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.

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.

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.

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 carburized at 880 ℃ and 900 ℃ 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.

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.

Apparent diffusion coefficient-based histogram analysis differentiates histological subtypes of periampullary adenocarcinoma

BACKGROUND For periampullary adenocarcinoma,the histological subtype is a better prognostic predictor than the site of tumor origin.Intestinal-type periampullary adenocarcinoma(IPAC)is reported to have a better prognosis than the pancreatobiliary-type periampullary adenocarcinoma(PPAC).However,the classification of histological subtypes is difficult to determine before surgery.Apparent diffusion coefficient(ADC)histogram analysis is a noninvasive,nonenhanced method with high reproducibility that could help differentiate the two subtypes.AIM To investigate whether volumetric ADC histogram analysis is helpful for distinguishing IPAC from PPAC.METHODS Between January 2015 and October 2018,476 consecutive patients who were suspected of having a periampullary tumor and underwent magnetic resonance imaging(MRI)were reviewed in this retrospective study.Only patients who underwent MRI at 3.0 T with different diffusion-weighted images(b-values=800 and 1000 s/mm^2)and who were confirmed with a periampullary adenocarcinoma were further analyzed.Then,the mean,5th,10th,25th,50th,75th,90th,and 95th percentiles of ADC values and ADCmin,ADCmax,kurtosis,skewness,and entropy were obtained from the volumetric histogram analysis.Comparisons were made by an independent Student's t-test or Mann-Whitney U test.Multiple-class receiver operating characteristic curve analysis was performed to determine and compare the diagnostic value of each significant parameter.RESULTS In total,40 patients with histopathologically confirmed IPAC(n=17)or PPAC(n=23)were enrolled.The mean,5th,25th,50th,75th,90th,and 95th percentiles and ADCmax derived from ADC1000 were significantly lower in the PPAC group than in the IPAC group(P<0.05).However,values derived from ADC800 showed no significant difference between the two groups.The 75th percentile of ADC1000 values achieved the highest area under the curve(AUC)for differentiating IPAC from PPAC(AUC=0.781;sensitivity,91%;specificity,59%;cut-off value,1.50×10^-3 mm^2/s).CONCLUSION Volumetric ADC histogram analysis at a b-value of 1000 s/mm2 might be helpful for differentiating the histological subtypes of periampullary adenocarcinoma before surgery.

Histogram analysis of apparent diffusion coefficient predicts response to radiofrequency ablation in hepatocellular carcinoma

Objective: The aim of this study was to predict tumor progression in patients with hepatocellular carcinoma(HCC) treated with radiofrequency ablation(RFA) using histogram analysis of apparent diffusion coefficients(ADC).Methods: Breath-hold diffusion weighted imaging(DWI) was performed in 64 patients(33 progressive and 31 stable) with biopsy-proven HCC prior to RFA. All patients had pre-treatment magnetic resonance imaging(MRI)and follow-up computed tomography(CT) or MRI. The ADC values(ADC_(10), ADC_(30_, ADC_(median) and ADC_(max))were obtained from the histogram's 10 th, 30 th, 50 th and 100 th percentiles. The ratios of ADC_(10), ADC_(30_,ADCmedian and ADCmax to the mean non-lesion area-ADC(RADC_(10), RADC_(30_, RADC_(median), and RADC_(max)) were calculated. The two patient groups were compared. Key predictive factors for survival were determined using the univariate and multivariate analysis of the Cox model. The Kaplan-Meier survival analysis was performed, and pairs of survival curves based on the key factors were compared using the log-rank test.Results: The ADC_(30_, ADCmedian, ADCmax, RADC_(30_, RADC_(median), and RADC_(max) were significantly larger in the progressive group than in the stable group(P<0.05). The median progression-free survival(PFS) was 22.9 months for all patients. The mean PFS for the stable and progressive groups were 47.7±1.3 and 9.8±1.3 months,respectively. Univariate analysis indicated that RADC_(10), RADC_(30_, and RADC_(median) were significantly correlated with the PFS [hazard ratio(HR)=31.02, 43.84, and 44.29, respectively, P<0.05 for all]. Multivariate analysis showed that RADCmedian was the only independent predictor of tumor progression(P=0.04). And the cutoff value of RADC_(median) was 0.71.Conclusions: Pre-RFA ADC histogram analysis might serve as a useful biomarker for predicting tumor progression and survival in patients with HCC treated with RFA.

Combined value of apparent diffusion coefficient-standardized uptake value max in evaluation of post-treated locally advanced rectal cancer

AIM:To assess the clinical diagnostic value of functional imaging,combining quantitative parameters of apparent diffusion coefficient(ADC) and standardized uptake value(SUV)max,before and after chemo-radiation therapy,in prediction of tumor response of patients with rectal cancer,related to tumor regression grade at histology.METHODS:A total of 31 patients with biopsy proven diagnosis of rectal carcinoma were enrolled in our study.All patients underwent a whole body ^(18)FDG positron emission tomography(PET)/computed tomography(CT) scan and a pelvic magnetic resonance(MR)examination including diffusion weighted(DW) imaging for staging(PET1,RM1) and after completion(6.6 wk)of neoadjuvant treatment(PET2,RM2).Subsequently all patients underwent total mesorectal excision and the histological results were compared with imaging findings.The MR scanning,performed on 1.5 T magnet(Philips,Achieva),included T2-weighted multiplanar imaging and in addition DW images with b-value of 0 and 1000 mm^2/s.On PET/CT the SUVmax of the rectal lesion were calculated in PET1 and PET2.The percentage decrease of SUVmax(△SUV) and ADC(△ADC) values from baseline to presurgical scan were assessed and correlated with pathologic response classified as tumor regression grade(Mandard's criteria;TRG1 = complete regression,TRG5 = no regression).RESULTS:After completion of therapy,all the patients were submitted to surgery.According to the Mandard's criteria,22 tumors showed complete(TRG1) or subtotal regression(TRG2) and were classified as responders;9tumors were classified as non responders(TRG3,4 and5).Considering all patients the mean values of SUVmax in PET 1 was higher than the mean value of SUVmax in PET 2(P < 0.001),whereas the mean ADC values was lower in RM1 than RM2(P < 0.001),with a △SUV and △ADC respectively of 60.2%and 66.8%.The best predictors for TRG response were SUV2(threshold of4.4) and ADC2(1.29 × 10^(-3) mm^2/s) with high sensitivity and specificity.Combining in a single analysis both the obtained median value,the positive predictive value,in predicting the different group category response in related to TRG system,presented R^2 of 0.95.CONCLUSION:The functional imaging combining ADC and SUVmax in a single analysis permits to detect changes in cellular tissue structures useful for the assessment of tumour response after the neoadjuvant therapy in rectal cancer,increasing the sensitivity in correct depiction of treatment response than either method alone.

Diffusion-weighted magnetic resonance imaging in cancer: Reported apparent diffusion coefficients,in-vitro and invivo reproducibility

There is considerable disparity in the published apparent diffusion coefficient(ADC) values across different anatomies. Institutions are increasingly assessing repeatability and reproducibility of the derived ADC to determine its variation,which could potentially be used as an indicator in determining tumour aggressiveness or assessing tumour response. In this manuscript,a review of selected articles published to date in healthy extracranial body diffusion-weighted magnetic resonance imaging is presented,detailing reported ADC values and discussing their variation across different studies. In total 115 studies were selected including 28 for liver parenchyma,15 for kidney(renal parenchyma),14 for spleen,13 for pancreatic body,6 for gallbladder,13 for prostate,13 for uterus(endometrium,myometrium,cervix) and 13 for fibroglandular breast tissue. Median ADC values in selected studies were found to be 1.28 × 10-3 mm2/s in liver,1.94 × 10-3 mm2/s in kidney,1.60 × 10-3 mm2/s in pancreatic body,0.85 × 10-3 mm2/s in spleen,2.73 × 10-3 mm2/s in gallbladder,1.64 × 10-3 mm2/s and 1.31 × 10-3 mm2/s in prostate peripheral zone and central gland respectively(combined median value of 1.54×10-3 mm2/s),1.44 × 10-3 mm2/s in endometrium,1.53 × 10-3 mm2/s in myometrium,1.71 × 10-3 mm2/s in cervix and 1.92 × 10-3 mm2/s in breast. In addition,six phantom studies and thirteen in vivo studies were summarized to compare repeatability and reproducibility of the measured ADC. All selected phantom studies demonstrated lower intra-scanner and inter-scanner variation compared to in vivo studies. Based on the findings of this manuscript,it is recommended that protocols need to be optimised for the body part studied and that system-induced variability must be established using a standardized phantom in any clinical study. Reproducibility of the measured ADC must also be assessed in a volunteer population,as variations are far more significant in vivo compared with phantom studies.

Fractal scaling of effective diffusion coefficient of solute in porous media

Fractal approach is used to derive a power law relation between effective diffusion coefficient of solute in porous media and the geometry parameter characterizing the media.The results are consistent with the empirical equations analogous to Archie’s law and are expected to be applied to prediction of effective diffusion coefficient.

CORRELATION AND PREDICTION OF LIQUID DIFFUSION COEFFICIENTS IN BINARY SYSTEMS

A theoretical model to correlate and predict the liquid diffusion coefficients in binary sys-tems has been developed.Based on this mode1 the diffusion coefficient of 73 binary systems have beencorrelated,the overall average deviation of the correlation for diffusion coefficients is 0.009.Forbinary systems the diffusion coefficients have been predicted from vapor liquid phase equilibrium(VLE)and vice versa.

STUDY ON THE DIFFUSION OF Cu^(2+)-H^+ COUPLE IN A CATION EXCHANGE MEMBRANE——A RAPID METHOD TO DETERMINE SELF-DIFFUSION COEFFICIENTS OF COUNTER-IONS WITH UNEQUAL VALENCE

1 INTRODUCTIONKnowledge of the basic transport phenomena of ions in an ion exchange membrane isimportant for the application of such a membrane.Various studies on the developmentof mathematical models for predicting and correlating membrane transport rate havebeen published in recent years.More exact estimation of the diffusion coefficientshas been the subject of chief concern in many of these papers.For a bi-ionic systemwith the same valence,Sato et al.gave a method for estimating diffusion coefficients

Drift Mobility, Diffusion Coefficient of Randomly Moving Charge Carriers in Metals and Other Materials with Degenerated Electron Gas

In this short review some aspects of applications of free electron theory on the ground of the Fermi statistics will be analyzed. There it is an intention to attempt somebody’s attention to problems in widespread literature of interpretation of conductivity of metals, superconductor in the normal state and semiconductors with degenerated electron gas. In literature there are many cases when to these materials the classical statistics is applied. It is well known that the electron heat capacity and thermal noise (and as a consequence the electrical conductivity) are determined by randomly moving electrons, which energy is close to the Fermi energy level, and the other part of electrons, which energy is well below the Fermi level can not be scattered and change its energy. Therefore there was tried as simple as possible on the ground of Fermi distribution, and on random motion of charge carriers, and on the well known experimental results to take general expressions for various kinetic parameters which are applicable for materials both without and with degenerated electron gas. It is shown, that drift mobility of randomly moving charge carriers, depending on the degree degeneracy, can considerably exceed the Hall mobility. Also it is shown that the Einstein relation between the diffusion coefficient and the drift mobility of charge carriers is valid even in the case of degeneracy. There also will be presented the main kinetic parameter values for different metals.

Effect of Curing Age on Chloride Diffusion Coefficient of Recycled Aggregate Concrete Subjected to Compressive Stresses

The effect of curing age on chloride diffusion coefficient of recycled aggregate concrete subjected to different compressive stresses was investigated.A compression loading setup was both designed and fabricated.The chloride diffusion coefficients of recycled aggregate concrete under compressive stresses were measured by the rapid chloride ion migration(RCM)method.The experimental results show that the chloride diffusion coefficients of recycled aggregate concrete(RAC)under different compressive stress ratios generally decrease with the increase of curing age.For RAC subjected to the same compressive stress ratios,the chloride diffusion coefficients approximately have power functions with curing ages and the relationship models are proposed.Moreover,the influence of curing age on chloride diffusion coefficient firstly decreases and then increases as the compressive stress ratio increases.

Correlation of magnetic resonance imaging quantitative parameters and apparent diffusion coefficient value with pathological breast cancer

BACKGROUND China ranks 120th worldwide for the incidence of breast cancer and 163rd for mortality.Early screening,diagnosis,and timely determination of the optimal treatment plan can help ensure clinical efficacy and prognosis.AIM To investigate the relationship between quantitative magnetic resonance imaging parameters,apparent diffusion coefficient value,pathological immunohistochemical status,and patient prognosis.METHODS A total of 108 patients with breast cancer(breast cancer group)and 110 patients with benign breast tumors(benign group)confirmed by pathological examination at our Hospital from September 2013 to August 2016 were selected.All patients had undergone preoperative magnetic resonance imaging(MRI)examinations,and the quantitative parameters of MRI and apparent diffusion coefficient(ADC)values for the two groups were compared.The MRI quantitative parameters and ADC values of patients with different estrogen receptor(ER),progesterone receptor,and human epidermal growth factor receptor-2 expression were statistically analyzed.The relationship between the quantitative parameters of MRI and ADC values and patient recurrence was analyzed using receiver operating curves.RESULTS The measured values of the quantitative parameters of MRI-Ktrans,Kep,and Ve in the breast cancer group were higher than those in the benign group;the ADC value in the breast cancer group was lower than that in the benign group,and the difference was statistically significant(P<0.05).The Ktrans,Ve,and ADC values in patients with ER-positive breast cancer were significantly lower than those in patients with negative ER expression(P<0.05).After 5 years of follow-up,22 patients with breast cancer experienced postoperative recurrence.The Kep,Ve,and ADC values of the recurrence group were significantly lower than those of the non-recurrence group,and the difference was statistically significant(P<0.05).CONCLUSION MRI quantitative parameters and ADC are related to the expression of breast cancer-related immunological receptor factors and have certain clinical value in assessing postoperative recurrence in patients.

Influence of Temperature and Frequency on Minority Carrier Diffusion Coefficient in a Silicon Solar Cell under Magnetic Field

In this study, the effects of temperature and frequency on minority carrier diffusion coefficient in silicon solar cell under a magnetic field are presented. Using two methods (analytic and graphical), the optimum temperature corresponding to maximum diffusion coefficient is determined versus cyclotronic frequency and magnetic field.

Whole lesion histogram analysis of apparent diffusion coefficient predicts therapy response in locally advanced rectal cancer

BACKGROUND Whole-tumor apparent diffusion coefficient(ADC)histogram analysis is relevant to predicting the neoadjuvant chemoradiation therapy(nCRT)response in patients with locally advanced rectal cancer(LARC).AIM To evaluate the performance of ADC histogram-derived parameters for predicting the outcomes of patients with LARC.METHODS This is a single-center,retrospective study,which included 48 patients with LARC.All patients underwent a pre-treatment magnetic resonance imaging(MRI)scan for primary tumor staging and a second restaging MRI for response evaluation.The sample was distributed as follows:18 responder patients(R)and 30 non-responders(non-R).Eight parameters derived from the whole-lesion histogram analysis(ADCmean,skewness,kurtosis,and ADC10^(th),25^(th),50^(th),75^(th),90^(th) percentiles),as well as the ADCmean from the hot spot region of interest(ROI),were calculated for each patient before and after treatment.Then all data were compared between R and non-R using the Mann-Whitney U test.Two measures of diagnostic accuracy were applied:the receiver operating characteristic curve and the diagnostic odds ratio(DOR).We also reported intra-and interobserver variability by calculating the intraclass correlation coefficient(ICC).RESULTS Post-nCRT kurtosis,as well as post-nCRT skewness,were significantly lower in R than in non-R(both P<0.001,respectively).We also found that,after treatment,R had a larger loss of both kurtosis and skewness than non-R(Δ%kurtosis and Δ skewness,P<0.001).Other parameters that demonstrated changes between groups were post-nCRT ADC10^(th),Δ%ADC10^(th),Δ%ADCmean,and ROIΔ%ADCmean.However,the best diagnostic performance was achieved byΔ%kurtosis at a threshold of 11.85%(Area under the receiver operating characteristic curve[AUC]=0.991,DOR=376),followed by post-nCRT kurtosis=0.78×10^(-3)mm^(2)/s(AUC=0.985,DOR=375.3),Δskewness=0.16(AUC=0.885,DOR=192.2)and post-nCRT skewness=1.59×10^(-3)mm^(2)/s(AUC=0.815,DOR=168.6).Finally,intraclass correlation coefficient analysis showed excellent intraobserver and interobserver agreement,ensuring the implementation of histogram analysis into routine clinical practice.CONCLUSION Whole-tumor ADC histogram parameters,particularly kurtosis and skewness,are relevant biomarkers for predicting the nCRT response in LARC.Both parameters appear to be more reliable than ADCmean from one-slice ROI.

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-off of 1.80×10–3 mm2/s could distinguish between stages I and II and an ADC value of≤1.36×10–3 mm2/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.