Time-dependent Diffusion Coefficient and Conventional Diffusion Constant of Nanoparticles in Polymer Melts by Mode-coupling Theory

Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa- tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site model with Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode- coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.

Molecular Dynamics, Diffusion Coefficients and Activation Energy of the Electrolyte (Anode) in Lithium (Li and Li+), Sodium (Na and Na+) and Potassium (K and K+)

This work is a simulation modelling with the LAMMPS calculation code of an electrode based on alkali metals (lithium, sodium and potassium) using the MEAM potential. For different multiplicities, two models were studied;with and without gap. In this work, we present the structural, physical and chemical properties of the lithium, sodium and potassium electrodes. For the structural properties, the cohesive energy and the mesh parameters were calculated, revealing that, whatever the chemical element selected, the compact hexagonal hcp structure is the most stable, followed by the face-centred cubic CFC structure, and finally the BCC structure. The most stable structure is lithium, with a cohesion energy of -6570 eV, and the lowest bcc-hcp transition energy of -0.553 eV/atom, followed by sodium. For physical properties, kinetic and potential energies were calculated for each of the sectioned chemical elements, with lithium achieving the highest value. Finally, for the chemical properties, we studied the diffusion coefficient and the activation energy. Only potassium followed an opposite order to the other two, with the quantities with lacunae being greater than those without lacunae, whatever the multiplicity. The order of magnitude of the diffusion coefficients is given by the relationship DLi > DNa > Dk for the multiplicity 6*6*6, while for the activation energy the order is reversed.

Molecular Dynamics, Physical Properties, Diffusion Coefficients and Activation Energy of the Lithium Oxide (Li-O) and Sodium Oxide (Na-O) Electrolyte (Cathode)

This work is a simulation model with the LAMMPS calculation code of an electrode based on alkali metal oxides (lithium, sodium and potassium) using the Lennard Jones potential. For a multiplicity of 8*8*8, we studied a gap-free model using molecular dynamics. Physical quantities such as volume and pressure of the Na-O and Li-O systems exhibit similar behaviors around the thermodynamic ensembles NPT and NVE. However, for the Na2O system, at a minimum temperature value, we observe a range of total energy values;in contrast, for the Li2O system, a minimum energy corresponds to a range of temperatures. Finally, for physicochemical properties, we studied the diffusion coefficient and activation energy of lithium and potassium oxides around their melting temperatures. The order of magnitude of the diffusion coefficients is given by the relation Dli-O >DNa-O for the multiplicity 8*8*8, while for the activation energy, the order is well reversed EaNa-O > EaLi-O.

Identification of the Diffusion Coefficients of Pollutants ( N O 3 - and Mn2+) through the Walls of Concrete Tank and Vulnerability of the Stored Water Quality

The populations of urban centers in Congo-Brazzaville have decided to develop various methods of water storage (concrete or masonry underground tanks) for domestic use, due to shortages in the distribution of water through the public network. However, questions remain as to the physico-chemical quality of the water stored in these tanks, when these structures are built in wet and relatively polluted areas. This paper presents a model of pollutant diffusion through the cementitious matrix (concrete) of tank walls simulated at a buried reservoir. The results of the experimental and numerical simulations show that certain concrete parameters, such as porosity, permeability and diffusivity, have a significant influence on the transfer of pollutants through the concrete walls, thus altering the physico-chemical quality of the stored water. The numerical models (1D) used to predict pollutant transfer and the quality of the stored water are consistent with those of the optimal control for identifying the diffusion coefficient. Major ion concentrations appear to be correlated with system porosity and diffusion coefficient. Nevertheless, the identification of the diffusion coefficient from the optimal control method, based on an explicit numerical resolution of a finite volume PDE for the approximation of the experiment, is not consistent with that of the optimal control method.

Effect of Size and Initial Water Content on the Effective Diffusion Coefficient during Convective Drying of Sweet Potato Cut into Cubic and Cylindrical Shapes

In this article, we investigated the influence of size and initial water content on the effective diffusion coefficient of sweet potatoes samples cut into cubic and cylindrical shapes. The sizes of the cubic samples are 0.5, 1, 1.5, 1.75, 2, 2.5 and 3 cm edge with a respective initial water content of 2.7, 3.76, 3.48, 2.68, 3.28, 2.17 and 2.29 kg/kgms. For cylindrical samples, the radius is set at 0.5 cm and sample heights are 1, 1.5, 2, 2.5, 3, 3.5 and 4 cm with respective water contents of 2.2, 3.19, 2.85, 2.1, 2.17, 2.39 and 2.03 kg/kgms. The effective diffusion coefficients of cubic samples are of the order of 10−10 and 10−9 m2∙s−1 grew with sample edge. As for the cylindrical samples, the effective diffusion coefficients were of the order of 10−9 m2∙s−1 and there was no linear correlation between cylinder height and their effective diffusion coefficient. As for the examination of the initial water content on the effective diffusion coefficient, it turned out that the initial water content had no influence on the effective diffusion coefficient of the sweet potato samples.

Determination of Natural Logarithm of Diffusion Coefficient and Activation Energy of Thin Layer Drying Process of Ginger Rhizome Slices

This study is an extension of the previous work done with ARS-680 Environmental Chamber. Drying is a complex operation that demands much energy and time. Drying is essentially important for preservation of ginger rhizome. Drying of ginger was modeled, and then the effective diffusion coefficient and activation energy were determined. For this purpose, the experiments were done at six levels of varied temperatures: 10°C, 20°C, 30°C, 40°C, 50°C and 60°C. The values of effective diffusion coefficients obtained in this work for the variously treated ginger rhizomes closely agreed with the average effective diffusion coefficients of other notable authors who determined the drying kinetics and convective heat transfer coefficients of ginger slices.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

Vertical Diffusion Coefficient with Stratification Effect for Silty Sediment Suspension Under Waves

To analyze previous experimental data of suspended sediment concentration for silty sediment with different sediment particle sizes due to waves, a new stratification correction coefficient is presented. The suspended sediment concentration gradient and sediment particle diameter are selected as parameters. Furthermore, a diffusion coefficient model with a stratification effect over the whole water depth for silty sediment suspension under waves is developed. The comparison between the suspended sediment concentration calculated by the presented model and several groups of experimental data shows that the model can reasonably reflect the vertical distribution of silty sediment suspension.The stratification effect calculated by the present model decreases with an increase in the sediment particle diameter,which indicates that the model can be extended to describe the suspended sediment concentration of fine to medium sand when the near-bottom sediment concentration is not very high. Although the original model needs to be iteratively solved, the approximate method without iteration is recommended for applications when the near bottom sediment concentration is between 10 and 20 kg/m~3 due to the small difference between the non-iterative and iterative solution for near bed layer suspended sediment concentration, which plays a major role in sediment transport.

ANALYSIS AND DISCRETIZATION FOR AN OPTIMAL CONTROL PROBLEM OF A VARIABLE-COEFFICIENT RIESZ-FRACTIONAL DIFFUSION EQUATION WITH POINTWISE CONTROL CONSTRAINTS

We present a mathematical and numerical study for a pointwise optimal control problem governed by a variable-coefficient Riesz-fractional diffusion equation.Due to the impact of the variable diffusivity coefficient,existing regularity results for their constantcoefficient counterparts do not apply,while the bilinear forms of the state(adjoint)equation may lose the coercivity that is critical in error estimates of the finite element method.We reformulate the state equation as an equivalent constant-coefficient fractional diffusion equation with the addition of a variable-coefficient low-order fractional advection term.First order optimality conditions are accordingly derived and the smoothing properties of the solutions are analyzed by,e.g.,interpolation estimates.The weak coercivity of the resulting bilinear forms are proven via the Garding inequality,based on which we prove the optimal-order convergence estimates of the finite element method for the(adjoint)state variable and the control variable.Numerical experiments substantiate the theoretical predictions.

Unveiling the Re,Cr,and I diffusion in saturated compacted bentonite using machine-learning methods

The safety assessment of high-level radioactive waste repositories requires a high predictive accuracy for radionuclide diffusion and a comprehensive understanding of the diffusion mechanism.In this study,a through-diffusion method and six machine-learning methods were employed to investigate the diffusion of ReO_(4)^(−),HCrO_(4)^(−),and I−in saturated compacted bentonite under different salinities and compacted dry densities.The machine-learning models were trained using two datasets.One dataset contained six input features and 293 instances obtained from the diffusion database system of the Japan Atomic Energy Agency(JAEA-DDB)and 15 publications.The other dataset,comprising 15,000 pseudo-instances,was produced using a multi-porosity model and contained eight input features.The results indicate that the former dataset yielded a higher predictive accuracy than the latter.Light gradient-boosting exhibited a higher prediction accuracy(R2=0.92)and lower error(MSE=0.01)than the other machine-learning algorithms.In addition,Shapley Additive Explanations,Feature Importance,and Partial Dependence Plot analysis results indicate that the rock capacity factor and compacted dry density had the two most significant effects on predicting the effective diffusion coefficient,thereby offering valuable insights.

Calculation of ion diffusion coefficient related to concrete deterioration based on Debye-Hückel-Onsager theory

This paper applies the Debye-Hückel-Onsager electrolyte solution theory to investigate the diffusivity of ions in concrete pore solutions.First,a model of the diffusion coefficient associated with the ionic species,solution concentration and ambient temperature is proposed in the saturated concrete.Secondly,as an example,the effects of sodium chloride solution concentration,which are associated with influencing factors such as the ionic cloud radius,electrophoresis and relaxation,on the chloride diffusion coefficient are analyzed.It is found that the diffusion coefficient decreases with the increase in solution concentration,and the electrophoresis and ionic cloud radius are two important factors influencing the ionic diffusivity.Finally,the experiments,in which the chloride diffusion coefficients in specimens under different water-cement ratios are measured by the rapid chloride migration（RCM）method,are carried out to validate the effectiveness of the proposed model,and the results indicate that there is a generally reasonable agreement between the experimental and the proposed model results.

Diffusion Equations of the Electric Charges and Magnetic Flux

Innovative definitions of the electric and magnetic diffusivities through conducting mediums and innovative diffusion equations of the electric charges and magnetic flux are verified in this article. Such innovations depend on the analogy of the governing laws of diffusion of the thermal, electrical, and magnetic energies and newly defined natures of the electric charges and magnetic flux as energy, or as electromagnetic waves, that have electric and magnetic potentials. The introduced diffusion equations of the electric charges and magnetic flux involve Laplacian operator and the introduced diffusivities. Both equations are applied to determine the electric and magnetic fields in conductors as the heat diffusion equation which is applied to determine the thermal field in steady and unsteady heat diffusion conditions. The use of electric networks for experimental modeling of thermal networks represents sufficient proof of similarity of the diffusion equations of both fields. By analysis of the diffusion phenomena of the three considered modes of energy transfer;the rates of flow of these energies are found to be directly proportional to the gradient of their volumetric concentration, or density, and the proportionality constants in such relations are the diffusivity of each energy. Such analysis leads also to find proportionality relations between the potentials of such energies and their volumetric concentrations. Validity of the introduced diffusion equations is verified by correspondence their solutions to the measurement results of the electric and magnetic fields in microwave ovens.

Transient elastography and diffusion-weighted magnetic resonance imaging for assessment of liver fibrosis in children with chronic hepatitis C

BACKGROUND Chronic hepatitis C(CHC)is a health burden with consequent morbidity and mortality.Liver biopsy is the gold standard for evaluating fibrosis and assessing disease severity and prognostic purposes post-treatment.Noninvasive altern-atives for liver biopsy such as transient elastography(TE)and diffusion-weighted magnetic resonance imaging(DW-MRI)are critical needs.AIM To evaluate TE and DW-MRI as noninvasive tools for predicting liver fibrosis in children with CHC.METHODS This prospective cross-sectional study initially recruited 100 children with CHC virus infection.Sixty-four children completed the full set of investigations including liver stiffness measurement(LSM)using TE and measurement of apparent diffusion coefficient(ADC)of the liver and spleen using DW-MRI.Liver biopsies were evaluated for fibrosis using Ishak scoring system.LSM and liver and spleen ADC were compared in different fibrosis stages and correlation analysis was performed with histopathological findings and other laboratory parameters.RESULTS Most patients had moderate fibrosis(73.5%)while 26.5%had mild fibrosis.None had severe fibrosis or cirrhosis.The majority(68.8%)had mild activity,while only 7.8%had moderate activity.Ishak scores had a significant direct correlation with LSM(P=0.008)and were negatively correlated with both liver and spleen ADC but with no statistical significance(P=0.086 and P=0.145,respectively).Similarly,histopatho-logical activity correlated significantly with LSM(P=0.002)but not with liver or spleen ADC(P=0.84 and 0.98 respectively).LSM and liver ADC were able to significantly discriminate F3 from lower fibrosis stages(area under the curve=0.700 and 0.747,respectively)with a better performance of liver ADC.CONCLUSION TE and liver ADC were helpful in predicting significant fibrosis in children with chronic hepatitis C virus infection with a better performance of liver ADC.

Effect of liquid diffusion coefficients on microstructure evolution during solidification of Al356.1 alloy

（The effect of liquid diffusion coefficients on the microstructure evolution during solidification of primary （Al） phase in Al356.1 alloy was investigated by means of the phase-field simulation using two sets of diffusion coefficients in liquid phase, while fixing other thermophysical and numerical parameters. The first set is only with impurity coefficients of liquid phase in Arrhenius formula representing only the temperature dependence. While the second set is with the well-established atomic mobility database representing both temperature and concentration dependence. For the second set of liquid diffusion coefficients, the effect of non-diagonal diffusion coefficients on the microstructure evolution in Al356.1 alloy during solidification was also analyzed. The differences were observed in the morphology, tip velocity and composition profile ahead of the tip of the dendrite due to the three cases of liquid diffusivities. The simulation results indicate that accurate databases of mobilities in the liquid phase are highly needed for the quantitative simulation of microstructural evolution during solidification.

Hydrogen diffusion coefficient in liquid metals evaluated by solid-gas eutectic unidirectional solidification

Based on the solid-gas eutectic unidirectional solidification technique and the principle of unidirectional solidification of single-phase alloy, a new method for evaluating the diffusion coefficient of hydrogen in liquid metals was proposed. Taking Cu-H2 system for example, the influences of argon partial pressure and superheat degree of melt on the diffusion coefficient of hydrogen in liquid metal were studied and the predicted values were similar to each other. The obtained temperature-dependent equation for diffusion coefficient of hydrogen in liquid copper is comparable with experimental data in literature, which validates the effectiveness of this method. The temperature-dependent equations for diffusion coefficient of hydrogen in liquid Mg, Si and Cu-34.6%Mn alloy were also evaluated by this method, along with the values at the melting point of each metal and alloy.

Effect of Rare Earths on Diffusion Coefficient and Transfer Coefficient of Carbon during Carburizing

The diffusion coefficient of carbon in surface layer of steel-20 rare earth carburixed at 880 degreesC and 900 degreesC for 8 h was calculated by substituting the measured layer depths into the diffusion equation. The mathematical model of the transfer coefficient of carbon was deduced based on the kinetics of weight gain during gas carburizing. The calculated results show that the main reason why the gas carburizing process is accelerated is due to the obvious increase in the diffusion coefficient and transfer coefficient of carbon resulted from the addition of RE.

Apparent diffusion coefficient by diffusion-weighted magnetic resonance imaging as a sole biomarker for staging and prognosis of gastric cancer

Objective： To investigate the role of apparent diffusion coefficient （ADC） from diffusion-weighted magnetic resonance imaging （DW-MRI） when applied to the 7th TNM classification in the staging and prognosis of gastric cancer （GC）. Methods： Between October 2009 and May 2014, a total of 89 patients with non-metastatic, biopsy proven GC underwent 1.5T DW-MRI, and then treated with radical surgery. Tumor ADC was measured retrospectively and compared with final histology following the 7th TNM staging （local invasion, nodal involvement and according to the different groups -- stage Ⅰ, Ⅱ and Ⅲ）. Kaplan-Meier curves were also generated. The follow-up period is updated to May 2016. Results： Median follow-up period was 33 months and 45/89 （51%） deaths from GC were observed. ADC was significantly different both for local invasion and nodal involvement （P〈0.001）. Considering final histology as the reference standard, a preoperative ADC cut-offof 1.80×10-3 mm^2/s could distinguish between stages I and Ⅱ and an ADC value of ≤1.36-10-3 mm^2/s was associated with stage Ⅲ（P〈0.001）. Kaplan-Meier curves demonstrated that the survival rates for the three prognostic groups were significantly different according to final histology and ADC cut-offs （P〈0.001）. Conclusions： ADC is different according to local invasion, nodal involvement and the 7th TNM stage groups for GC, representing a potential, additional prognostic biomarker. The addition of DW-MRI could aid in the staging and risk stratification of GC.

Influence of Binder Composition and Concrete Pore Structure on Chloride Diffusion Coefficient in Concrete

The influence of binder composition and pore structure of concrete on chloride diffusion coefficient in concrete were investigated by the natural immersion test, MIP test, SEM and EDS test, respectively. The experimental results showed that the effect of binder composition on chloride diffusion coefficient was the comprehensive result of concrete pore structure and binder hydration products, and the porosity and pore size distribution were the main factors that influence the changes of diffusion coefficient. The chloride diffusion coefficient decreased with increasing the curing temperature and the relative humidity. The hydration degree were promoted by improving curing temperatures, and then the porosity of concrete decreased and the proportion of gel pore and transitional pore increased, respectively. But the water evaporation decreased with increasing the relative humidity and then decreased porosity and increased the proportion of gel pore and transitional pore. Additionally, The chloride diffusion coefficient of concrete got the lower value when the appropriate replacement of fly ash in the ranges of 10%-20%, when the double-adding fly ash and slag content was 50%. The porosity increased and the ratio of C/S in C-S-H decreased with further increasing the fly ash content, which led to increase the chloride diffusion coefficient in concrete.

Apparent diffusion coefficient values of normal testis and variations with age

The usefulness of diffusion-weighted magnetic resonance imaging （DWI） in the evaluation of scrotal pathology has recently been reported. A standard reference of normal testicular apparent diffusion coefficient （ADC） values and their variations with age is necessary when interpreting normal testicular anatomy and pathology. We evaluated 147 normal testes using DWI, including 71 testes from 53 men aged 20-39years （group 1）, 67 testes from 42 men aged 40-69 years （group 2） and nine testes from six men older than 70years （group 3）. DWI was performed along the axial plane, using a single shot, multislice spin-echo planar diffusion pulse sequence and b-values of 0 and 900 s mm-2. The mean and standard deviation of the ADC values of normal testicular parenchyma were calculated for each age group separately. Analysis of variance （ANOVA） followed by post hoc analysis （Dunnett T3） was used for statistical purposes. The ADC values （x 10-3 mm2s-1） of normal testicular tissue were different among age groups （group 1：1.08 ± 0.13; group 2：1.15 ±0.15 and group 3：1.31± 0.22）. ANOVA revealed differences in mean ADC among age groups （F= 11.391, P〈 0.001）. Post hoc analysis showed differences between groups 1 and 2 （P= 0.008） and between groups 1 and 3 （P= 0.043）, but not between groups 2 and 3 （P= 0.197）. Our findings suggest that ADC values of normal testicular tissue increase with advancing age.

Prediction of different stages of rectal cancer: Texture analysis based on diffusion-weighted images and apparent diffusion coefficient maps

BACKGROUND It is evident that an accurate evaluation of T and N stage rectal cancer is essential for treatment planning.It has not been extensively investigated whether texture features derived from diffusion-weighted imaging(DWI)images and apparent diffusion coefficient(ADC)maps are associated with the extent of local invasion(pathological stage T1-2 vs T3-4)and nodal involvement(pathological stage N0 vs N1-2)in rectal cancer.AIM To predict different stages of rectal cancer using texture analysis based on DWI images and ADC maps.METHODS One hundred and fifteen patients with pathologically proven rectal cancer,who underwent preoperative magnetic resonance imaging,including DWI,were enrolled,retrospectively.The ADC measurements(ADCmean,ADCmin,ADCmax)as well as texture features,including the gray level co-occurrence matrix parameters,the gray level run-length matrix parameters and wavelet parameters were calculated based on DWI(b=0 and b=1000)images and the ADC maps.Independent sample t-tests or Mann-Whitney U tests were used for statistical analysis.Multivariate logistic regression analysis was conducted to establish the models.The predictive performance was validated by receiver operating characteristic curve analysis.RESULTS Dissimilarity,sum average,information correlation and run-length nonuniformity from DWIb=0 images,gray level nonuniformity,run percentage and run-length nonuniformity from DWIb=1000 images,and dissimilarity and run percentage from ADC maps were found to be independent predictors of local invasion(stage T3-4).The area under the operating characteristic curve of the model reached 0.793 with a sensitivity of 78.57%and a specificity of 74.19%.Sum average,gray level nonuniformity and the horizontal components of symlet transform(SymletH)from DWIb=0 images,sum average,information correlation,long run low gray level emphasis and SymletH from DWIb=1000 images,and ADCmax,ADCmean and information correlation from ADC maps were identified as independent predictors of nodal involvement.The area under the operating characteristic curve of the model reached 0.802 with a sensitivity of 80.77%and a specificity of 68.25%.CONCLUSION Texture features extracted from DWI images and ADC maps are useful clues for predicting pathological T and N stages in rectal cancer.