The increase to the proportion of fluxed pellets in the blast furnace burden is a useful way to reduce the carbon emissions in the ironmaking process.In this study,the interaction between calcium carbonate and iron or...The increase to the proportion of fluxed pellets in the blast furnace burden is a useful way to reduce the carbon emissions in the ironmaking process.In this study,the interaction between calcium carbonate and iron ore powder and the mineralization mechanism of fluxed iron ore pellet in the roasting process were investigated through diffusion couple experiments.Scanning electron microscopy with energy dispersive spectroscopy was used to study the elements’diffusion and phase transformation during the roasting process.The results indicated that limestone decomposed into calcium oxide,and magnetite was oxidized to hematite at the early stage of preheating.With the increase in roasting temperature,the diffusion rate of Fe and Ca was obviously accelerated,while the diffusion rate of Si was relatively slow.The order of magnitude of interdiffusion coefficient of Fe_(2)O_(3)-CaO diffusion couple was 10^(−10) m^(2)·s^(−1) at a roasting temperature of 1200℃for 9 h.Ca_(2)Fe_(2)O_(5) was the initial product in the Fe_(2)O_(3)-CaO-SiO_(2) diffusion interface,and then Ca_(2)Fe_(2)O_(5) continued to react with Fe_(2)O_(3) to form CaFe_(2)O_(4).With the expansion of the diffusion region,the sillico-ferrite of calcium liquid phase was produced due to the melting of SiO_(2) into CaFe_(2)O_(4),which can strengthen the consolidation of fluxed pellets.Furthermore,andradite would be formed around a small part of quartz particles,which is also conducive to the consolidation of fluxed pellets.In addition,the principle diagram of limestone and quartz diffusion reaction in the process of fluxed pellet roasting was discussed.展开更多
For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geomet...For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geometries may lead to difficulties in the accuracy when discretizing the high-order derivatives on grid points near the boundary.It is very challenging to design numerical methods that can efficiently and accurately handle both difficulties.Applying an implicit scheme may be able to remove the stability constraints on the time step,however,it usually requires solving a large global system of nonlinear equations for each time step,and the computational cost could be significant.Integration factor(IF)or exponential time differencing(ETD)methods are one of the popular methods for temporal partial differential equations(PDEs)among many other methods.In our paper,we couple ETD methods with an embedded boundary method to solve a system of reaction-diffusion equations with complex geometries.In particular,we rewrite all ETD schemes into a linear combination of specificФ-functions and apply one state-of-the-art algorithm to compute the matrix-vector multiplications,which offers significant computational advantages with adaptive Krylov subspaces.In addition,we extend this method by incorporating the level set method to solve the free boundary problem.The accuracy,stability,and efficiency of the developed method are demonstrated by numerical examples.展开更多
Ta/NiFe film is deposited on Si substrate precoated with SiO_2 by magnetron sputtering.SiO_2/Ta interface and Ta_5Si_3 standard sample are investigated by using X-ray photoelectron spectroscopy (XPS) and peak decompos...Ta/NiFe film is deposited on Si substrate precoated with SiO_2 by magnetron sputtering.SiO_2/Ta interface and Ta_5Si_3 standard sample are investigated by using X-ray photoelectron spectroscopy (XPS) and peak decomposition technique.The results show that there is a thermodynamically favorable reaction at the SiO_2/Ta interface:37Ta+15SiO_2=5Ta_5Si_3+6Ta_2O_5.The more stable products Ta_5Si_3 and Ta_2O_5 may be beneficial to stop the diffusion of Cu into SiO_2.展开更多
A mathematical model of CE reaction schemes under first or pseudo-first order conditions with different diffusion coefficients at a spherical electrode under non-steady-state conditions is described. The model is base...A mathematical model of CE reaction schemes under first or pseudo-first order conditions with different diffusion coefficients at a spherical electrode under non-steady-state conditions is described. The model is based on non-stationary diffusion equation containing a non-linear reaction term. This paper presents the complex numerical method (Homotopy perturbation method) to solve the system of non-linear differential equation that describes the homogeneous processes coupled to electrode reaction. In this paper the approximate analytical expressions of the non-steady-state concentrations and current at spherical electrodes for homogeneous reactions mechanisms are derived for all values of the reaction diffusion parameters. These approximate results are compared with the available analytical results and are found to be in good agreement.展开更多
A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems i...A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.展开更多
A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of ...A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied.展开更多
A class of nonlinear singularly perturbed problems for reaction diffusion equations are considered. Under suitable conditions, by using the theory of differential inequalities, the asymptotic behavior of solutions for...A class of nonlinear singularly perturbed problems for reaction diffusion equations are considered. Under suitable conditions, by using the theory of differential inequalities, the asymptotic behavior of solutions for the initial boundary value problems are studied, reduced problems of which possess two intersecting solutions.展开更多
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Unsing the iteration method and the comparison theorem, the existence, uniqueness and i...In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Unsing the iteration method and the comparison theorem, the existence, uniqueness and its asymptotic behavior of solution for the problem are studied.展开更多
A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations is considered. Under suitable conditions, firstly, the outer solution of the original probl...A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed.展开更多
In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for th...In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.展开更多
In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the re...In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.展开更多
A class of nonlinear predator prey reaction diffusion systems for singularly pe rturbed problems are considered.Under suitable conditions, by using theory of di fferential inequalities the existence and asymptotic be...A class of nonlinear predator prey reaction diffusion systems for singularly pe rturbed problems are considered.Under suitable conditions, by using theory of di fferential inequalities the existence and asymptotic behavior of solution for in itial boundary value problems are studied.展开更多
A class of singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison theorem the asymptotic behavior of solution for the initial boundary value problems is studied.
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original pr...The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.展开更多
BACKGROUND About 10%-31% of colorectal liver metastases(CRLM)patients would concomitantly show hepatic lymph node metastases(LNM),which was considered as sign of poor biological behavior and a relative contraindicatio...BACKGROUND About 10%-31% of colorectal liver metastases(CRLM)patients would concomitantly show hepatic lymph node metastases(LNM),which was considered as sign of poor biological behavior and a relative contraindication for liver resection.Up to now,there’s still lack of reliable preoperative methods to assess the status of hepatic lymph nodes in patients with CRLM,except for pathology examination of lymph node after resection.AIM To compare the ability of mono-exponential,bi-exponential,and stretchedexponential diffusion-weighted imaging(DWI)models in distinguishing between benign and malignant hepatic lymph nodes in patients with CRLM who received neoadjuvant chemotherapy prior to surgery.METHODS In this retrospective study,97 CRLM patients with pathologically confirmed hepatic lymph node status underwent magnetic resonance imaging,including DWI with ten b values before and after chemotherapy.Various parameters,such as the apparent diffusion coefficient from the mono-exponential model,and the true diffusion coefficient,the pseudo-diffusion coefficient,and the perfusion fraction derived from the intravoxel incoherent motion model,along with distributed diffusion coefficient(DDC)andαfrom the stretched-exponential model(SEM),were measured.The parameters before and after chemotherapy were compared between positive and negative hepatic lymph node groups.A nomogram was constructed to predict the hepatic lymph node status.The reliability and agreement of the measurements were assessed using the coefficient of variation and intraclass correlation coefficient.RESULTS Multivariate analysis revealed that the pre-treatment DDC value and the short diameter of the largest lymph node after treatment were independent predictors of metastatic hepatic lymph nodes.A nomogram combining these two factors demonstrated excellent performance in distinguishing between benign and malignant lymph nodes in CRLM patients,with an area under the curve of 0.873.Furthermore,parameters from SEM showed substantial repeatability.CONCLUSION The developed nomogram,incorporating the pre-treatment DDC and the short axis of the largest lymph node,can be used to predict the presence of hepatic LNM in CRLM patients undergoing chemotherapy before surgery.This nomogram was proven to be more valuable,exhibiting superior diagnostic performance compared to quantitative parameters derived from multiple b values of DWI.The nomogram can serve as a preoperative assessment tool for determining the status of hepatic lymph nodes and aiding in the decision-making process for surgical treatment in CRLM patients.展开更多
The singularly perturbed initial boundary value problems for the reaction diffusion system are raised. Firstly, under suitable conditions, using a iteration technique, the differential inequalities theorem is construc...The singularly perturbed initial boundary value problems for the reaction diffusion system are raised. Firstly, under suitable conditions, using a iteration technique, the differential inequalities theorem is constructed and introducing two auxiliary functions the existence and uniqueness theorem of solution for the basic reaction diffusion system is proved. Using the singularly perturbed method the formal asymptotic expressions of the solution are constructed with power series theory. By using the comparison theorem the existence and its asymptotic behavior of solution for the original problem are studied. Finally, using method of estimate inequalities, the structure of solutions for the problem is discussed thoroughly in three cases and asymptotic solution of the original problem is given. The asymptotic behavior of solution in the three cases is proved.展开更多
Manufacturing process,diffusion co-efficient and areal capacity are the three main criteria for regulating thick electrodes for lithium-ion batteries(LIBs).However,simultaneously regulating these criteria for LIBs is ...Manufacturing process,diffusion co-efficient and areal capacity are the three main criteria for regulating thick electrodes for lithium-ion batteries(LIBs).However,simultaneously regulating these criteria for LIBs is desirable but remains a significant challenge.In this work,niobium pentoxide(Nb_(2)O_(5))anode and lithium iron phosphate(LiFePO_(4))cathode materials were chosen as the model materials and demonstrate that these three parameters can be simultaneously modulated by incorporation of micro-carbon fibers(MCF)and carbon nanotubes(CNT)with both Nb_(2)O_(5) and LFP via vacuum filtration approach.Both as-prepared MNC-20 anode and MLC-20 cathode achieves high reversible areal capacity of≈5.4 m A h cm^(-2)@0.1 C and outstanding Li-ion diffusion coefficients of≈10~(-8)cm~2 s~(-1)in the half-cell configuration.The assembled MNC-20‖MLC-20 full cell LIB delivers maximum energy and power densities of244.04 W h kg^(-1)and 108.86 W kg^(-1),respectively.The excellent electrochemical properties of the asprepared thick electrodes can be attributed to the highly conductive,mechanical compactness and multidimensional mutual effects of the MCF,CNT and active materials that facilitates rapid Li-ion diffusion kinetics.Furthermore,electrochemical impedance spectroscopy(EIS),symmetric cells analysis,and insitu Raman techniques clearly validates the enhanced Li-ion diffusion kinetics in the present architecture.展开更多
The formation mechanism of calcium vanadate and manganese vanadate and the difference between calcium and manganese in the reaction with vanadium are basic issues in the calcification roasting and manganese roasting p...The formation mechanism of calcium vanadate and manganese vanadate and the difference between calcium and manganese in the reaction with vanadium are basic issues in the calcification roasting and manganese roasting process with vanadium slag.In this work,CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples were prepared and roasted for different time periods to illustrate and compare the diffusion reaction mechanisms.Then,the changes in the diffusion product and diffusion coefficient were investigated and calculated based on scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS) analysis.Results show that with the extension of the roasting time,the diffusion reaction gradually proceeds among the CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples.The regional boundaries of calcium and vanadium are easily identifiable for the CaO–V_(2)O_(5) diffusion couple.Meanwhile,for the MnO_(2)–V_(2)O_(5) diffusion couple,MnO_(2) gradually decomposes to form Mn_(2)O_(3),and vanadium diffuses into the interior of Mn_(2)O_(3).Only a part of vanadium combines with manganese to form the diffusion production layer.CaV_(2)O_(6) and MnV_(2)O_(6) are the interfacial reaction products of the CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples,respectively,whose thicknesses are 39.85 and 32.13μm when roasted for 16 h.After 16 h,both diffusion couples reach the reaction equilibrium due to the limitation of diffusion.The diffusion coefficient of the CaO–V_(2)O_(5) diffusion couple is higher than that of the MnO_(2)–V_(2)O_(5) diffusion couple for the same roasting time,and the diffusion reaction between vanadium and calcium is easier than that between vanadium and manganese.展开更多
基金support of Shanxi Province Major Science and Technology Projects,China (No.20191101002).
文摘The increase to the proportion of fluxed pellets in the blast furnace burden is a useful way to reduce the carbon emissions in the ironmaking process.In this study,the interaction between calcium carbonate and iron ore powder and the mineralization mechanism of fluxed iron ore pellet in the roasting process were investigated through diffusion couple experiments.Scanning electron microscopy with energy dispersive spectroscopy was used to study the elements’diffusion and phase transformation during the roasting process.The results indicated that limestone decomposed into calcium oxide,and magnetite was oxidized to hematite at the early stage of preheating.With the increase in roasting temperature,the diffusion rate of Fe and Ca was obviously accelerated,while the diffusion rate of Si was relatively slow.The order of magnitude of interdiffusion coefficient of Fe_(2)O_(3)-CaO diffusion couple was 10^(−10) m^(2)·s^(−1) at a roasting temperature of 1200℃for 9 h.Ca_(2)Fe_(2)O_(5) was the initial product in the Fe_(2)O_(3)-CaO-SiO_(2) diffusion interface,and then Ca_(2)Fe_(2)O_(5) continued to react with Fe_(2)O_(3) to form CaFe_(2)O_(4).With the expansion of the diffusion region,the sillico-ferrite of calcium liquid phase was produced due to the melting of SiO_(2) into CaFe_(2)O_(4),which can strengthen the consolidation of fluxed pellets.Furthermore,andradite would be formed around a small part of quartz particles,which is also conducive to the consolidation of fluxed pellets.In addition,the principle diagram of limestone and quartz diffusion reaction in the process of fluxed pellet roasting was discussed.
文摘For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geometries may lead to difficulties in the accuracy when discretizing the high-order derivatives on grid points near the boundary.It is very challenging to design numerical methods that can efficiently and accurately handle both difficulties.Applying an implicit scheme may be able to remove the stability constraints on the time step,however,it usually requires solving a large global system of nonlinear equations for each time step,and the computational cost could be significant.Integration factor(IF)or exponential time differencing(ETD)methods are one of the popular methods for temporal partial differential equations(PDEs)among many other methods.In our paper,we couple ETD methods with an embedded boundary method to solve a system of reaction-diffusion equations with complex geometries.In particular,we rewrite all ETD schemes into a linear combination of specificФ-functions and apply one state-of-the-art algorithm to compute the matrix-vector multiplications,which offers significant computational advantages with adaptive Krylov subspaces.In addition,we extend this method by incorporating the level set method to solve the free boundary problem.The accuracy,stability,and efficiency of the developed method are demonstrated by numerical examples.
文摘Ta/NiFe film is deposited on Si substrate precoated with SiO_2 by magnetron sputtering.SiO_2/Ta interface and Ta_5Si_3 standard sample are investigated by using X-ray photoelectron spectroscopy (XPS) and peak decomposition technique.The results show that there is a thermodynamically favorable reaction at the SiO_2/Ta interface:37Ta+15SiO_2=5Ta_5Si_3+6Ta_2O_5.The more stable products Ta_5Si_3 and Ta_2O_5 may be beneficial to stop the diffusion of Cu into SiO_2.
文摘A mathematical model of CE reaction schemes under first or pseudo-first order conditions with different diffusion coefficients at a spherical electrode under non-steady-state conditions is described. The model is based on non-stationary diffusion equation containing a non-linear reaction term. This paper presents the complex numerical method (Homotopy perturbation method) to solve the system of non-linear differential equation that describes the homogeneous processes coupled to electrode reaction. In this paper the approximate analytical expressions of the non-steady-state concentrations and current at spherical electrodes for homogeneous reactions mechanisms are derived for all values of the reaction diffusion parameters. These approximate results are compared with the available analytical results and are found to be in good agreement.
文摘A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.
基金The Project Supported by National Natural Science Foundation of China(10071045)
文摘A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied.
基金The Importent Study Profect of the National Natural Science Poundation of China(90211004)The Natural Sciences Foundation of Zheiiang(102009)
文摘A class of nonlinear singularly perturbed problems for reaction diffusion equations are considered. Under suitable conditions, by using the theory of differential inequalities, the asymptotic behavior of solutions for the initial boundary value problems are studied, reduced problems of which possess two intersecting solutions.
基金The project is supported by The National Natural Science Foundation of China(10071048)"Hundred People Project" of Chinese Academy of Sciences
文摘In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Unsing the iteration method and the comparison theorem, the existence, uniqueness and its asymptotic behavior of solution for the problem are studied.
文摘A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed.
基金Supported by the National Natural Sciences Foundation of China(40676016 and 10471039)the National Key Project for Basic Research(2003CB415101-03 and 2004CB418304)+2 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission(N.E03004)the Natural Science Foundation of Zeijiang,China(Y606268).
文摘In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.
基金Project supported by the National Natural Science Foundation of China (Nos. 40676016, 10471039), the National Key Basic Research Special Foundation of China (No. 2004CB418304), the Key Basic Research Foundation of the Chinese Academy of Sciences (No. KZCX3-SW-221) and in part by EInstitutes of Shanghai Municipal Education Commission (No. E03004)
文摘In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
基金Supported by important study project of the National Natural Science Foundation of China(9 0 2 1 1 0 0 4 ) and by the"Hundred Talents'Project"of Chinese Academy of Sciences
文摘A class of nonlinear predator prey reaction diffusion systems for singularly pe rturbed problems are considered.Under suitable conditions, by using theory of di fferential inequalities the existence and asymptotic behavior of solution for in itial boundary value problems are studied.
文摘A class of singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison theorem the asymptotic behavior of solution for the initial boundary value problems is studied.
基金Supported by the National Natural Science Foundation of China (90111011 and 10471039)the National Key Project for Basics Research (2003CB415101-03 and 2004CB418304)the Key Project of the Chinese Academy of Sciences (KZCX3-SW-221)the Natural Science Foundation of Zhejiang (Y604127).
文摘The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
基金Supported by Beijing Hospitals Authority Youth Program,No.QML20231103Beijing Hospitals Authority Ascent Plan,No.DFL20191103National Key R&D Program of China,No.2023YFC3402805.
文摘BACKGROUND About 10%-31% of colorectal liver metastases(CRLM)patients would concomitantly show hepatic lymph node metastases(LNM),which was considered as sign of poor biological behavior and a relative contraindication for liver resection.Up to now,there’s still lack of reliable preoperative methods to assess the status of hepatic lymph nodes in patients with CRLM,except for pathology examination of lymph node after resection.AIM To compare the ability of mono-exponential,bi-exponential,and stretchedexponential diffusion-weighted imaging(DWI)models in distinguishing between benign and malignant hepatic lymph nodes in patients with CRLM who received neoadjuvant chemotherapy prior to surgery.METHODS In this retrospective study,97 CRLM patients with pathologically confirmed hepatic lymph node status underwent magnetic resonance imaging,including DWI with ten b values before and after chemotherapy.Various parameters,such as the apparent diffusion coefficient from the mono-exponential model,and the true diffusion coefficient,the pseudo-diffusion coefficient,and the perfusion fraction derived from the intravoxel incoherent motion model,along with distributed diffusion coefficient(DDC)andαfrom the stretched-exponential model(SEM),were measured.The parameters before and after chemotherapy were compared between positive and negative hepatic lymph node groups.A nomogram was constructed to predict the hepatic lymph node status.The reliability and agreement of the measurements were assessed using the coefficient of variation and intraclass correlation coefficient.RESULTS Multivariate analysis revealed that the pre-treatment DDC value and the short diameter of the largest lymph node after treatment were independent predictors of metastatic hepatic lymph nodes.A nomogram combining these two factors demonstrated excellent performance in distinguishing between benign and malignant lymph nodes in CRLM patients,with an area under the curve of 0.873.Furthermore,parameters from SEM showed substantial repeatability.CONCLUSION The developed nomogram,incorporating the pre-treatment DDC and the short axis of the largest lymph node,can be used to predict the presence of hepatic LNM in CRLM patients undergoing chemotherapy before surgery.This nomogram was proven to be more valuable,exhibiting superior diagnostic performance compared to quantitative parameters derived from multiple b values of DWI.The nomogram can serve as a preoperative assessment tool for determining the status of hepatic lymph nodes and aiding in the decision-making process for surgical treatment in CRLM patients.
基金Supported by the National Natural Science Foundation of China (40676016 and 10471039)the National Program for Basic Science Researches of China (2003CB415101-03 and 2004CB418304)+1 种基金the Key Project of the Chinese Academy of Sciences (KZCX3-SW-221)E-Insitutes of Shanghai Municipal Education Commission (N.E03004)
文摘The singularly perturbed initial boundary value problems for the reaction diffusion system are raised. Firstly, under suitable conditions, using a iteration technique, the differential inequalities theorem is constructed and introducing two auxiliary functions the existence and uniqueness theorem of solution for the basic reaction diffusion system is proved. Using the singularly perturbed method the formal asymptotic expressions of the solution are constructed with power series theory. By using the comparison theorem the existence and its asymptotic behavior of solution for the original problem are studied. Finally, using method of estimate inequalities, the structure of solutions for the problem is discussed thoroughly in three cases and asymptotic solution of the original problem is given. The asymptotic behavior of solution in the three cases is proved.
基金supported by the Science and Technology Innovation Program of Hunan Province(2022WZ1012)the Hunan Joint International Laboratory of Advanced Materials and Technology for Clean Energy(2020CB1007)the Natural Science Foundation of Guangzhou(202201020147)。
文摘Manufacturing process,diffusion co-efficient and areal capacity are the three main criteria for regulating thick electrodes for lithium-ion batteries(LIBs).However,simultaneously regulating these criteria for LIBs is desirable but remains a significant challenge.In this work,niobium pentoxide(Nb_(2)O_(5))anode and lithium iron phosphate(LiFePO_(4))cathode materials were chosen as the model materials and demonstrate that these three parameters can be simultaneously modulated by incorporation of micro-carbon fibers(MCF)and carbon nanotubes(CNT)with both Nb_(2)O_(5) and LFP via vacuum filtration approach.Both as-prepared MNC-20 anode and MLC-20 cathode achieves high reversible areal capacity of≈5.4 m A h cm^(-2)@0.1 C and outstanding Li-ion diffusion coefficients of≈10~(-8)cm~2 s~(-1)in the half-cell configuration.The assembled MNC-20‖MLC-20 full cell LIB delivers maximum energy and power densities of244.04 W h kg^(-1)and 108.86 W kg^(-1),respectively.The excellent electrochemical properties of the asprepared thick electrodes can be attributed to the highly conductive,mechanical compactness and multidimensional mutual effects of the MCF,CNT and active materials that facilitates rapid Li-ion diffusion kinetics.Furthermore,electrochemical impedance spectroscopy(EIS),symmetric cells analysis,and insitu Raman techniques clearly validates the enhanced Li-ion diffusion kinetics in the present architecture.
基金supported by the National Natural Science Foundation of China(Nos.52174277 and 51874077)the Fundamental Funds for the Central Universities,China(No.N2225032)+1 种基金the China Postdoctoral Science Foundation(No.2022M720683)the Postdoctoral Fund of Northeastern University,China。
文摘The formation mechanism of calcium vanadate and manganese vanadate and the difference between calcium and manganese in the reaction with vanadium are basic issues in the calcification roasting and manganese roasting process with vanadium slag.In this work,CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples were prepared and roasted for different time periods to illustrate and compare the diffusion reaction mechanisms.Then,the changes in the diffusion product and diffusion coefficient were investigated and calculated based on scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS) analysis.Results show that with the extension of the roasting time,the diffusion reaction gradually proceeds among the CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples.The regional boundaries of calcium and vanadium are easily identifiable for the CaO–V_(2)O_(5) diffusion couple.Meanwhile,for the MnO_(2)–V_(2)O_(5) diffusion couple,MnO_(2) gradually decomposes to form Mn_(2)O_(3),and vanadium diffuses into the interior of Mn_(2)O_(3).Only a part of vanadium combines with manganese to form the diffusion production layer.CaV_(2)O_(6) and MnV_(2)O_(6) are the interfacial reaction products of the CaO–V_(2)O_(5) and MnO_(2)–V_(2)O_(5) diffusion couples,respectively,whose thicknesses are 39.85 and 32.13μm when roasted for 16 h.After 16 h,both diffusion couples reach the reaction equilibrium due to the limitation of diffusion.The diffusion coefficient of the CaO–V_(2)O_(5) diffusion couple is higher than that of the MnO_(2)–V_(2)O_(5) diffusion couple for the same roasting time,and the diffusion reaction between vanadium and calcium is easier than that between vanadium and manganese.