near-surface effects that we can expect at all ranges. We use the average coda amplitude at ranges from 120 to 125° to correct coda amplitudes at other ranges. PKP coda waves show a strong dependence on time and range and are clearly influenced by scattering in the lower mantle. PKP coda waves, however, do not provide a tighter constraint on the vertical distribution of mantle heterogeneity than is provided by precursors. This is due, in part, to relatively large scatter in coda amplitudes as revealed by a resampling analysis. Modeling using Rayleigh–Born scattering theory and an exponential autocorrelation function shows that PKP coda amplitudes are not highly sensitive to the vertical distribution of heterogeneity in the mantle. To illustrate this we consider single-scattering in two extreme models of mantle heterogeneity. One allows heterogeneity just at the CMB; the other includes heterogeneity throughout the mantle. The amplitudes of precursors are tightly constrained by our stack and support our earlier conclusion that small-scale heterogeneity is uniformly distributed throughout the lower mantle. The best-fit model includes 8 km scale length heterogeneity with an rms velocity contrast throughout the mantle of 1%.