Heterogeneous Diffusion Research Articles

Kinetics of Nickel Diffusion into Austenitic Stainless Steels AISI 304 and 316L and Calculation of Diffusion Coefficients.

Diffusion bonding has many advantages, but it also has its specifics. When creating heterogeneous joints, problems arise with the creation of intermetallic phases. For this reason, an interlayer is needed to prevent the creation of these unfavorable phases. It is important to ensure that the interlayer is of sufficient thickness to prevent the elements from diffusing through the entire interlayer and the intermetallic phases from being formed again. Conversely, too thick an interlayer causes an increase in the heterogeneity of the bond properties. The creation of the initial diffusion bonds in a heterogeneous diffusion joint of AISI 304 and AISI 316L steel with a 0.2 mm thick nickel interlayer was made in a Gleeble 3500. The experiments to determine the diffusion kinetics were carried out in a vacuum furnace, with subsequent evaluation by EDX (Energy Dispersive X-ray Spectroscopy) analysis. Subsequently, the diffusion coefficients of nickel into both steels were determined, and generalized equations were formulated to calculate the diffusion coefficients for temperatures in the range of 950 to 1150 °C and holding times in the range of 3600 to 18,000 s. Equations are also given to determine the width of the diffused zone between each steel and the Ni interlayer.

Symmetries and Conservation Laws for a Class of Fourth-Order Reaction–Diffusion–Advection Equations

We have studied a class of (1+1)-dimensional equations that models phenomena with heterogeneous diffusion, advection, and reaction. We have analyzed these fourth-order partial differential equations within the framework of group methods. In this class, the diffusion coefficient is constant, while the coefficients of advection and the reaction term are assumed to depend on the unknown density u(t,x). We have identified the Lie symmetries extending the Principal Algebra along with all the conservation laws corresponding to the different forms of the coefficients, and have derived several brief applications.

Inhomogeneous oxidation behaviors of FeCoNiTiCu high-entropy alloy nanoparticles confined within graphite shells

The oxidation of magnetic high-entropy alloy nanoparticles (HEA-NPs) is an inevitable process in service environments, which can induce unexpected properties and result in the failure of devices. Graphite shells coating is an effective approach to prevent the oxidation of nanoparticles, and the defects on graphite shells can also have a significant impact on the physical and chemical properties of nanoparticles. Thus, it is significant to uncover the oxidation process and understand the change of magnetic properties of HEA-NPs encapsulated in graphite shells (HEA@C-NPs). Herein, we demonstrate the microstructure evolution of HEA@C-NPs under different annealing temperatures. With the increase of annealing temperatures, the graphite shell is broken gradually and then oxygen atoms enter into the HEA core across the defects in graphite shell. An inhomogeneous partial-empty structure is observed at 300 ℃, which can result from the heterogeneous diffusion of different elements across graphite shell with ununiform defects. Accompanied with the formation of the oxide, the saturation magnetization decreases linearly and the exchange bias effect increases gradually. Our results give some understanding for the oxidation process and thus provide a guidance for designing HEA-NPs on complex service environments.

Boundary Conditions for the Parametric Kalman Filter Forecast

AbstractThis paper is a contribution to the exploration of the parametric Kalman filter (PKF), which is an approximation of the Kalman filter, where the error covariances are approximated by a covariance model. Here we focus on the covariance model parameterized from the variance and the anisotropy of the local correlations, and whose parameters dynamics provides a proxy for the full error‐covariance dynamics. For this covariance model, we aim to provide the boundary condition to specify in the prediction of PKF for bounded domains, focusing on Dirichlet and Neumann conditions when they are prescribed for the physical dynamics. An ensemble validation is proposed for the transport equation and for the heterogeneous diffusion equation over a bounded 1D domain. This ensemble validation requires to specify the auto‐correlation time‐scale needed to populate boundary perturbation that leads to prescribed uncertainty characteristics. The numerical simulations show that the PKF is able to reproduce the uncertainty diagnosed from the ensemble of forecast appropriately perturbed on the boundaries, which show the ability of the PKF to handle boundaries in the prediction of the uncertainties. It results that Dirichlet condition on the physical dynamics implies Dirichlet condition on the variance and on the anisotropy.

Value of placental virtual magnetic resonance elastography and intravoxel incoherent motion-based diffusion and perfusion in predicting adverse outcomes of small-for-gestational-age infants

ObjectiveIt is critical to early monitor and manage small-for-gestational age (SGA) infants with truly adverse outcomes not detected by conventional methods. We aimed to explore the value of diffusion-weighted imaging (DWI)-based virtual magnetic resonance elastography (vMRE) and intravoxel incoherent motion (IVIM)-based biexponential and stretched exponential parameters in predicting adverse outcomes of SGA infants.MethodsTwenty SGA infants with adverse outcomes and forty without adverse outcomes were included in this prospective study. One DWI-based vMRE parameter [the stiffness value (μdiff)], five IVIM–based parameters [true diffusion coefficient (D), pseudo-diffusion coefficient (D*), perfusion fraction (f), diffusion distribution coefficient (DDC), and diffusion heterogeneity index (Alpha)] and apparent diffusion coefficient (ADC) were calculated and compared between groups. The predictive efficiency was compared by the logistic regression analysis and receiver operating characteristic curve analysis. The relationship between the μdiff value with gestational age was also evaluated.ResultsThe placental μdiff value was remarkably higher, and the f, DDC, and ADC values were considerably lower in the SGA infants with adverse outcomes compared with those without adverse outcomes. The μdiff and f value were predictive risk factors for SGA infants with adverse outcomes. A combined predictive model (μdiff and f) improved the predictive efficacy. Moreover, there was no statistically significant correlation between the placental stiffness value and gestational age.ConclusionsFunctional MRI parameters to quantify placenta elastography and microcirculation in SGA patients. This might be a useful tool to assess placental function and a vital non-invasive supplement for predicting adverse outcomes of SGA infants.Critical relevance statementThis prospective study shows DWI-based virtual magnetic resonance elastography and intravoxel incoherent motion-based functional parameters to quantify placenta elastography and microcirculation in small-for-gestational-age patients, which could complement existing non-invasive methods for monitoring and predicting neonatal perinatal adverse outcome.Key points• vMRE is an emerging non-invasive imaging technique for evaluating placenta stiffness.• SGA infants with adverse outcome have stiffer placental elasticity and lower microcirculation.• Risk factors combination displayed better efficacy in predicting adverse outcomes of SGA.Graphical

Diffusion heterogeneity and vascular perfusion in tumor and peritumoral areas for prediction of overall survival in patients with high-grade glioma

ObjectiveTo evaluation of diffusion heterogeneity and vascular perfusion in tumor and peritumoral areas for prognostic prediction in high-grade glioma (HGG, WHO III/IV grade). MethodsForty patients with HGG underwent diffusion kurtosis imaging (DKI), intravoxel incoherent motion (IVIM), and arterial spin labeling (ASL) MRI before operation. After normalization, the parameters were divided into diffusion heterogeneity parameters (rD, rMD, rMK, rKr, rKa) and vascular perfusion parameters (rD*, rF, rCBF). Univariate and multivariate Cox regression analyses were used to evaluate associations between overall survival (OS) and the above parameters, clinical factors, and IDH1 status. The Mann-Whitney test was used to evaluate differences in the parameters between different IDH1 states. ResultsIn the univariate Cox regression analysis, OS was significantly associated with tumor resection range, IDH1 status, tumor heterogeneity parameters (rD, rMD, rMK, rKr, rKa), and rCBF in tumor area(all p < 0.05). In addition, rD and rCBF measured in the peritumoral region were also predictors of poor OS (both p < 0.01). Multivariate Cox regression analysis indicated that rMK in the tumor area and rCBF in the peritumoral area (hazard ratio = 7.900 and 5.466, respectively, for each 0.1 increase in the normalized value) were independent predictors of OS. ConclusionThe rMK of tumor area and rCBF of peritumoral area had independent predictive value for OS in patients with HGG. Advances in knowledgeThis study explored useful imaging biomarkers from the diffusion heterogeneity and vascular perfusion of tumor and peritumoral areas in HGG, which is useful to help clinician to make precise therapeutic plans, and predict the prognostic for glioma patients.

Dynamic heterogeneity of atomic transport in a body-centered cubic WTaVCr non-equiatomic high-entropy alloy

Compared to face-centered cubic (fcc) high-entropy alloys (HEAs), body-centered cubic (bcc) HEAs generally possess larger lattice distortion, resulting in distinct point defect properties. In this work, molecular dynamics (MD) simulations and molecular statics (MS) calculations were performed to study the dynamic heterogeneity in a bcc W40Ta35V10Cr15 non-equiatomic HEA with large lattice distortion. Defect energies in W40Ta35V10Cr15 HEA show a strong preference for a specific element and possess large energy spreads, resulting in dynamic heterogeneity of atomic transport in the process of defect diffusion and evolution. V and Cr interstitials exhibit higher occurrence probability and faster diffusion compared to W and Ta interstitials. Such diffusion heterogeneity brings about high recombination probabilities of W and Ta interstitials and large fractions of V and Cr in surviving interstitials during displacement cascades. The binding ability of interstitials correlates with the magnitude of interstitial formation energies. The smaller the interstitial formation energies, the weaker the binding abilities. A large number of surviving V and Cr interstitials with smaller interstitial formation energies exhibit weak binding abilities and discrete distribution. Our findings suggest that the dynamic heterogeneity in W40Ta35V10Cr15 HEA with large lattice distortion may be the underlying mechanism of outstanding irradiation resistance.

Interplay between particle trapping and heterogeneity in anomalous diffusion

Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction with position-dependent diffusion, potentially leading to erroneous conclusions. Here, we introduce a hybrid diffusion model that merges a position-dependent diffusion coefficient with the trapping mechanism of the comb model. We derive exact solutions for position distributions and mean squared displacements, validated through simulations of Langevin equations. Our model shows that the trapping mechanism attenuates the impact of media heterogeneity. Superdiffusion occurs when the position-dependent coefficient increases superlinearly, while subdiffusion occurs for sublinear and inverse power-law relations. This nontrivial interplay between heterogeneity and state-independent mechanisms also leads to anomalous yet Brownian, and non-Brownian yet Gaussian regimes. These findings emphasize the need for cautious interpretations of experiments and highlight the limitations of relying solely on mean squared displacements or position distributions for diffusion characterization.

Entropy induced flow model for solar radiation through nanomaterials with cubic autocatalysis reaction

Background and objectiveHere we analyze entropy optimized magnetohydrodynamic flow of Reiner- Rivlin fluid nanomaterial. Flow by stretched cylinder is induced. Energy expression is scrutinized by addressing radiation, Ohmic heating and dissipation. Features for Brownian motion and thermophoresis have been accounted. Characteristics of nano fluid is added through Buongiorno’s model. Additionally, presence of homogeneous-heterogeneous chemical reaction is considered. MethodologyRelated governing expressions of problem (partial differential system) are converted into non-dimensional differential system. Governing problems are tackled through ND-solve technique. ResultsVelocity, entropy production, concentration and thermal field against sundry parameters are analyzed. Performances of Nusselt number and gradient of velocity are evaluated. Higher fluid variable lead to enhance velocity. Velocity and skin friction for magnetic field have reverse trends. Qualitatively same trend of temperature and concentration holds regarding thermophoresis. Behavior of magnetic field on temperature and entropy rate is similar. Nusselt number and thermal field for Prandtl number have reverse outcome. Entropy optimization boosted for heterogeneous diffusion variable. Radiation impact increases entropy generation.

A family of edge-centered finite volume schemes for heterogeneous and anisotropic diffusion problems on unstructured meshes

A family of edge-centered finite volume schemes for heterogeneous and anisotropic diffusion problems on unstructured meshes

Measurement of helium diffusion in Lotsberg Salt cores: A proxy to evaluate hydrogen diffusion

Hydrogen can be a critical part of the energy transition and salt caverns have been considered for underground hydrogen storage. Although there have been some successful experiences of hydrogen storage in salt caverns in Europe and the United States, it is essential to exercise caution when selecting caverns for storage to ensure safe operations. This study investigates the relationship between rock heterogeneity and helium diffusion by testing salt-rock cores from the Lotsberg Formation, Alberta, Canada. We characterized salt rock heterogeneity by analyzing the results of X-ray diffraction (XRD) analysis, thin-section microscopy, scanning electron microscopy/energy dispersive X-ray spectrometry (SEM/EDS), and high-resolution CT scans. Then, diffusion tests were conducted using a custom-designed HPHT visualization cell on core samples with different compositions and crystal sizes. The samples in this study were categorized as Lotsberg Salt and Lotsberg Marlstone. Lotsberg Salt mainly consisted of halite with trace amounts of carbonate impurities, while Lotsberg Marlstone comprised halite with a carbonate matrix containing carbonates, clays, quartz, and muscovite. Helium diffusion through pure and intact halite crystals was negligible, and the micro-scale halite crystal boundaries are non-open or poorly unconnected for helium diffusion. Halite samples with macro-scale grain boundaries and carbonate impurities exhibited more interconnected pore networks, resulting in increased rates of helium diffusion. However, the formation of secondary halite veins between grain boundaries can lead to tightly sealed boundaries that have poor connectivity, limiting helium diffusion within the sample. Salt-rock cores with intergranular fractures and unsealed grain boundaries showed accelerated pressure declines, attributed to the preferential diffusion of helium through these fracture and crack pathways.

Sulfation Effects of Chondroitin Sulfate to Bind a Chemokine in Aqueous Medium: Conformational Heterogeneity and Dynamics from Molecular Simulation.

The sulfation patterns and degree of sulfation of chondroitin sulfate (CS), an important class of glycosaminoglycans (GAG), and their interactions with chemokines are accountable for various diseases. To realize the underlying mechanism of such complex biological phenomena at a molecular level and their application in rational drug design, a study on conformations and dynamics of CSs is necessary. To explore this, in this study, we performed a series of atomistic molecular dynamics (MD) simulations with different sulfated variants of octadecasaccharide CS, like CS-C, CS-E, and CS-T, in their free forms and when bound to the protein chemokine CXCL8 dimer in an aqueous medium. The calculated binding free energy of CSs with the CXCL8 dimer is favorable, and the degree of sulfation favors the complexation process further with prominent hydrophobic and hydrogen-bonded interactions. We find that the recognition is associated with the configurational entropy loss of the CS molecules as calculated from the Gaussian mixture approach, which supports that the degree of sulfation regulates the process. Cluster analysis through the k-means algorithm and end-to-end distance measurement revealed that although the free CS molecules adopted linear conformations, the nonlinear conformations during binding with protein were noted. Adaptation of nonlinear forms in the bound forms is noteworthy for the less-sulfated CS-C and CS-E. Apart from favorable 4C1 conformations, the occasional appearance of skew-boat forms from the free-energy map of ring pucker for the GlcUA unit was observed, which remains unaffected by the sulfation. We find that during recognition, the average relaxation time of intra-CS and inter-CS-CXCL8 hydrogen bonds (HBs) is about a magnitude lesser than that of CS-water HBs, most prominent on the involvement of higher sulfated CS-T analogues. The translational motion of surrounded water molecules in CSs exhibited sublinear diffusion, and the degree of sublinearity increases around the heavily sulfated molecules due to the hindrance created by them as well as the presence of the chemokine and exhibited markedly slow heterogeneous diffusion.

Potential Value of the Stretched Exponential and Fractional Order Calculus Model in Discriminating Between Hepatocellular Carcinoma and Intrahepatic Cholangiocarcinoma: an Animal Experiment of Orthotopic Xenograft Nude Mice.

In clinical practice, Preoperative differentiation between hepatocellular carcinoma and intrahepatic cholangiocarcinoma is challenging but critical for treatment decisions. This study investigated the discriminatory power of the stretched-exponential model and fractional-order calculus model parameters for hepatocellular carcinoma versus intrahepatic cholangiocarcinoma in orthotopic xenograft nude mice. Prototype orthotopic xenograft models of hepatocellular carcinoma and intrahepatic cholangiocarcinoma were developed using 20 nude mice divided into two groups and separately transplanted with MHCC97H and HUCCT1 cells. Readout-segmented diffusion-weighted imaging with multiple b-values (0-2000 s/mm2) was obtained using a 3.0-T magnetic resonance imaging scanner. The apparent diffusion coefficient was calculated using the mono-exponential model. The distributed diffusion coefficient and intravoxel water molecular diffusion heterogeneity (α) were calculated using the stretched-exponential model. The diffusion coefficient (D), fractional-order derivative in space (β), and spatial parameter (μ) were calculated using the fractional-order calculus model. The liver and tumor specimens of nude mice were immunostained after euthanasia to clarify the liver cancer type. Differences in diffusion-related parameters between the groups were evaluated using Mann-Whitney U-test and univariate logistic analysis. Receiver operating characteristic curves were used to assess the diagnostic efficacy of each parameter. P<0.05 was deemed significant. α, D, and β were significant discriminators between the groups. The area under the curve for these three variables was 0.890, 0.830, and 0.870, respectively, with cutoff values of 0.491, 0.435, and 0.782, respectively. The stretched-exponential model parameters α and the fractional-order calculus model parameters D and β showed high diagnostic efficacy in discriminating intrahepatic cholangiocarcinoma from hepatocellular carcinoma in orthotopic xenograft nude mouse models.

The fate and supply capacity of potassium in biochar used in agriculture

We used chemical extraction, X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM-EDX) to study the potassium (K) in biochar prepared from corn straw at different temperatures (300 °C, 500 °C, 700 °C and 900 °C). The characteristics of biochar were analyzed through Fourier transform infrared spectroscopy (FTIR) and specific surface area analysis. We found that the potassium in biochar can be divided into water soluble potassium, exchangeable potassium, non-exchangeable potassium, and insoluble potassium according to the availability of agricultural potassium. The fate of potassium in straw changed as follows: with increasing pyrolysis temperature, the proportion of the sum of exchangeable and non-exchangeable potassium decreased, and the proportions of insoluble and lost potassium increased. The total, water soluble and exchangeable potassium contents in biochar were highest at 700 °C. The non-exchangeable and insoluble potassium contents were highest at 300 °C and 900 °C, respectively. Kinetics experiments were conducted to determine the different fates of potassium released from biochar at different temperatures; pot experiments were also undertaken. The release of different forms of potassium in biochar at different temperatures is mainly dominated by heterogeneous diffusion. Biochar increased not only the content of different forms of potassium in soil but also the potassium content of soybean stems and leaves. We calculated the potassium supply capacity of biochar by two strategies, measurements of the potassium content in biochar and the conversion rate of potassium in straw during pyrolysis. The most active and efficient potassium supply capacities were 33.60 g·kg−1 and 9.53 g·kg−1 at 700 °C and 300 °C, respectively. Biochar provides readily available (water soluble and exchangeable) potassium and a long-term (non-exchangeable) potassium supply to soil.

Structured multiagent decision-making in information diffusion: The model and dynamics

In recent years, studies in many fields have widely explored diffusion in social networks, which refers to the collective behavior of a set of autonomous social actors who interact with something (such as opinions, viruses, or innovations) in social networks. Many researchers have utilized a multiagent method to explore the effects of social actor characteristics and behavioral complexity on information diffusion. This method performs well in modeling the complex characteristics and decision-making of social actors. Although this subject has been intensively studied, analyses have typically been limited to concerns about the effects of entire social network structures, such as the small-world and scale-free aspects. Few empirical information diffusion studies have systematically investigated causal effects and decision-making mechanisms under the constraints of the interaction structures of agents. In practice, we observed that the decision-making of each agent in information diffusion was significantly influenced and constrained by its contextual network structures. To solve this problem, this study utilizes the cause–effect graph method to model the interaction structures of agents in social networks and presents agent decision-making models under the constraints of local network structures in information diffusion. The proposed models and methods can be used to effectively analyze the mechanism of the influence of structured interaction relations of agents on the process of decision-making and diffusion results. Moreover, the presented decision-making model can comprehensively consider the factors of social positions of heterogeneous agents, interaction strengths, and diffusion strategies, and thus, can better match the features of real-world influence diffusion in social networks.

A linearity-preserving diamond scheme with extended least square interpolation for the heterogeneous and anisotropic diffusion problems on polyhedral meshes

A linearity-preserving diamond scheme with extended least square interpolation for the heterogeneous and anisotropic diffusion problems on polyhedral meshes

A conservative network element method for diffusion-advection-reaction problems

We derive a conservative network element method for heterogeneous and anisotropic diffusion problems by modifying the non-conservative version, and extend it to the approximation of an additional advection term. The numerical scheme possesses the flux formulation reminiscent of classical finite volume methods. Its convergence is naturally governed by the network element theory. Numerical results illustrate the good behavior of the method even on distorted point clouds.

On heterogeneous diffusion processes and the formation of spatial-temporal nonlocality.

Heterogeneous diffusion processes defined as a solution to the overdamped Langevin equation with multiplicative noise, the amplitude of which has a power-law space-dependent form, are studied. Particular emphasis is on discrete analogs of these processes, for which, in particular, an asymptotic estimate of their variance behavior in time is obtained. In addition, a class of processes formed by deformation of the discrete analog of the fractional Brownian motion using the Cantor ladder and its inverse transformation is considered. It is found that such a class turns out to be close in structure to discrete analogs of heterogeneous processes. This class of processes allows us to illustrate geometrically the emergence of sub- and superdiffusion transport regimes. On the basis of discrete analogs of heterogeneous processes and memory flow phenomenology, we construct a class of random processes that allows us to model nonlocality in time and space taking into account spatial heterogeneity.

Evaluation of a Simulation Model for Deep-Bed Drying of Hybrid Rice Seeds

This study evaluates a simulation model for drying hybrid rice seeds in deep-bed set-up. This model is based on a heterogeneous diffusion model for predicting grain moisture at different levels on a deep-bed drying set-up was developed. To evaluate this, hybrid rice seeds were dried in a laboratory dryer with a 50-cm depth test cell. Three drying setups (45°C, 55°C, and stepwise) were used. During drying, moisture content was measured at different levels of the cell and at specified time intervals. Around four months after storage, germination percentage of samples from different drying setting and grain locations were obtained. The drying experiment revealed that the fastest drying time is achieved with the 55°C drying temperature. Parameter estimation and model validation of the simulation have revealed that the model used can well predict the moisture content of the seeds across the deep-cell drying bin at any given time. This can be further supported by the mean relative error of the model which is below its acceptable values. Germination results have also shown that the drying procedures used have no negative effect on the seed quality. Thus, using the simulation model could be an accurate way to predict the moisture content with no effect on its seed quality.

Epidemic dynamics and spatial segregation driven by cognitive diffusion and nonlinear incidence

AbstractWe propose susceptible‐infected‐susceptible epidemic reaction–diffusion models with cognitive movement and nonlinear incidence in a spatially heterogeneous environment. The cognitive dispersal term takes either random diffusion or symmetric diffusion. Building upon the ‐estimates of positive solutions under , we state the asymptotic dynamics for , . The numerical results reveal spatial segregation of susceptible and infected populations: (a) the heterogeneous random diffusion can segregate the population and reduce the infection fraction significantly; (b) the segregation phenomenon disappears as the ratio approaches one from below; (c) the disease‐free region strengthens the segregation induced by heterogeneous random diffusion; (d) the segregation governed by random diffusion is more sensitive to the incidence mechanism; (e) the distribution of steady states driven by symmetric diffusion is always similar to that by homogeneous diffusion.