Spatial scaling laws of velocity kinetic energy spectra for the compressible turbulence flow and the density-weighted counterparts are formulated in terms of the wavenumber, dissipation rate, and Mach number by using ...Spatial scaling laws of velocity kinetic energy spectra for the compressible turbulence flow and the density-weighted counterparts are formulated in terms of the wavenumber, dissipation rate, and Mach number by using a dimensional analysis. We apply the Barenblatt＇s incomplete similarity theory to both kinetic and density-weighted energy spectra. It shows that, within the initial subrange, both energy spectra approach the -5/3 and -2 power laws of the wavenumber when the Mach number tends to unity and infinity, respectively.展开更多
We study a conflict of two individuals over a valuable resource.We construct a sequential game where the first individual,the Owner,decides whether to defend the resource and the other individual,the Intruder,decides ...We study a conflict of two individuals over a valuable resource.We construct a sequential game where the first individual,the Owner,decides whether to defend the resource and the other individual,the Intruder,decides whether to attack and try to steal the resource.Individuals know the value of the resource to themselves.This provides the individuals an estimate of the value of the resource to the opponent.We build a mathematical model that allows us to quantify and vary the accuracy of this estimate.We study how the outcomes of the game depend on the accuracy.We show that,in our setting,the accuracy does not matter to the Intruder but it does to the Owner.For resources of a large value,the Owner benefits from a smaller accuracy.However,for resources of a small value,the Owner benefits from a bigger accuracy.展开更多
基金Project supported by the National Research Foundation of South Africa(No.93918)
文摘Spatial scaling laws of velocity kinetic energy spectra for the compressible turbulence flow and the density-weighted counterparts are formulated in terms of the wavenumber, dissipation rate, and Mach number by using a dimensional analysis. We apply the Barenblatt＇s incomplete similarity theory to both kinetic and density-weighted energy spectra. It shows that, within the initial subrange, both energy spectra approach the -5/3 and -2 power laws of the wavenumber when the Mach number tends to unity and infinity, respectively.
文摘We study a conflict of two individuals over a valuable resource.We construct a sequential game where the first individual,the Owner,decides whether to defend the resource and the other individual,the Intruder,decides whether to attack and try to steal the resource.Individuals know the value of the resource to themselves.This provides the individuals an estimate of the value of the resource to the opponent.We build a mathematical model that allows us to quantify and vary the accuracy of this estimate.We study how the outcomes of the game depend on the accuracy.We show that,in our setting,the accuracy does not matter to the Intruder but it does to the Owner.For resources of a large value,the Owner benefits from a smaller accuracy.However,for resources of a small value,the Owner benefits from a bigger accuracy.
