We consider solving the forward and inverse partial differential equations(PDEs)which have sharp solutions with physics-informed neural networks(PINNs)in this work.In particular,to better capture the sharpness of the ...We consider solving the forward and inverse partial differential equations(PDEs)which have sharp solutions with physics-informed neural networks(PINNs)in this work.In particular,to better capture the sharpness of the solution,we propose the adaptive sampling methods(ASMs)based on the residual and the gradient of the solution.We first present a residual only-based ASM denoted by ASMⅠ.In this approach,we first train the neural network using a small number of residual points and divide the computational domain into a certain number of sub-domains,then we add new residual points in the sub-domain which has the largest mean absolute value of the residual,and those points which have the largest absolute values of the residual in this sub-domain as new residual points.We further develop a second type of ASM(denoted by ASMⅡ)based on both the residual and the gradient of the solution due to the fact that only the residual may not be able to efficiently capture the sharpness of the solution.The procedure of ASMⅡis almost the same as that of ASMⅠ,and we add new residual points which have not only large residuals but also large gradients.To demonstrate the effectiveness of the present methods,we use both ASMⅠand ASMⅡto solve a number of PDEs,including the Burger equation,the compressible Euler equation,the Poisson equation over an Lshape domain as well as the high-dimensional Poisson equation.It has been shown from the numerical results that the sharp solutions can be well approximated by using either ASMⅠor ASMⅡ,and both methods deliver much more accurate solutions than the original PINNs with the same number of residual points.Moreover,the ASMⅡalgorithm has better performance in terms of accuracy,efficiency,and stability compared with the ASMⅠalgorithm.This means that the gradient of the solution improves the stability and efficiency of the adaptive sampling procedure as well as the accuracy of the solution.Furthermore,we also employ the similar adaptive sampling technique for the data points of boundary conditions(BCs)if the sharpness of the solution is near the boundary.The result of the L-shape Poisson problem indicates that the present method can significantly improve the efficiency,stability,and accuracy.展开更多
Physics-informed deep learning has recently emerged as an effective tool for leveraging both observational data and available physical laws.Physics-informed neural networks(PINNs)and deep operator networks(DeepONets)a...Physics-informed deep learning has recently emerged as an effective tool for leveraging both observational data and available physical laws.Physics-informed neural networks(PINNs)and deep operator networks(DeepONets)are two such models.The former encodes the physical laws via the automatic differentiation,while the latter learns the hidden physics from data.Generally,the noisy and limited observational data as well as the over-parameterization in neural networks(NNs)result in uncertainty in predictions from deep learning models.In paper“MENG,X.,YANG,L.,MAO,Z.,FERRANDIS,J.D.,and KARNIADAKIS,G.E.Learning functional priors and posteriors from data and physics.Journal of Computational Physics,457,111073(2022)”,a Bayesian framework based on the generative adversarial networks(GANs)has been proposed as a unified model to quantify uncertainties in predictions of PINNs as well as DeepONets.Specifically,the proposed approach in“MENG,X.,YANG,L.,MAO,Z.,FERRANDIS,J.D.,and KARNIADAKIS,G.E.Learning functional priors and posteriors from data and physics.Journal of Computational Physics,457,111073(2022)”has two stages:(i)prior learning,and(ii)posterior estimation.At the first stage,the GANs are utilized to learn a functional prior either from a prescribed function distribution,e.g.,the Gaussian process,or from historical data and available physics.At the second stage,the Hamiltonian Monte Carlo(HMC)method is utilized to estimate the posterior in the latent space of GANs.However,the vanilla HMC does not support the mini-batch training,which limits its applications in problems with big data.In the present work,we propose to use the normalizing flow(NF)models in the context of variational inference(VI),which naturally enables the mini-batch training,as the alternative to HMC for posterior estimation in the latent space of GANs.A series of numerical experiments,including a nonlinear differential equation problem and a 100-dimensional(100D)Darcy problem,are conducted to demonstrate that the NFs with full-/mini-batch training are able to achieve similar accuracy as the“gold rule”HMC.Moreover,the mini-batch training of NF makes it a promising tool for quantifying uncertainty in solving the high-dimensional partial differential equation(PDE)problems with big data.展开更多
Cemented tailings backfill(CTB) have increasingly been used in recent years to improve the stability of mining stopes in deep underground mines. Deep mining processes are often associated with rock bursting and high-s...Cemented tailings backfill(CTB) have increasingly been used in recent years to improve the stability of mining stopes in deep underground mines. Deep mining processes are often associated with rock bursting and high-speed dynamic loading conditions. Therefore, it is important to investigate the characteristics and dynamic mechanical behavior of CTB. This paper presents the results of dynamic tests on CTB specimens with different cement and solid contents using a split Hopkinson pressure bar(SHPB). The results showed that some CTB specimens exhibited one to two lower stress peaks after reaching dynamic peak stress before they completely failed. The greater the cement-to-tailings ratio is, the more obvious the strain reaction. This property mainly manifested as follows. First,the dynamic peak stress increased with the increase of the cement-to-tailings ratio when the impact velocity was fixed. Second, the dynamic peak stress had a quadratic relationship with the average stress rate. Third, the cement-to-tailings ratio could enhance the increase rate of dynamic peak stress with strain rate. In addition, the dynamic strength enhancement factor K increased with the increase of strain rate, and its value was larger than that of the rock samples. The failure modes of CTB specimens under low-speed impact were tensile failure and X conjugate shear failure, where were nearly the same as those under static uniaxial and triaxial compression. The CTB specimens were crushed and broken under critical strain, a failure mode similar to that of low-strength concrete. The results of the experimental research can improve the understanding of the dynamic mechanical properties of CTB and guide the strength design of deep mining backfills.展开更多
Cemented tailings backfill(CTB)structures are important components of underground mine stopes.It is important to investigate the characteristics and dynamic behavior of CTB materials because they are susceptible to di...Cemented tailings backfill(CTB)structures are important components of underground mine stopes.It is important to investigate the characteristics and dynamic behavior of CTB materials because they are susceptible to disturbance by dynamic loading,such as excavation and blasting.In this study,the authors present the results of a series of Split-Hopkinson pressure bar(SHPB)single and cyclic impact loading tests on CTB specimens to investigate the long-term dynamic mechanical properties of CTB.The stress-strain relationship,dynamic strength,and dynamic failure characteristics of CTB specimens are analyzed and discussed to provide valuable conclusions that will improve our knowledge of CTB long-term mechanical behavior and characteristics.For instance,the dynamic peak stress under cyclic impact loading is approximately twice that under single impact loading,and the CTB specimens are less prone to fracture when cyclically loaded.These findings and conclusions can provide a new set of references for the stability analysis of CTB materials and help guide mine designers in reducing the amount of binding agents and the associated mining cost.展开更多
An empirical formula for composition demixing analysis in cathodic arc ion plating using alloy target is established based on the concepts of average charged state and relative demixing parameter. The level of composi...An empirical formula for composition demixing analysis in cathodic arc ion plating using alloy target is established based on the concepts of average charged state and relative demixing parameter. The level of composition demixing effect is presented by demixing degree of one element. For binary constituent alloy target, the composition change trend in coating is discussed and the limit of demixing degree for each element is determined. The content of one element with higher average charged state gets larger in coating than in alloy target, at meantime, the content of one element with lower average charged state gets less. For each one of the two constituents, the less the atom percent in alloy target, the larger the difference of its contents between the coating and the target. For triple constituent alloy target, the content change of one element with moderate average charged state is discussed in detail. Its content in coating getting larger or less is determined by the combination result of the contents of the other two elements in alloy target. For a given content of the element with moderate average charged state in triple alloy target, the content deviation level of that element from coating to alloy target will be not larger than that using binary alloy target containing only that element and one of the two others. According to the wanted coating composition, the composition design of alloy target is easily deduced from the formula.展开更多
The influences of interphase on dynamic effective properties of composites reinforced by randomly dispersed spherical particles were studied. A thin homogeneous elastic interphase with different shear and bulk moduli,...The influences of interphase on dynamic effective properties of composites reinforced by randomly dispersed spherical particles were studied. A thin homogeneous elastic interphase with different shear and bulk moduli, located between the reinforced particle and the host matrix, was introduced to model the interfacial bonding state. The effects of such an interphase on the coherent plane waves were studied numerically. Numerical simulations were carried out for SiC-Al composites with four typical cases of interphase. It was found that the property of interphase has significant influences on the effective propagation constants of coherent waves and the dynamic effective elastic moduli of the composites. The influences on the coherent longitudinal wave and the coherent shear waves were different and dependent upon the frequency range. Moreover, several imperfect interface models, i.e., the spring model, mass model, and spring-mass model, were studied numerically and compared with the interphase model, It was found that the spring model is a more suitable model than the mass model for the light and weak interphase whereas the mass model is a more suitable model than the spring model for the heavy and strong interphase.展开更多
A theoretical investigation was done for the generalized Berman problem, which arises in steady laminar flow of an incompressible viscous fluid along a channel with accelerating rigid porous walls. The existence of mu...A theoretical investigation was done for the generalized Berman problem, which arises in steady laminar flow of an incompressible viscous fluid along a channel with accelerating rigid porous walls. The existence of multiple solutions and its conditions were established by taking into account exponentially small terms in matched asymptotic expansion. The correctness of the analytical predictions was verified by numerical results.展开更多
A new method was reported for surface modification of an up-conversion luminescence material with hydrosulfide group. The factors that may influence the surface modification,such as reaction time,amount of catalyzer a...A new method was reported for surface modification of an up-conversion luminescence material with hydrosulfide group. The factors that may influence the surface modification,such as reaction time,amount of catalyzer and modifier,and reaction solvent,were investigated. The optimal conditions were that the reaction time,the quantity of the basic catalyzer,the quantity of modifier and the volume of reaction solvent were 40 min,1.0,1.0,and 40 mL,respectively. The results indicated that hydrosulfide group content modified on the surface of up-conversion luminescence material reached to 0.1430 mmol/g,and this modified up-conversion luminescence material could be widely used in the study of structure of protein and the property of microenvironment.展开更多
In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homot...In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homotopy analysis method （HAM） is employed to obtain the expres- sions for velocity fields. Graphs are sketched for values of parameters and associated dynamic characteristics, especially the expansion ratio, are analyzed in detail.展开更多
Objective:To analyze economic feasibility for investing in nursing care.Method:The number of practicing nurses'density per 1000 population as a proxy for nursing staff and Gross Domestic Product(GDP)per capita(cur...Objective:To analyze economic feasibility for investing in nursing care.Method:The number of practicing nurses'density per 1000 population as a proxy for nursing staff and Gross Domestic Product(GDP)per capita(current US$)were collected in 35 member countries of Organization for Economic Co-operation and Development(OECD)over 2000-2016 period.The statistical technique of panel data analysis including unit root test,cointegration analysis,Granger causality test,dynamic long-run model analysis and error correction model were applied to measure economic impact of nursing-related services.Results:There was a committed bilateral relationship between nurse-staffing level and GDP with longrun magnitudes of 1.39 and 0A1 for GDP-lead-nurse and nurse-lead-GDP directions in OECD countries,respectively.Moreover,the highest long-run magnitudes of the effect nursing staff has on increasing GDP per capita were calculated in Finland(2.07),Sweden(1.92),Estonia(1.68),Poland(1.52),Czech Republic(1.48),Norway(1.47)and Canada(1.24).Conclusion:Our findings verify that although the dependency of nursing characteristics to GDP per capita is higher than the reliance of GDP to number of nurses'density per 1000 population,investing in nursing care is economically feasible in OECD countries i.e.nursing is not only a financial burden(or cost)on health care systems,but also an economic stimulus in OECD countries.Hence,we alert governments and policy makers about the risk of underestimating the economic impacts of nurses on economic systems of OECD countries.展开更多
An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution...An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.展开更多
The planar texture of glassy cholesteric siloxane cyclic side-chain liquid crystals was fixed by quenching initially. Then the polymer network formed by the optically active polymerizable monomers imposed additional c...The planar texture of glassy cholesteric siloxane cyclic side-chain liquid crystals was fixed by quenching initially. Then the polymer network formed by the optically active polymerizable monomers imposed additional constraints on the motion of chain segments of the glassy liquid crystal and then further stabilized the molecule arrangement. A cholesteric liquid crystal film with stable optical properties was developed by this method.展开更多
The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstr...The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstream with Uw 〉〉 U∞, or alternatively when the plate surface velocity is kept fixed but the stream speed is reduced to zero. A theoretical analysis for a boundary layer flow is made and the self-similar equation is determined. Solutions are presented numerically for special power index and the associated transfer behavior is discussed.展开更多
基金Project supported by the National Key R&D Program of China(No.2022YFA1004504)the National Natural Science Foundation of China(Nos.12171404 and 12201229)the Fundamental Research Funds for Central Universities of China(No.20720210037)。
文摘We consider solving the forward and inverse partial differential equations(PDEs)which have sharp solutions with physics-informed neural networks(PINNs)in this work.In particular,to better capture the sharpness of the solution,we propose the adaptive sampling methods(ASMs)based on the residual and the gradient of the solution.We first present a residual only-based ASM denoted by ASMⅠ.In this approach,we first train the neural network using a small number of residual points and divide the computational domain into a certain number of sub-domains,then we add new residual points in the sub-domain which has the largest mean absolute value of the residual,and those points which have the largest absolute values of the residual in this sub-domain as new residual points.We further develop a second type of ASM(denoted by ASMⅡ)based on both the residual and the gradient of the solution due to the fact that only the residual may not be able to efficiently capture the sharpness of the solution.The procedure of ASMⅡis almost the same as that of ASMⅠ,and we add new residual points which have not only large residuals but also large gradients.To demonstrate the effectiveness of the present methods,we use both ASMⅠand ASMⅡto solve a number of PDEs,including the Burger equation,the compressible Euler equation,the Poisson equation over an Lshape domain as well as the high-dimensional Poisson equation.It has been shown from the numerical results that the sharp solutions can be well approximated by using either ASMⅠor ASMⅡ,and both methods deliver much more accurate solutions than the original PINNs with the same number of residual points.Moreover,the ASMⅡalgorithm has better performance in terms of accuracy,efficiency,and stability compared with the ASMⅠalgorithm.This means that the gradient of the solution improves the stability and efficiency of the adaptive sampling procedure as well as the accuracy of the solution.Furthermore,we also employ the similar adaptive sampling technique for the data points of boundary conditions(BCs)if the sharpness of the solution is near the boundary.The result of the L-shape Poisson problem indicates that the present method can significantly improve the efficiency,stability,and accuracy.
基金Project supported by the National Natural Science Foundation of China(No.12201229)。
文摘Physics-informed deep learning has recently emerged as an effective tool for leveraging both observational data and available physical laws.Physics-informed neural networks(PINNs)and deep operator networks(DeepONets)are two such models.The former encodes the physical laws via the automatic differentiation,while the latter learns the hidden physics from data.Generally,the noisy and limited observational data as well as the over-parameterization in neural networks(NNs)result in uncertainty in predictions from deep learning models.In paper“MENG,X.,YANG,L.,MAO,Z.,FERRANDIS,J.D.,and KARNIADAKIS,G.E.Learning functional priors and posteriors from data and physics.Journal of Computational Physics,457,111073(2022)”,a Bayesian framework based on the generative adversarial networks(GANs)has been proposed as a unified model to quantify uncertainties in predictions of PINNs as well as DeepONets.Specifically,the proposed approach in“MENG,X.,YANG,L.,MAO,Z.,FERRANDIS,J.D.,and KARNIADAKIS,G.E.Learning functional priors and posteriors from data and physics.Journal of Computational Physics,457,111073(2022)”has two stages:(i)prior learning,and(ii)posterior estimation.At the first stage,the GANs are utilized to learn a functional prior either from a prescribed function distribution,e.g.,the Gaussian process,or from historical data and available physics.At the second stage,the Hamiltonian Monte Carlo(HMC)method is utilized to estimate the posterior in the latent space of GANs.However,the vanilla HMC does not support the mini-batch training,which limits its applications in problems with big data.In the present work,we propose to use the normalizing flow(NF)models in the context of variational inference(VI),which naturally enables the mini-batch training,as the alternative to HMC for posterior estimation in the latent space of GANs.A series of numerical experiments,including a nonlinear differential equation problem and a 100-dimensional(100D)Darcy problem,are conducted to demonstrate that the NFs with full-/mini-batch training are able to achieve similar accuracy as the“gold rule”HMC.Moreover,the mini-batch training of NF makes it a promising tool for quantifying uncertainty in solving the high-dimensional partial differential equation(PDE)problems with big data.
基金financially supported by the National Key R&D Program of China (No. 2018YFC0604602)the Fundamental Research Funds for the Central Universities of China (No. FRF-TP-17-029A2)the Open fund of Key Laboratory of High-Efficient Mining and Safety of Metal Mines, Ministry of Education of China (No. ustbmslab201803)
文摘Cemented tailings backfill(CTB) have increasingly been used in recent years to improve the stability of mining stopes in deep underground mines. Deep mining processes are often associated with rock bursting and high-speed dynamic loading conditions. Therefore, it is important to investigate the characteristics and dynamic mechanical behavior of CTB. This paper presents the results of dynamic tests on CTB specimens with different cement and solid contents using a split Hopkinson pressure bar(SHPB). The results showed that some CTB specimens exhibited one to two lower stress peaks after reaching dynamic peak stress before they completely failed. The greater the cement-to-tailings ratio is, the more obvious the strain reaction. This property mainly manifested as follows. First,the dynamic peak stress increased with the increase of the cement-to-tailings ratio when the impact velocity was fixed. Second, the dynamic peak stress had a quadratic relationship with the average stress rate. Third, the cement-to-tailings ratio could enhance the increase rate of dynamic peak stress with strain rate. In addition, the dynamic strength enhancement factor K increased with the increase of strain rate, and its value was larger than that of the rock samples. The failure modes of CTB specimens under low-speed impact were tensile failure and X conjugate shear failure, where were nearly the same as those under static uniaxial and triaxial compression. The CTB specimens were crushed and broken under critical strain, a failure mode similar to that of low-strength concrete. The results of the experimental research can improve the understanding of the dynamic mechanical properties of CTB and guide the strength design of deep mining backfills.
基金financially supported by the National Key R&D Program of China (No. 2017YFC0602900)the Fundamental Research Funds for the Central Universities (No. FRF-TP-17-029A2)the Open Fund of Key Laboratory of High-Efficient Mining and Safety of Metal Mines (Ministry of Education of China, No. ustbmslab201803)
文摘Cemented tailings backfill(CTB)structures are important components of underground mine stopes.It is important to investigate the characteristics and dynamic behavior of CTB materials because they are susceptible to disturbance by dynamic loading,such as excavation and blasting.In this study,the authors present the results of a series of Split-Hopkinson pressure bar(SHPB)single and cyclic impact loading tests on CTB specimens to investigate the long-term dynamic mechanical properties of CTB.The stress-strain relationship,dynamic strength,and dynamic failure characteristics of CTB specimens are analyzed and discussed to provide valuable conclusions that will improve our knowledge of CTB long-term mechanical behavior and characteristics.For instance,the dynamic peak stress under cyclic impact loading is approximately twice that under single impact loading,and the CTB specimens are less prone to fracture when cyclically loaded.These findings and conclusions can provide a new set of references for the stability analysis of CTB materials and help guide mine designers in reducing the amount of binding agents and the associated mining cost.
文摘An empirical formula for composition demixing analysis in cathodic arc ion plating using alloy target is established based on the concepts of average charged state and relative demixing parameter. The level of composition demixing effect is presented by demixing degree of one element. For binary constituent alloy target, the composition change trend in coating is discussed and the limit of demixing degree for each element is determined. The content of one element with higher average charged state gets larger in coating than in alloy target, at meantime, the content of one element with lower average charged state gets less. For each one of the two constituents, the less the atom percent in alloy target, the larger the difference of its contents between the coating and the target. For triple constituent alloy target, the content change of one element with moderate average charged state is discussed in detail. Its content in coating getting larger or less is determined by the combination result of the contents of the other two elements in alloy target. For a given content of the element with moderate average charged state in triple alloy target, the content deviation level of that element from coating to alloy target will be not larger than that using binary alloy target containing only that element and one of the two others. According to the wanted coating composition, the composition design of alloy target is easily deduced from the formula.
基金This work was financially supported by the National Natural Science Foundation of China (No.10272003) and the Talent Foundationof University of Science & Technology Beijing.
文摘The influences of interphase on dynamic effective properties of composites reinforced by randomly dispersed spherical particles were studied. A thin homogeneous elastic interphase with different shear and bulk moduli, located between the reinforced particle and the host matrix, was introduced to model the interfacial bonding state. The effects of such an interphase on the coherent plane waves were studied numerically. Numerical simulations were carried out for SiC-Al composites with four typical cases of interphase. It was found that the property of interphase has significant influences on the effective propagation constants of coherent waves and the dynamic effective elastic moduli of the composites. The influences on the coherent longitudinal wave and the coherent shear waves were different and dependent upon the frequency range. Moreover, several imperfect interface models, i.e., the spring model, mass model, and spring-mass model, were studied numerically and compared with the interphase model, It was found that the spring model is a more suitable model than the mass model for the light and weak interphase whereas the mass model is a more suitable model than the spring model for the heavy and strong interphase.
基金This work was financially supported by the National Natural Science Foundations of China (No.50476083).
文摘A theoretical investigation was done for the generalized Berman problem, which arises in steady laminar flow of an incompressible viscous fluid along a channel with accelerating rigid porous walls. The existence of multiple solutions and its conditions were established by taking into account exponentially small terms in matched asymptotic expansion. The correctness of the analytical predictions was verified by numerical results.
基金the National Natural Science Foundations of China (No50372006 and No20273007)
文摘A new method was reported for surface modification of an up-conversion luminescence material with hydrosulfide group. The factors that may influence the surface modification,such as reaction time,amount of catalyzer and modifier,and reaction solvent,were investigated. The optimal conditions were that the reaction time,the quantity of the basic catalyzer,the quantity of modifier and the volume of reaction solvent were 40 min,1.0,1.0,and 40 mL,respectively. The results indicated that hydrosulfide group content modified on the surface of up-conversion luminescence material reached to 0.1430 mmol/g,and this modified up-conversion luminescence material could be widely used in the study of structure of protein and the property of microenvironment.
基金supported by the National Natural Science Foundations of China (50936003, 50905013)The Open Project of State Key Lab. for Adv. Matals and Materials (2009Z-02)Research Foundation of Engineering Research Institute of USTB
文摘In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homotopy analysis method （HAM） is employed to obtain the expres- sions for velocity fields. Graphs are sketched for values of parameters and associated dynamic characteristics, especially the expansion ratio, are analyzed in detail.
文摘Objective:To analyze economic feasibility for investing in nursing care.Method:The number of practicing nurses'density per 1000 population as a proxy for nursing staff and Gross Domestic Product(GDP)per capita(current US$)were collected in 35 member countries of Organization for Economic Co-operation and Development(OECD)over 2000-2016 period.The statistical technique of panel data analysis including unit root test,cointegration analysis,Granger causality test,dynamic long-run model analysis and error correction model were applied to measure economic impact of nursing-related services.Results:There was a committed bilateral relationship between nurse-staffing level and GDP with longrun magnitudes of 1.39 and 0A1 for GDP-lead-nurse and nurse-lead-GDP directions in OECD countries,respectively.Moreover,the highest long-run magnitudes of the effect nursing staff has on increasing GDP per capita were calculated in Finland(2.07),Sweden(1.92),Estonia(1.68),Poland(1.52),Czech Republic(1.48),Norway(1.47)and Canada(1.24).Conclusion:Our findings verify that although the dependency of nursing characteristics to GDP per capita is higher than the reliance of GDP to number of nurses'density per 1000 population,investing in nursing care is economically feasible in OECD countries i.e.nursing is not only a financial burden(or cost)on health care systems,but also an economic stimulus in OECD countries.Hence,we alert governments and policy makers about the risk of underestimating the economic impacts of nurses on economic systems of OECD countries.
基金This work was financially supported by the National Natural Science Foundation of China (No.50476083).
文摘An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.
基金The work was financially supported by the National Natural Science Foundation of China (No.50476083) and the Cross-CenturyTalents Projects of the Educational Ministry of China.
基金This work was financially supported by the National High-Tech Research and Development Program of China (No. 2003AA327050).
文摘The planar texture of glassy cholesteric siloxane cyclic side-chain liquid crystals was fixed by quenching initially. Then the polymer network formed by the optically active polymerizable monomers imposed additional constraints on the motion of chain segments of the glassy liquid crystal and then further stabilized the molecule arrangement. A cholesteric liquid crystal film with stable optical properties was developed by this method.
基金This work is supported by the National Natural Science Foundation of China (No.50476083) and the Cross-Century Talents Projectsby the Ministry Education of China.
文摘The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstream with Uw 〉〉 U∞, or alternatively when the plate surface velocity is kept fixed but the stream speed is reduced to zero. A theoretical analysis for a boundary layer flow is made and the self-similar equation is determined. Solutions are presented numerically for special power index and the associated transfer behavior is discussed.
基金The project supported by National Natural Science Foundation of China under Grant No. 70271068, the Foundation for University Key Teachers, and the Research Fund for the Doctoral Program of Higher Education of the Ministry of Education of China under Grant No. 200200080004
