We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical ex...We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of n. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O（n） branch for n 〈 2 and the results obtained by previous transfer matrix calculations. For n = 2, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical 0（2） loop model. These results confirm that the cubic anisotropy is marginal at n = 2 but irrelevant for n〈2.展开更多
Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology ...Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology has become particularly important and widely used in the field of optimization.In this study,a new CG method was put forward,which combined subspace technology and a cubic regularization model.Besides,a special scaled norm in a cubic regularization model was analyzed.Under certain conditions,some significant characteristics of the search direction were given and the convergence of the algorithm was built.Numerical comparisons show that for the 145 test functions under the CUTEr library,the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods.展开更多
Immiscible water-alternating-gas（WAG） flooding is an EOR technique that has proven successful for water drive reservoirs due to its ability to improve displacement and sweep efficiency.Nevertheless,considering the c...Immiscible water-alternating-gas（WAG） flooding is an EOR technique that has proven successful for water drive reservoirs due to its ability to improve displacement and sweep efficiency.Nevertheless,considering the complicated phase behavior and various multiphase flow characteristics,gas tends to break through early in production wells in heterogeneous formations because of overriding,fingering,and channeling,which may result in unfavorable recovery performance.On the basis of phase behavior studies,minimum miscibility pressure measurements,and immiscible WAG coreflood experiments,the cubic B-spline model（CBM） was employed to describe the three-phase relative permeability curve.Using the Levenberg-Marquardt algorithm to adjust the vector of unknown model parameters of the CBM sequentially,optimization of production performance including pressure drop,water cut,and the cumulative gas-oil ratio was performed.A novel numerical inversion method was established for estimation of the water-oil-gas relative permeability curve during the immiscible WAG process.Based on the quantitative characterization of major recovery mechanisms,the proposed method was validated by interpreting coreflood data of the immiscible WAG experiment.The proposed method is reliable and can meet engineering requirements.It provides a basic calculation theory for implicit estimation of oil-water-gas relative permeability curve.展开更多
Three-dimensional(3-D)Markov cubic random mesh models are presented andproved in the form of two theorems in details.Its applications to the modeling and description of3-D images are described.The model presented here...Three-dimensional(3-D)Markov cubic random mesh models are presented andproved in the form of two theorems in details.Its applications to the modeling and description of3-D images are described.The model presented here is a appropriate mathematical tool for thesegmentation,modeling,classification and other processing.Finally,an example is given.展开更多
Cubic equation-of-state solid models are one of the most widely used models to predict asphaltene precipitation behavior.Thermodynamic parameters are needed to model precipitation under different pressures and tempera...Cubic equation-of-state solid models are one of the most widely used models to predict asphaltene precipitation behavior.Thermodynamic parameters are needed to model precipitation under different pressures and temperatures and are usually obtained through tuning with multi asphaltene onset experiments.For the purpose of enhancing the cubic Peng–Robinson solid model and reducing its dependency on asphaltene experiments,this paper tests the use of aromatics and waxes correlations to obtain these thermodynamic parameters.In addition,weighted averages between both correlations are introduced.The averaging is based on reported saturates,aromatics,resins,asphaltene(SARA)fractions,and wax content.All the methods are tested on four oil samples,with previously published data,covering precipitation and onset experiments.The proposed wax-asphaltene average showed the best match with experimental data,followed by a SARA-weighted average.This new addition enhances the model predictability and agrees with the general molecular structure of asphaltene molecules.展开更多
A dislocation interaction model has been proposed for cyclic deformation of fcc crystals.Ac- cording to this model,cyclic stress-strain responses and saturation dislocation structures of a crystal are associated with ...A dislocation interaction model has been proposed for cyclic deformation of fcc crystals.Ac- cording to this model,cyclic stress-strain responses and saturation dislocation structures of a crystal are associated with the modes and intensities of dislocation interactions between slip systems active in the crystal; and,hence,may be predicted by the location of its tensile axis in the crystallographic triangle.This model has successfully explained the different behaviours of double-slip crystals and multi-slip behaviours of some crystals with orientations usually con- sidered as single-slip ones.展开更多
For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic splin...For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables.展开更多
In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubi...In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.展开更多
The paper introduces a method for displaying cubic volume cells (voxels) resulting frompartitioning given objectS with orthogonal planes for finite difference calculation. The method representS ablock of voxels as a B...The paper introduces a method for displaying cubic volume cells (voxels) resulting frompartitioning given objectS with orthogonal planes for finite difference calculation. The method representS ablock of voxels as a B-rep solid model and conStrUcts the B-rep geometric clementS with an approach frombottom to up. Once the B-rep model is established, it is efficient in displaying because inner voxels areomitted and many coplanar facetS are merged together. By displaying the interSeCtion lines of theconstructed B-reP model and the partitioning planes, the tessellation image can be generated.展开更多
As a typical configuration in plastic deformations, dislocation arrays possess a large variation of the separation of the partial dislocation pairs in face-centered cubic（fcc） metals. This can be manifested convenie...As a typical configuration in plastic deformations, dislocation arrays possess a large variation of the separation of the partial dislocation pairs in face-centered cubic（fcc） metals. This can be manifested conveniently by an effective stacking fault energy（SFE）. The effective SFE of dislocation arrays is described within the elastic theory of dislocations and verified by atomistic simulations. The atomistic modeling results reveal that the general formulae of the effective SFE can give a reasonably satisfactory prediction for all dislocation types, especially for edge dislocation arrays. Furthermore, the predicted variation of the effective SFE is consistent with several previous experiments, in which the measured SFE is not definite, changing with dislocation density. Our approach could provide better understandings of cross-slip and the competition between slip and twinning during plastic deformations in fcc metals.展开更多
Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and repr...Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.展开更多
Progress in hydrate thermodynamic study necessitates robust and fast models to be incorporated in reservoir simulation softwares. However, numerous models presented in the literature makes selection of the best,proper...Progress in hydrate thermodynamic study necessitates robust and fast models to be incorporated in reservoir simulation softwares. However, numerous models presented in the literature makes selection of the best,proper predictive model a cumbersome task. It is of industrial interest to make use of cubic equations of state(EOS) for modeling hydrate equilibria. In this regard, this study focuses on evaluation of three common EOSs including Peng–Robinson, Soave–Redlich–Kwong and Valderrama–Patel–Teja coupled with van der Waals and Platteeuw theory to predict hydrate P–T equilibrium of a real natural gas sample. Each EOS was accompanied with three mixing rules, including van der Waals(vd W),Avlonitis non-density dependent(ANDD) and general nonquadratic(GNQ). The prediction of cubic EOSs was in sufficient agreement with experimental data and with overall AARD% of less than unity. In addition, PR plus ANDD proved to be the most accurate model in this study for prediction of hydrate equilibria with AARD% of 0.166.It was observed that the accuracy of cubic EOSs studied in this paper depends on mixing rule coupled with them,especially at high-pressure conditions. Lastly, the present study does not include any adjustable parameter to be correlated with hydrate phase equilibrium data.展开更多
目的:探讨混合教学模式下医学生学习沉浸体验对其系统思维的影响。方法:选取2022至2023学年完成医学统计学课程学习的医学生为研究对象,采用SATS 36量表、青少年学习沉浸体验问卷、系统思考量表调查医学生的学习态度、学习沉浸体验和系...目的:探讨混合教学模式下医学生学习沉浸体验对其系统思维的影响。方法:选取2022至2023学年完成医学统计学课程学习的医学生为研究对象,采用SATS 36量表、青少年学习沉浸体验问卷、系统思考量表调查医学生的学习态度、学习沉浸体验和系统思维。采用线性相关分析学习态度、学习沉浸体验与系统思维之间的相关关系;采用多重线性回归和限制性立方样条(Restricted cubic spline,RCS)模型分析控制性别、专业和学习态度影响后,学习沉浸体验与系统思维之间的线性和非线性关系。结果:349名医学生的学习态度均分为(4.31±0.59)分,学习沉浸体验均分为(3.33±0.65)分,均处于中等偏上水平;系统思维得分为(59.01±13.57)分,处于中等水平。医学生的学习沉浸体验、学习态度和系统思维间均呈正相关。学习沉浸体验存在性别和专业差异。在控制了性别、专业和学习态度影响后,多重线性回归结果显示,学习沉浸体验和系统思维存在线性趋势关系(P<0.01);RCS模型分析显示,学习沉浸体验和系统思维之间存在J型的非线性关系(P for non-linearity<0.01);以中位数3.16为拐点,学习沉浸体验得分<3.16分时,对医学生的系统思维不产生影响(P=0.51);当得分≥3.16分时,随着学习沉浸体验增加,医学生的系统思维随之增加(Beta per SD=0.56,95%CI:0.44~0.68,P<0.01)。结论:混合模式下医学生的学习沉浸体验会对系统思维产生促进作用,当学习沉浸体验得分≥3.16分时,医学生的学习沉浸体验越高,系统思维随之增加。不同维度学习沉浸体验与系统思维的密切程度不一样。展开更多
In this paper,we show that for any given planar cubic algebraic curves defined by a quadratic Hamiltonian vector field,we can always have their exact explicit parametric representations. We use a model of micro-struct...In this paper,we show that for any given planar cubic algebraic curves defined by a quadratic Hamiltonian vector field,we can always have their exact explicit parametric representations. We use a model of micro-structured solid to show an application of our conclusions.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.10675021)the New Century Excellent Talents in University of China,the Natural Science Foundation of Anhui Province of China (Grant No.090416224)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20103402110053)
文摘We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of n. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O（n） branch for n 〈 2 and the results obtained by previous transfer matrix calculations. For n = 2, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical 0（2） loop model. These results confirm that the cubic anisotropy is marginal at n = 2 but irrelevant for n〈2.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11901561).
文摘Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology has become particularly important and widely used in the field of optimization.In this study,a new CG method was put forward,which combined subspace technology and a cubic regularization model.Besides,a special scaled norm in a cubic regularization model was analyzed.Under certain conditions,some significant characteristics of the search direction were given and the convergence of the algorithm was built.Numerical comparisons show that for the 145 test functions under the CUTEr library,the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods.
基金the financial support of the Important National Science and Technology Specific Projects of China (Grant No. 2011ZX05010-002)the Important Science and Technology Specific Projects of Petro China (Grant No. 2014E-3203)
文摘Immiscible water-alternating-gas（WAG） flooding is an EOR technique that has proven successful for water drive reservoirs due to its ability to improve displacement and sweep efficiency.Nevertheless,considering the complicated phase behavior and various multiphase flow characteristics,gas tends to break through early in production wells in heterogeneous formations because of overriding,fingering,and channeling,which may result in unfavorable recovery performance.On the basis of phase behavior studies,minimum miscibility pressure measurements,and immiscible WAG coreflood experiments,the cubic B-spline model（CBM） was employed to describe the three-phase relative permeability curve.Using the Levenberg-Marquardt algorithm to adjust the vector of unknown model parameters of the CBM sequentially,optimization of production performance including pressure drop,water cut,and the cumulative gas-oil ratio was performed.A novel numerical inversion method was established for estimation of the water-oil-gas relative permeability curve during the immiscible WAG process.Based on the quantitative characterization of major recovery mechanisms,the proposed method was validated by interpreting coreflood data of the immiscible WAG experiment.The proposed method is reliable and can meet engineering requirements.It provides a basic calculation theory for implicit estimation of oil-water-gas relative permeability curve.
文摘Three-dimensional(3-D)Markov cubic random mesh models are presented andproved in the form of two theorems in details.Its applications to the modeling and description of3-D images are described.The model presented here is a appropriate mathematical tool for thesegmentation,modeling,classification and other processing.Finally,an example is given.
文摘Cubic equation-of-state solid models are one of the most widely used models to predict asphaltene precipitation behavior.Thermodynamic parameters are needed to model precipitation under different pressures and temperatures and are usually obtained through tuning with multi asphaltene onset experiments.For the purpose of enhancing the cubic Peng–Robinson solid model and reducing its dependency on asphaltene experiments,this paper tests the use of aromatics and waxes correlations to obtain these thermodynamic parameters.In addition,weighted averages between both correlations are introduced.The averaging is based on reported saturates,aromatics,resins,asphaltene(SARA)fractions,and wax content.All the methods are tested on four oil samples,with previously published data,covering precipitation and onset experiments.The proposed wax-asphaltene average showed the best match with experimental data,followed by a SARA-weighted average.This new addition enhances the model predictability and agrees with the general molecular structure of asphaltene molecules.
文摘A dislocation interaction model has been proposed for cyclic deformation of fcc crystals.Ac- cording to this model,cyclic stress-strain responses and saturation dislocation structures of a crystal are associated with the modes and intensities of dislocation interactions between slip systems active in the crystal; and,hence,may be predicted by the location of its tensile axis in the crystallographic triangle.This model has successfully explained the different behaviours of double-slip crystals and multi-slip behaviours of some crystals with orientations usually con- sidered as single-slip ones.
基金supported by the Natural Science Foundation of Hubei Province of China(Grant No.2010CDB10804)
文摘For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables.
文摘In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.
文摘The paper introduces a method for displaying cubic volume cells (voxels) resulting frompartitioning given objectS with orthogonal planes for finite difference calculation. The method representS ablock of voxels as a B-rep solid model and conStrUcts the B-rep geometric clementS with an approach frombottom to up. Once the B-rep model is established, it is efficient in displaying because inner voxels areomitted and many coplanar facetS are merged together. By displaying the interSeCtion lines of theconstructed B-reP model and the partitioning planes, the tessellation image can be generated.
基金support of this work by the Program of ‘‘One Hundred Talented People’’ of the Chinese Academy of Sciences (JBY) and the National Natural Science Foundation of China (Nos. 51571198, 51771206, 51331007, 51501197 and 51401207)
文摘As a typical configuration in plastic deformations, dislocation arrays possess a large variation of the separation of the partial dislocation pairs in face-centered cubic（fcc） metals. This can be manifested conveniently by an effective stacking fault energy（SFE）. The effective SFE of dislocation arrays is described within the elastic theory of dislocations and verified by atomistic simulations. The atomistic modeling results reveal that the general formulae of the effective SFE can give a reasonably satisfactory prediction for all dislocation types, especially for edge dislocation arrays. Furthermore, the predicted variation of the effective SFE is consistent with several previous experiments, in which the measured SFE is not definite, changing with dislocation density. Our approach could provide better understandings of cross-slip and the competition between slip and twinning during plastic deformations in fcc metals.
文摘Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.
文摘Progress in hydrate thermodynamic study necessitates robust and fast models to be incorporated in reservoir simulation softwares. However, numerous models presented in the literature makes selection of the best,proper predictive model a cumbersome task. It is of industrial interest to make use of cubic equations of state(EOS) for modeling hydrate equilibria. In this regard, this study focuses on evaluation of three common EOSs including Peng–Robinson, Soave–Redlich–Kwong and Valderrama–Patel–Teja coupled with van der Waals and Platteeuw theory to predict hydrate P–T equilibrium of a real natural gas sample. Each EOS was accompanied with three mixing rules, including van der Waals(vd W),Avlonitis non-density dependent(ANDD) and general nonquadratic(GNQ). The prediction of cubic EOSs was in sufficient agreement with experimental data and with overall AARD% of less than unity. In addition, PR plus ANDD proved to be the most accurate model in this study for prediction of hydrate equilibria with AARD% of 0.166.It was observed that the accuracy of cubic EOSs studied in this paper depends on mixing rule coupled with them,especially at high-pressure conditions. Lastly, the present study does not include any adjustable parameter to be correlated with hydrate phase equilibrium data.
文摘目的:探讨混合教学模式下医学生学习沉浸体验对其系统思维的影响。方法:选取2022至2023学年完成医学统计学课程学习的医学生为研究对象,采用SATS 36量表、青少年学习沉浸体验问卷、系统思考量表调查医学生的学习态度、学习沉浸体验和系统思维。采用线性相关分析学习态度、学习沉浸体验与系统思维之间的相关关系;采用多重线性回归和限制性立方样条(Restricted cubic spline,RCS)模型分析控制性别、专业和学习态度影响后,学习沉浸体验与系统思维之间的线性和非线性关系。结果:349名医学生的学习态度均分为(4.31±0.59)分,学习沉浸体验均分为(3.33±0.65)分,均处于中等偏上水平;系统思维得分为(59.01±13.57)分,处于中等水平。医学生的学习沉浸体验、学习态度和系统思维间均呈正相关。学习沉浸体验存在性别和专业差异。在控制了性别、专业和学习态度影响后,多重线性回归结果显示,学习沉浸体验和系统思维存在线性趋势关系(P<0.01);RCS模型分析显示,学习沉浸体验和系统思维之间存在J型的非线性关系(P for non-linearity<0.01);以中位数3.16为拐点,学习沉浸体验得分<3.16分时,对医学生的系统思维不产生影响(P=0.51);当得分≥3.16分时,随着学习沉浸体验增加,医学生的系统思维随之增加(Beta per SD=0.56,95%CI:0.44~0.68,P<0.01)。结论:混合模式下医学生的学习沉浸体验会对系统思维产生促进作用,当学习沉浸体验得分≥3.16分时,医学生的学习沉浸体验越高,系统思维随之增加。不同维度学习沉浸体验与系统思维的密切程度不一样。
基金Supported by the National Natural Science Foundation of China（11471289,11162020）
文摘In this paper,we show that for any given planar cubic algebraic curves defined by a quadratic Hamiltonian vector field,we can always have their exact explicit parametric representations. We use a model of micro-structured solid to show an application of our conclusions.
