Volume 43, Issue 6
December 1994, pages 411-508
pp 411-420 December 1994
The periodic motion of the classical anharmonic oscillator characterized by the potentialV(x)=1/2x2+λ/2k x2k is considered. The period is first determined to all orders inλ in a perturbative series. Making use of this, the solution of the nonlinear equation of motion is then expressed in the form of a Fourier series. The Fourier coefficients are obtained by solving simple algebraic relations. Secular terms are inherently absent in this perturbative scheme. Explicit solution is presented for generalk up to the second order, from which the Duffing and the sextic oscillator results follow as special cases.
pp 421-429 December 1994
We establish numerically the validity of Huberman-Rudnick scaling relation for Lyapunov exponents during the period doubling route to chaos in one dimensional maps. We extend our studies to the context of a combination map, where the scaling index is found to be different.
pp 431-442 December 1994
In this paper we have tried to stabilize the unstable fixed points for a class of 1-D maps by using a multiplicative nonlinear feedback control mechanism. We have also used such control to create new attractors (which did not exist in the original system), to suit our requirement. The control is also found to work in the presence of noise.
pp 443-451 December 1994
We show that the temperature-generalization of a popular model of quark-confinement seems to provide a rather interesting insight into the origin of mass of elementary particles: as the universe cooled, there was an era when particles did not have an identity since their masses were variable; the temperature at which the conversion of these ‘nomadic’ particles into ‘elementary’ particles took place seems to have been governed by the value of a dimension-less coupling constantCc. ForCc=0.001(0.1) this temperature is of the order of 109 K (1011 K), below which the particle masses do not change.
pp 453-465 December 1994
We suggest a new answer to the problem of the solar neutrinos: a neutrino-photon interaction that would cause the neutrinos to disappear before they leave the sun or make them lose energy towards detection thresholds. We calculate the available energy in the system of the centre of mass, and show that the photons may be endowed with a pseudo-cross-section in the system of the sun. Under the assumption of an absorption, made to simplify the neutrino transport calculation, the chlorine experiment yields:σa=1.8(−1.0+0.7)*10−9 barn, which is close togβ/(ℏc)=4·49*10−9 barn. The escape probability is substantially larger for the gallium neutrinos than for the chlorine neutrinos. Thermal radiation in the core of a supernova is suppressed by electrical conductivity, therefore the neutrinos from SN1987A could escape; they interacted with the photon piston in the outer layers of the supernova and the interaction has to be a scattering. The cosmological implications of a neutrino-photon interaction are discussed; Hubble’s constant may have to be modified. The case of an elastic scattering between neutrino and photon is discussed in more detail.
pp 467-476 December 1994
Screening of a moving infinite color sheet source is examined in a quark plasma at finite temperature. The classical chromohydrodynamic equations for quarks are integrated, to obtain profiles for quark current density, which in turn are used to solve the SU(2) Yang-Mills equations numerically. This provides a classical but non-perturbative treatment for the screening of a moving source in quark plasma.
The results show two interesting features. We observe that if the test source is at rest the screening does not depend on the color dynamics and the behavior is very similar to that in Coulomb plasma. When the test source is moving with non-relativistic velocity the non-abelian features manifest themselves by weakening the screening and also by exhibiting an oscillatory profile with distance.
pp 477-485 December 1994
Line strengthsS for the dipole allowed transitions within then=2 complex of the oxygen isoelectronic sequence have been fitted in the formZ2S=A+B/(Z −C), whereZ is the nuclear charge of a particular ion. The constantsA, B andC are determined by using a non-linear least square method. The data forS are taken from the configuration interaction calculations which included internal, semi-internal and all external type correlations for ions in the rangeZ=8 − 25. It is shown that the values ofA obtained from the fit for all the transitions are in excellent accord with the ab-initio values obtained in the hydrogenic limitZ → ∞ provided near degeneracy effects are included in the ground state multiplet 1s22s22p41S.
pp 487-493 December 1994
EinsteinA-values for the electric dipole transitions between the rotational levels up to 540 cm−1 andJ=11 in the ground vibrational state of the protonated N2O (i.e., HN2O+) are calculated. The coefficients are used to compute the mean radiative lifetimes of the levels. TheseA-values can be used for analysing the spectra from astronomical objects, if observed.
pp 495-502 December 1994
Vibrationally elastic total cross-sections ofe−—H2O scattering are calculated at intermediate energiesEi=10–300 eV. The interaction potentials are treated in spherical models. The dipole rotational excitation, which is significant but not dominant above 10 eV, is treated incoherently. Effects of electronic excitation-ionization, significant above 30 eV or so, are considered through a complex optical potential. A dynamically distorted charge-density is employed to calculate the imaginary part of the complex potential. Comparisons are made with recent theoretical and experimental data. The mutual agreement is better in total cross-sections than in differential cross-sections.
pp 503-508 December 1994 Addendum
A study on string theory has been done in five dimensional flat space-time. Barotropic equation of state andp-string model are discussed. Also a polynomial relation between the two scale factors is assumed. In some special cases the solution reduces to generalized Kasner metric. Further diminision of extra dimension with the evolution of universe is exhibited. A detailed study of phase-space analysis is done for geometric string model.
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