Based on many overseas experimental researches conducted concerning square columns confined by FRP,the section shape, confining strength, stress concentration of corners and critical value of strong confinement are analyzed。 According as the stress and strain of confined concrete are considered to be relevant to its loading paths or not,the simplified model of average axial stress-strain, which consists of a parabola and a dash line,is presented。

The structure of the solar convection zone was calculated by E.Vitense with the mixing length theory of turbulence.A fundamental formula in her calculations is the formula for the energy flux of turbulent convection [eq.(2.1)],or W.Schmidt's formula [eq.(2.1)].This formula should be modified by the following two corrections: (1)According to the argument of S.A.Zhevakin,the specific heat at constant pressure c_p in this formula should be replaced by (1/2)C=(1/2)(C_p—A_p),where A_p is the work required for the...

The structure of the solar convection zone was calculated by E.Vitense with the mixing length theory of turbulence.A fundamental formula in her calculations is the formula for the energy flux of turbulent convection [eq.(2.1)],or W.Schmidt's formula [eq.(2.1)].This formula should be modified by the following two corrections: (1)According to the argument of S.A.Zhevakin,the specific heat at constant pressure c_p in this formula should be replaced by (1/2)C=(1/2)(C_p—A_p),where A_p is the work required for the compression of one gram of medium when cooled for one degree at constant pressure.In this paper are derived the formulas of the factor C,for the hydrogen ionization zone [eq.(2.20)] and for the single ionization zone of helium [eq.(2.29)]in the envelope of a star.Eq.(2.32)is the formula for C in the critical double ionization zone of helium. (2)According to the investigation of E.J.Opik,in order to take account of the lateral exchange of heat between the turbulent elements,W.Schmidt's formula (2.1) should be multiplied by the factor f/B=0.188. The finally corrected formula is eq.(2.33).The ratio of the convective energy flux computed by eq.(2.33)to that computed by the original eq.(2.1)is 0.094C/c_p≈0.094/γ, since C is approximately equal to the specific heat at constant volume c_v and γ=c_p/c_v. This ratio is 0.0564 for ideal monatomic gas since γ=5/3 and is 0.0705 for fully ionized gas since γ=4/3.Obviously the convective energy flux computed by the original eq.(2.1) is overestimated by a factor 14—18. On the basis of the corrected formula (2.33),or(2.34),we derived anew in §4 some formulas for the calculation Of the solar convection zone as used by E.Vitense. It is obvious that E.Vitense's method and all the formulas in §§2,3 and 4 may be applied not only to the sun but also to other stars.The application to the sun is made in §5.The results are as follows: Fig.1 shows the variations of the gas pressure P_g as function of the geometrical depth t in the solar convection zone.The solid curve(——)corresponds to the model in which the mixing length l of the turbulent element is equal to H,the equivalent height of the atmosphere.The dashed curve(……)is for the model with l=2H.The thick- ness of the solar convection zone with l=H is found to be 3700km and the correspon- ding value of 65000kin found by E.Vitense with the original eq.(2.1)is 17.6 times overestimated.The thickness of the solar convection zone with l=2H is 8790km and the corresponding value of 160,000km found by E.Vitense is overestimated by a fac- tor 18.2. Fig.2 shows the temperature T as function of the gas pressure P_g.The solid curve stands for l=H and the dashed curve for l=2H as in other figures. In Fig.3 is shown T4 as function of the mean optical depth .The dashed line with dots (—·—·—) is for the model in radiative equilibrium. Fig.4 is the entropy diagram for the layers in the solar atmosphere.The left-hand solid curve shows the outermost layer in radiative equilibrium, then begins the convection zone in two models with l=H (——) and l=2H (……),and the right-hand falling parts of the curves correspond to the inner radiative layer. Fig.5 shows the ratio of πF_c to πF as function of P_g,where πF_c is the convective energy flux and πF is the total energy flux,i.e.,πF_c plus the radiative energy flux πF_rad. Therefore,it may be concluded that the thickness of the solar convection zone is some thousand kilometers in order of magnitude.

本文对经日瓦金改正过的对流能通量公式做了进一步的修改,并根据改正后的公式,重推了费坦瑟计算太阳对流层时所用的一些公式.然后计算了太阳对流层.得到的结果是:对于混合长 l 等于大气等值高度 H 的模型,对流层厚度是3700公里;对于 l =2H 的模型,对流层厚度是8790公里.

An important astrophysical consequent of the experiments regarding a nonzero rest mass of neutrinos is the possible existence of self-gravitating systems of neutrinos. The masses of stable equilibrium configurations of such systems are of the order of the mass of clusters of galaxies. On the other hand, in the standard model of big bang cosmology the mass density in the universe is dominated by neutrinos if it has a nonzero mass, say, mv - 14-46 ev. Hence it might be expected that the clustering of matter in...

An important astrophysical consequent of the experiments regarding a nonzero rest mass of neutrinos is the possible existence of self-gravitating systems of neutrinos. The masses of stable equilibrium configurations of such systems are of the order of the mass of clusters of galaxies. On the other hand, in the standard model of big bang cosmology the mass density in the universe is dominated by neutrinos if it has a nonzero mass, say, mv - 14-46 ev. Hence it might be expected that the clustering of matter in the early universe should be affected substantially by such neutrinos.The clustering of pure neutrinos content in expanding universe has been investigated in several works, but in which the clustering of cosmological matter has not been involved yet, Since the results of direct measures on galaxies or on clusters of galaxies, for example, the mass, the size and the velocity dispersion are always the properties of matter components themselves, it is necessary to analyse the interaction between the clustering processes of the neutrinos and the matter,1, In the case of mv=0 the clustering theory of the Jeans instability stage in the early universe can be summarized in the Figs 1 and 2.Fig 1 show the Jeans wave length λm of ionized hydrogen plus blackbody radiation as a function of cosmological radiation temperature Tr. The corresponding time of the drop in the Jeans, length is the hydrogen recombination at Tr - 4000 K. Before the recombination both ionized hydrogen and radiation are in thermal equilibrium by collisions with each, other, after the recombination the matter decoupled from radiation. Dashed line Mm in Fig 2 shows the Jeans mass as a function of radiation temperature. A drop in the time of recombination occures as well. The dashed line Mhor in Fig. 2 gives the mass contained within the horizon of the cosmological model.The mass range of the Jeans instability is given by Mm < M < Mhor. Then it can be obtained from the Fig. 2 that no preferential clustering size exists in this model, i.e. all systems with mass from about 106 to 1017 M⊙ are unstable against the Jeans mechanism in the early universe and all unstable developments start from the time of recombination. That is often considered as a shortage of the theory of early clustering in the big bang model. In this work we have shown that if neutrinos have a nonzero rest mass the conclusions mentioned above should become to advantage the big bang theory.2, As the age of the universe was longer than td or the temperature dropped below Td-1.3×1011 K, the neutrinos and antineutrinos decoupled from the other particles so that we might adopt the two-components perfect-fluid to represent the contents of the universe, one of the components is the neutrinos and the other is the matter and the radiation.For the component of matter and radiation, the thermodynamieal properties are still described by the results given in section 1. The component of neutrinos is a col-lisionless self-gravitating gas, for which the distribution function N(t, xi pi) satisfies the Vlasov equation. In the Eobertson-Walker metric, using the distribution in the time td as the initial condition, the solution of the Vlasov equation can be found as follows:where B(t) is the cosmic scale factor in the R-W metric and Rd =R(td).All thermodynamieal properties of the neutrinos systems can be obtained from the distribution (1). For instance, in the nonrelativistic case the effective temperature Teff of neutrinos arewhere mv is in the unit of ev. In the same way we can derived the Jeans wave length of the neutrino system (see Fig. 1).3, The two-components in the early universe interact with each other through gravitational force. When we want to examine the Jeans instability, the two components system should be treated as a whole. Strictly speaking, we must deal with this problem in the relastivistic and expansive cosmological model. We can, however, safely employ classical and non-expansive model if our interests cover only the Jeans length and mass, but not the growing rate of small fluctuations. N

Neutral magnetic field was found wide important applications in space physics and satrophysics[1-4].In a rectangular coordinate system x y and z,the neutral magnetic field is,given by Eq.(2-1),where h is a small northward magnetic field[5],a and e are the parameters of the field.When ε=0 the field is a neutral sheet.An analytical trajectory of the charged particle moving in this field has been calculated The results are:(1)By means of a perturbation method[5],we found that the motion of the charged particle...

Neutral magnetic field was found wide important applications in space physics and satrophysics[1-4].In a rectangular coordinate system x y and z,the neutral magnetic field is,given by Eq.(2-1),where h is a small northward magnetic field[5],a and e are the parameters of the field.When ε=0 the field is a neutral sheet.An analytical trajectory of the charged particle moving in this field has been calculated The results are:(1)By means of a perturbation method[5],we found that the motion of the charged particle in a neutral sheet field can be defined by the first approximation of motions either in a neutral magnetic field or in a neutral sheet field with a small northward component.The first,second and third approximation of the motion in a neutral magnetic field satify respectively the Eqs.(2-7);(2-8)and(2-9),and in neutral sheet with northward component they satify Eqs.(2-12),(2-13)and(2-14).(2) In the neutral sheet field,the whole region can be devided into a perturba-tion region and non-perturbation region(|x|≤L).Innon-perturbation region,the Alfven's perturbation method can not be used,the analytical solution of the motion equation(2-7)is given by Eqs.(3-7)and(3-16),where z' and the drift velocity Vz are given by Eqs.(3-17)and(3-15).In the perturbation region,the anlytical solution of Eq.(2-7)is given by Eqs.(4-8)and(4-22),where z' and Vz are given by(4-23)and(4-18).The thrid approximation of the analytical trajectory and the trajectory evaluation by computer agree quite well,except for a slight deviation around the boundary of the perturbation region and the non-perturbation region.(3)The trajectory of the particle moving in a neutral sheet field can be devided into two motions,one is along a closed oscillation trajectory in the plane perpendicular with the magnetic field while its center drifts in a direction parallel to the neutral line,and the other along the magnetic line with an uniform velocity.In the non-perturbation region,the closed oscillation trajectory of particles with diference initial conditions are shown in Fig.2 by lines(1),(2),(3),(4)and(5)They are derived from Eqs.(3-7)and(3-17),and take a "8" shape motion.Lines(5),(6),(7)and(8)are derived from Eq.(4-8)and(4-23)in the perturbation region,and take a circular motion.There is a slight deviation between(5)and(5)The drift velocity in non-perturbation region determined by Eq.(3-15)has an opposite direction and a much higher value than that in the perturbation region.The projection of the trajectories on x-y plane corresponds to the particles with different initial conditions are shown in Pigs.1 and 3 by full lines,and the dashed lines denote the founda-mental and higer harmonic of the corresponding trajectories.A complete analytical form has been obtained from the above results.