The refraction of rays in the Savart polariscope is different from the isotropic medium. We have analysed and discussed the refraction of rays in the Savart polariscope on the basis of the Snell law. The refraction fo...The refraction of rays in the Savart polariscope is different from the isotropic medium. We have analysed and discussed the refraction of rays in the Savart polariscope on the basis of the Snell law. The refraction formulae of the extraordinary rays and ordinary rays were derived. Results obtained may provide theoretical and practical guide lines for studying, developing and engineering of polarization interference imaging spectrometer.展开更多
The reflection in the Savart polariscope is different from the isotropic medium. The double reflection of rays in the Savart polariscope is analyzed and discussed on the basis of the Snell law. The double reflection f...The reflection in the Savart polariscope is different from the isotropic medium. The double reflection of rays in the Savart polariscope is analyzed and discussed on the basis of the Snell law. The double reflection formulae of the extraordinary ray and the ordinary ray are given. These results may provide a theoretical and practical guide for studying, developing and engineering polarization interference imaging spectrometers.展开更多
Certain prerequisite information on the component fluxes is necessary for solution of the Stefan-Maxwell equation in multicomponent diffusion systems and the Graham's law of diffusion and effusion is often resorte...Certain prerequisite information on the component fluxes is necessary for solution of the Stefan-Maxwell equation in multicomponent diffusion systems and the Graham's law of diffusion and effusion is often resorted for this purpose. This article addresses solution of the Stefan-Maxwell equation in binary gas systems and explores the necessary conditions for definite solution of concentration profiles and pertinent component fluxes. It is found that there are multiple solutions for component fluxes in contradiction to what specified by the Graham's law of diffusion.The theorem of minimum entropy production in the non-equilibrium thermodynamics is believed instructive in determining the stable steady state solution out of infinite multiple solutions possible under the specified conditions.It is suggested that only when the boundary condition of component concentration is symmetrical in an isothermal binary system, the counter-diffusion becomes equimolar. The Graham's law of diffusion seems not generally valid for the case of isothermal ordinary diffusion.展开更多
The stand density index,one of the most important metrics for managing site occupancy,is generally calculated from empirical data by means of a coefficient derived from the“self-thinning rule”or stand density model....The stand density index,one of the most important metrics for managing site occupancy,is generally calculated from empirical data by means of a coefficient derived from the“self-thinning rule”or stand density model.I undertook an exploratory analysis of model fitting based on simulated data.I discuss the use of the logarithmic transformation(i.e.,linearisation)of the relationship between the total number of trees per hectare(N)and the quadratic mean diameter of the stand(QMD).I compare the classic method used by Reineke(J Agric Res 46:627–638,1933),i.e.,linear OLS model fitting after logarithmic transformation of data,with the“pure”powerlaw model,which represents the native mathematical structure of this relationship.I evaluated the results according to the correlation between N and QMD.Linear OLS and nonlinear fitting agreed in the estimation of coefficients only for highly correlated(between-1 and-0.85)or poorly correlated([-0.39)datasets.At average correlation values(i.e.,between-0.75 and-0.4),it is probable that for practical applications,the differences were relevant,especially concerning the key coefficient for Reineke’s stand density index calculation.This introduced a non-negligible bias in SDI calculation.The linearised log–log model always estimated a lower slope term than did the exponent of the nonlinear function except at the extremes of the correlation range.While the logarithmic transformation is mathematically correct and always equivalent to a nonlinear model in case of prediction of the dependent variable,the difference detected in my studies between the two methods(i.e.,coefficient estimation)was directly related to the correlation between N and QMD in each simulated/disturbed dataset.In general,given the power law as the“natural”structure of the N versus QMD relationship,the nonlinear model is preferred,with a logarithmic transformation used only in the case of violation of parametric assumptions(e.g.data distributed non-normally).展开更多
This paper extends Hojman＇s conservation law to the third-order differential equation. A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion. The gener...This paper extends Hojman＇s conservation law to the third-order differential equation. A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion. The generators contain variations of the time and generalized coordinates. Two independent non-trivial conserved quantities of the third-order ordinary differential equation are obtained. A simple example is presented to illustrate the applications of the results.展开更多
基金supported by the State Key Program of National Natural Science of China (Grant No 40537031)the National Natural Science Foundation of China (Grant Nos 40375010 and 60278019)+2 种基金the Science and Technology Plan Foundation of Shaanxi Province of China (Contract No 2005K04-G18)the special research project of Shaanxi Provincial Educational Department of China (Grant Nos 07JK261 and 05JK197)the research project of Xi’an Polytechnic University of China (Grant No 2006XG34)
文摘The refraction of rays in the Savart polariscope is different from the isotropic medium. We have analysed and discussed the refraction of rays in the Savart polariscope on the basis of the Snell law. The refraction formulae of the extraordinary rays and ordinary rays were derived. Results obtained may provide theoretical and practical guide lines for studying, developing and engineering of polarization interference imaging spectrometer.
基金Supported by the National Natural Science Foundation of China (Grant Nos 40375010 and 60278019)the Science and Technology Plan Foundation of Shaanxi Province (Grant No 2005K04-G18)the Special Research Project of Shaanxi Provincial Educational Department (Grant No 07JK261)
文摘The reflection in the Savart polariscope is different from the isotropic medium. The double reflection of rays in the Savart polariscope is analyzed and discussed on the basis of the Snell law. The double reflection formulae of the extraordinary ray and the ordinary ray are given. These results may provide a theoretical and practical guide for studying, developing and engineering polarization interference imaging spectrometers.
基金Supported by the National Natural Science Foundation of China(No.29792074)and SINOPEC.
文摘Certain prerequisite information on the component fluxes is necessary for solution of the Stefan-Maxwell equation in multicomponent diffusion systems and the Graham's law of diffusion and effusion is often resorted for this purpose. This article addresses solution of the Stefan-Maxwell equation in binary gas systems and explores the necessary conditions for definite solution of concentration profiles and pertinent component fluxes. It is found that there are multiple solutions for component fluxes in contradiction to what specified by the Graham's law of diffusion.The theorem of minimum entropy production in the non-equilibrium thermodynamics is believed instructive in determining the stable steady state solution out of infinite multiple solutions possible under the specified conditions.It is suggested that only when the boundary condition of component concentration is symmetrical in an isothermal binary system, the counter-diffusion becomes equimolar. The Graham's law of diffusion seems not generally valid for the case of isothermal ordinary diffusion.
基金fully funded by the Italian National Rural Network project,in the framework of the European Network for Rural Development(ENRD)by EU,in the framework of the Horizon 2020 B4EST project ‘‘Adaptive BREEDING for productive,sustainable and resilient FORESTs under climate change’’,UE Grant Agreement 773383(http://b4est.eu/)
文摘The stand density index,one of the most important metrics for managing site occupancy,is generally calculated from empirical data by means of a coefficient derived from the“self-thinning rule”or stand density model.I undertook an exploratory analysis of model fitting based on simulated data.I discuss the use of the logarithmic transformation(i.e.,linearisation)of the relationship between the total number of trees per hectare(N)and the quadratic mean diameter of the stand(QMD).I compare the classic method used by Reineke(J Agric Res 46:627–638,1933),i.e.,linear OLS model fitting after logarithmic transformation of data,with the“pure”powerlaw model,which represents the native mathematical structure of this relationship.I evaluated the results according to the correlation between N and QMD.Linear OLS and nonlinear fitting agreed in the estimation of coefficients only for highly correlated(between-1 and-0.85)or poorly correlated([-0.39)datasets.At average correlation values(i.e.,between-0.75 and-0.4),it is probable that for practical applications,the differences were relevant,especially concerning the key coefficient for Reineke’s stand density index calculation.This introduced a non-negligible bias in SDI calculation.The linearised log–log model always estimated a lower slope term than did the exponent of the nonlinear function except at the extremes of the correlation range.While the logarithmic transformation is mathematically correct and always equivalent to a nonlinear model in case of prediction of the dependent variable,the difference detected in my studies between the two methods(i.e.,coefficient estimation)was directly related to the correlation between N and QMD in each simulated/disturbed dataset.In general,given the power law as the“natural”structure of the N versus QMD relationship,the nonlinear model is preferred,with a logarithmic transformation used only in the case of violation of parametric assumptions(e.g.data distributed non-normally).
基金supported by the National Natural Science Foundation of China (Grant No 10872037)the Natural Science Foundation of Anhui Province of China (Grant No 070416226)
文摘This paper extends Hojman＇s conservation law to the third-order differential equation. A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion. The generators contain variations of the time and generalized coordinates. Two independent non-trivial conserved quantities of the third-order ordinary differential equation are obtained. A simple example is presented to illustrate the applications of the results.
