Two-dimesional electromagnetic fields guided by plasma layers. II

Radiophysics and Quantum Electronics -     

Dynamics of a system exhibiting the global bifurcation of a limit cycle at infinity

This paper concerns the dynamics of a class of non-linear oscillators of the form:

$\text{x″ + x ? ?x′(1?ax}{}^2\text{?bx′}{}^2\text{) = 0}$

. The non-linear term contains two parameters a and b which may be varied to give the Rayleigh and Van der Pol differential equations as special cases.The existence and approximation of limit cycles in this system are investigated using the Poincare-Bendixson theorem and the Lindstedt perturbation method. Analysis of the system at infinity is used to study the global bifurcation through which the limit cycle is created from four saddle-saddle connections between equilibrium points at infinity. Center manifold theory is used to determine the stability of the equilibrium points at infinity. Numerical integration is used to verify the analytical results.It is shown that an arbitrarily small perturbation to the damping term of the Rayleigh equation results in points close to the stable limit cycle escaping to infinity.     

Separable coordinates for four-dimensional Riemannian spaces

We present a complete list of all separable coordinate systems for the equations and with special emphasis on nonorthogonal coordinates. Applications to general relativity theory are indicated.     

Charged particle multiplicity distributions ine + e − annihilation at 29 GeV: a comparison with hadronic data

The charged particle multiplicity distributions for two-jet events ine ⁺ e ^? annihilation at 29 GeV have been measured using the High Resolution Spectrometer at PEP. A Poisson distribution describes the data for both the complete event and for the single jets. In addition, no correlation is observed between the multiplicities in the two jets of an event. For fixed values of the prong number of the complete event, the multiplicity sharing between the two jets is in good agreement with a binomial distribution. The rapidity gap distribution is exponential with a slope equal to the mean rapidity density. These observations, which are consistent with a picture of independent emission of single particles, are contrasted to the results from soft hadronic collisions and conclusions are drawn about the nature of clusters.     

High temperature phase transition in NH4H2PO4

NH₄H₂PO₄ (ADP) has been investigated by infrared spectroscopy, differential scanning calorimetry, thermogravimetric analysis and d.c. conductivity in the temperature range of 25–180° C. Sharp reversible changes were observed in the region from 400 to 500 cm^?1 of the infrared spectra in the temperature range of 138–174° C. Similar and supportive data were obtained with DSC, TGA and DC conductivity measurements. The results clearly suggest a high temperature phase transition for ADP before its melting point.