Spatial Distribution Of Solutes Research Articles

Radiation-induced segregation at grain boundaries of alloy 800H: Experimentally-informed atomistic simulations

The irradiation of alloys can alter the spatial distribution of solute and impurity elements. The redistribution of alloying elements can cause local chemical changes at surfaces and interfaces, which may degrade the mechanical and chemical properties of alloys. In this paper, a combination of microscopic experiments and atomistic simulations are employed to study the effect of irradiation damage on radiation-induced segregation (RIS) at grain boundaries (GBs) of the alloy 800H. The grain boundary character distribution in alloy 800H was determined by electron backscatter diffraction, and proton-irradiation-induced defects were identified by transmission electron microscopy. The experimentally-observed GBs were recreated in atomistic simulations to further study their atomistic structure, grain boundary energies, and local element concentration. The effects of radiation-induced defects on the redistribution of alloying elements at various GBs were investigated. A mechanism is proposed to explain the local chemical changes at GBs after the interaction with radiation-induced dislocation loops, which is of importance to nuclear reactor performance.

Combination of Hyperspectral and Machine Learning to Invert Soil Electrical Conductivity

An accurate estimation of soil electrical conductivity (EC) using hyperspectral techniques is of great significance for understanding the spatial distribution of solutes and soil salinization. Although spectral transformation has been widely used in data pre-processing, the performance of different pre-processing techniques (or combination methods) on different models of the same data set is still ambiguous. Moreover, extremely randomized trees (ERT) and light gradient boosting machine (LightGBM) models are new learning algorithms with good generalization performance (soil moisture and above-ground biomass), but are less studied in estimating soil salinity in the visible and near-infrared spectra. In this study, 130 soil EC data, soil measured hyperspectral data, topographic factors, conventional salinity indices such as Salinity Index 1, and two-band (2D) salinity indices such as ratio indices, were introduced. The five spectral pre-processing methods of standard normal variate (SNV), standard normal variate and detrend (SNV-DT), inverse (1/OR) (OR is original spectrum), inverse-log (Log(1/OR) and fractional order derivative (FOD) (range 0–2, with intervals of 0.25) were performed. A gradient boosting machine (GBM) was used to select sensitive spectral parameters. Models (extreme gradient boosting (XGBoost), LightGBM, random forest (RF), ERT, classification and regression tree (CART), and ridge regression (RR)) were used for inversion soil EC and model validation. The results reveal that the two-dimensional correlation coefficient highlighted EC more effectively than the one-dimensional. Under SNV and the second order derivative, the two-dimensional correlation coefficient increased by 0.286 and 0.258 compared to the one-dimension, respectively. The 13 characteristic factors of slope, NDI, SI-T, RI, profile curvature, DOA, plane curvature, SI (conventional), elevation, Int2, aspect, S1 and TWI provided 90% of the cumulative importance for EC using GBM. Among the six machine models, the ERT model performed the best for simulation (R2 = 0.98) and validation (R2 = 0.96). The ERT model showed the best performance among the EC estimation models from the reference data. The kriging map based on the ERT simulation showed a close relationship with the measured data. Our study selected the effective pre-processing methods (SNV and the 2 order derivative) using one- and two-dimensional correlation, 13 important factors and the ERT model for EC hyperspectral inversion. This provides a theoretical support for the quantitative monitoring of soil salinization on a larger scale using remote sensing techniques.

Dissolved carbon and CDOM in lake ice and underlying waters along a salinity gradient in shallow lakes of Northeast China

The variations of DOC and DIC concentrations in lake ice and underlying waters were examined in 40 shallow lakes across the Songnen Plain, Northeast China. The lakes, frozen annually during winter, included freshwater and brackish systems (EC > 1000 μS cm−1; range: 171–12607 μS cm−1 in underlying water). Results showed that lake ice contained lower DOC (7.2 mg L−1) and DIC (6.7 mg L−1) concentration compared to the underlying waters (58.2 and 142.4 mg L−1, respectively). Large differences in DOC and DIC concentrations of underlying waters were also observed between freshwater (mean ± SD: 22.3 ± 11.5 mg L−1, 50.7 ± 20.6 mg L−1) and brackish lakes (83.3 ± 138.0 mg L−1, 247.0 ± 410.5 mg L−1). A mass balance model was developed to describe the relative distribution of solutes and chemical attributes between ice and the underlying waters. Results showed that water depth and ice thickness were the key factors regulating the spatial distribution of solutes in the frozen lakes. Chromophoric dissolved organic matter (CDOM) absorption coefficient at 320 nm, aCDOM(320) and specific UV absorbance (SUVA254) were used to characterize CDOM composition and quality. Compared to the underlying waters, CDOM present in ice largely included low aromaticity organic substances, an outcome perhaps facilitated by ice formation and photo-degradation. In ice and underlying freshwaters, CDOM predominantly included organic C fractions of high aromaticity, while low aromaticity organic substances were observed for brackish lakes. Results of this study suggest that, if water salinity increases due to climate change and anthropogenic activities, significant changes can occur in the dissolved carbon and fate of CDOM in these shallow lakes.

Microstructure evolution during homogenization of Al-Mg-Si-Mn-Fe alloys: Modelling and experimental results

Microstructure evolution during the homogenization heat treatment of an Al-Mg-Si-Fe-Mn (AA6xxx) alloy was investigated using a combination of modelling and experimental studies. The model is based on the CALPHAD-coupled homogenization heat treatment model originally developed for AA3xxx alloys (i.e., Al-Mn-Fe-Si). In this work, the model was adapted to the more complex AA6xxx system (Al-Mg-Si-Mn-Fe) to predict the evolution of critical microstructural features such as the spatial distribution of solute, the type and fraction of constituent particles and dispersoid number density and size distribution. Experiments were also conducted using three direct chill (DC) cast AA6xxx alloys with different Mn levels subjected to various homogenization treatments. The resulting microstructures were characterized using a range of techniques including scanning electron microscopy, electron microprobe analysis (EPMA), XRD, and electrical resistivity measurements. The model predictions were compared with the experimental measurements, and reasonable agreement was found.

Dislocation cross-slip in fcc solid solution alloys

Cross-slip is a fundamental process of screw dislocation motion and plays an important role in the evolution of work hardening and dislocation structuring in metals. Cross-slip has been widely studied in pure FCC metals but rarely in FCC solid solutions. Here, the cross-slip transition path in solid solutions is calculated using atomistic methods for three representative systems of Ni-Al, Cu-Ni and Al-Mg over a range of solute concentrations. Studies using both true random alloys and their corresponding average-alloy counterparts allow for the independent assessment of the roles of (i) fluctuations in the spatial solute distribution in the true random alloy randomness and (ii) average alloy properties such as stacking fault energy. The results show that the solute fluctuations dominate the activation energy barrier, i.e. there are large sample-to-sample variations around the average activation barrier. The variations in activation barrier correlate linearly with the energy difference between the initial and final states. The distribution of this energy difference can be computed analytically in terms of the solute/dislocation interaction energies. Thus, the distribution of cross-slip activation energies can be accurately determined from a parameter-free analytic model. The implications of the statistical distribution of activation energies on the rate of cross-slip in real alloys are then identified.

Dynamic properties of the Fisher–Kolmogorov–Petrovskii–Piscounov equation with the deviation of the spatial variable

We consider the problem of the density wave propagation of a logistic equation with the deviation of the spatial variable and diffusion (the Fisher–Kolmogorov equation with the deviation of the spatial variable). The Ginzburg–Landau equation was constructed in order to study the qualitative behavior of the solution near the equilibrium state. We analyzed the profile of the wave equation and found conditions for the appearance of oscillatory regimes. The numerical analysis of the wave propagation shows that, for a fairly small spatial deviation, this equation has a solution similar to that the classical Fisher–Kolmogorov equation. An increase in this spatial deviation leads to the existence of the oscillatory component in the spatial distribution of solutions. A further increase in the spatial deviation leads to the destruction of the traveling wave. This is expressed in the fact that undamped spatiotemporal fluctuations exist in a neighborhood of the initial perturbation. These fluctuations are close to the solution of the corresponding boundary value problem with periodic boundary conditions. Finally, when the spatial deviation is large enough we observe intensive spatiotemporal fluctuations in the whole area of wave propagation.

Spatially inhomogeneous structures in the solution of Fisher-Kolmogorov equation with delay

We consider the problem of density wave propagation in a logistic equation with delay and diffusion (Fisher-Kolmogorov equation with delay). A Ginzburg-Landau equation was constructed in order to study the qualitative behavior of the solution near the equilibrium state. The numerical analysis of wave propagation shows that for a sufficiently small delay this equation has a solution similar to the solution of a classical Fisher-Kolmogorov equation. The delay increasing leads to existence of the oscillatory component in spatial distribution of solutions. A further increase of delay leads to destruction of the traveling wave. That is expressed in the fact that undamped spatio-temporal fluctuations exist in a neighborhood of the initial perturbation. These fluctuations are close to the solution of the corresponding boundary value problem with periodic boundary conditions. Finally, when the delay is sufficiently large we observe intensive spatio-temporal fluctuations in the whole area of wave propagation.

Dynamical Properties of the Fisher–Kolmogorov–Petrovskii–Piscounov Equation with Deviation of the Spatial Variable

We consider the problem of density wave propagation of a logistic equation with deviation of the spatial variable and diffusion (Fisher-Kolmogorov equation with deviation of the spatial variable). A Ginzburg–Landau equation was constructed in order to study the qualitative behavior of the solution near the equilibrium state. We analyzed the profile of the wave equation and found conditions for the appearance of oscillatory regimes. The numerical analysis of wave propagation shows that for a suficiently small spatial deviation this equation has a solution similar to the solution of the classical Fisher–Kolmogorov equation. The spatial deviation increasing leads to the existence of the oscillatory component in the spatial distribution of solutions. A further increase of the spatial deviation leads to destruction of the traveling wave. That is expressed in the fact that undamped spatio-temporal fluctuations exist in a neighborhood of the initial perturbation. These fluctuations are close to the solution of the corresponding boundary value problem with periodic boundary conditions. Finally, when the spatial deviation is suficiently large we observe intensive spatio-temporal fluctuations in the whole area of wave propagation.

Phase transitions in small-world systems: application to functional brain networks

In the present paper the problem of symmetry breaking in the systems with a small- world property is considered. The obtained results are applied to the description of the functional brain networks. Origin of the entropy of fractal and multifractal small-world systems is discussed. Applying the maximum entropy principle the topology of these networks has been determined. The symmetry of the regular subgroup of a small-world system is described by a discrete subgroup of the Galilean group. The algorithm of determination of this group and transformation properties of the order parameter have been proposed. The integer basis of the irreducible representation is constructed and a free energy functional is introduced. It has been shown that accounting the presence of random connections leads to an integro- differential equation for the order parameter. For q-exponential distributions an equation of motion for the order parameter takes the form of a fractional differential equation. We consider the system that is described by a two-component order parameter and discuss the features of the spatial distribution of solutions.

Fisher–Kolmogorov–Petrovskii–Piscounov Equation with Delay

We considered the problem of density wave propagation in a logistic equation with delay and diffusion (Fisher–Kolmogorov equation with delay). It was constructed a Ginzburg–Landau equation in order to study the qualitative behavior of the solution near the equilibrium state. The numerical analysis of wave propagation shows that for a sufficiently small delay this equation has a solution similar to the solution of a classical Fisher–Kolmogorov equation. The delay increasing leads to existence of the oscillatory component in spatial distribution of solutions. A further increase of delay leads to the destruction of the traveling wave. That is expressed in the fact that undamped spatio-temporal fluctuations exist in a neighborhood of the initial perturbation. These fluctuations are close to the solution of the corresponding boundary value problem with periodic boundary conditions. Finally, when the delay is sufficiently large we observe intensive spatio-temporal fluctuations in the whole area of wave propagation.

Microbial ecology of biogeochemical interfaces - diversity, structure, and function of microhabitats in soil

In soils, a multitude of inorganic, organic, and biological constituents build up extremely large, heterogeneous, and hierarchically organized biogeochemical interfaces (BGIs). These interfaces affect a variety of soil processes, such as the formation and the stability of soil aggregates; the movement and the spatial distribution of solutes, colloids, and gases; or the bioavailability of inorganic and organic compounds. As environmental conditions prevailing in soil frequently change over time and in space, the structural and the compositional heterogeneity of BGIs offers a multitude of microhabitats and supports growth of highly diverse microbial communities. Yet, microorganisms not only inhabit these interfaces, but they also actively participate in their formation and reorganization, as well as in their destabilization and destruction. They may thus be seen as both “architects” and “actors” …

Spatial distribution of solute leaching with snowmelt and irrigation: measurements and simulations

Abstract. Transport of a tracer and a degradable solute in a heterogeneous soil was measured in the field, and simulated with several transient and steady state infiltration rates. Leaching surfaces were used to investigate the solute leaching in space and time simultaneously. In the simulations, a random field for the scaling factor in the retention curve was used for the heterogeneous soil, which was based on the spatial distribution of drainage in an experiment with a multi-compartment sampler. As a criterion to compare the results from simulations and observations, the sorted and cumulative total drainage in a cell was used. The effect of the ratio of the infiltration rate over the degradation rate on leaching of degradable solutes was investigated. Furthermore, the spatial distribution of the leaching of degradable and non-degradable solutes was compared. The infiltration rate determines the amount of leaching of the degradable solute. This can be partly explained by a decreasing travel time with an increasing infiltration rate. The spatial distribution of the leaching also depends on the infiltration rate. When the infiltration rate is high compared to the degradation rate, the leaching of the degradable solute is similar as for the tracer. The fraction of the pore space of the soil that contributes to solute leaching increases with an increasing infiltration rate. This fraction is similar for a tracer and a degradable solute. With increasing depth, the leaching becomes more homogeneous, as a result of dispersion. The spatial distribution of the solute leaching is different under different transient infiltration rates, therefore, also the amount of leaching is different. With independent stream tube approaches, this effect would be ignored.

Spatial Distribution of Solutes in Aquifer Outcrop Zones along the Brazos River, East-Central Texas

Concentrations of several solutes – nitrate, arsenic, sulfate, boron, chloride, and bromide – along with total dissolved solids (TDS) in ten counties bordering the Brazos River in east-central Texas were compiled, mapped, and analyzed relative to regional land use and geology. Agriculture and oil/gas production are major activities and potential sources of groundwater contamination in the study area. Data were compiled from 104 water wells with a median depth of 446 ft (136 m) in the outcrop zones of six sedimentary aquifers: Carizzo-Wilcox, Queen City, Sparta, Yegua-Jackson, Gulf Coast, and Brazos Alluvium. Only two observations surpassed the 44.3 mg/L drinking water standard for nitrate, and four observations exceeded the 10 ug/L standard for arsenic. The median chloride concentration was 53 mg/L; however, the maximum level was almost three times the secondary drinking water standard of 250 mg/L. Chloride, bromide, sulfate, and boron concentrations resembled TDS patterns, with numerous samples exceeding secondary TDS drinking water standards in the Yegua-Jackson Aquifer. Most chloride/bromide ratios were between 100 and 300. Overall, results of this study suggest that natural processes exert a primary control on solute concentrations in the above aquifers, with a potential for modest anthropogenic impacts from agriculture and oil/gas production.

Nutrient cycling in bedform induced hyporheic zones

The hyporheic zone is an ecotone connecting the stream and groundwater ecosystem that plays a significant role for stream biogeochemistry. Water exchange across the stream-sediment interface and biogeochemical reactions in the streambed concur to affect subsurface solute concentrations and eventually nutrient cycling in the fluvial corridor. In this paper we investigate the interplay of hydrological and biogeochemical processes in a duned streambed and their effect on spatial distribution of solutes. We employ a numerical model to simulate the turbulent water flow and the pressure distribution over the dunes, and then to evaluate the flow field and the biogeochemical reactions in the hyporheic sediments. Sensitivity analyses are performed to analyze the influence of hydrological and chemical properties of the system on solute reaction rates. The results demonstrate the effect of stream velocity and sediment permeability on the chemical zonation. Changing sediment permeability as well as stream velocity directly affects the nutrient supply and the residence times in the streambed, thus controlling the reaction rates under the dune. Stream-water quality is also shown to influence the reactive behavior of the sediments. In particular, the availability of dissolved organic carbon determines whether the streambed acts as a net sink or source of nitrate. This study represents a step towards a better understanding of the complex interactions between hydrodynamical and biogeochemical processes in the hyporheic zone.

Parameterizing the Leaching Surface by Combining Curve-Fitting for Solute Breakthrough and for Spatial Solute Distribution

Multi-compartment samplers (MCSs) measure unsaturated solute transport in space and time at a given depth. Sorting the breakthrough curves (BTCs) for individual compartments in descending order of total solute amount and plotting in 3D produces the leaching surface. The leaching surface is a useful tool to organize, present, and analyze MCS data. We present a novel method to quantitatively characterize leaching surfaces. We fitted a mean pore-water velocity and a dispersion coefficient to each BTC, and then approximated their values by functions of the rank order of the BTCs. By combining the parameters of these functions with those of the Beta distribution fitted to the spatial distribution of solutes, we described an entire leaching surface by four to eight parameters. This direct characterization method allows trends to be subtracted from the observations, and incorporates the effects of local heterogeneity. The parametric fit creates the possibility to quantify concisely the leaching behavior of a soil in a given climate under given land use, and eases the quantitative comparison of spatio-temporal leaching behavior in different soils and climates.

Dispersion of solutes in porous media

A recently introduced theory of solute transport in porous media is tested by comparison with experiment. The solute transport is predicted using an adaptation of the cluster statistics of percolation theory to critical path analysis together with knowledge of how the structure of such percolation clusters affects the time of transport across them. Only the effects of a single scale of medium heterogeneity are incorporated, and a minimal amount of information regarding the structure of the medium is required. This framework is used to find effectively the distributions of solute velocities and travel distances and thus generate arrival time distributions. The comparison with experiment focuses on the dispersivity (the ratio of the second to the first moment of the spatial solute distribution). The predictions of the theory in the absence of diffusion are verified by comparing with over 2200 experiments over length scales from a few microns to 100 km. At larger length scales (centimeters on up) about 95% of the data lie within our predicted bounds. At smaller length scales approximately 99.8% of the data lie where we predict. These comparisons are not trivial as the typical values of the dispersivity increase by ten orders of magnitude over ten orders of magnitude of length scale. Noteworthy is that the classical advection-dispersion (ADE) equation predicts that the dispersivity should be independent of length scale! This agreement with experiment requires rethinking of the relevance of diffusion and multi-scale heterogeneity and would also appear to signal the complete inappropriateness of using the classical ADE or any of its derivatives to model solute transport.

Incorporation of Effects of Diffusion into Advection-Mediated Dispersion in Porous Media

The distribution of solute arrival times, W(t;x), at position x in disordered porous media does not generally follow Gaussian statistics. A previous publication determined W(t;x) in the absence of diffusion from a synthesis of critical path, percolation scaling, and cluster statistics of percolation. In that publication, W(t;x) as obtained from theory, was compared with simulations in the particular case of advective solute transport through a two-dimensional model porous medium at the percolation threshold for various lengths x. The simulations also did not include the effects of diffusion. Our prediction was apparently verified. In the current work we present numerical results related to moments of W(x;t), the spatial solute distribution at arbitrary time, and extend the theory to consider effects of molecular diffusion in an asymptotic sense for large Peclet numbers, Pe. However, results for the scaling of the dispersion coefficient in the range 1<Pe<100 agree with those of other authors, while results for the dispersivity as a function of spatial scale also appear to explain experiment.

Specifying Scale‐dependent Dispersivity in Numerical Solutions of the Convection–Dispersion Equation

Many studies have incorporated various scale‐dependent dispersivity functions into the convection–dispersion equation (CDE). For a given function, there are different ways of specifying the dispersivity values in the discretized subdomains of a numerical solution. These ways would depend on how the function's time or space variable is built into the numerical scheme and on how the different ways may be interrelated. No study has addressed how these different ways may affect resulting breakthrough curves (BTCs) or their applicability to solute transport problems. In this study, five ways were specified and designated as local time, average time, apparent time, local distance, or apparent distance dependent dispersivity in the numerical scheme. The main objective was to demonstrate relationships among these ways by assuming that dispersion in the scale‐dependent CDE was quasi‐Fickian and implicitly based on an estimation of the first moment of the BTC at the given location. How these ways affected calculated BTCs was numerically tested using generalized linear and power scale–dependent dispersivity functions for a one‐dimensional problem with initial solute distribution represented as a Dirac delta function. For either type of function, differences were obvious in BTCs obtained for solute transport conditions with small apparent Peclet numbers using the alternative ways of specifying scale‐dependent dispersivity in the numerical scheme. The differences decreased with increasing apparent Peclet number. The numerical test results also showed that the derived relationships were not applicable for numerically calculating the spatial solute distribution at a given time. These test results were expected to be generally applicable because any other initial‐value solute transport problem can be solved as a superposition of this test problem.

Spatial Distribution of Solutes and Water in Sucrose Solution Dehydrated Apples

Half-fresh apples were immersed in sucrose solution (50% w/w, 27°C) during different times of exposition (2, 4, and 8 h). Then each fruit was sliced from the transversal exposed surface. Density, water, and sugar content were determined for each slice. A mathematical model was fitted to experimental data of water and sucrose content considering the global flux and the tissue shrinkage. By numerical analysis, the binary effective diffusion coefficients as a function of concentration were calculated, using material coordinates and integrating simultaneously two differential equations (for water and sucrose). The coefficients obtained are one or even two orders of magnitude lower than the ones for pure solutions and present an unusual concentration dependence. This comparison shows the influence of the tissue resistance to the diffusion.

The influence of earthworm community structure on the distribution and movement of solutes in a chisel-tilled soil

Although it is known that deep-burrowing earthworms can increase the depth of penetration of solutes in soil, their comparative effect on solute transport when they are added to communities composed solely of epigeic and endogeic species is not clear. Ionic tracers were applied as artificial rainfall to the surface of plots with or without added deep-burrowing earthworms ( n=3). We determined the soil water content, total nitrogen, soil organic carbon (SOC), strontium, and bromide concentrations in soil samples taken from a 320 mm×380 mm, 56-position grid with 40 mm sample spacing. Earthworm inoculations increased populations of deep-burrowing Lumbricus terrestris L., and decreased those of the surface-dwelling L. rubellus Hoffmeister, and had no impact on geophagous species; compared to the earthworm communities in control plots. The average soil concentrations of SOC, bromide and strontium were higher where earthworms were inoculated compared to controls. Solute concentrations, SOC, and soil water content all decreased with depth. Synthetic data derived from multivariate analyses were used as an index of solute transport intensity. Solute transport intensity was greater at any given depth in response to earthworm inoculations, compared to that in controls. Although we observed a characteristic breakthrough of solutes to greater depths where deep-burrowing earthworms were inoculated, there were no differences in the spatial distribution of solutes between the two earthworm communities studied. We concluded that although the activity of deep-burrowing species allowed solute breakthrough to greater depth, the more diffuse distribution of solutes was the result of the dominant random burrowing activity of epigeic and endogeic earthworm species, which comprised the larger proportion of earthworms in these communities.