An integral approach has been used to analyze the development of the free convection boundary layer on heated concave surfaces,such as those in horizontal cylinders or a sphere.Based on the non-dimensional laminar and...An integral approach has been used to analyze the development of the free convection boundary layer on heated concave surfaces,such as those in horizontal cylinders or a sphere.Based on the non-dimensional laminar and turbulent velocity and temperature profiles closed form expressions for the boundary layer thickness,velocity scale as well as the boundary layer commencement after the point of instability are obtained.In addition,the mass flowrate to the thermal stratified region is given.展开更多
In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions ...In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions to this problem is obtained.展开更多
Past researches have shown that the non-smooth body surfaces of soil burrowing animals help to reduce soil resistance. In this research, this concept of bionic non-smooth surface was applied to disc ploughs and an exp...Past researches have shown that the non-smooth body surfaces of soil burrowing animals help to reduce soil resistance. In this research, this concept of bionic non-smooth surface was applied to disc ploughs and an experiment was conducted in an indoor soil bin to find out the effects of different bionic units on reducing soil resistance to disc ploughing. Horizontal force acting on the disc plough during soil deformation was measured using a 5 kN sensor. Convex and concave bionic units were used and the material used for making convex ones is ultra high molecular weight polyethylene (UHMWPE) which is hydrophobic. From the experiment results, higher or deeper bionic units always resulted in less soil resistance. Convex bionic units gave the highest resistance reduction reaching a maximum of 19% reduction (from 1715.36 N to 1383.65 N) compared to concave bi-onic units. Also, samples with a bionic unit density of 30% gave the highest resistance reduction compared to the other two, which were either plain or had 10% density. In conclusion, the concept of bionic non-smooth units can be applied to disc ploughs in order to reduce soil resistance.展开更多
In this study, we explore the application of ACP (asymptotic curve based and proportionality oriented) Alpha Beta (αβ) Nonlinear Math to analyze arithmetic and radiation transmission data. Specifically, we investiga...In this study, we explore the application of ACP (asymptotic curve based and proportionality oriented) Alpha Beta (αβ) Nonlinear Math to analyze arithmetic and radiation transmission data. Specifically, we investigate the relationship between two variables. The novel approach involves collecting elementary “y” data and subsequently analyzing the asymptotic cumulative or demulative (opposite of cumulative) Y data. In part I, we examine the connection between the common linear numbers and ideal nonlinear numbers. In part II, we delve into the relationship between X-ray energy and the radiation transmission for various thin film materials. The fundamental physical law asserts that the nonlinear change in continuous variable Y is negatively proportional to the nonlinear change in continuous variable X, expressed mathematically as dα = −Kdβ. Here: dα {Y, Yu, Yb} represents the change in Y, with Yu and Yb denoting the upper and baseline asymptote of Y. dβ {X, Xu, Xb} represents the change in X, with Xu and Xb denoting the upper and baseline asymptote of X. K represents the proportionality constant or rate constant, which varies based on equation arrangement. K is the key inferential factor for describing physical phenomena.展开更多
Experimental study of the local and average heat transfer characteristics of a single round jet impinging on the concave surfaces was conducted in this work to gain in-depth knowledge of the curvature effects.The expe...Experimental study of the local and average heat transfer characteristics of a single round jet impinging on the concave surfaces was conducted in this work to gain in-depth knowledge of the curvature effects.The experiments were conducted by employing a piccolo tube with one single jet hole over a wide range of parameters：jet Reynolds number from 27000 to 130000,relative nozzle to surface distance from 3.3 to 30,and relative surface curvature from 0.005 to 0.030.Experimental results indicate that the surface curvature has opposite effects on heat transfer characteristics.On one hand,an increase of relative nozzle to surface distance（increasing jet diameter in fact）enhances the average heat transfer around the surface for the same curved surface.On the other hand,the average Nusselt number decreases as relative nozzle to surface distance increases for a fixed jet diameter.Finally,experimental data-based correlations of the average Nusselt number over the curved surface were obtained with consideration of surface curvature effect.This work contributes to a better understanding of the curvature effects on heat transfer of a round jet impingement on concave surfaces,which is of high importance to the design of the aircraft anti-icing system.展开更多
In most models of population dynamics, diffusion between patches is assumedto be continuous or discrete, but in practice many species diffuse only during a single period. Inthis paper we propose a single species model...In most models of population dynamics, diffusion between patches is assumedto be continuous or discrete, but in practice many species diffuse only during a single period. Inthis paper we propose a single species model with impulsive diffusion between two patches, whichprovides a more natural description of population dynamics. By using the discrete dynamical systemgenerated by a monotone, concave map for the population, we prove that the map always has a globallystable positive fixed point. This means that a single species system with impulsive diffusionalways has a globally stable positive periodic solution. This result is further substantiated bynumerical simulation. Under impulsive diffusion the single species survives in the two patches.展开更多
In order to gain a sufficient wear resistance for applications, the biomimetic non-smooth units in concave were fabricated on the surfaces of 20CrMnTi steel using a biomimetic laser remelting technology. The diameter ...In order to gain a sufficient wear resistance for applications, the biomimetic non-smooth units in concave were fabricated on the surfaces of 20CrMnTi steel using a biomimetic laser remelting technology. The diameter and distribution of the concaves were optimized using orthogonal experiment. The microstructures of the biomimetic non-smooth units were examined. The anti-wear behaviors were investigated by the rolling wear test with lubricant. The results of wear tests indicated that the biomimetic surfaces exhibit a higher anti-wear ability than the smooth surfaces. The biomimetic surface with concaves of 250 μm in diameter and transverse distance of 270 μm and longitudinal distance of 400 μm exhibits the best anti-wear property. The enhancement of wear resistance can be mainly attributed to the action of biomimetic non-smooth units and the super fined microstructure and hardness in the biomimetic unit zones.展开更多
The Schur convexity and concavity of a class of symmetric functions are discussed, and an open problem proposed by Guan in "Some properties of a class of symmetric functions" is answered. As consequences, so...The Schur convexity and concavity of a class of symmetric functions are discussed, and an open problem proposed by Guan in "Some properties of a class of symmetric functions" is answered. As consequences, some inequalities are established by use of the theory of majorization.展开更多
Controlled syntheses of PtNi metal nanocrystals with unique structures for catalyzing oxygen reduction reactions （ORRs） have attracted great interest. Here, we report the one-step synthesis of single-crystal PtNi oc...Controlled syntheses of PtNi metal nanocrystals with unique structures for catalyzing oxygen reduction reactions （ORRs） have attracted great interest. Here, we report the one-step synthesis of single-crystal PtNi octahedra with in situ-developed highly concave features and self-confined composition that are optimal for ORR. Detailed studies revealed that the Pt-rich seeding, subsequent Pt/Ni co-reduction, and Pt-Ni interfusion resulted in uniform single-crystal PtNi octahedra, and that the combination of Ni facet segregation and oxygen etching of a Ni-rich surface led to the concavity and confined Ni content. The concave PtNi nanocrystals exhibited much higher ORR performance than the commercially available Pt/C catalyst in terms of both specific activity （29.1 times higher） and mass activity （12.9 times higher） at 0.9 V （vs. reversible hydrogen electrode （RHE））. The performance was also higher than that of PtNi octahedra without concavity, confirming that the higher activity was closely related to its morphology. Moreover, the concave octahedra also exhibited remarkable stability in ORR （93% mass activity remained after 10,000 cycles between 0.6 and 1.1 V vs. RHE） owing to the passivation of the unstable sites.展开更多
The Schur convexity or concavity problem of the Gini mean values S(a, b; x, y) with respect to (x, y) ∈ (0, ∞) × (0, ∞) for fixed (a, b) ∈ ? × ? is still open. In this paper, we prove that S(a, b; x, y) ...The Schur convexity or concavity problem of the Gini mean values S(a, b; x, y) with respect to (x, y) ∈ (0, ∞) × (0, ∞) for fixed (a, b) ∈ ? × ? is still open. In this paper, we prove that S(a, b; x, y) is Schur convex with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b): a ? 0, b ? 0, a + b ? 1}, and Schur concave with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b): b ? 0, b ? a, a + b ? 1} ∩ {(a, b): a ? 0, a ? b, a + b ? 1}.展开更多
文摘An integral approach has been used to analyze the development of the free convection boundary layer on heated concave surfaces,such as those in horizontal cylinders or a sphere.Based on the non-dimensional laminar and turbulent velocity and temperature profiles closed form expressions for the boundary layer thickness,velocity scale as well as the boundary layer commencement after the point of instability are obtained.In addition,the mass flowrate to the thermal stratified region is given.
文摘In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions to this problem is obtained.
基金supported by the National Natural Science Foundation of China (Grant No 50175045)National High Technology Research and Development Program of China (‘863’ Project) (Grant No 2010AA101401-3)the scientific and technological development plan of Jilin Province, China (Grant No 20050539)
文摘Past researches have shown that the non-smooth body surfaces of soil burrowing animals help to reduce soil resistance. In this research, this concept of bionic non-smooth surface was applied to disc ploughs and an experiment was conducted in an indoor soil bin to find out the effects of different bionic units on reducing soil resistance to disc ploughing. Horizontal force acting on the disc plough during soil deformation was measured using a 5 kN sensor. Convex and concave bionic units were used and the material used for making convex ones is ultra high molecular weight polyethylene (UHMWPE) which is hydrophobic. From the experiment results, higher or deeper bionic units always resulted in less soil resistance. Convex bionic units gave the highest resistance reduction reaching a maximum of 19% reduction (from 1715.36 N to 1383.65 N) compared to concave bi-onic units. Also, samples with a bionic unit density of 30% gave the highest resistance reduction compared to the other two, which were either plain or had 10% density. In conclusion, the concept of bionic non-smooth units can be applied to disc ploughs in order to reduce soil resistance.
文摘In this study, we explore the application of ACP (asymptotic curve based and proportionality oriented) Alpha Beta (αβ) Nonlinear Math to analyze arithmetic and radiation transmission data. Specifically, we investigate the relationship between two variables. The novel approach involves collecting elementary “y” data and subsequently analyzing the asymptotic cumulative or demulative (opposite of cumulative) Y data. In part I, we examine the connection between the common linear numbers and ideal nonlinear numbers. In part II, we delve into the relationship between X-ray energy and the radiation transmission for various thin film materials. The fundamental physical law asserts that the nonlinear change in continuous variable Y is negatively proportional to the nonlinear change in continuous variable X, expressed mathematically as dα = −Kdβ. Here: dα {Y, Yu, Yb} represents the change in Y, with Yu and Yb denoting the upper and baseline asymptote of Y. dβ {X, Xu, Xb} represents the change in X, with Xu and Xb denoting the upper and baseline asymptote of X. K represents the proportionality constant or rate constant, which varies based on equation arrangement. K is the key inferential factor for describing physical phenomena.
基金supported by the National Natural Science Foundation of China(No.51206008)the EU Marie Curie Actions-International Incoming Fellowships(No.FP7PEOPLE-2013-IIF-626576)
文摘Experimental study of the local and average heat transfer characteristics of a single round jet impinging on the concave surfaces was conducted in this work to gain in-depth knowledge of the curvature effects.The experiments were conducted by employing a piccolo tube with one single jet hole over a wide range of parameters：jet Reynolds number from 27000 to 130000,relative nozzle to surface distance from 3.3 to 30,and relative surface curvature from 0.005 to 0.030.Experimental results indicate that the surface curvature has opposite effects on heat transfer characteristics.On one hand,an increase of relative nozzle to surface distance（increasing jet diameter in fact）enhances the average heat transfer around the surface for the same curved surface.On the other hand,the average Nusselt number decreases as relative nozzle to surface distance increases for a fixed jet diameter.Finally,experimental data-based correlations of the average Nusselt number over the curved surface were obtained with consideration of surface curvature effect.This work contributes to a better understanding of the curvature effects on heat transfer of a round jet impingement on concave surfaces,which is of high importance to the design of the aircraft anti-icing system.
基金Supported by the National Natural Science Foundation of China (No.10171106)
文摘In most models of population dynamics, diffusion between patches is assumedto be continuous or discrete, but in practice many species diffuse only during a single period. Inthis paper we propose a single species model with impulsive diffusion between two patches, whichprovides a more natural description of population dynamics. By using the discrete dynamical systemgenerated by a monotone, concave map for the population, we prove that the map always has a globallystable positive fixed point. This means that a single species system with impulsive diffusionalways has a globally stable positive periodic solution. This result is further substantiated bynumerical simulation. Under impulsive diffusion the single species survives in the two patches.
基金supported by the National Nature Science Foundation of China (Grant No 50635030)the Key Scientific and Technological Project of Jilin Province (Grant No 09ZDGG001)
文摘In order to gain a sufficient wear resistance for applications, the biomimetic non-smooth units in concave were fabricated on the surfaces of 20CrMnTi steel using a biomimetic laser remelting technology. The diameter and distribution of the concaves were optimized using orthogonal experiment. The microstructures of the biomimetic non-smooth units were examined. The anti-wear behaviors were investigated by the rolling wear test with lubricant. The results of wear tests indicated that the biomimetic surfaces exhibit a higher anti-wear ability than the smooth surfaces. The biomimetic surface with concaves of 250 μm in diameter and transverse distance of 270 μm and longitudinal distance of 400 μm exhibits the best anti-wear property. The enhancement of wear resistance can be mainly attributed to the action of biomimetic non-smooth units and the super fined microstructure and hardness in the biomimetic unit zones.
基金supported by National Natural Science Foundation of China (Grant Nos.60850005, 10771195)the Natural Science Foundation of Zhejiang Province (Grant Nos. D7080080, Y7080185,Y607128)
文摘The Schur convexity and concavity of a class of symmetric functions are discussed, and an open problem proposed by Guan in "Some properties of a class of symmetric functions" is answered. As consequences, some inequalities are established by use of the theory of majorization.
基金We acknowledge support from the National Science Foundation （NSF） through award DMR-1437263 on catalysis studies and the Office of Naval Research （ONR） under award N00014-15-1-2146 for synthesis efforts. X. F. D. acknowledges support from the U.S. Department of Energ34 Office of Basic Energy Sciences, Division of Materials Science and Engineering through award DE-SC0008055. E. B. Z. received additional support from China Scholarship Council （CSC） scholarships. We also thank the Electron Imaging Center of Nanomachines at CNSI for TEM support.
文摘Controlled syntheses of PtNi metal nanocrystals with unique structures for catalyzing oxygen reduction reactions （ORRs） have attracted great interest. Here, we report the one-step synthesis of single-crystal PtNi octahedra with in situ-developed highly concave features and self-confined composition that are optimal for ORR. Detailed studies revealed that the Pt-rich seeding, subsequent Pt/Ni co-reduction, and Pt-Ni interfusion resulted in uniform single-crystal PtNi octahedra, and that the combination of Ni facet segregation and oxygen etching of a Ni-rich surface led to the concavity and confined Ni content. The concave PtNi nanocrystals exhibited much higher ORR performance than the commercially available Pt/C catalyst in terms of both specific activity （29.1 times higher） and mass activity （12.9 times higher） at 0.9 V （vs. reversible hydrogen electrode （RHE））. The performance was also higher than that of PtNi octahedra without concavity, confirming that the higher activity was closely related to its morphology. Moreover, the concave octahedra also exhibited remarkable stability in ORR （93% mass activity remained after 10,000 cycles between 0.6 and 1.1 V vs. RHE） owing to the passivation of the unstable sites.
基金supported by National Natural Science Foundation of China (Grant Nos. 60850005, 10771195)the Natural Science Foundation of Zhejiang Province (Grant Nos. D7080080, Y607128, Y7080185)
文摘The Schur convexity or concavity problem of the Gini mean values S(a, b; x, y) with respect to (x, y) ∈ (0, ∞) × (0, ∞) for fixed (a, b) ∈ ? × ? is still open. In this paper, we prove that S(a, b; x, y) is Schur convex with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b): a ? 0, b ? 0, a + b ? 1}, and Schur concave with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b): b ? 0, b ? a, a + b ? 1} ∩ {(a, b): a ? 0, a ? b, a + b ? 1}.
