Vol. 25, No. 6 (1976)
1976-03-20
CONTENT
1976, 25 (6): 465-471.
doi: 10.7498/aps.25.465
Abstract +
An orthogonal-loop-coupling YIG tunable filter is analyzed by using the equivalent circuit. By introducing a suitable expression for the self-inductance of the coupling loop, applicable formulae for designing multi-stage YIG filters are given. Using these formulae, an example for designing the two-stage filter is presented. Also, the influence of the parameters of the coupling loops on the passband response is analyzed for a single-stage YIG resonance filter.
1976, 25 (6): 472-480.
doi: 10.7498/aps.25.472
Abstract +
The problem of the non-linear interaction between two fully collimated plane-wave beams travelling in different directions has given rise to much of the controversy to date as to whether the secondary scattered radiation exists outside the interaction region. Ingard et al. expressed the primary beams with a type of discontinuous function ρ={ej(w-ky),|x|a. Through calculations, they claimed that a scattered radiation is shown to exist outside the region of interaction. Assuming primary fields are plane waves of infinite extent, Westervelt studied the same problem, but a negative conclusion was obtained. By dividing co-ordinate space into the inside and outside of the common volume, Al-Temimi solved Westervelt's equation for both cases and concluded that the two conflicting results could relatively be brought together.Although in this paper only ideal beams interacting at right angles are discussed, the author suggests that this type of discontinuity can be more adequately described with a certain combination of unit-step functions. By applying and solving Westervelt's equation, the author obtains an interesting result, i.e., the secondary scattered radiations outside the common volume originate not from a volume source as claimed by Al-Temimi, but from a δ-function surface-dipole. However, this surface source is. artificial, because discontinuous functions which do not satisfy the homogeneous wave equation have been used to describe the primary waves. It is shown that the solution obtained by the author is the same as that of Al-Temimi, therefore, a relative agreement cannot be reached between the two conflicting results. A comment is also made on the latter's paper concerning the inappropriateness of the continuous conditions assumed at the boundaries. Based on the above discussions, the author predicts that if the primary beams are to be described by discontinuous functions, then the theories of the parametric transmitting and recieving arrays will be similarly affected.
1976, 25 (6): 481-486.
doi: 10.7498/aps.25.481
Abstract +
In this paper, the effect of a random fluctuation surface on the sound field of a harmonic point source in positive sound velocity gradient shallow water is consideved. Approximate expressions for the pole equations and amplitude functions are obtained. It is found that the results of reference [1] are the limiting case of the results of this paper.
1976, 25 (6): 487-493.
doi: 10.7498/aps.25.487
Abstract +
For a three-dimensional eight-vertex model with energy parameters satisfying the condition ε1+ε2=ε3+ε4, all the critical exponents have been calculated:α=α′=0,β=1/4,δ=7,γ=1/2,γ′=3/2,ν=ν′=1,η=3/2. These do not satisfy the scaling law, the reason is that the correlative region of polarization contracts from the crystal planes (1, 1, 1) and (1, 1, 1) to the crystal axis [1, 0, 1] at the critical point.
1976, 25 (6): 494-506.
doi: 10.7498/aps.25.494
Abstract +
An equation of the Bethe-Salpeter type is used to obtain the internal wave function of mesons. It is found that if the potential well between the straton and anti-straton is of the pseudo-scalar type, then the 0- and 1- mesons will satisfy the same approximate radial wave function, and thus lead to SU6 symmetry. We have shown previously that pseudo-scalar potential is the only single type of potential which leads to this symmetry. The potential is V = V0+ V1, where V0 represents a super-strong deep well, the effect of which is to reduce the very large mass M of the free straton to a small effective value. The motion of the straton inside the meson is therefore relativistic. V1 represents a small potential of the order of 1/M of a simple harmonic oscillator. A tensor force is also introduced to account for the splitting of energy levels of the states with the same spin and orbital angular momentum. Our solutions for the ground and angular excited states of 0- and 1- mesons practically explain all the observed meson states. Our theory can apply equally to the baryon states if the phenomenological potential V0 is reduced by a factor of 2.
1976, 25 (6): 507-513.
doi: 10.7498/aps.25.507
Abstract +
Starting from the integral definition of gauge fields, and using a formularesembling the Gauss-Bonnet theorem - a theorem in differential geometryon compact manifolds, we derive a general conjugate relationship between the gauge charge and the dual charge. The relation between electronic charge and the magnetic monopole is an example of this conjugate relationship. For an SO (3) gauge group with a U (1) group as its invariant subgroup, we obtain the 't Hooft monopole solution as a special solution, without introducing any concept of singular strings or any mechanism such as the spontaneous breaking of symmetries.
1976, 25 (6): 514-520.
doi: 10.7498/aps.25.514
Abstract +
The gauge inrariant expressions and relations of various physical quantities in the non-Abelian SU (2) gauge field, such as electric charge, dual charge (magnetic charge), electromagnetic field and massive vector field, are studied, The relation between magnetic charge and the large scale topological property of the isotopic directions of the charge operator is shown.
