Classification of all electrovac specetimes permitting the separation of variables in the Hamilton-Jacobi equation for a charged test particle is carried out. This separation requires the existence of a complete set consisting of Killing’s vectors and tensors of a special kind. Every complete set defines its own type of metric and electromagnetic potential in the separable coordinate system. There exist seven types of separation of variables for electromagnetic spaces. For every type an additional classification is carried out by transformation of coordinates without any disturbance of the separation conditions, the gradient transformation of electromagnetic potential and the conformal-constant transformation of metric.

The key step in solving the problem is the extraction of an autonomous subsystem which determines the metric from only the Einstein-Maxwell equations for every type of separation of variables.

Representatives of all classes of metrics and electromagnetic potential are given for every type of separation of variables with the exception of the spaces found in the well-known work by Carter.

The problem is solved in terms of metric formalism. The classes of electrovac spacetimes obtained are found to be related to Petrov’s classification.

The construction of the second constant of motion of second order for two-dimensional classical systems is carried out in terms ofz=q₁ +iq₂ andq=q₁ −iq₂. As a result a class of Toda-type potentials admitting second order invariants is explored.

New analytic solutions for rotational perturbations of the Robertson-Walker metric are found in order to incorporate the possibility of a rotating viscous universe. The field equations impose restrictions on the matter rotationω(r, t), and some of the solutions for Ω(r, t) which is related to the local dragging of inertial frames are studied. In all the cases the rotational velocity is found to decay with increase of time. Geodesics of the metric are studied to reveal the intrinsic nature of rotation and to elucidate the role of Ω.

The observed oscillatory linewidths of theV′=3 level ofB³Π₀₊ state of I³⁵Cl and I³⁷Cl are explained as due to heterogeneous predissociation caused by the crossing of an unstableZ¹Π state. The crossing point and the slopes of the curves have been fixed to predict the observed linewidths.

Some interesting aspects of the temperature dependence of the Planck’s functionφ and heat capacities of metals exhibiting the h.c.p. ⇄ b.c.c. transformation have been brought to light by the use of reduced temperature (T*) and Planck’s function (-φ T*). It has been shown that tangents drawn to the -φ T* vsT* plots of these metals at any chosen value ofT* intersect at a point whose coordinates are defined by the slope and intercept ofφ vs entropy plots at any homologous temperature and the selectedT* value. A generalized expression obtained for the temperature dependence ofφ has been used to demonstrate that the heat capacity of these metals may be visualized to have structural and material components.

The impurity-induced charge density in jellium is calculated by solving the Schrödinger equation self-consistently. The resulting phase shifts have been used to estimate the value of residual resistivity for dilute Zr-H system, which comes out to be 0.50 µΘ cm/at.%. An alternative form of one-parameter-screened Coulomb potential, which is more suitable than the customary Thomas-Fermi potential, is suggested. The calculated self-energy by using new potential is found close to its value obtained by Darbyet al.

Copper crystals have been grown by Czochralski technique in a 6-bar argon gas environment. X-ray analysis shows that these are single crystals and are strain-free. A slight pressure environment that is truly hydrostatic seems to improve the quality of the crystals. Thermal profile estimation results show that the values of temperature which decrease upto the neck region are same in magnitude as those measured during the experiments and that necking improves the thermal profile and, consequently, the crystal quality. No facet formation has been observed in these crystals.

We present the analytical expression to determine the static structure factorS(q) of liquid alkali metals based on the semi-analytic theory of Baus and Hansen. The calculations were motivated to point out the anomalies exhibited by one-component plasma system (ocp) in describing the structure factor. The numerical example of Na illustrates our results.ocp structure factor is also compared with those obtained by the hard sphere system.