Within the context of Newton’s theory of gravitation, restricted to point-like test particles and central bodies, stable circular orbits in ordinary space are related to stable circular paths on a massless, unmovable...Within the context of Newton’s theory of gravitation, restricted to point-like test particles and central bodies, stable circular orbits in ordinary space are related to stable circular paths on a massless, unmovable, undeformable vortex-like surface, under the action of a tidal gravitational field along the symmetry axis. An interpretation is made in the light of a holographic principle, in the sense that motions in ordinary space are connected with motions on a selected surface and vice versa. Then ordinary space is conceived as a 3-hypersurface bounding a n-hypervolume where gravitation takes origin, within a n-hyperspace. The extension of the holographic principle to extra dimensions implies the existence of a minimum distance where test particles may still be considered as distinct from the central body. Below that threshold, it is inferred test particles lose theirs individuality and “glue” to the central body via unification of the four known interactions and, in addition, 1) particles can no longer be conceived as point-like but e.g., strings or membranes, and 2) quantum effects are dominant and matter turns back to a pre-big bang state. A more detailed formulation including noncircular motions within the context of general relativity, together with further knowledge on neutron stars, quark stars and black holes, would provide further insight on the formulation of quantum gravity.展开更多
In this paper,we studied the metric mean dimension in Feldman–Katok(FK for short)metric.We introduced the notions of FK-Bowen metric mean dimension and FK-Packing metric mean dimension on subsets.And we established t...In this paper,we studied the metric mean dimension in Feldman–Katok(FK for short)metric.We introduced the notions of FK-Bowen metric mean dimension and FK-Packing metric mean dimension on subsets.And we established two variational principles.展开更多
The paper shows that the variational principle serves as an element of the mathematical structure of a quantum theory. The experimentally confirmed properties of the corpuscular-wave duality of a quantum particle are ...The paper shows that the variational principle serves as an element of the mathematical structure of a quantum theory. The experimentally confirmed properties of the corpuscular-wave duality of a quantum particle are elements of the analysis. A Lagrangian density that yields the equations of motion of a given quantum theory of a massive particle is analyzed. It is proved that if this Lagrangian density is a Lorentz scalar whose dimension is ?then the associated action consistently defines the required phase of the quantum particle. The dimension of this Lagrangian density proves that also the quantum function ?has dimension. This result provides new criteria for the acceptability of quantum theories. An examination of the first order Dirac equation demonstrates that it satisfies the new criteria whereas the second order Klein-Gordon equation fails to do that.展开更多
电网换相换流器型高压直流输电(line commutated converter high voltage direct current,LCC-HVDC)的强非线性导致其内部频率耦合复杂多样,传统建模方法难以兼顾准确性与实用性。为此,提出了一种基于相移原理的降维谐波状态空间(harmon...电网换相换流器型高压直流输电(line commutated converter high voltage direct current,LCC-HVDC)的强非线性导致其内部频率耦合复杂多样,传统建模方法难以兼顾准确性与实用性。为此,提出了一种基于相移原理的降维谐波状态空间(harmonic state space,HSS)建模方法,将谐波域相移原理与HSS理论相结合,建立了LCC-HVDC系统的降维HSS模型。通过PSCAD/EMTDC平台搭建LCC-HVDC系统的时域仿真算例,验证了所建模型的正确性。在此基础上分析了LCC-HVDC系统的小扰动稳定性,并采用参与因子对失稳模态的主导因素进行了辨识。基于所建立的模型进一步研究了HSS截断阶数对模型精度及稳定性分析的影响,并给出了LCC-HVDC系统HSS模型截断阶数选取的建议。结果表明,所提模型具有较高的完整性与准确性,且相较于传统HSS模型的维度降低了一半,大大缩短了计算时间,有效降低了理论分析的复杂度。展开更多
文摘Within the context of Newton’s theory of gravitation, restricted to point-like test particles and central bodies, stable circular orbits in ordinary space are related to stable circular paths on a massless, unmovable, undeformable vortex-like surface, under the action of a tidal gravitational field along the symmetry axis. An interpretation is made in the light of a holographic principle, in the sense that motions in ordinary space are connected with motions on a selected surface and vice versa. Then ordinary space is conceived as a 3-hypersurface bounding a n-hypervolume where gravitation takes origin, within a n-hyperspace. The extension of the holographic principle to extra dimensions implies the existence of a minimum distance where test particles may still be considered as distinct from the central body. Below that threshold, it is inferred test particles lose theirs individuality and “glue” to the central body via unification of the four known interactions and, in addition, 1) particles can no longer be conceived as point-like but e.g., strings or membranes, and 2) quantum effects are dominant and matter turns back to a pre-big bang state. A more detailed formulation including noncircular motions within the context of general relativity, together with further knowledge on neutron stars, quark stars and black holes, would provide further insight on the formulation of quantum gravity.
基金Supported by NNSF of China(Grant No.12031019,11871188)。
文摘In this paper,we studied the metric mean dimension in Feldman–Katok(FK for short)metric.We introduced the notions of FK-Bowen metric mean dimension and FK-Packing metric mean dimension on subsets.And we established two variational principles.
文摘The paper shows that the variational principle serves as an element of the mathematical structure of a quantum theory. The experimentally confirmed properties of the corpuscular-wave duality of a quantum particle are elements of the analysis. A Lagrangian density that yields the equations of motion of a given quantum theory of a massive particle is analyzed. It is proved that if this Lagrangian density is a Lorentz scalar whose dimension is ?then the associated action consistently defines the required phase of the quantum particle. The dimension of this Lagrangian density proves that also the quantum function ?has dimension. This result provides new criteria for the acceptability of quantum theories. An examination of the first order Dirac equation demonstrates that it satisfies the new criteria whereas the second order Klein-Gordon equation fails to do that.
文摘电网换相换流器型高压直流输电(line commutated converter high voltage direct current,LCC-HVDC)的强非线性导致其内部频率耦合复杂多样,传统建模方法难以兼顾准确性与实用性。为此,提出了一种基于相移原理的降维谐波状态空间(harmonic state space,HSS)建模方法,将谐波域相移原理与HSS理论相结合,建立了LCC-HVDC系统的降维HSS模型。通过PSCAD/EMTDC平台搭建LCC-HVDC系统的时域仿真算例,验证了所建模型的正确性。在此基础上分析了LCC-HVDC系统的小扰动稳定性,并采用参与因子对失稳模态的主导因素进行了辨识。基于所建立的模型进一步研究了HSS截断阶数对模型精度及稳定性分析的影响,并给出了LCC-HVDC系统HSS模型截断阶数选取的建议。结果表明,所提模型具有较高的完整性与准确性,且相较于传统HSS模型的维度降低了一半,大大缩短了计算时间,有效降低了理论分析的复杂度。
