Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechan...Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS （M2DDSWWS） is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.展开更多
The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the dist...The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations （ODEs） are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles ~, and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type.展开更多
The steady laminar boundary layer flow adjacent to a vertical plate with prescribed surface temperature immersed in an incompressible viscous fluid,where the effect of thermal radiation was taken into consideration,wa...The steady laminar boundary layer flow adjacent to a vertical plate with prescribed surface temperature immersed in an incompressible viscous fluid,where the effect of thermal radiation was taken into consideration,was investigated.The governing partial differential equations were transformed into a system of ordinary differential equations using similarity transformation,before being solved numerically by the shooting method.Both assisting and opposing buoyant flows were considered.It is found that dual solutions exist for both cases. Moreover,numerical results show that the heat transfer rate at the surface decreases in the presence of the radiation effect.展开更多
The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model. To find some exact solutions of a nonintegrable model with some arbitrary paramete...The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model. To find some exact solutions of a nonintegrable model with some arbitrary parameters is much more difficult than to find the solutions of a model with some special parameters. In this paper, we make a modification for the usual direct method to find some conditional similarity solutions of a (2+1)-dimensional general nonintegrable KdV equation.展开更多
A suitable similarity transformation is introduced to reduce the laminarboundary layer equations of power law fluids to a class of singular nonlinear two-point boundaryvalue problems. The kin friction and shear stress...A suitable similarity transformation is introduced to reduce the laminarboundary layer equations of power law fluids to a class of singular nonlinear two-point boundaryvalue problems. The kin friction and shear stress distributions for boundary layer flow over amoving flat plate are investigated by utilizing the shooting technique. Results indicate that foreach fixed value of the power law exponent n or the velocity ratio parameter xi, the skin frictionand shear stress decrease with the increasing of n or xi respectively.展开更多
A more general assumption than that in the classical one-dimensional large strain consolidation theory is adopted and the exact analytical solution of nonlinear finite strain self-weight consolidation based on this as...A more general assumption than that in the classical one-dimensional large strain consolidation theory is adopted and the exact analytical solution of nonlinear finite strain self-weight consolidation based on this assumption is obtained. By applying the same experimental data, the comparison of the solutions of linear and nonlinear finite strain theory, as well as the numerical calculating results based on finite element method is presented. The results of the comparison show that the analytical solution obtained here takes on better agreement with practical cases than that of linear one, and they also show that, compared with the solutions based on nonlinear theory, the settlement and the consolidation degree based on linear theory are smaller.展开更多
The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact soluti...The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact solutions)have ever been found.In the light of Blasius’pioneer works,we extend Blasius similarity transformation to the two dimensional turbulent boundary layers,and for a special case of flow modelled by Prandtl mixing-length,we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation.The ordinary differential equation is numerically solved and some useful quantities are produced.For numerical calculations,a complete Maple code is provided.展开更多
We study the symmetries of a （2＋1）-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of sim...We study the symmetries of a （2＋1）-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of similarity solutions are obtained.展开更多
Lie point symmetry analysis is performed to a recently proposed(2+1)-dimensional nonlinear system,theresonant Davey-Stewartson equation.Some similarity solutions of the RDS equation are thus obtained.
This paper considers the problem of hydrodynamics and thermal boundary layers of Darcy flow over horizontal surface embedded in a porous medium. The solutions of such problems for the cases of uniform surface temperat...This paper considers the problem of hydrodynamics and thermal boundary layers of Darcy flow over horizontal surface embedded in a porous medium. The solutions of such problems for the cases of uniform surface temperature and variable surface temperature have been studied and analysed in many papers. This paper, however, attempts to find similarity solutions for the Darcy flow problem with a convective boundary condition at the plate surface. It is found that the solution is possible when the heat transfer coefficient is proportional to x<sup>–2/3</sup>. The numerical solutions thus obtained are analyzed for a range of values of the parameter characterizing the hot fluid convection process. Analytical expressions are provided for local surface heat flux and total surface heat transfer rate while the flow variables are discussed graphically.展开更多
Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed in...Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.展开更多
The exact (1+1)\|dimensional similarity solutions of the Broadwell model are studied in a concise way. A new type of exact (1+1)\|dimensional similarity solutions of the Broadwell model are obtained. The conclusion th...The exact (1+1)\|dimensional similarity solutions of the Broadwell model are studied in a concise way. A new type of exact (1+1)\|dimensional similarity solutions of the Broadwell model are obtained. The conclusion that one\|dimensional Broadwell model cannot have multi\|dimensional similarity solutions is proved and the proof is simplified.展开更多
This work is devoted to get a new family of analytical solutions of the(2+1)-coupled dispersive long wave equations propagating in an infinitely long channel with constant depth,and can be observed in an open sea or i...This work is devoted to get a new family of analytical solutions of the(2+1)-coupled dispersive long wave equations propagating in an infinitely long channel with constant depth,and can be observed in an open sea or in wide channels.The solutions are obtained by using the invariance property of the similarity transformations method via one-parameter Lie group theory.The repeated use of the similarity transformations method can transform the system of PDEs into system of ODEs.Under adequate restrictions,the reduced system of ODEs is solved.Numerical simulation is performed to describe the solutions in a physically meaningful way.The profiles of the solutions are simulated by taking an appropriate choice of functions and constants involved therein.In each animation,a frame for dominated behavior is captured.They exhibit elastic multisolitons,single soliton,doubly solitons,stationary,kink and parabolic nature.The results are significant since these have confirmed some of the established results of S.Kumar et al.(2020)and K.Sharma et al.(2020).Some of their solutions can be deduced from the results derived in this work.Other results in the existing literature are different from those in this work.展开更多
The science of strategy(game theory)is known as the optimal decision-making of autonomous and challenging players in a strategic background.There are different strategies to complete the optimal decision.One of these ...The science of strategy(game theory)is known as the optimal decision-making of autonomous and challenging players in a strategic background.There are different strategies to complete the optimal decision.One of these strategies is the similarity technique.Similarity technique is a generalization of the symmetric strategy,which depends only on the other approaches employed,which can be formulated by altering diversities.One of these methods is the fractal theory.In this investigation,we present a new method studying the similarity analytic solution(SAS)of a 3D-fractal nanofluid system(FNFS).The dynamic evolution is completely given by the concept of differential subordination and majorization.Subordination andmajorization relationships are the sets of observable individualities.Game theory can simplify the conditions under which particular sets combine.We offer an explicit construction for the complex possible velocity,energy and thermal functions of two-dimensional fluid flow(the complex variable is suggested in the open unit disk,where the disk is selected at a constant temperature and concentration with uniform velocity).We establish that whenever the 3D-fractal nanofluid systemis approximated by a fractal function,the solution has the same property,so a class of fractal tangent function gives SAS.Finally,we demonstrate some simulations and examples that give the consequences of this methodology.展开更多
Marangoni convection occurs along any liquid vapor interface that has a surface tension gradient. The surface tension gradient can result from either temperature or concentration gradients along the surface. Maran...Marangoni convection occurs along any liquid vapor interface that has a surface tension gradient. The surface tension gradient can result from either temperature or concentration gradients along the surface. Marangoni convection is of importance in crystal growth melts and during boiling as it influences the flow around the vapor bubbles. The influence of Marangoni induced convection is more obvious under microgravity but also occurs in earth gravity. This paper presents a similarity solution for Marangoni induced flow for both the velocity and temperature profiles, assuming developing boundary layer flow along a surface with various imposed temperature profiles. The surface velocity, the total flow rate, and the heat transfer characteristics are given for various temperature profiles and various Prandtl numbers. Since the predicted boundary layer thickness would be much less than the diameter of vapor bubbles during nucleate boiling, the bubble surface curvature effects can be neglected and this analysis can also be used as a first estimate of the effect of Marangoni flow around a vapor bubble.展开更多
Land suitability assessment is a prerequisite phase in land use planning; it guides toward optimal land use by providing information on the opportunities and constraints involved in the use of a given land area. A geo...Land suitability assessment is a prerequisite phase in land use planning; it guides toward optimal land use by providing information on the opportunities and constraints involved in the use of a given land area. A geographic information system-based procedure, known as rural settlement suitability evaluation(RSSE) using an improved technique for order preference by similarity to ideal solution(TOPSIS), was adopted to determine the most suitable area for constructing rural settlements in different geographical locations. Given the distribution and independence of rural settlements, a distinctive evaluation criteria system that differed from that of urban suitability was established by considering the level of rural infrastructure services as well as living and working conditions. The unpredictable mutual interference among evaluation factors has been found in practical works. An improved TOPSIS using Mahalanobis distance was applied to solve the unpredictable correlation among the criteria in a suitability evaluation. Uncertainty and sensitivity analyses obtained via Monte Carlo simulation were performed to examine the robustness of the model. Daye, a resource-based city with rapid economic development, unsatisfied rural development, and geological environmental problems caused by mining, was used as a case study. Results indicate the following findings: 1) The RSSE model using the improved TOPSIS can assess the suitability of rural settlements, and the suitability maps generated using the improved TOPSIS have higher information density than those generated using traditional TOPSIS. The robustness of the model is improved, and the uncertainty is reduced in the suitability results. 2) Highly suitable land is mainly distributed in the northeast of the study area, and the majority of which is cultivated land, thereby leading to tremendous pressure on the loss of cultivated land. 3) Lastly, 12.54% of the constructive expansion permitted zone and 8.36% of the constructive expansion conditionally permitted zone are situated in an unsuitable area, which indicates that the general planning of Daye lacks the necessary verification of suitability evaluation. Guidance is provided on the development strategy of rural settlement patches to support decision making in general land use planning.展开更多
Network maintenance strategy selection is a multi-objective decision making topic. It mostly depends on the uncertainty and fuzziness of decision makers and conditions. In this paper, based on analytic hierarchy proce...Network maintenance strategy selection is a multi-objective decision making topic. It mostly depends on the uncertainty and fuzziness of decision makers and conditions. In this paper, based on analytic hierarchy process(AHP) and technique for order preference by similarity to ideal solution(TOPSIS), TOPSIS partial order method is proposed to choose the optimal maintenance strategy. This method uses AHP to determine the weights of evaluation indexes. The optimal maintenance strategy choice is given as an example to demonstrate the effectiveness of the method.展开更多
In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system...In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras.Secondly,by analyzing the reduced equation,three types of similarity solutions are derived,such as multi-soliton like solutions,variable separations solutions,and KdV type solutions.展开更多
The magnetohydrodynamic （MHD） Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD bo...The magnetohydrodynamic （MHD） Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method （DTM） with the Pade approximation called DTM-Pade. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.展开更多
为了客观评价地下空间开发地质适宜性并为评价工作提供一种新思路和参考,提出了一种基于三角模糊数的模糊层次分析法(fuzzy analytic hierarchy process based on triangular fuzzy numbers,FAHP)和优劣解距离法(technique for order pr...为了客观评价地下空间开发地质适宜性并为评价工作提供一种新思路和参考,提出了一种基于三角模糊数的模糊层次分析法(fuzzy analytic hierarchy process based on triangular fuzzy numbers,FAHP)和优劣解距离法(technique for order preference by similarity to ideal solution,TOPSIS)相结合的评价方法。通过地质调查研究构建基于土体工程地质性质、水文地质条件、不良地质作用、地形地貌等影响因素为主的层次分析关系模型。基于专家判别利用FAHP计算各评价因素的权重,以各评价指标层的分级临界值作为典型评价样本,利用TOPSIS法对适宜性等级进行非等分划分,基于区间值优化的TOPSIS法建立最终评价模型,通过ArcGIS的空间分析功能等确定每个评价单元适宜性等级。该方法与传统方法相比一定程度上减少了评价过程中专家评判的过多主观影响,评价过程更倾向于定量化,结果更为客观。利用该方法对无锡市区浅层地下空间开发地质适宜性进行评价,评价结果与实际工程经验相符,证明了该方法的有效性,因此该方法对地下空间开发适宜性评价工作具有一定借鉴意义。展开更多
基金Project supported by the Natural Science Foundation of Guangdong Province of China (Grant No.10452840301004616)the National Natural Science Foundation of China (Grant No.61001018)the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institute (Grant No.408YKQ09)
文摘Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS （M2DDSWWS） is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.
文摘The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations （ODEs） are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles ~, and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type.
基金supported by a research grant from Universiti Kebangsaan Malaysia(No.UKM-GUP-BTT-07-25-174)
文摘The steady laminar boundary layer flow adjacent to a vertical plate with prescribed surface temperature immersed in an incompressible viscous fluid,where the effect of thermal radiation was taken into consideration,was investigated.The governing partial differential equations were transformed into a system of ordinary differential equations using similarity transformation,before being solved numerically by the shooting method.Both assisting and opposing buoyant flows were considered.It is found that dual solutions exist for both cases. Moreover,numerical results show that the heat transfer rate at the surface decreases in the presence of the radiation effect.
文摘The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model. To find some exact solutions of a nonintegrable model with some arbitrary parameters is much more difficult than to find the solutions of a model with some special parameters. In this paper, we make a modification for the usual direct method to find some conditional similarity solutions of a (2+1)-dimensional general nonintegrable KdV equation.
基金This work was financially supported by the Cross-Century Talents Projects of Educational Ministry, China and the "973" Key Item(
文摘A suitable similarity transformation is introduced to reduce the laminarboundary layer equations of power law fluids to a class of singular nonlinear two-point boundaryvalue problems. The kin friction and shear stress distributions for boundary layer flow over amoving flat plate are investigated by utilizing the shooting technique. Results indicate that foreach fixed value of the power law exponent n or the velocity ratio parameter xi, the skin frictionand shear stress decrease with the increasing of n or xi respectively.
文摘A more general assumption than that in the classical one-dimensional large strain consolidation theory is adopted and the exact analytical solution of nonlinear finite strain self-weight consolidation based on this assumption is obtained. By applying the same experimental data, the comparison of the solutions of linear and nonlinear finite strain theory, as well as the numerical calculating results based on finite element method is presented. The results of the comparison show that the analytical solution obtained here takes on better agreement with practical cases than that of linear one, and they also show that, compared with the solutions based on nonlinear theory, the settlement and the consolidation degree based on linear theory are smaller.
基金Xi’an University of Architecture and Technology(Grant no.002/2040221134).
文摘The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact solutions)have ever been found.In the light of Blasius’pioneer works,we extend Blasius similarity transformation to the two dimensional turbulent boundary layers,and for a special case of flow modelled by Prandtl mixing-length,we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation.The ordinary differential equation is numerically solved and some useful quantities are produced.For numerical calculations,a complete Maple code is provided.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10475055 and 10547124 and partly by Shanghai Leading Academic Discipline Project under Grant No. T0401.Acknowledgments The authors would like to thank Prof. S.Y. Lou for his helpful discussions.
文摘We study the symmetries of a （2＋1）-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of similarity solutions are obtained.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10735030 and 90503006National Key Basic Research Program of China (973 Program) under Grant No.2007CB814800Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20070248120
文摘Lie point symmetry analysis is performed to a recently proposed(2+1)-dimensional nonlinear system,theresonant Davey-Stewartson equation.Some similarity solutions of the RDS equation are thus obtained.
文摘This paper considers the problem of hydrodynamics and thermal boundary layers of Darcy flow over horizontal surface embedded in a porous medium. The solutions of such problems for the cases of uniform surface temperature and variable surface temperature have been studied and analysed in many papers. This paper, however, attempts to find similarity solutions for the Darcy flow problem with a convective boundary condition at the plate surface. It is found that the solution is possible when the heat transfer coefficient is proportional to x<sup>–2/3</sup>. The numerical solutions thus obtained are analyzed for a range of values of the parameter characterizing the hot fluid convection process. Analytical expressions are provided for local surface heat flux and total surface heat transfer rate while the flow variables are discussed graphically.
文摘Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.
基金Supported by National Natural Science Foundation ofChina(No. 196 310 6 0 ) and Post Doctor Science Foun-dation of China
文摘The exact (1+1)\|dimensional similarity solutions of the Broadwell model are studied in a concise way. A new type of exact (1+1)\|dimensional similarity solutions of the Broadwell model are obtained. The conclusion that one\|dimensional Broadwell model cannot have multi\|dimensional similarity solutions is proved and the proof is simplified.
文摘This work is devoted to get a new family of analytical solutions of the(2+1)-coupled dispersive long wave equations propagating in an infinitely long channel with constant depth,and can be observed in an open sea or in wide channels.The solutions are obtained by using the invariance property of the similarity transformations method via one-parameter Lie group theory.The repeated use of the similarity transformations method can transform the system of PDEs into system of ODEs.Under adequate restrictions,the reduced system of ODEs is solved.Numerical simulation is performed to describe the solutions in a physically meaningful way.The profiles of the solutions are simulated by taking an appropriate choice of functions and constants involved therein.In each animation,a frame for dominated behavior is captured.They exhibit elastic multisolitons,single soliton,doubly solitons,stationary,kink and parabolic nature.The results are significant since these have confirmed some of the established results of S.Kumar et al.(2020)and K.Sharma et al.(2020).Some of their solutions can be deduced from the results derived in this work.Other results in the existing literature are different from those in this work.
文摘The science of strategy(game theory)is known as the optimal decision-making of autonomous and challenging players in a strategic background.There are different strategies to complete the optimal decision.One of these strategies is the similarity technique.Similarity technique is a generalization of the symmetric strategy,which depends only on the other approaches employed,which can be formulated by altering diversities.One of these methods is the fractal theory.In this investigation,we present a new method studying the similarity analytic solution(SAS)of a 3D-fractal nanofluid system(FNFS).The dynamic evolution is completely given by the concept of differential subordination and majorization.Subordination andmajorization relationships are the sets of observable individualities.Game theory can simplify the conditions under which particular sets combine.We offer an explicit construction for the complex possible velocity,energy and thermal functions of two-dimensional fluid flow(the complex variable is suggested in the open unit disk,where the disk is selected at a constant temperature and concentration with uniform velocity).We establish that whenever the 3D-fractal nanofluid systemis approximated by a fractal function,the solution has the same property,so a class of fractal tangent function gives SAS.Finally,we demonstrate some simulations and examples that give the consequences of this methodology.
基金Supported by the National Natural Science Foundationof China( No. 5 9995 5 5 0 - 3 )
文摘Marangoni convection occurs along any liquid vapor interface that has a surface tension gradient. The surface tension gradient can result from either temperature or concentration gradients along the surface. Marangoni convection is of importance in crystal growth melts and during boiling as it influences the flow around the vapor bubbles. The influence of Marangoni induced convection is more obvious under microgravity but also occurs in earth gravity. This paper presents a similarity solution for Marangoni induced flow for both the velocity and temperature profiles, assuming developing boundary layer flow along a surface with various imposed temperature profiles. The surface velocity, the total flow rate, and the heat transfer characteristics are given for various temperature profiles and various Prandtl numbers. Since the predicted boundary layer thickness would be much less than the diameter of vapor bubbles during nucleate boiling, the bubble surface curvature effects can be neglected and this analysis can also be used as a first estimate of the effect of Marangoni flow around a vapor bubble.
基金Under the auspices of National Natural Science Foundation of China(No.41371429,41401196)
文摘Land suitability assessment is a prerequisite phase in land use planning; it guides toward optimal land use by providing information on the opportunities and constraints involved in the use of a given land area. A geographic information system-based procedure, known as rural settlement suitability evaluation(RSSE) using an improved technique for order preference by similarity to ideal solution(TOPSIS), was adopted to determine the most suitable area for constructing rural settlements in different geographical locations. Given the distribution and independence of rural settlements, a distinctive evaluation criteria system that differed from that of urban suitability was established by considering the level of rural infrastructure services as well as living and working conditions. The unpredictable mutual interference among evaluation factors has been found in practical works. An improved TOPSIS using Mahalanobis distance was applied to solve the unpredictable correlation among the criteria in a suitability evaluation. Uncertainty and sensitivity analyses obtained via Monte Carlo simulation were performed to examine the robustness of the model. Daye, a resource-based city with rapid economic development, unsatisfied rural development, and geological environmental problems caused by mining, was used as a case study. Results indicate the following findings: 1) The RSSE model using the improved TOPSIS can assess the suitability of rural settlements, and the suitability maps generated using the improved TOPSIS have higher information density than those generated using traditional TOPSIS. The robustness of the model is improved, and the uncertainty is reduced in the suitability results. 2) Highly suitable land is mainly distributed in the northeast of the study area, and the majority of which is cultivated land, thereby leading to tremendous pressure on the loss of cultivated land. 3) Lastly, 12.54% of the constructive expansion permitted zone and 8.36% of the constructive expansion conditionally permitted zone are situated in an unsuitable area, which indicates that the general planning of Daye lacks the necessary verification of suitability evaluation. Guidance is provided on the development strategy of rural settlement patches to support decision making in general land use planning.
基金the Weapons and Equipment Preresearch Fund(No.9140A27040414JB34079)the Specialized Research Fund for the Doctoral Program of the Military Education(No.2015JY354)
文摘Network maintenance strategy selection is a multi-objective decision making topic. It mostly depends on the uncertainty and fuzziness of decision makers and conditions. In this paper, based on analytic hierarchy process(AHP) and technique for order preference by similarity to ideal solution(TOPSIS), TOPSIS partial order method is proposed to choose the optimal maintenance strategy. This method uses AHP to determine the weights of evaluation indexes. The optimal maintenance strategy choice is given as an example to demonstrate the effectiveness of the method.
基金Supported by Shandong Provincial Natural Science Foundation under Grant Nos. ZR2011AQ017 and ZR2010AM028
文摘In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras.Secondly,by analyzing the reduced equation,three types of similarity solutions are derived,such as multi-soliton like solutions,variable separations solutions,and KdV type solutions.
基金supported by the National Natural Science Foundation of China (Nos. 50936003 and 51076012)the Open Project of State Key Laboratory for Advanced Metals and Materials (No. 2009Z-02)
文摘The magnetohydrodynamic （MHD） Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method （DTM） with the Pade approximation called DTM-Pade. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.
文摘为了客观评价地下空间开发地质适宜性并为评价工作提供一种新思路和参考,提出了一种基于三角模糊数的模糊层次分析法(fuzzy analytic hierarchy process based on triangular fuzzy numbers,FAHP)和优劣解距离法(technique for order preference by similarity to ideal solution,TOPSIS)相结合的评价方法。通过地质调查研究构建基于土体工程地质性质、水文地质条件、不良地质作用、地形地貌等影响因素为主的层次分析关系模型。基于专家判别利用FAHP计算各评价因素的权重,以各评价指标层的分级临界值作为典型评价样本,利用TOPSIS法对适宜性等级进行非等分划分,基于区间值优化的TOPSIS法建立最终评价模型,通过ArcGIS的空间分析功能等确定每个评价单元适宜性等级。该方法与传统方法相比一定程度上减少了评价过程中专家评判的过多主观影响,评价过程更倾向于定量化,结果更为客观。利用该方法对无锡市区浅层地下空间开发地质适宜性进行评价,评价结果与实际工程经验相符,证明了该方法的有效性,因此该方法对地下空间开发适宜性评价工作具有一定借鉴意义。
