A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density(SD)of random phase fluctuations,which is the inversion of the classic transformation formu...A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density(SD)of random phase fluctuations,which is the inversion of the classic transformation formula from SD to Allan variance.Due to the fact that Allan variance does not always determine a unique SD function,power-law model of the SD of oscillator phase fluctuations is introduced to the translating algorithm and a constrained maximum likelihood solution is presented.Considering that the inversion is an ill-posed problem,a regularization method is brought forward in the process.Simulation results show that the converted SD of phase fluctuations from Allan variance parameters agrees well with the real SD function.Furthermore,the effects of the selected regularization factors and the input Allan variances are analyzed in detail.展开更多
An alternate non-Fourier heat conduction equation is derived from consideration of translation motion of spinless electron under a driving force due to an applied temperature gradient. This equation is a eapite ad cal...An alternate non-Fourier heat conduction equation is derived from consideration of translation motion of spinless electron under a driving force due to an applied temperature gradient. This equation is a eapite ad calcem,temperature. Elimination of the rate of change of velocity with respect to time leads to a non-Fourier heat conduction equation with a accumulation of temperature or ballistic term in it. The new constitutive heat conduction equation is combined with the energy balance equation in one dimension. The governing equation for transient temperature a partial differential equation （Eq. （23）） is solved for by the method of Laplace transforms. The problem considered is the semi-infinite medium with constant thermo physical properties with constant wall temperature boundary condition. A closed form analyticalexpression for the transient temperature was obtained （Eq. （36）） after truncation of higher order terms in the infinite binomial series and use of convolution and lag properties. This solution is compared with that obtained using the parabolic Fourier model and the damped wave model as presented in an earlier study. The predictions of Eq. （36） are closer to the Fourier model. The convex nature of the temperature curve is present.展开更多
The leaf area index(LAI) is a critical biophysical variable that describes canopy geometric structures and growth conditions.It is also an important input parameter for climate,energy and carbon cycle models.The scali...The leaf area index(LAI) is a critical biophysical variable that describes canopy geometric structures and growth conditions.It is also an important input parameter for climate,energy and carbon cycle models.The scaling effect of the LAI has always been of concern.Considering the effects of the clumping indices on the BRDF models of discrete canopies,an effective LAI is defined.The effective LAI has the same function of describing the leaf density as does the traditional LAI.Therefore,our study was based on the effective LAI.The spatial scaling effect of discrete canopies significantly differed from that of continuous canopies.Based on the directional second-derivative method of effective LAI retrieval,the mechanism responsible for the spatial scaling effect of the discrete-canopy LAI is discussed and a scaling transformation formula for the effective LAI is suggested in this paper.Theoretical analysis shows that the mean values of effective LAIs retrieved from high-resolution pixels were always equal to or larger than the effective LAIs retrieved from corresponding coarse-resolution pixels.Both the conclusions and the scaling transformation formula were validated with airborne hyperspectral remote sensing imagery obtained in Huailai County,Zhangjiakou,Hebei Province,China.The scaling transformation formula agreed well with the effective LAI retrieved from hyperspectral remote sensing imagery.展开更多
文摘A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density(SD)of random phase fluctuations,which is the inversion of the classic transformation formula from SD to Allan variance.Due to the fact that Allan variance does not always determine a unique SD function,power-law model of the SD of oscillator phase fluctuations is introduced to the translating algorithm and a constrained maximum likelihood solution is presented.Considering that the inversion is an ill-posed problem,a regularization method is brought forward in the process.Simulation results show that the converted SD of phase fluctuations from Allan variance parameters agrees well with the real SD function.Furthermore,the effects of the selected regularization factors and the input Allan variances are analyzed in detail.
文摘An alternate non-Fourier heat conduction equation is derived from consideration of translation motion of spinless electron under a driving force due to an applied temperature gradient. This equation is a eapite ad calcem,temperature. Elimination of the rate of change of velocity with respect to time leads to a non-Fourier heat conduction equation with a accumulation of temperature or ballistic term in it. The new constitutive heat conduction equation is combined with the energy balance equation in one dimension. The governing equation for transient temperature a partial differential equation （Eq. （23）） is solved for by the method of Laplace transforms. The problem considered is the semi-infinite medium with constant thermo physical properties with constant wall temperature boundary condition. A closed form analyticalexpression for the transient temperature was obtained （Eq. （36）） after truncation of higher order terms in the infinite binomial series and use of convolution and lag properties. This solution is compared with that obtained using the parabolic Fourier model and the damped wave model as presented in an earlier study. The predictions of Eq. （36） are closer to the Fourier model. The convex nature of the temperature curve is present.
基金supported by the National Natural Science Foundation of China(Grant Nos.91025006,40871186,40730525)National Basic Research Program of China(Grant No.2007CB714402)National High Technology Research and Development Program of China(Grant Nos.2009AA12Z143,2009AA122103)
文摘The leaf area index(LAI) is a critical biophysical variable that describes canopy geometric structures and growth conditions.It is also an important input parameter for climate,energy and carbon cycle models.The scaling effect of the LAI has always been of concern.Considering the effects of the clumping indices on the BRDF models of discrete canopies,an effective LAI is defined.The effective LAI has the same function of describing the leaf density as does the traditional LAI.Therefore,our study was based on the effective LAI.The spatial scaling effect of discrete canopies significantly differed from that of continuous canopies.Based on the directional second-derivative method of effective LAI retrieval,the mechanism responsible for the spatial scaling effect of the discrete-canopy LAI is discussed and a scaling transformation formula for the effective LAI is suggested in this paper.Theoretical analysis shows that the mean values of effective LAIs retrieved from high-resolution pixels were always equal to or larger than the effective LAIs retrieved from corresponding coarse-resolution pixels.Both the conclusions and the scaling transformation formula were validated with airborne hyperspectral remote sensing imagery obtained in Huailai County,Zhangjiakou,Hebei Province,China.The scaling transformation formula agreed well with the effective LAI retrieved from hyperspectral remote sensing imagery.
