Variation Of Diffusion Coefficient Research Articles

Coupled model on the variation of diffusion coefficient and surface chloride concentration in reinforced concrete structures over time

Durability analyses and service life estimates of structures in a marine environment can be developed through the modeling of chloride concentration profiles. However, as surface chloride concentration and diffusion coefficient vary over time, especially due to the cement hydration process, modeling chloride profiles from structures with recent degradation ages requires an adjustment for the temporal dependence of these two physical parameters. The variation of the surface chloride concentration (Cs) as a function of time tends to show an increasing asymptotic behavior, while the diffusion coefficient (D) has a decreasing asymptotic tendency. For this reason, the power function, usually used to describe the diffusion coefficient, has problems for advanced ages, while the exponential function has difficulties at recent ages. Therefore, the key issue in this problem is the rate of change of Cs and D over time. This article presents the development of a single time-dependence model to simultaneously describe the decrease in D and the increase in Cs over time. The coupled model is a piecewise-defined function, with continuity of the function and its first derivative in the transition time between recent ages and more advanced ages, defined as 10 years. To validate the new model, data from structures under natural degradation were used. The results demonstrated the applicability of the coupled model with individual adjustments of the exponent α, which implicitly represents material properties and environmental parameters. However, in the absence of sufficient information, a standard α exponent of 0.25 per year can be adopted, demonstrating a moderate to strong adherence of the coupled model to the Cs and D data over time. Three stages of temporal dependence were identified: I – up to 10 years: marked increase in Cs and decrease in D over time; II – between 10 and 25 years: decrease in the variation rate of Cs and D; and III – from 25 years: stabilization of Cs and D.

Modular shape-switching architected materials toward programmable acoustic properties

Next-generation acoustic devices and systems have utilized the recent advances in shape-switching and reconfigurable origami-inspired architected materials. Motivated by those efforts, we herein develop a hybrid material design strategy by combining two types of architected materials for their potential applications in tunable acoustic diffusion. The bilayered modular material consists of bistable/multistable blocks as the actuation layer and the origami sheet as the function layer. Guided by numerical simulations and physical prototyping, we proved the feasibility of controllable acoustic properties induced by programmable shape-switching sequences and customized corrugations in prototypes of linear units and planar units. Such programmability could offer the on-demand modification of scattering field directivity and variation of diffusion coefficients at various states compared to their traditional fixed counterparts. Overall, the proposed strategy opens the route to developing acoustic devices and systems with tailorable properties at different length scales.

Unraveling Photothermal-Enhanced bulk charge transport and surface oxygen reactions in TiO2 photoanodes for highly efficient photoelectrochemical water oxidation

Titanium dioxide (TiO2) has been extensively used as an important photoanode material for photoelectrochemical (PEC) water splitting, but its activity is greatly hindered by the low charge transport and sluggish oxygen evolution reaction (OER) kinetics. Herein, we demonstrate spinel oxide NiCo2O4 (NCO) acted as both photothermal material and oxygen evolution cocatalyst could significantly promote the PEC performance of TiO2 photoanodes, and a high photocurrent of 2.34 mA cm−2 at 1.23 V vs. reversible hydrogen electrode has been achieved by NCO/TiO2 photoanodes assisted by the photothermal effect. Importantly, a mechanism is proposed to explain the enhanced bulk charge transport and surface OER activity by an integrated various operando characterizations and density functional theory (DFT) study. Intensity-modulated photocurrent spectroscopy (IMPS) analysis and DFT calculations imply the relatively high temperature induced by the photothermal effect could accelerate small polaron hopping in the bulk of TiO2, which is verified by the electron diffusion coefficient variation of TiO2 with oxygen vacancies at different temperatures. Operando cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) reveal that photothermal conversion facilitates the oxidation of Ni2+ at lower potential and promotes the adsorption of *OH and deprotonation of *OOH intermediates. This work provides deep insight into the photothermal-enhanced PEC performance by observing the bulk small polaron hopping and surface dynamic evolution during the PEC process, which may underpin future advances in promoting PEC and photocatalytic performances of small-polaron-type semiconductors.

Evolution of microstructure and CO2 diffusion coefficient of compacted recycled aggregates during carbonation investigated by X-ray tomography

Recycled aggregates compacted in road layers are made of a majority of concrete aggregates which can mineralize atmospheric CO2. Previous studies showed that carbonation modifies the microstructure of recycled concrete aggregates, but little information is available in the case of compacted recycled aggregates. Furthermore, carbonation kinetics depends on CO2 diffusion through the compacted material, which is linked its microstructure. This paper presents an investigation of the evolution of both microstructure and CO2 diffusion coefficient of compacted recycled aggregates during carbonation in two different environments by X-ray tomography. Segmented 3D images were analyzed to fully extract resolved pore structures. In addition, the CO2 diffusion coefficient variations were investigated by calculating the macroscopic diffusivity tensor in the segmented 3D images. We show that the numerical results are very similar to previous experimental results from gas diffusion tests and that the diffusivity coefficients can be estimated by using only the larger pore network (pore size > 5.5 µm). These findings suggest that nondestructive imaging approaches, such as micro-Computed Tomography (µCT), are a relevant alternative to experimental characterization methods.

Spatio-temporal pattern formation due to host-circuit interplay in gene expression dynamics

Biological systems are majorly dependent on their property of bistability in order to exhibit nongenetic heterogeneity in terms of cellular morphology and physiology. Spatial patterns of phenotypically heterogeneous cells, arising due to underlying bistability, may play significant role in phenomena like biofilm development, adaptation, cell motility etc. While nonlinear positive feedback regulation, like cooperative heterodimer formation are the usual reason behind bistability, similar dynamics can also occur as a consequence of host-circuit interaction. In this paper, we have investigated the pattern formation by a motif with non-cooperative positive feedback, that imposes a metabolic burden on its host due to its expression. In a cellular array set inside diffusible environment, we investigate in-silico spatio-temporal diffusion in one dimension as well as in two dimension in the context of various initial conditions respectively. Moreover, the number of cells exhibiting the same steady state, as well as their spatial distribution has been quantified in terms of connected component analysis. The effect of diffusion coefficient variation has been studied in terms of stability of related states and time evolution of patterns.

Design, Development And Evaluation Of Transdermal Drug Delivery System For Treatment Of Diabetes

The current research aims to formulate and evaluated Cinnamaldehyde transdermal patches to treat diabetes. A good penetration enhancer Oleic Acid, would improve drug delivery from various polymer-based transdermal patches. Transdermal patches of the matrix type were made by solvent casting techniques using various polymer PVP K30, HPMC K100, and solvent. All prepared formulations were tested for folding endurance, weight variation, thickness, drug content, moisture content, moisture loss, in vitro drug release and In- vivo studies. Batch TDP1 was optimised formula from all formulation batches shows zero order release for 24 hours, with a cumulative percentage of drug diffusion of 97.68% from 2cm2 patches. It has been determined that polymer concentration HPMC films showed better release which may be attributed to the reason of high water vapour permeability of HPMC films for enhancing diffusion rate of drug through rat skin, oleic acid were incorporated as permeation enhancers in the HPMC films since they showed better release. It allows for controlled drug release from the patch. Drug content of the patches was found to be more than 98%. Variations in flux and Diffusion Coefficient were observed among various formulations. The drug–polymer interaction results suggested no interaction between drug and polymers. The in vivo results revealed that the patches successfully prevented the hyperglycaemia and they were also effective on chronic application. The transdermal route exhibited negligible skin irritation and produced better improvement with all the tested in vivo parameters compared to oral administration.

Multiscale measurements of gas diffusion coefficient of coal using counter-diffusion and image-based methods

Coal seam gas (CSG), also known as Coalbed Methane (CBM), is an important natural gas resource owing to its abundance and high energy density. During production, the gas desorbs from the coal matrix owing to pressure depletion. It then diffuses primarily within the micropores of the coal matrix toward the coal fractures and then migrates to the wellbore. Therefore, diffusivity plays a significant role in the gas production process, and this process needs to be explicitly characterized. However, experimental gas diffusion measurements are commonly based on coal particles rather than bulk coal samples, and thus, the impacts of coal fractures are typically neglected. This study aims to test the diffusion coefficients of fractured and tight bulk coal samples to provide insights into gas diffusion within the different pores and fractured structures. Diffusion coefficients of bulk coal samples were measured at different diffusion times, confining pressures, and gas pressures using counter-diffusion experiments. The results show that the bulk diffusion coefficient varies with confining pressure and gas pressure, which demonstrates the impacts of internal pore/fracture structure of coal on the diffusivity. The time-dependent diffusion coefficient results show that the diffusion coefficients became constant after 24 h, ranging from 1 × 10−10 m2/s to 2 × 10−10 m2/s. Local diffusion coefficients were obtained using X-ray micro-computed tomography images of krypton gas diffusing through a coal sample. These were higher than the diffusion coefficients of bulk samples, which were in the order of ∼10−9 m2/s. The variations in local diffusion coefficients indicated the heterogeneity of coal, thereby validating the importance of both local and bulk diffusion measurements in coal characterization.

Study on the behavior and mechanism of methane desorption-diffusion for multi-scale coal samples under multi-temperature conditions

• Obvious methane release by thermal in large specimen and low pressure. • More activation energy is required for methane diffusion in columnar coal. • Methane diffusion from coal matrix to the fracture is enhanced by thermal action. • Pressure-depleted reservoirs of CBM extraction could be improved by thermal action. Based on the background of coalbed methane thermal mining and mine gas control, this paper mainly investigates the effect of thermal action on the enhanced methane desorption-diffusion characteristics of multi-scale coal samples under different conditions and the corresponding mechanism through a series of methane dispersion experiments and theoretical analysis. The results show that the relationship between temperature and diffusion coefficient can be described by the modified Arrhenius equation, and the activation energy required for gas diffusion in columnar coal is greater than that in granular coal; The diffusion coefficient decreases linearly with increasing adsorption pressure under non-thermal action, while the pressure-dependent diffusion coefficient variation relationship under thermal action can be described by a quadratic function; The variation law of diffusion coefficient with coal size can be explained in terms of pore distribution and effective diffusion cross-sectional area in coal. In addition, the concept of “extreme particle size” has been used to explain the significant size effect exhibited by methane desorption, and the extreme particle size of the coal sample used in this experiment is inferred to be about 1 mm. Thermal action has a significant enhanced effect on methane release in large size coal samples and at low adsorption pressure. For low-pressure reservoirs, applying appropriate thermal measures to stimulate the coal matrix can significantly promote residual methane desorption, more importantly, enhance the diffusion ability of methane from coal matrix to the fracture, increasing the matrix methane diffusion flux, which is expected to improve the capacity performance of pressure-depleted reservoirs in the middle and late stages of CBM extraction, thus achieving efficient recovery of CBM. This study has improved gas transport theory in porous media to a certain extent, and also provides a certain theoretical basis for CBM thermal mining and gas disaster prevention and control.

Diffusion and memory effect in a stochastic process and the correspondence to an information propagation in a social system

A generalized Langevin equation is suggested to describe a diffusion particle system with memory. The equation can be transformed into the Fokker–Planck equation by using the Kramers–Moyal expansion. The solution of Fokker–Planck equation can describe not only the diffusion of particles but also that of opinion particles based on the similarities between the two. We find that the memory can restrain some non-equilibrium phenomena of velocity distribution in the system, without memory, induced by correlation between the noise and space (Wang et al., 2021). However, the memory can enhance the effective collision among particles as shown by the variation of diffusion coefficients, and changes the diffusion mode between the dissipative and pumping region by comparing with that in the aforementioned system without memory. As the discussions in this physical system is paralleled to a social system, the random diffusion of social ideology, such as the information propagation, can be suppressed by the correlation between the noise and space.

Simultaneous Acquisition of Diffusion Tensor and Dynamic Diffusion MRI.

Dynamic diffusion magnetic resonance imaging (ddMRI) metrics can assess transient microstructural alterations in tissue diffusivity but requires additional scan time hindering its clinical application. To determine whether a diffusion gradient table can simultaneously acquire data to estimate dynamic and diffusion tensor imaging (DTI) metrics. Prospective. Seven healthy subjects, 39 epilepsy patients (15 female, 31 male, age ± 15). Two-dimensional diffusion MRI (b=1000 s/mm2 ) at a field strength of 3T. Sessions in healthy subjects-standard ddMRI (30 directions), standard DTI (15 and 30 directions), and nested cubes scans (15 and 30 directions). Sessions in epilepsy patients-two 30 direction (standard ddMRI, 10 nested cubes) or two 15 direction scans (standard DTI, 5 nested cubes). Fifteen direction DTI was repeated twice for within-session test-retest measurements in healthy subjects. Bland-Altman analysis computed bias and limits of agreement for DTI metrics using test-retest scans and standard 15 direction vs. 5 nested cubes scans. Intraclass correlation (ICC) analysis compared tensor metrics between 15 direction DTI scans (standard vs. 5 nested cubes) and the coefficients of variation (CoV) of trace and apparent diffusion coefficient (ADC) between 30 direction ddMRI scans (standard vs. 10 nested cubes). Bland-Altman and ICC analysis using a P-value of 0.05 for statistical significance. Correlations of mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) were strong and significant in gray (ICC > 0.95) and white matter (ICC > 0.95) between standard vs. nested cubes DTI acquisitions. Correlation of white matter fractional anisotropy was also strong (ICC > 0.95) and significant. ICCs of the CoV of dynamic ADC measured using repeated cubes and nested cubes acquisitions were modest (ICC >0.60), but significant in gray matter. A nested cubes diffusion gradient table produces tensor-based and dynamic diffusion measurements in a single acquisition. 2 TECHNICAL EFFICACY: Stage 1.

Diffusion coefficients of an extensive set of pharmaceutical compounds in supercritical fluid chromatography over a wide range of mobile phase compositions

Diffusion data are essential for adequate analysis of the kinetic separation performance of any chromatographic system. Unfortunately, for Supercritical Fluid Chromatography (SFC), very little data is available of the diffusion coefficients in mobile phases typically used in contemporary methods, i.e. with a non-negligible amount of polar modifier such as methanol. In this work, a relative simple method which only requires minor modifications to a standard commercially available SFC instrument is used to determine the diffusion coefficient of an extensive set of pharmaceutical compounds in the range of 10–50 vol% of modifier (methanol) in CO2. By using a traditional SFC column, the solute is first separated from the sample solvent plug, before entering a long capillary, where the band broadening can be linked to its diffusion coefficient using the Taylor-Aris equation. By using two UV-detectors, before and after the capillary, the effect of the dispersion in the column can be eliminated and the true volumetric flow rate determined. It was found that in the investigated range of conditions, the change in mobile phase viscosity in a first approximation allows to predict the variation in diffusion coefficient. Chemical structure and more particularly functional groups can however have a significant effect on the diffusion coefficient.

Robust Interior Penalty Discontinuous Galerkin Methods

A new variant of the IPDG method is presented, involving carefully constructed weighted averages of the gradient of the approximate solution. The method is shown to be robust even for the most extreme simultaneous local mesh, polynomial degree and diffusion coefficient variation scenarios, without resulting into unreasonably large penalization. The new IPDG method, henceforth termed as robust IPDG (RIPDG), offers typically significantly better error behaviour and conditioning than the standard IPDG method when applied to scenarios with strong mesh/polynomial degree/diffusion local variation, especially when the underlying approximation space does not contain a sufficiently rich conforming subspace. The latter is of particular importance in the context of IPDG methods on polygonal/polyhedral meshes. On the other hand, when using uniform meshes, constant polynomial degree for problems with constant diffusion coefficients the RIPDG method is identical to the classical IPDG. Numerical experiments indicate the favourable performance of the new RIPDG method over the classical version in terms of conditioning and error.

Effect of ultrasound amplitude and frequency on nanoparticle diffusion in an agarose hydrogel

Exposure of nanoparticles in a porous medium, such as a hydrogel, to low-intensity ultrasound has been observed to dramatically enhance particle penetration rate. Enhancement of nanoparticle penetration is a key issue affecting applications such as biofilm mitigation and targeted drug delivery in human tissue. The current study used fluorescent imaging to obtain detailed experimental measurements of the effect of ultrasound amplitude and frequency on diffusion of nanoparticles of different diameters in an agarose hydrogel, which is often used as a simulant for biofilms and biological tissues. We demonstrate that the acoustic enhancement occurs via the phenomenon of oscillatory diffusion, in which a combination of an oscillatory flow together with random hindering of the particles by interaction with hydrogel proteins induces a stochastic random walk of the particles. The measured variation of acoustic diffusion coefficients with amplitude and frequency were used to validate a previous statistical theory of oscillatory diffusion based on the continuous time random walk approach.

Investigation of the Effect of Cutting Directions On the Improvement of Mechanical Parameters of Treated Cork by THT: Experimental Measurement, Modelling and Optimization of Mass Transfer

This work aims to investigate the impact of the cutting direction on the transfer properties of both the native cork and the treated by an optimized cycle at high temperature and boiling for the purpose to improve its mechanical characteristics in all three orthotropic directions. The study of the insulation performance is based on tracking the apparent mass diffusion coefficient (Dapp) variation in order to evolve a new material with the thermal, mass, acoustic and vibratory properties needed for various applications. TGA, IR and SEM analyzes are used to confirm the enhancement of the treated cork. The Dapp of the diffusing chemical species, NaCl (0.7M), is determined by conductimetric method. In transient mode, a mathematical model of mass transfer, which includes the diffusion parameters of the chemical species, is developed. Through the calibration of the model with the experimental measurements the Dapp values ​​were determined and then refined numerically by optimization using the Bat-Algorithm. The obtained results showed that the treatment improves the diffusion property of the native (DN) compared to the treaty (DA) with the values in the order of 10-12 and 10-13 m2.s-1 respectively with a relative uncertainty of 10-7. In addition, this investigation reveals that the radial diffusion coefficient (DR) is significantly higher than the tangential diffusion (DT) and longitudinal (DL) diffusion coefficients which both are almost of the same.

Probabilistic Repair Cost Simulation for RC Structures Repaired With Bacteria Coating Material Under Sulfate Attack

Concrete sewage structures are difficult to maintain since they are constructed under the ground and their surfaces inside are exposed to various deteriorations such as acid and sulfate ingress. In this study, their repair costs were evaluated both deterministically and probabilistically considering the extended service life through repairing of conventional repair mortar and a newly developed bacteria repair material. Unlike the conventional deterministic method, the probabilistic manner evaluates repair cost continuously, taking into account variations in the initial service life and extended service life through repair. For the work, variations in the sulfate ion diffusion coefficient and protection parameters (cover depth and repair layer thickness) were obtained experimentally. Based on the target service life (60 years), the repair cost increased to 123% as the maintenance-free period (MFP) decreased by half, and decreased to 77% as the MFP increased to 1.5 times. As the extended service life through repair decreased by half, the repair cost increased to 180% due to the increasing repair frequency. When the repair-extended service life increased to 1.5 times, the repair cost decreased to 73%. Considering exterior sulfate concentrations (120 and 200 ppm) and entire sewage pipelines (3268 m), the bacteria repair material showed the lowest repair cost (1376 K$ and 1498 K$ with the deterministic and probabilistic method, respectively) since the repair-service life increased from 10.4 to 25.3 years and the number of repairs decreased from 9 to 4 due to the low diffusion coefficient of the bacteria repair material.

A multiscale approach for stable relaxation parameter values in lattice Boltzmann simulations of heat and mass transport in porous media

Present work proposes a multiple time-scale lattice-Boltzmann method (LBM) for solving coupled convection-diffusion equations with large variation in diffusion coefficients. The key to the proposed approach is to vary the computational time-step over the solution domain according to the value of the diffusion coefficient. The proposed approach removes the limited applicability of classical LBM in simulating coupled transport phenomena with high diffusivity ratios. The proposed method is also found to be very efficient in solving heat and mass transfer problems in systems involving a combination of clear and porous media. The results indicate the efficacy of the proposed method in handling coupled flow, heat and mass transport in systems where diffusion coefficients values vary over several orders of magnitude.

Dynamic brain ADC variations over the cardiac cycle and their relation to tissue strain assessed with DENSE at high‐field MRI

PurposeThe ADC of brain tissue slightly varies over the cardiac cycle. This variation could reflect physiology, including mixing of the interstitial fluid, relevant for brain waste clearance. However, it is known from cardiac diffusion imaging that tissue deformation by itself affects the magnitude of the MRI signal, leading to artificial ADC variations as well. This study investigates to what extent tissue deformation causes artificial ADC variations in the brain.Theory and MethodsWe implemented a high‐field MRI sequence with stimulated echo acquisition mode that simultaneously measures brain tissue deformation and ADC. Based on the measured tissue deformation, we simulated the artificial ADC variation by combining established theoretical frameworks and compared the results with the measured ADC variation. We acquired data in 8 healthy volunteers with diffusion weighting b = 300 and b = 1000 s/mm2.ResultsApparent diffusion coefficient variation was largest in the feet‐to‐head direction and showed the largest deviation from the mean ADC at peak systole. Artificial ADC variation estimated from tissue deformation was 1.3 ± 0.37·10−5 mm2/s in the feet‐to‐head direction for gray matter, and 0.75 ± 0.29·10−5 mm2/s for white matter. The measured ADC variation in the feet‐to‐head direction was 5.6·10−5 ± 1.5·10−5 mm2/s for gray matter and 3.2·10−5 ± 1.0·10−5 mm2/s for white matter, which was a factor of 3.5 ± 0.82 and 3.4 ± 0.57 larger than the artificial diffusion variations. The measured diffusion variations in the right‐to‐left/anterior‐to‐posterior direction were a factor of 1.5 ± 1.0/1.7 ± 1.4 and 2.0 ± 0.91/2.5 ± 0.94 larger than the artificial diffusion variations for gray matter and white matter, respectively.ConclusionApparent diffusion coefficient variations in the brain likely largely reflect physiology.

Influence of the substitution with rare earth elements on the properties of layered lanthanum nickelate – Part 1: Structure, oxygen transport and electrochemistry evaluation

This study is aimed at studying the properties of La2NiO4+δ (LNO) substituted with rare earth elements to increase its oxygen over-stoichiometry and enhance oxygen transport thus improving electrochemical properties of the related electrodes. Materials of the La1.6Ln0.4NiO4+δ series (where Ln = Pr (LPNO), Nd (LNNO), Sm (LSNO), Eu (LENO), Gd (LGNO)) are synthesized by a nitrate combustion technique and their structural features, oxygen over-stoichiometry, and oxygen transport properties are investigated by different methods such as X-ray diffraction, TGA, temperature programmed isotopic oxygen exchange with C18O2 (TPIE) in a flow reactor. The unit cell volume in the La1.6Ln0.4NiO4+δ series decreases from Pr (V = 188.3 Å3) to Gd (V = 186.7 Å3). According to the TGA data, the LNO value of oxygen over-stoichiometry, δ, is equal to 0.15, while all substituted materials, except LGNO, show higher values: 0.16 for LENO, 0.17 for LSNO and LNNO, and the highest value equal to 0.18 has been revealed for LPNO. Oxygen mobility and surface reactivity are studied by the temperature-programmed isotope exchange of oxygen with C18O2 in a flow reactor. All samples can be characterized by a fast oxygen diffusivity provided by cooperative mechanism of oxygen migration involving both regular and highly mobile interstitial oxygen. Variation of oxygen tracer diffusion coefficient with dopant cation nature is probably associated with interstitial oxygen content. The best characteristics have been acquired for Ln = Eu (D⁎ = 2.4∙10−9 cm2/s at 700 °C). Electrochemical properties of the related La1.6Ln0.4NiO4+δ electrodes are investigated in a contact with a Ce0.8Sm0.2O1.9 solid-state electrolyte. The influence of the temperature of the electrode formation and the effect of the collector layer on the electrode electrochemical activity are considered. The LENO, LPNO and LSNO-based electrodes demonstrate low polarization resistance related to the enhanced oxygen diffusion properties. Substitution with Gd, contrarily, significantly deteriorates electrochemical properties of LNO.

Prediction of local diffusion coefficient based on images of fractured coal cores

Diffusion is a transport phenomenon in coal that plays a significant role in the productivity of coal seam gas (CSG) reservoirs. The diffusion coefficient quantifies the extent of gas diffusion in a coal sample. Diffusion coefficient is commonly measured as a bulk value for a core; however, it can vary spatially in a core, and its local variation is commonly ignored. We present an automated method to calculate local diffusion coefficients of krypton in a coal core using 3D microcomputed X-ray tomography (micro-CT) images. Fractures are identified from greyscale micro-CT images automatically and compared with the conventional watershed segmentation method. Local diffusion coefficients within the matrix are calculated automatically considering different fluid states. As gas within a coal core may be in the free state or adsorbed state, our method calculates the total diffusion coefficient taking into account the state of the fluid. We observe a variation of diffusion coefficient with time suggesting that as the gas accesses different regions of the pore matrix the diffusion rate changes. 3D diffusion coefficient maps are generated from the automated calculation, which shows the heterogeneity of the coal sample. The fractions of free and adsorbed gases are calculated, which allows further analysis of their individual impact on transport. Additionally, the proposed method can be applied to other fractured materials for automated diffusion coefficient measurements.

Pattern formation in a reaction–diffusion rumor propagation system with Allee effect and time delay

This paper analyzes the diffusion behavior of the suspicious and the infected cabins in cyberspace by establishing a rumor propagation reaction–diffusion model with Allee effect and time delay. The Turing instability conditions of the system are emphatically studied. After considering the effect of time delay on the rumor propagation system, we have studied the correlation between the stability of the system under the influence of small time delay and the homogeneous system near the equilibrium point; the critical condition of the delay-induced spatial instability is given as well. Then, we prove the existence of Hopf bifurcation induced by time delay in some cases. Further considering the possibility of diffusion coefficient changing with time, the critical parameter curves of stability and instability of approximate systems are given by means of Floquet theory, and the necessary conditions of Turing instability of periodic coefficient are studied. In the numerical simulations, we find that the variation in diffusion coefficient and time delay will change the pattern type, and the periodical diffusion behavior will affect the arrangement of the crowd gathering area in the pattern.