We extend the impulse theory for unsteady aerodynamics, from its classic global form to finite-domain formulation, then to a minimum-domain version for discrete wake. Each extension has been confirmed numerically. The...We extend the impulse theory for unsteady aerodynamics, from its classic global form to finite-domain formulation, then to a minimum-domain version for discrete wake. Each extension has been confirmed numerically. The minimum-domain theory indicates that the numerical finding of Li and Lu（2012） is of general significance： The entire force is completely determined by only the time rate of impulse of those vortical structures still connecting to the body, along with the Lamb-vector integral thereof that captures the contribution of all the rest disconnected vortical structures.展开更多
A recent development in climate research is the recognition that space activity such as solar flares, gamma ray bursts, supernovas etc. can have a significant impact on the Earth. The existing methods of modelling spa...A recent development in climate research is the recognition that space activity such as solar flares, gamma ray bursts, supernovas etc. can have a significant impact on the Earth. The existing methods of modelling space activity do not model these phenomena explicitly. Instead, their effect on ionization rates is formulated and then built into existing climate models. In this paper, based on the authors’ earlier work, several analytical approaches for modelling a solar flare hitting the Earth are presented. These methods can also be used for modelling gamma-ray bursts or cosmic rays striking our planet. In addition, a method of calculating the total amount of radiation received during a solar flare is proposed. The future use of the proposed modelling approaches within comprehensive global climate models allows for explicit modelling of space activity and provides a new pathway for studying the possible effects of this activity on the Earth.展开更多
Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Litt...Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Littlewood-Paley g-function gr （r ∈ [2, ∞）） is bounded from Hardy space H1（u） into L1（u）. Moreover, the authors show that, if f ∈ RBMO（u）, then [gr（f）]r is either infinite everywhere or finite almost everywhere, and in the latter case, [gr（f）]r belongs to RBLO（u） with the norm no more than ｜｜f｜｜ RBMO（u） multiplied by a positive constant which is independent of f. As a corollary, the authors obtain the boundedness of gr from RBMO（u） into RBLO（u）. The vector valued Calderon-Zygmund theory over （X, d, u） is also established with details in this paper.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.10921202,11221062,11521091 and 11472016)
文摘We extend the impulse theory for unsteady aerodynamics, from its classic global form to finite-domain formulation, then to a minimum-domain version for discrete wake. Each extension has been confirmed numerically. The minimum-domain theory indicates that the numerical finding of Li and Lu（2012） is of general significance： The entire force is completely determined by only the time rate of impulse of those vortical structures still connecting to the body, along with the Lamb-vector integral thereof that captures the contribution of all the rest disconnected vortical structures.
文摘A recent development in climate research is the recognition that space activity such as solar flares, gamma ray bursts, supernovas etc. can have a significant impact on the Earth. The existing methods of modelling space activity do not model these phenomena explicitly. Instead, their effect on ionization rates is formulated and then built into existing climate models. In this paper, based on the authors’ earlier work, several analytical approaches for modelling a solar flare hitting the Earth are presented. These methods can also be used for modelling gamma-ray bursts or cosmic rays striking our planet. In addition, a method of calculating the total amount of radiation received during a solar flare is proposed. The future use of the proposed modelling approaches within comprehensive global climate models allows for explicit modelling of space activity and provides a new pathway for studying the possible effects of this activity on the Earth.
基金Supported by National Natural Science Foundation of China(Grant No.11471040)the Fundamental Research Funds for the Central Universities(Grant No.2014KJJCA10)
文摘Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Littlewood-Paley g-function gr （r ∈ [2, ∞）） is bounded from Hardy space H1（u） into L1（u）. Moreover, the authors show that, if f ∈ RBMO（u）, then [gr（f）]r is either infinite everywhere or finite almost everywhere, and in the latter case, [gr（f）]r belongs to RBLO（u） with the norm no more than ｜｜f｜｜ RBMO（u） multiplied by a positive constant which is independent of f. As a corollary, the authors obtain the boundedness of gr from RBMO（u） into RBLO（u）. The vector valued Calderon-Zygmund theory over （X, d, u） is also established with details in this paper.
