We propose that thed-d fusion rate in palladium can be enhanced by the combined screening of the electrostatic interactions by the itinerant deuterons and the conduction electrons. The model assumes that, under certain conditions, deuterium exists as a D⁺ ion in palladium. The combined screening by electrons and the D⁺ ions (deuterons) is found to be more effective than that due to electrons alone. The calculated values of thed-d fusion rates, considering screening, for composition PdD at 300 K are 10⁻¹⁶ s⁻¹ and 10⁻¹⁴ s⁻¹ for D₂⁺ ion and D₂ molecule respectively. These values lie in the range suggested by the recent electrochemical experiments.

Mass regularities forS- andP-wave mesons and relations between their masses are discussed. A detailed analysis is given forS-wave mesons which extends the investigations onP-wave mesons reported earlier. Masses for theS- andP-states of all interesting$$q\bar q$$-systems (including toponium states) are predicted. Partial understanding of the mass formulae is obtained within a general potential model approach. Scaling arguments are presented which support the empirical scaling behaviour found for the expectation values determining the spin-splittings in the potential picture.

The Gaussian effective potential of the sine-Gordon model is calculated in 1+1 and 2+1 dimensions. Issues like renormalization, vacuum energy and stability of the vacuum are discussed in detail.

We look at the confinement of tensor gluons (f_μν^(c) field) in a strong gravity background and find that the strong gravity provides a trap for the confinement of colour waves of selected frequencies. We assume that the tensorf_μν^(c) field (mediating quanta: tensor 2⁺f-meson) satisfies Einstein-like equations with a cosmological constant. The colour field satisfy equations resembling Maxwell form of the linear theory of gravitation and see the effect off_μν^(c) field as playing the role of a medium having space dependent dielectric permeabilities. The solution of colour field equations resemble harmonic oscillator type wave functions with equispaced energy levels (no continuum) leading to confinement.

A confinement model of hadron with its constituent quarks bound in a strong gravitational field is presented. The gravitational field plays the role of a medium having, as if, space dependent permeabilities from a fixed centre. The massless Dirac equation modified by the gravitational field is solved. The solution for the wavefunction of the quarks obtained shows the characteristic features of confinement, i.e., (i) wavefunction with higher energy states lying closer to the centre, (ii) equispaced energy levels without continuum, (iii) the quark orbits lying within a distance ∼ 10⁻¹⁴ cm, the characteristic radius of a typical hadron.

The existence of a remanent magnetization (M_rem) on switching off the field of a field cooled (FC) sample of a highT_c superconductor is often reported. It has recently been argued thatM_rem should equal the difference in FC and zero field cooled (ZFC) magnetizations (M_FC —M_ZFC) in hard superconductors and this has been demonstrated to hold in single crystals of YBCO at 4.2K over a limited range ofH values. We report the detailed magnetization measurements under various thermomagnetic histories (of whichM_rem is one special case) on two specimens of Nb, which show different extents of flux trapping. We find that there are in general three regions inH, T space, corresponding toM_rem+M_ZFC−M_FC=0,M_rem<(M_FC−M_ZFC) andM_rem>(M_FC−M_ZFC). At anyT, the equality holds forH<H_c1(T), and forH→H_c2 (M_FC−M_ZFC) asymptotically vanishes and thereM_rem>(M_FC−M_ZFC). We show that there exists an intermediate region in all hard superconductors, whereM_rem<(M_FC−M_ZFC). The range over which this situation persists, however, depends on the degree of irreversibility in a sample. We can explain qualitatively all the history dependent magnetization data in terms of the critical state model. We point out an inconsistency in an earlier analysis to determineH_c1(T) from such data in YBCO. We also propose a new criterion for putting limits onH_c1(T) in hard superconductors.

The study of the analytic structure of nonlinear ordinary and partial differential equations is shown to provide a unified approach to determining their properties and finding their solutions.