A method for static aeroelastic trim analysis and flight loads computation of a flexible aircraft with large deformations has been presented in this paper,which considers the geometric nonlinearity of the structure an...A method for static aeroelastic trim analysis and flight loads computation of a flexible aircraft with large deformations has been presented in this paper,which considers the geometric nonlinearity of the structure and the nonplanar effects of aerodynamics.A nonplanar vortex lattice method is used to compute the nonplanar aerodynamics.The nonlinear finite element method is introduced to consider the structural geometric nonlinearity.Moreover,the surface spline method is used for structure/aerodynamics coupling.Finally,by combining the equilibrium equations of rigid motions of the deformed aircraft,the nonlinear trim problem of the flexible aircraft is solved by iterative method.For instance,the longitudinal trim analysis of a flexible aircraft with large-aspect-ratio wings is carried out by both the nonlinear method presented and the linear method of MSC Flightloads.Results obtained by these two methods are compared,and it is indicated that the results agree with each other when the deformation is small.However,because the linear method of static aeroelastic analysis does not consider the nonplanar aerodynamic effects or structural geometric nonlinearity,it is not applicable as the deformations increase.Whereas the nonlinear method presented could solve the trim problem accurately,even the deformations are large,which makes the nonlinear method suitable for rapid and efficient analysis in engineering practice.It could be used not only in the preliminary stage but also in the detail stage of aircraft design.展开更多
Two new concepts, the generalized support function and restricted chord function, both referring to a convex set, were introduced in [1]. General formulae to yield the kinematic measure of a segment of fixed length in...Two new concepts, the generalized support function and restricted chord function, both referring to a convex set, were introduced in [1]. General formulae to yield the kinematic measure of a segment of fixed length in a convex set were established based on these concepts. In this article , using the partial intersection method, we consider the generalized Buffon problem for three kinds of lattices. We determine the probability of intersection of a body test needle of length l, l a.展开更多
The microstructure of granular media, including grain's shape- and size-polydispersities, orientation, and area fraction can potentially affect its permeability. However, few studies consider the coupling effects ...The microstructure of granular media, including grain's shape- and size-polydispersities, orientation, and area fraction can potentially affect its permeability. However, few studies consider the coupling effects of these features. This work employs geometrical probability and stereology to establish quantitative relationships between the above microstructural features and the geometric tortuosity of the two-dimensional granular media containing superellipse, superoval, and polygon grains. Then the lattice Boltzmann method (LBM) is used to determine the permeabilities of these granular media. By combining the tortuosity model and the LBM-derived permeabilities, modified K–C equations are formulated to predict the permeability and the shape factor, considering the grain's shape- and size-polydispersities, orientation, and area fraction. The reliability of these methods can be verified by comparing them with both our simulations and available experimental, theoretical, and numerical data reported in the literature. The findings implicate that the tortuosity and permeability of the granular media are strongly correlated with the grain's shape, orientation, and area fraction but unaffected by the size polydispersity and spatial arrangement of grains. Only circularity is not enough to derive a unified formula for considering the impact of grain shape on tortuosity and permeability, other shape parameters need to be explored in the future.展开更多
In 2010,Gábor Czédli and E.Tamás Schmidt mentioned that the best cover-preserving embedding of a given semimodular lattice is not known yet[A cover-preserving embedding of semimodular lattices into geom...In 2010,Gábor Czédli and E.Tamás Schmidt mentioned that the best cover-preserving embedding of a given semimodular lattice is not known yet[A cover-preserving embedding of semimodular lattices into geometric lattices.Advances in Mathematics,225,2455-2463(2010)].That is to say:What are the geometric lattices G such that a given finite semimodular lattice L has a cover-preserving embedding into G with the smallest|G|?In this paper,we propose an algorithm to calculate all the best extending cover-preserving geometric lattices G of a given semimodular lattice L and prove that the length and the number of atoms of every best extending cover-preserving geometric lattice G equal the length of L and the number of non-zero join-irreducible elements of L,respectively.Therefore,we solve the problem on the best cover-preserving embedding of a given semimodular lattice raised by Gábor Czédli and E.Tamás Schmidt.展开更多
To explain the anomaly (τ<sub>b</sub> ≠ τ<sub>f</sub>) of the neutron lifetime τ in some experiments, in “bottle” τ<sub>b</sub> and in “beam” τ<sub>f</sub>, we...To explain the anomaly (τ<sub>b</sub> ≠ τ<sub>f</sub>) of the neutron lifetime τ in some experiments, in “bottle” τ<sub>b</sub> and in “beam” τ<sub>f</sub>, we resort to an anomalous form of the neutron n<sub>a</sub>. This form belongs to one of two different states of the structure of the quark configurations making up the neutron (nucleon): first, an ordinary form Ψ<sub>o</sub>, while the second is an “anomalous” form Ψ<sub>a</sub>, difficult to detect and decay. If the ordinary configuration is present in everyone nuclear processes, to strong and weak interactions, and in diffusion processes, the anomalous form can emerge, in casual way and probabilistic, in some processes of fusion with production of neutrons and can be highlighted in some experiments as those in “bottle” and in “beam”, see the anomaly of the neutron lifetime. We show that the anomalous form Ψ<sub>a</sub> can be highlighted in the coupling between a dipoles’ lattice of virtual bosons W and the neutron (nucleon) because the neutron into anomalous configuration does not decays. Finally, we interpret the anomalous neutron as a “dark” neutron, presenting, so, the dark matter as an anomalous form of hadron matter.展开更多
We assume that M is a phase space and H an Hilbert space yielded by a quantization scheme. In this paper we consider the set of all “experimental propositions” of M and we look for a model of quantum logic in relati...We assume that M is a phase space and H an Hilbert space yielded by a quantization scheme. In this paper we consider the set of all “experimental propositions” of M and we look for a model of quantum logic in relation to the quantization of the base manifold M. In particular we give a new interpretation about previous results of the author in order to build an “asymptotics quantum probability space” for the Hilbert lattice L(H).展开更多
In this paper, some properties of the image of the geometric lattice of a graphic matroid under a strong map are discussed, and a negative answer to the related open question of Welsh’s book is given.
Let F be a field and V= V<sub>n</sub>（F）={（a<sub>1</sub>,…, a<sub>n</sub>）|a<sub>i</sub>∈F} be the row vector space of finite dimension n over F. Let be a finite s...Let F be a field and V= V<sub>n</sub>（F）={（a<sub>1</sub>,…, a<sub>n</sub>）|a<sub>i</sub>∈F} be the row vector space of finite dimension n over F. Let be a finite set ofsubspaces of Vsuch that U=（0）. And let L= L（（?）） be the set of intersections of dements of. Partial order L by reverse inclusion has V as its minimal element and as its set of atoms. We denote the partial order-展开更多
Let be a n-dimensional row vector space over a finite field For , let be a d-?dimensional subspace of . denotes the set of all the spaces which are the subspaces of and not the subspaces of except . We define the part...Let be a n-dimensional row vector space over a finite field For , let be a d-?dimensional subspace of . denotes the set of all the spaces which are the subspaces of and not the subspaces of except . We define the partial order on by ordinary inclusion (resp. reverse inclusion), and then is a poset, denoted by (resp. ). In this paper we show that both and are finite atomic lattices. Further, we discuss the geometricity of and , and obtain their characteristic polynomials.展开更多
A rapid and efficient method for static aeroelastic analysis of a flexible slender wing when considering the structural geometric nonlinearity has been developed in this paper. A non-planar vortex lattice method herei...A rapid and efficient method for static aeroelastic analysis of a flexible slender wing when considering the structural geometric nonlinearity has been developed in this paper. A non-planar vortex lattice method herein is used to compute the non-planar aerodynamics of flexible wings with large deformation. The finite element method is introduced for structural nonlinear statics analysis. The surface spline method is used for structure/aerodynamics coupling. The static aeroelastic characteristics of the wind tunnel model of a flexible wing are studied by the nonlinear method presented, and the nonlinear method is also evaluated by comparing the results with those obtained from two other methods and the wind tunnel test. The results indicate that the traditional linear method of static aeroelastic analysis is not applicable for cases with large deformation because it produces results that are not realistic. However, the nonlinear methodology, which involves combining the structure finite element method with the non-planar vortex lattice method, could be used to solve the aeroelastic deformation with considerable accuracy, which is in fair agreement with the test results. Moreover, the nonlinear finite element method could consider complex structures. The non-planar vortex lattice method has advantages in both the computational accuracy and efficiency. Consequently, the nonlinear method presented is suitable for the rapid and efficient analysis requirements of engineering practice. It could be used in the preliminary stage and also in the detailed stage of aircraft design.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11172025,91116005)the Research Fund for the Doctoral Program of Higher Education of China (Grant No.20091102110015)
文摘A method for static aeroelastic trim analysis and flight loads computation of a flexible aircraft with large deformations has been presented in this paper,which considers the geometric nonlinearity of the structure and the nonplanar effects of aerodynamics.A nonplanar vortex lattice method is used to compute the nonplanar aerodynamics.The nonlinear finite element method is introduced to consider the structural geometric nonlinearity.Moreover,the surface spline method is used for structure/aerodynamics coupling.Finally,by combining the equilibrium equations of rigid motions of the deformed aircraft,the nonlinear trim problem of the flexible aircraft is solved by iterative method.For instance,the longitudinal trim analysis of a flexible aircraft with large-aspect-ratio wings is carried out by both the nonlinear method presented and the linear method of MSC Flightloads.Results obtained by these two methods are compared,and it is indicated that the results agree with each other when the deformation is small.However,because the linear method of static aeroelastic analysis does not consider the nonplanar aerodynamic effects or structural geometric nonlinearity,it is not applicable as the deformations increase.Whereas the nonlinear method presented could solve the trim problem accurately,even the deformations are large,which makes the nonlinear method suitable for rapid and efficient analysis in engineering practice.It could be used not only in the preliminary stage but also in the detail stage of aircraft design.
文摘Two new concepts, the generalized support function and restricted chord function, both referring to a convex set, were introduced in [1]. General formulae to yield the kinematic measure of a segment of fixed length in a convex set were established based on these concepts. In this article , using the partial intersection method, we consider the generalized Buffon problem for three kinds of lattices. We determine the probability of intersection of a body test needle of length l, l a.
基金extend their appreciation to Researcher Supporting Project number(RSPD2024R692),King Saud University,Riyadh,Kingdomof SaudiArabia.
文摘The microstructure of granular media, including grain's shape- and size-polydispersities, orientation, and area fraction can potentially affect its permeability. However, few studies consider the coupling effects of these features. This work employs geometrical probability and stereology to establish quantitative relationships between the above microstructural features and the geometric tortuosity of the two-dimensional granular media containing superellipse, superoval, and polygon grains. Then the lattice Boltzmann method (LBM) is used to determine the permeabilities of these granular media. By combining the tortuosity model and the LBM-derived permeabilities, modified K–C equations are formulated to predict the permeability and the shape factor, considering the grain's shape- and size-polydispersities, orientation, and area fraction. The reliability of these methods can be verified by comparing them with both our simulations and available experimental, theoretical, and numerical data reported in the literature. The findings implicate that the tortuosity and permeability of the granular media are strongly correlated with the grain's shape, orientation, and area fraction but unaffected by the size polydispersity and spatial arrangement of grains. Only circularity is not enough to derive a unified formula for considering the impact of grain shape on tortuosity and permeability, other shape parameters need to be explored in the future.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11901064 and 12071325)。
文摘In 2010,Gábor Czédli and E.Tamás Schmidt mentioned that the best cover-preserving embedding of a given semimodular lattice is not known yet[A cover-preserving embedding of semimodular lattices into geometric lattices.Advances in Mathematics,225,2455-2463(2010)].That is to say:What are the geometric lattices G such that a given finite semimodular lattice L has a cover-preserving embedding into G with the smallest|G|?In this paper,we propose an algorithm to calculate all the best extending cover-preserving geometric lattices G of a given semimodular lattice L and prove that the length and the number of atoms of every best extending cover-preserving geometric lattice G equal the length of L and the number of non-zero join-irreducible elements of L,respectively.Therefore,we solve the problem on the best cover-preserving embedding of a given semimodular lattice raised by Gábor Czédli and E.Tamás Schmidt.
文摘To explain the anomaly (τ<sub>b</sub> ≠ τ<sub>f</sub>) of the neutron lifetime τ in some experiments, in “bottle” τ<sub>b</sub> and in “beam” τ<sub>f</sub>, we resort to an anomalous form of the neutron n<sub>a</sub>. This form belongs to one of two different states of the structure of the quark configurations making up the neutron (nucleon): first, an ordinary form Ψ<sub>o</sub>, while the second is an “anomalous” form Ψ<sub>a</sub>, difficult to detect and decay. If the ordinary configuration is present in everyone nuclear processes, to strong and weak interactions, and in diffusion processes, the anomalous form can emerge, in casual way and probabilistic, in some processes of fusion with production of neutrons and can be highlighted in some experiments as those in “bottle” and in “beam”, see the anomaly of the neutron lifetime. We show that the anomalous form Ψ<sub>a</sub> can be highlighted in the coupling between a dipoles’ lattice of virtual bosons W and the neutron (nucleon) because the neutron into anomalous configuration does not decays. Finally, we interpret the anomalous neutron as a “dark” neutron, presenting, so, the dark matter as an anomalous form of hadron matter.
文摘We assume that M is a phase space and H an Hilbert space yielded by a quantization scheme. In this paper we consider the set of all “experimental propositions” of M and we look for a model of quantum logic in relation to the quantization of the base manifold M. In particular we give a new interpretation about previous results of the author in order to build an “asymptotics quantum probability space” for the Hilbert lattice L(H).
基金Foundation item:The NSF(99SL02)of Shaanxi Province and the SF(20609)of China for Postdoctoral Fellow.
文摘In this paper, some properties of the image of the geometric lattice of a graphic matroid under a strong map are discussed, and a negative answer to the related open question of Welsh’s book is given.
文摘Let F be a field and V= V<sub>n</sub>（F）={（a<sub>1</sub>,…, a<sub>n</sub>）|a<sub>i</sub>∈F} be the row vector space of finite dimension n over F. Let be a finite set ofsubspaces of Vsuch that U=（0）. And let L= L（（?）） be the set of intersections of dements of. Partial order L by reverse inclusion has V as its minimal element and as its set of atoms. We denote the partial order-
文摘Let be a n-dimensional row vector space over a finite field For , let be a d-?dimensional subspace of . denotes the set of all the spaces which are the subspaces of and not the subspaces of except . We define the partial order on by ordinary inclusion (resp. reverse inclusion), and then is a poset, denoted by (resp. ). In this paper we show that both and are finite atomic lattices. Further, we discuss the geometricity of and , and obtain their characteristic polynomials.
基金National Natural Science Foundation of China(Nos.11172025,91116005)Research Fund for the Doctoral Program of Higher Education of China(No.20091102110015)
文摘A rapid and efficient method for static aeroelastic analysis of a flexible slender wing when considering the structural geometric nonlinearity has been developed in this paper. A non-planar vortex lattice method herein is used to compute the non-planar aerodynamics of flexible wings with large deformation. The finite element method is introduced for structural nonlinear statics analysis. The surface spline method is used for structure/aerodynamics coupling. The static aeroelastic characteristics of the wind tunnel model of a flexible wing are studied by the nonlinear method presented, and the nonlinear method is also evaluated by comparing the results with those obtained from two other methods and the wind tunnel test. The results indicate that the traditional linear method of static aeroelastic analysis is not applicable for cases with large deformation because it produces results that are not realistic. However, the nonlinear methodology, which involves combining the structure finite element method with the non-planar vortex lattice method, could be used to solve the aeroelastic deformation with considerable accuracy, which is in fair agreement with the test results. Moreover, the nonlinear finite element method could consider complex structures. The non-planar vortex lattice method has advantages in both the computational accuracy and efficiency. Consequently, the nonlinear method presented is suitable for the rapid and efficient analysis requirements of engineering practice. It could be used in the preliminary stage and also in the detailed stage of aircraft design.
