Diffusive Equilibrium Research Articles

Combined Gel Probes for the In Situ Determination of Dissolved Reactive Phosphorus in Porewaters and Characterization of Sediment Reactivity

Diffusive equilibrium in thin films (DET) and diffusive gradients in thin films (DGT) were applied in situ to obtain high spatial resolution dissolved reactive phosphorus (DRP) sediment porewater profiles in two lagoons of the Gippsland Lakes (SE Australia) during summer. Although the DRP depth profiles were different in each lake, highlighting the sensitivity of DRP to the redox state of the sediment spatial DRP variations obtained from DET and DGT showed striking similarities with depth in each lake. Comparison of DRP concentrations obtained from DGT and DET allows an assessment of the reactivity of the sediment. A dynamic numerical model of DGT-induced flux in sediments (DIFS) quantified reactivity kinetics. Sediment response time (Tc) related to sedimentary phosphorus resupply resulting from DGT-induced lowering of the porewater DRP concentration was calculated. Values of Tc ranged from 4128 to 183 400 s and from 55 to 149 400 s for Lakes Victoria and Wellington, respectively. These results indicate the limited capacity of the sediment to quickly resupply DRP to the porewater, especially in surface sediment which was always characterized by the highest Tc. Adsorption and desorption rate constants were also calculated from DIFS with values ranging from 2 x 10(-3) to 2 x 10(-2) day(-1) and from 0.3 to 21 day(-1) for Lake Victoria and from 2 x 10(-4) to 0.8 day(-1) and from 0.6 to 1558 day(-1) for Lake Wellington, respectively. Diffusive fluxes estimated from the in situ DRP gradient at the sediment-water interface by DET were 558 and 1.2 micromol m(-2) day(-1) in lakes Victoria and Wellington, respectively. Despite only a single measurement, these fluxes highlight a substantial contribution of P from the sediment to the water column in summer for Lake Victoria which is likely to contribute to the recurring blooms of blue-green algae. These calculated fluxes obtained with minimal sediment disturbance and high spatial resolution were substantially different (by a factor of 6-180) from other reported values using more conventional quantitative assessments such as diffusive fluxes (from core slicing) and benthic chambers.

Radiative levitation: a likely explanation for pulsations in the unique hot O subdwarf star SDSS J160043.6+074802.9

Context: SDSS J160043.6+074802.9 (J1600+0748 for short) is the only hot sdO star for which unambiguous multiperiodic luminosity variations have been reported so far. These rapid variations, with periods in the range from ~60 s to ~120 s, are best qualitatively explained in terms of pulsational instabilities, but the exact nature of the driving mechanism has remained a puzzle. Aims: Our primary goal is to examine quantitatively how pulsation modes can be excited in an object such as J1600+0748. Given the failure of uniform-metallicity models as well documented in the recent Ph.D. thesis of C. Rodriguez-Lopez, we consider the effects of radiative levitation on iron as a means to boost the efficiency of the opacity-driving mechanism in models of J1600+0748. Methods: We combine high sensitivity time-averaged optical spectroscopy and full nonadiabatic calculations to carry out our study. In the first instance, this is used to estimate the location of J1600+0748 in the log g-T_eff plane. Given this essential input, we pulsate stellar models consistent with these atmospheric parameters. We construct both uniform-metallicity models and structures in which the iron abundance is specified by the condition of diffusive equilibrium between gravitational settling and radiative levitation. Results: On the basis of NTLE H/He synthetic spectra, we find that the target star has the following atmospheric parameters: log g = 5.93 ± 0.11, T_eff = 71 070 ± 2725 K, and log N(He)/N(H) = -0.85 ± 0.08. This takes into account our deconvolution of the spectrum of J1600+0748 as it is polluted by the light of a main sequence companion. We confirm that uniform-metallicity stellar models with Z in the range from 0.02 to 0.10 cannot excite pulsation modes of the kind observed. On the other hand, we find that the inclusion of radiative levitation, as we implemented it, leads to pulsational instabilities in a period range that overlaps with, although it is narrower than, the observed range in J1600+0748. The excited modes correspond to low-order, low-degree p-modes. Conclusions: We infer that radiative levitation is a likely essential ingredient in the excitation physics at work in J1600+0748.

Assessing sulfate reduction and methane cycling in a high salinity pore water system in the northern Gulf of Mexico

Pore waters extracted from 18 piston cores obtained on and near a salt-cored bathymetric high in Keathley Canyon lease block 151 in the northern Gulf of Mexico contain elevated concentrations of chloride (up to 838 mM) and have pore water chemical concentration profiles that exhibit extensive departures (concavity) from steady-state (linear) diffusive equilibrium with depth. Minimum δ 13C dissolved inorganic carbon (DIC) values of −55.9‰ to −64.8‰ at the sulfate–methane transition (SMT) strongly suggest active anaerobic oxidation of methane (AOM) throughout the study region. However, the nonlinear pore water chemistry-depth profiles make it impossible to determine the vertical extent of active AOM or the potential role of alternate sulfate reduction pathways. Here we utilize the conservative (non-reactive) nature of dissolved chloride to differentiate the effects of biogeochemical activity (e.g., AOM and/or organoclastic sulfate reduction) relative to physical mixing in high salinity Keathley Canyon sediments. In most cases, the DIC and sulfate concentrations in pore waters are consistent with a conservative mixing model that uses chloride concentrations at the seafloor and the SMT as endmembers. Conservative mixing of pore water constituents implies that an undetermined physical process is primarily responsible for the nonlinearity of the pore water-depth profiles. In limited cases where the sulfate and DIC concentrations deviated from conservative mixing between the seafloor and SMT, the δ 13C-DIC mixing diagrams suggest that the excess DIC is produced from a 13C-depleted source that could only be accounted for by microbial methane, the dominant form of methane identified during this study. We conclude that AOM is the most prevalent sink for sulfate and that it occurs primarily at the SMT at this Keathley Canyon site.

Stability of a sonoluminescing nitrogen bubble in chilled water

Bubbles are levitated in a resonator driven by an ultrasound wave. Their highly nonlinear oscillations feature a strong collapse, where fluidlike densities and temperatures of several thousand degrees Kelvin are reached, resulting in the emission of ultrashort light pulses. Previous experiments and theories explained the observed stable bubble dynamic and emission on long time scales with the requirement of a noble gas. Recent experiments reveal stable sonoluminescent emission of nitrogen bubbles in chilled water without the presence of a noble gas. Numerical calculations show that a diffusive and dissociative equilibrium can be reached when the temperature within a nitrogen bubble is limited due to the presence of water vapor. Calculated stability lines agree with published experimental results. The results show that noble-gas-free stable single bubble sonoluminescence of nitrogen bubbles is possible.

Simulations of Surface Forces in Polyelectrolyte Solutions

We have simulated interactions between charged surfaces in the presence of oppositely charged polyelectrolytes by coupling perturbations in the isotension ensemble to a free energy variance minimization scheme. For polymeric systems, this method completely outperforms configurationally biased versions of grand canonical simulations. Proper diffusive equilibrium between bulk and slit has been established for polyelectrolytes with up to 60 monomers per chain. A consequence of imposing diffusive equilibrium conditions, in contrast to previous more restricted models, is the possibility of surface charge inversion; ion-ion correlation and the cooperativity of monomer adsorption drive the formation of a polyion layer close to the surface, that overcompensates the nominal surface charge. This is observed even at modest surface charge densities, and leads to a build up of a long ranged electrostatic barrier. In addition, the onset of charge inversion requires very low bulk polymer densities. Due to screening effects, this leads to a higher and more long-ranged free energy barrier at low, compared to high, bulk densities. Oscillatory forces, reminiscent of those found in simple hard sphere systems, are resolved in the high concentration regime. As a consequence of a second surface charge inversion, the system "stratifies" to form a stable polyelectrolyte layer in the central part of the slit, stabilized by the adsorbed surface layers.

Buffered Diffusion around a Spherical Proton Pumping Cell: A Theoretical Analysis

H + ions are a substrate of many active and passive membrane transporters in all cells. Absolute proton fluxes are often quantified using intracellular pH sensitive microelectrodes or pH sensitive dyes. These measurements, however, rely on a priori estimates of the intracellular buffer capacity and on the assumption of diffusive equilibrium inside the cell. Here, assuming local equilibrium of protons with a single mobile buffer, we model the diffusion of H + in the extracellular medium around an H + pumping cell to estimate the expected pH changes as a function of time, distance from the cell, extracellular buffer capacity, and the absolute proton flux across the membrane. In particular, using accurate numerical simulation, we gauge the range of validity of an explicit, analytical solution of the linearized, nonstationary diffusion equation. Our results provide a framework to quantify the absolute membrane proton flux, if spatiotemporal information about the extracellular pH change is available, e.g., using imaging of pH dependent fluorescent dyes.

Thermal structure and dynamics of the Martian upper atmosphere at solar minimum from global circulation model simulations

Abstract. Simulations of the Martian upper atmosphere have been produced from a self-consistent three-dimensional numerical model of the Martian thermosphere and ionosphere, called MarTIM. It covers an altitude range of 60 km to the upper thermosphere, usually at least 250 km altitude. A radiation scheme is included that allows the main sources of energy input, EUV/UV and IR absorption by CO2 and CO, to be calculated. CO2, N2 and O are treated as the major gases in MarTIM, and are mutually diffused (though neutral chemistry is ignored). The densities of other species (the minor gases), CO, Ar, O2 and NO, are based on diffusive equilibrium above the turbopause. The ionosphere is calculated from a simple photoionisation and charge exchange routine though in this paper we will only consider the thermal and dynamic structure of the neutral atmosphere at solar minimum conditions. The semi-diurnal (2,2) migrating tide, introduced at MarTIM's lower boundary, affects the dynamics up to 130 km. The Mars Climate Database (Lewis et al., 2001) can be used as a lower boundary in MarTIM. The effect of this is to increase wind speeds in the thermosphere and to produce small-scale structures throughout the thermosphere. Temperature profiles are in good agreement with Pathfinder results. Wind velocities are slightly lower compared to analysis of MGS accelerometer data (Withers, 2003). The novel step-by-step approach of adding in new features to MarTIM has resulted in further understanding of the drivers of the Martian thermosphere.

Measurement of soluble reactive phosphorus concentration profiles and fluxes in river-bed sediments using DET gel probes

DET (diffusive equilibrium in thin films) gel probes were used for sampling river-bed sediment porewaters, to characterise in situ soluble reactive phosphorus (SRP) concentration profiles and fluxes. DET probes were deployed in three contrasting rural streams: (1) a headwater ‘pristine’ stream, with minimal P inputs from low intensity grassland and no point sources, (2) an intensively cultivated arable catchment, and (3) a stream subject to high P loadings from sewage effluent and intensive arable farming. The DET results showed highly enriched porewater SRP concentrations of between ca. 400 and 5000 ug-P/1 in the sewage-impacted stream. In contrast, the arable and pristine streams had porewater SRP concentrations <70 ug-P/1 and <20 ug-P/1, respectively. Porewater SRP concentration profiles in both the sewage-impacted and arable-impacted streams showed well-defined vertical structure, indicating internal sources and sinks of SRP within the sediment. However, there was little variability in porewater SRP concentrations in the pristine stream. The DET porewater profiles indicated net diffusion of SRP (a) from the overlying river water into the surface sediment and (b) from subsurface sediment upwards towards the sediment–water interface. A mass balance for the sewage-impacted site showed that the influx of SRP into the surface sediments from the overlying river water was small (ca. 1% of the daily river SRP load). The DET results indicated that, in the arable and sewage-impacted streams, the surface ‘cap’ of fine sediment may play an important role in inhibiting upward movement of SRP from subsurface porewaters into the overlying river water, under steady-state, low-flow conditions.

Interactions between Charged Surfaces Immersed in a Polyelectrolyte Solution

With grand canonical simulations invoking a configurationally weighted scheme, we have calculated interactions between charged surfaces immersed in a polyelectrolyte solution. In contrast to previous simulations of such systems, we have imposed full equilibrium conditions (i.e., we have included diffusive equilibrium with a bulk solution). This has a profound impact on the resulting interactions: even at modest surface charge densities, oppositely charged chains will, at sufficiently large separations, adsorb strongly enough to overcompensate for the nominal surface charge. This phenomenon, known as charge inversion, generates a double-layer repulsion and a free-energy barrier. Simpler canonical approaches, where the chains are assumed to neutralize the surfaces perfectly, will not capture this stabilizing barrier. The barrier height increases with the length of the polyions. Interestingly enough, the separation at which the repulsion becomes attractive is independent of chain length. The short chains here are unable to reach across from one surface to the other. We therefore conclude that the transition to an attractive regime is not provided by the formation of such "intersurface" bridges. With long chains and at large separations, charge inversion displays decaying oscillatory behavior (i.e., the apparent surface charge switches sign once again). This is due to polyion packing effects. We have also investigated responses to salt addition and changes in polyelectrolyte concentration. Our results are in qualitative and semiquantitative agreement with experimental findings, although it should be noted that our chains are comparatively short, and the experimental surface charge density is poorly established.

Insights into redox cycling of sulfur and iron in peatlands using high-resolution diffusive equilibrium thin film (DET) gel probe sampling

High spatial resolution vertical profiles of pore-water chemistry have been obtained for a peatland using diffusive equilibrium in thin films (DET) gel probes. Comparison of DET pore-water data with more traditional depth-specific sampling shows good agreement and the DET profiling method is less invasive and less likely to induce mixing of pore-waters. Chloride mass balances as water tables fell in the early summer indicate that evaporative concentration dominates and there is negligible lateral flow in the peat. Lack of lateral flow allows element budgets for the same site at different times to be compared. The high spatial resolution of sampling also enables gradients to be observed that permit calculations of vertical fluxes. Sulfate concentrations fall at two sites with net rates of 1.5 and 5.0nmol cm − 3 day − 1, likely due to a dominance of bacterial sulfate reduction, while a third site showed a net gain in sulfate due to oxidation of sulfur over the study period at an average rate of 3.4nmol cm − 3 day − 1. Behaviour of iron is closely coupled to that of sulfur; there is net removal of iron at the two sites where sulfate reduction dominates and addition of iron where oxidation dominates. The profiles demonstrate that, in addition to strong vertical redox related chemical changes, there is significant spatial heterogeneity. Whilst overall there is evidence for net reduction of sulfate within the peatland pore-waters, this can be reversed, at least temporarily, during periods of drought when sulfide oxidation with resulting acid production predominates.

Quiescence as a mechanism for cyclical hypoxia and acidosis

Tumour tissue characteristically experiences fluctuations in substrate supply. This unstable microenvironment drives constitutive metabolic changes within cellular populations and, ultimately, leads to a more aggressive phenotype. Previously, variations in substrate levels were assumed to occur through oscillations in the haemodynamics of nearby and distant blood vessels. In this paper we examine an alternative hypothesis, that cycles of metabolite concentrations are also driven by cycles of cellular quiescence and proliferation. Using a mathematical modelling approach, we show that the interdependence between cell cycle and the microenvironment will induce typical cycles with the period of order hours in tumour acidity and oxygenation. As a corollary, this means that the standard assumption of metabolites entering diffusive equilibrium around the tumour is not valid; instead temporal dynamics must be considered.

High resolution profiles of thallium, manganese and iron assessed by DET and DGT techniques in riverine sediment pore waters

High resolution profiles of Mn, Tl and Fe concentrations have been assessed in the pore waters of river Leie sediments at Warneton and Menen (at the border of Belgium and France) by DET (Diffusive Equilibrium in Thin Films) and DGT (Diffusive Gradients in Thin Films) techniques. The oxidized, solid Mn (IV), Tl (III) and Fe (III) compounds were reduced in the suboxic (+255 to -20 mV versus Standard Hydrogen Electrode (SHE)) riverine sediments and since these reduced species are much more soluble also they are released into the pore waters. The highest DET (total dissolved) concentrations of Fe (76 mg l(-1)), Mn (2 mg l(-1)) were observed at the station of Menen, while Tl maxima differed only slightly between the 3 surveys (21 to 27 microg l(-1)). The average ratios of Fe/Mn/Tl in the pore waters at the 3 sampling stations are fairly constant for both the DET and DGT samplings. However, the results indicate that compared to Fe and Tl a greater proportion of the Mn measured by DET is accumulated by DGT, reflecting the ready supply of Mn from solid phase to solution.

Neutral density response to the solar flares of October and November, 2003

In this paper we report the first measurements of the thermosphere neutral density response to a solar EUV flare. Two X17 flares are considered: The first on 28 October, 2003, and the second on 4 November, 2003. The density measurements are provided by accelerometers on the GRACE and CHAMP satellites near 490 km and 400 km, respectively. X‐ray fluxes are provided by GOES‐12, and EUV fluxes by the SEE instrument on TIMED. The thermosphere density increases associated with the first flare are about 50–60% at low to mid‐latitudes. The time to peak response is 72 ± 47 minutes with respect to the peak EUV flux emitted by the flare, while the recovery to prior quiescent levels takes nearly 12 hours with an approximate decay time constant of 8 hours. The response to the second flare is about 35–45% with similar response and recovery times. The above density enhancements correspond to exosphere temperature increases of about 125–175 K and 100–125 K, respectively. These results provide new opportunities for the testing and validation of models over time scales similar to those of basic mechanisms governing the thermosphere response, such as thermal conduction, radiative cooling, and restoration of diffusive equilibrium.

First whistler observed in the magnetosphere of Saturn

[1] This paper describes and analyzes the first whistler observed in the magnetosphere of Saturn. The whistler was detected by the Radio and Plasma Wave Science (RPWS) instrument on the Cassini spacecraft during the inbound pass on October 28, 2004, at a radial distance of 6.18 RS (Saturn radii). Based on the measured dispersion, a travel time computation shows that the whistler originated from lightning in the northern hemisphere of Saturn. Using a simple centrifugal potential model for the plasma distribution along the magnetic field line, we have determined the scale height and fractional concentrations of water group ions and protons that give the best fit to the observed dispersion. In addition, a more complex diffusive equilibrium model was also analyzed. The inferred electron density profiles for the two models are very similar. Representative scale heights and equatorial ion fractional concentrations that provided good fits to the dispersion of the whistler were found to be = 0.89 RS and = 0.7 for water group ions, and = 2.67 RS and = 0.3 for protons.

Technique for determining midlatitude O+/H+ transition heights from topside ionograms

The midlatitude O+/H+ transition height (where the H+ and O+ number densities are equal) is of importance because it is where the topside altitude distribution of the dominant ions transitions from the ionospheric F region into the plasmasphere, which is considered the inner region of the magnetosphere. This transition height can be determined by fitting ionospheric topside sounder–derived electron density (Ne) profiles to analytical H+ and O+ functions. There are four variables involved in this process, two involving ion number densities and two involving the electron temperature Te. The density variables are the H+ density at the height of the satellite and the O+ density at the base of the profile (taken as 400 km). The temperature variables have been treated using different approaches. In an earlier investigation, diffusive equilibrium ion density profiles, based on an earlier Titheridge height‐varying electron temperature function, were used to fit the Ne profiles in which the electron temperature Te and the Te altitude gradient at a base height of 400 km, denoted by T0 and G0, respectively, were free variables. In the present work, T0 and G0 are constrained by using a later Titheridge empirical temperature model. Alternatively, when in situ Langmuir probe Te determinations are available, the problem reduces to one with only one free temperature variable. All three of these approaches, using Titheridge's revised height‐varying electron temperature function, are applied to a sequence of midlatitude ISIS 2–derived Ne profiles obtained during a period of prolonged high magnetic activity. The results indicate that in the inner plasmasphere, where the transition height is slowly varying, the approach based on the two free Te parameters (T0 and G0) agrees well with the one using the Langmuir probe input. In the region where the transition height is rapidly increasing, however, the approach based on the empirical temperature model produced the most consistent results for the O+/H+ transition height.

Fe isotope fractionation in iron meteorites: New insights into metal-sulphide segregation and planetary accretion

Magmatic iron meteorites are considered to be remnants of the metallic cores of differentiated asteroids, and may be used as analogues of planetary core formation. The Fe isotope compositions (δ57/54Fe) of metal fractions separated from magmatic and non-magmatic iron meteorites span a total range of 0.39‰, with the δ57/54Fe values of metal fractions separated from the IIAB irons (δ57/54Fe 0.12 to 0.32‰) being significantly heavier than those from the IIIAB (δ57/54Fe 0.01 to 0.15‰), IVA (δ57/54Fe − 0.07 to 0.17‰) and IVB groups (δ57/54Fe 0.06 to 0.14‰). The δ57/54Fe values of troilites (FeS) separated from magmatic and non-magmatic irons range from − 0.60 to − 0.12‰, and are isotopically lighter than coexisting metal phases. No systematic relationships exist between metal-sulphide fractionation factor (Δ57/54FeM-FeS = δ57/54Femetal − δ57/54FeFeS) metal composition or meteorite group, however the greatest Δ57/54FeM-FeS values recorded for each group are strikingly similar: 0.79, 0.63, 0.76 and 0.74‰ for the IIAB, IIIAB, IAB and IIICD irons, respectively. Δ57/54FeM-FeS values display a positive correlation with kamacite bandwidth, i.e. the most slowly-cooled meteorites, which should be closest to diffusive equilibrium, have the greatest Δ57/54FeM-FeS values. These observations provide suggestive evidence that Fe isotopic fractionation between metal and troilite is dominated by equilibrium processes and that the maximum Δ57/54FeM-FeS value recorded (0.79 ± 0.09‰) is the best estimate of the equilibrium metal-sulphide Fe isotope fractionation factor. Mass balance models using this fractionation factor in conjunction with metal δ57/54Fe values and published Fe isotope data for pallasites can explain the relatively heavy δ57/54Fe values of IIAB metals as a function of large amounts of S in the core of the IIAB parent body, in agreement with published experimental work. However, sequestering of isotopically light Fe into the S-bearing parts of planetary cores cannot explain published differences in the average δ57/54Fe values of mafic rocks and meteorites derived from the Earth, Moon and Mars and 4-Vesta. The heavy δ57/54Fe value of the Earth's mantle relative to that of Mars and 4-Vesta may reflect isotopic fractionation due to disproportionation of ferrous iron present in the proto-Earth mantle into isotopically heavy ferric iron hosted in perovskite, which is released into the magma ocean, and isotopically light native iron, which partitions into the core. This process cannot take place at significant levels on smaller planets, such as Mars, as perovskite is only stable at pressures > 23 GPa. Interestingly, the average δ57/54Fe values of mafic terrestrial and lunar samples are very similar if the High-Ti mare basalts are excluded from the latter. If the Moon's mantle is largely derived from the impactor planet then the isotopically heavy signature of the Moon's mantle requires that the impacting planet also had a mantle with a δ57/54Fe value heavier than that of Mars or 4-Vesta, which then implies that the impactor planet must have been greater in size than Mars.

High-resolution profiles of trace metals in the pore waters of riverine sediment assessed by DET and DGT

The techniques of DET (diffusive equilibrium in thin films) and DGT (diffusive gradients in thin films) were applied to obtain high-resolution vertical profiles of trace metals in freshwater sediments. In the framework of the EU-Interreg project Stardust ( http://www.vliz.be/projects/stardust/) between France and Belgium, in which the mobility of sediment bound metals is investigated, sediment samples were collected from the Upper Scheldt River (at Helkijn, Belgium) and the Leie River (at Warneton, located at the Belgian–French border). Intra- and inter-laboratory comparisons of the gel techniques were carried out between the two laboratories involved. In general, a good agreement was observed, taking sediment heterogeneity into account. At both stations, metal pore water profiles show more or less similar tendencies although the sediment at Warneton was more anoxic than at Helkijn. A strong correlation between Fe and Co was found at Helkijn as well as at Warneton. The metal gradients at the water/sediment interface were calculated from the high resolution profiles and the conventional, low resolution profiles. Significant differences were observed.

Determination of High Resolution Pore Water Profiles of Trace Metals in Sediments of the Rupel River (Belgium) using Det (Diffusive Equilibrium in Thin Films) and DGT (Diffusive Gradients in Thin Films) Techniques

The techniques of diffusional equilibrium in thin films (DET) and diffusional gradients in thin films (DGT) were used to obtain high resolution pore water profiles of total dissolved and labile trace (mobilizable) metals in the sediments of the Rupel River, Belgium. DGT measures labile metal species in situ by immobilizing them on a resin gel after diffusion through a diffusive gel whereas for DET an equilibrium is established between the DET gel and the pore water. Concentrations of Pb and Zn obtained by DGT were in good agreement with the results obtained by centrifugation, and thus were well buffered by rapid equilibrium with the solid phase, whereas Fe, Mn and Cd were very tightly bound to the sediment phase and large differences were observed between the labile and the total metal concentrations. Cu, Zn, Co and Ni show intermediated behavior. Good correlations were found between the profiles of As and Fe and Mn and Co for DET as well as DGT showing a close link between the geochemical behavior of these elements. Cu, Zn, Pb and Cd are also influenced by the reductive mobilization of Fe and Mn oxides but are also closely linked to the bacterial degradation of organic matter in the surface sediments as to the precipitation of metal sulfides in the deeper layers.

Three‐dimensional ionospheric tomography using observation data of GPS ground receivers and ionosonde by neural network

In this paper we present a new method based on a Residual Minimization Training Neural Network (RMTNN) to reconstruct the three‐dimensional electron density distribution of the local ionosphere with high spatial resolution (about 50 km × 50 km in east/west and 30 km in altitude) using GPS and ionosonde observation data. In this method we reconstruct an approximate three‐dimensional electron density distribution as a computer tomographic image by making use of the excellent capability of a multilayer neural network to approximate an arbitrary function. For this application the network training is carried out by minimizing the squared residuals of an integral equation. We combine several additional techniques with the new method, i.e., input space discretization, use of ionosonde observation data to improve the vertical resolution, automatic estimation of the biases of the satellite and the ground receivers by using the parameter estimation method, and estimation of plasmasphere contributions to the total electron content on the basis of an assumption of diffusive equilibrium with constant scale height. Numerical experiments for the actual positions of the GPS satellites and the ground receivers are used to validate the reliability of the method. We also applied the method to the analysis of real observation data and compared the results with ionosonde observations which were not used for the network training.

Contractive Metrics for a Boltzmann Equation for Granular Gases: Diffusive Equilibria

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t → ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial datum has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L1-norm, as well as various Sobolev norms.