We study elastic α-particle scattering offp,α-particle and¹²C targets at 17.9 GeV/c incident momentum in the rigid projectile approximation of the Glauber model. Differential and total cross-sections are computed and compared with the data. Reasonable agreement with the observed differential cross-sections is found for small momentum transfers but short-range dynamical correlations in the target will probably have to be taken into account to get better agreement at larger momentum transfers, particularly in the case of α-¹²C scattering.

The finite-temperature Schrödinger equation, derived recently from the Bethe-Salpeter equation for the bound states of an electron and a proton interacting via the instantaneous Coulomb interaction, is studied in the coordinate space. An expression for the temperature-modified Coulomb potential is obtained and briefly discussed.

The Hartree-Fock procedure is used to study the behaviour of the ground state of a system ofM spinless electrons distributed overN equivalent and equidistant sites (M ⩽N) as a function of the strength of the mutual repulsion between the electrons. Below a critical strength, all initial configurations are seen, after repeated iterations, to converge to a unique solution. Above this critical strength, in addition to the initial configurations which lead to a unique solution, there exist configurations which on repeated iterations give rise to stable two-period solutions. Although the number of independent stable two-period solutions depends on the coupling strength, for no value of the coupling are stable solutions of periodicity higher than two seen.

The occurrence of discontinuities in the energy spectrum of thes-wave Hamiltonian in three dimensionsH(μ, λ) =p²/2 − 1/r + 2µr + 2λ²r² has been reported by us. In this communication we develop a unified understanding, based principally on the topography of the energy surfaces, of the different discontinuities we reported earlier. These discontinuities do not in general occur wherever the corresponding classical system would display catastrophic behaviour.

The existence of finite discontinuities in the energy eigenvalue spectra of certain multiterm potentials when their coupling parameters attain suitably chosen limiting values has been reported in the literature. We show that such discontinuities are also characteristic of such well-known systems as generalized anharmonic oscillators and the doubly anharmonic oscillator in one dimension. The present study strengthens the general conjecture that eigenvalue spectra are likely to display discontinuities in situations where a potential undergoes an abrupt change in shape with smooth variation of its coupling parameters.

We study discrete nonlinear maps in which the control parameter is itself “modulated” by another discrete nonlinear map. We show that for a certain class of such maps, which includes for example the logistic map, the periodicity of the modulated signal is either one, independent of the periodicity of the modulating signal, or its periodicity is an integral multiple of the periodicity of the modulating signal or it is chaotic.

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.

We demonstrate that chaos can be controlled using multiplicative exponential feedback control. Unstable fixed points, unstable limit cycles and unstable chaotic trajectories can all be stabilized using such control which is effective both for maps and flows. The control is of particular significance for systems with several degrees of freedom, as knowledge of only one variable on the desired unstable orbit is sufficient to settle the system onto that orbit. We find in all cases that the transient time is a decreasing function of the stiffness of control. But increasing the stiffness beyond an optimum value can increase the transient time. We have also used such a mechanism to control spatiotemporal chaos is a well-known coupled map lattice model.

We review the subject of control of chaotic systems paying special attention to exponential control. We also discuss the application of synchronization of chaotic systems to security in communications.