Taking both dipole and exchange interaction into aceount we have deduced the secular equation for the dipole-exchange spin waves in an axially magnetized cylin-drical ferromagnet. Numerical results of frequency spectra are also given. When the wave vector of the spin wave is small, dipole energy is the most important term and our results coincide with that of magnetostatic modes. When the wave vector becomes large, exchange energy plays a greatrole, and our results approach those of the theory of macroscopic exchange waves.
Taking both dipole and exchange interaction into aceount we have deduced the secular equation for the dipole-exchange spin waves in an axially magnetized cylin-drical ferromagnet. Numerical results of frequency spectra are also given. When the wave vector of the spin wave is small, dipole energy is the most important term and our results coincide with that of magnetostatic modes. When the wave vector becomes large, exchange energy plays a greatrole, and our results approach those of the theory of macroscopic exchange waves.
The abnormal phenomena in the transmitted light passing through α-LiIO3 single crystals under the application of a DC field parallel to the c-axis have been further investigated by means of the direct projection method, the optical Fourier transfor-mation method and the Schlieren method. The change in the spacial frequency spectrum of a z-cut crystal plate with the increase of the applied field intensity was examined. It was observed that the diffraction efficiency of the transmitted light shows a linear dependence on the applied voltage, but is independent of the polariza-tion of the incident light. It was also found that the light polarization is not changed by the action of the DC field and the effect of absorption is negligible. The relaxa-tion process of the change in diffraction efficiency with time was recorded quantita-tively. A tentative explanation of these phenomena has been given.
The abnormal phenomena in the transmitted light passing through α-LiIO3 single crystals under the application of a DC field parallel to the c-axis have been further investigated by means of the direct projection method, the optical Fourier transfor-mation method and the Schlieren method. The change in the spacial frequency spectrum of a z-cut crystal plate with the increase of the applied field intensity was examined. It was observed that the diffraction efficiency of the transmitted light shows a linear dependence on the applied voltage, but is independent of the polariza-tion of the incident light. It was also found that the light polarization is not changed by the action of the DC field and the effect of absorption is negligible. The relaxa-tion process of the change in diffraction efficiency with time was recorded quantita-tively. A tentative explanation of these phenomena has been given.
The measuring time permitted for a pressure bar transducer is usually limited by the length of the pressure bar itself. To overcome this, we have studied the dyna-mic transmitting behavior of the pressure bar. Our results show that to obtain the correct pressure profile, one must reduce both the radial vibration in the neigh-borhod of the top end of the pressure bar, and the interference of reflected waves from the lower end with the incident wave. This paper presents a design for a pres-sure bar based on the principle of wave velocity dispersion, by which the perfor-mance of the transducer is greatly improved. The chief merit of the present design is that the permitted measuring time is no Longer limited by the length of the pres-sure bar.
The measuring time permitted for a pressure bar transducer is usually limited by the length of the pressure bar itself. To overcome this, we have studied the dyna-mic transmitting behavior of the pressure bar. Our results show that to obtain the correct pressure profile, one must reduce both the radial vibration in the neigh-borhod of the top end of the pressure bar, and the interference of reflected waves from the lower end with the incident wave. This paper presents a design for a pres-sure bar based on the principle of wave velocity dispersion, by which the perfor-mance of the transducer is greatly improved. The chief merit of the present design is that the permitted measuring time is no Longer limited by the length of the pres-sure bar.
This paper advocates a new approach to the theory of finite group representa-tions by applying exclusively the method of commuting operators in quantum me-chanics. The basic problems of group representation theory such as the labeling of irreducible representations, the finding of characters, irreducible bases and matrix ele-ments and the CG coefficients et al are all simplified to the solving of the eigenfunc-tions of a certain complete set of commuting operators. This method has the advan-tage of being concise in theory and easily manageable in practice.
This paper advocates a new approach to the theory of finite group representa-tions by applying exclusively the method of commuting operators in quantum me-chanics. The basic problems of group representation theory such as the labeling of irreducible representations, the finding of characters, irreducible bases and matrix ele-ments and the CG coefficients et al are all simplified to the solving of the eigenfunc-tions of a certain complete set of commuting operators. This method has the advan-tage of being concise in theory and easily manageable in practice.
This paper studies explicitly the Abelian spontaneously broken gauge model for scalar and gauge bosons by using perturbation expansions . It is discovered that in various renormalizable gauges (R gauge) the gauge dependent part contributed by unphysical components of inner lines in the sum of all Feynman diagrams of the same order coexists only with the outer mass shell components of outer lines. On the mass shell only the contribution by physical components is left, just as in the unitary gauge (U gauge). Thus, the identitical nature of the R gauge and U gauge on the mass shell has been shown explicitly, hence may be seen the unitarity of the R gauge. It is also shown why residue divergences appear in the U gauge, and why these residue divergences will necessarily cancal each other out, thus revealing the crypto-renormali-zability of the U gauge.
This paper studies explicitly the Abelian spontaneously broken gauge model for scalar and gauge bosons by using perturbation expansions . It is discovered that in various renormalizable gauges (R gauge) the gauge dependent part contributed by unphysical components of inner lines in the sum of all Feynman diagrams of the same order coexists only with the outer mass shell components of outer lines. On the mass shell only the contribution by physical components is left, just as in the unitary gauge (U gauge). Thus, the identitical nature of the R gauge and U gauge on the mass shell has been shown explicitly, hence may be seen the unitarity of the R gauge. It is also shown why residue divergences appear in the U gauge, and why these residue divergences will necessarily cancal each other out, thus revealing the crypto-renormali-zability of the U gauge.
This paper extends the Goldfarb-Buttle method which is used to treat the single particle transfer reactions induced by heavy ions to multi-particle transfer reactions. The 12C(7Li, t)16O and 20Ne(d, 6Li)16O reactions are calculated by using the coherent wave function for 16O, with due consideration to certain recoil effects. The results are compared with those obtained by experiment.
This paper extends the Goldfarb-Buttle method which is used to treat the single particle transfer reactions induced by heavy ions to multi-particle transfer reactions. The 12C(7Li, t)16O and 20Ne(d, 6Li)16O reactions are calculated by using the coherent wave function for 16O, with due consideration to certain recoil effects. The results are compared with those obtained by experiment.
On the basis of physical considerations and computational experience, it is poin-ted out that the initial value problem of the Maxwell equations as a set of first order hyperbolic differential equations could become an effective numerical method for the solution of antenna radiation fields. An alternating direction implicit difference scheme is proposed in combination with extrapolated treatment of the conditions on the outer boundary. To demonstrate the potentialities of the proposed method, nu-merical results for a cylindrical antenna are discussed.
On the basis of physical considerations and computational experience, it is poin-ted out that the initial value problem of the Maxwell equations as a set of first order hyperbolic differential equations could become an effective numerical method for the solution of antenna radiation fields. An alternating direction implicit difference scheme is proposed in combination with extrapolated treatment of the conditions on the outer boundary. To demonstrate the potentialities of the proposed method, nu-merical results for a cylindrical antenna are discussed.
In this paper, we proposed an improved theory for the microwave-induced step phenomenon. With this theory, we studied in detail the effect of an magnetic field and microwave power on the height of the microwave-induced step. Theoretical pre-dictions and the existed experimental facts are consistent.
In this paper, we proposed an improved theory for the microwave-induced step phenomenon. With this theory, we studied in detail the effect of an magnetic field and microwave power on the height of the microwave-induced step. Theoretical pre-dictions and the existed experimental facts are consistent.