On some educational and psychological aspects of problem solving

An attempt has been made to present an overview of various learning theories keeping in view the psychological aspect of problem solving behaviours of children and to explain the processes by which problem solving skills are acquired and applied. The four important research variables—as described by Lester (task, subject, process and instructional variables)—have been discussed and some research questions have been formulated for further research investigations in the area of problem solving.     

Energy-dispersive X-ray fluorescence – A tool for interdisciplinary research

Trace elements have been at the focus of attention for decades with considerable emphasis on their role in biology and biomedical sciences, environmental sciences, geology, archaeology and material sciences. They comprise a large number of elements, some having essential physiological functions, whereas others are toxic, mutagenic or carcinogenic. A few even have antiproliferative and anticarciniogenic properties. The advent of various instrumental techniques and sophisticated instrumentations has made their detection to very low limits possible, making this a very important multidisciplinary study. Among these techniques the energy-dispersive X-ray fluorescence (EDXRF) technique is being widely used for trace element detection in various fields of science. Keeping the importance of trace elements in mind, the Kolkata centre of UGC-DAE Consortium for Scientific Research initiated several research schemes in different fields of trace element research using various techniques, EDXRF being one of the main techniques. A Xenemetrix (erstwhile Jordan Valley) EX 3600 EDXRF spectrometer is being used to carry out the research. This presentation aims to highlight some of the very recent applications of EDXRF in the study of the role of trace elements in pre-cancerous tissues, medicinal plants and also in some environmental studies.     

The effect of nonlinearity in relativistic nucleon–nucleon potential

A simple form for nucleon–nucleon (NN) potential is introduced as an alternative to the popular M3Y form using the relativistic mean field theory (RMFT) with the non-linear terms in σ-meson for the first time. In contrast to the M3Y form, the new interaction becomes exactly zero at a finite distance and the expressions are analogous with the M3Y terms. Further, its applicability is examined by the study of proton and cluster radioactivity by folding it with the RMFT-densities of the cluster and daughter nuclei to obtain the optical potential in the region of proton-rich nuclides just above the double magic core¹⁰⁰Sn. The results obtained were found comparable with the widely used M3Y NN interactions.     

Comprehensive decay law for emission of charged particles and exotic cluster radioactivity

A general decay formula for the emission of charged particles from metastable nuclei is developed based on the basic phenomenon of resonances occurring in quantum scattering process under Coulomb-nuclear potential. It relates the half-lives of radioactive decays with the Q values of the outgoing elements with masses and charges of the nuclei involved in the decay. The relation is found to be a generalization of the Geiger–Nuttall law in α radioactivity and explains well all the known emissions of charged particles including clusters, alpha and proton.     

Neutron star in the presence of strong magnetic field

Compact stars such as neutron stars (NS) can have either hadronic or exotic states like strange quark or colour superconducting matter. Stars can also have a quark core surrounded by hadronic matter, known as hybrid stars (HS). The HS is likely to have a mixed phase in between the hadron and the quark phases. Observational results suggest huge surface magnetic field in certain NS. Therefore, we study here the effect of strong magnetic field on the respective equation of states (EOS) of matter under extreme conditions. We further study the hadron–quark phase transition in the interiors of NS giving rise to HS in the presence of strong magnetic field. The hadronic matter EOS is described based on RMF theory and we include the effects of strong magnetic fields leading to Landau quantization of the charged particles. For quark phase, we use the simple Massachusetts Institute of Technology (MIT) bag model, assuming density-dependent bag pressure and magnetic field. The magnetic field strength increases from the surface to the centre of the star. We construct the intermediate mixed phase using Glendenning conjecture. The magnetic field softens the EOS of both the matter phases. We finally study, the mass–radius relationship for such types of mixed HS, calculating their maximum mass, and compare them with the recent observations of pulsar PSR J1614-2230, which is about 2 solarmass.     

Nuclear quantum effects in calculated NMR shieldings of benzene; a Feynman path integral study

The Feynman path integral Monte Carlo approach has been coupled to the gauge including atomic orbital formalism in order to analyse the absolute magnetic shieldings of the benzene nuclei under the conditions of thermal equilibrium. The Hamiltonian employed in the derivation of ensemble averaged NMR quantities is of the Hartree-Fock type. The basis set used is of 6–31G quality. The spatial delocalization of the atoms leads to a deshielding of both types of benzene nuclei relative to the shieldings experienced at the minimum of the potential energy surface. This deshielding has to be traced back to bond length elongations in thermal equilibrium. The influence of the nuclear fluctuations on the NMR parameters of benzene is quantum driven up to temperatures of 400 K; classical fluctuations are of minor importance in this low-temperature window.     

Vibrational properties of vacancy in bcc transition metals using embedded atom method potentials

The embedded atom method (EAM) potentials, with the universal form of the embedding function along with the Morse form of pair potential, have been employed to determine the potential parameters for three bcc transition metals: Fe, Mo, and W, by fitting to Cauchy pressure (C ₁₂???C ₄₄)/2, shear constants $G_\textrm{v} =({C_{11} -C_{12} +3C_{44}})/5$ and C ₄₄, cohesive energy and the vacancy formation energy. The obtained potential parameters are used to calculate the phonon dispersion spectra of these metals. Large discrepancies are found between the calculated results of phonon dispersion using the EAM and the experimental phonon dispersion results. Therefore, to overcome this inadequacy of the EAM model, we employ the modified embedded atom method (MEAM) in which a modified term along with the pair potential and embedding function is added in the total energy. The phonon dispersions calculated using potential parameters obtained from the MEAM show good agreement with experimental results compared to those obtained from the EAM. Using the calculated phonons, we evaluate the local density of states of the neighbours of vacancy using the Green’s function method. The local frequency spectrum of first neighbours of vacancy in Mo shows an increase at higher frequencies and a shift towards the lower frequencies whereas in Fe and W, the frequency spectrum shows a small decrease towards higher frequency and small shift towards lower frequency. For the second neighbours of vacancy in all the three metals, the local frequency spectrum is not much different from that of the host atom. The local density of states of the neighbours of the vacancy has been used to calculate the mean square displacements and the formation entropy of vacancy. The calculated mean square displacements of the first neighbours of vacancy are found to be higher than that of the host atom, whereas it is lower for the second neighbours. The calculated results of the formation entropy of the vacancy compared well with other available results.     

Anisotropic cosmological models with bulk viscosity and particle creation in Saez–Ballester theory of gravitation

The paper deals with the study of particle creation and bulk viscosity in the evolution of spatially homogeneous and anisotropic Bianchi type-V cosmological models in the framework of Saez–Ballester theory of gravitation. Particle creation and bulk viscosity are considered as separate irreversible processes. The energy–momentum tensor is modified to accommodate the viscous pressure and creation pressure which is associated with the creation of matter out of gravitational field. A special law of variation of Hubble parameter is applied to obtain exact solutions of field equations in two types of cosmologies, one with power-law expansion and the other with exponential expansion. Cosmological model with power-law expansion has a Big-Bang singularity at time t = 0, whereas the model with exponential expansion has no finite singularity. We study bulk viscosity and particle creation in each model in four different cases. The bulk viscosity coefficient is obtained for full causal, Eckart’s and truncated theories. All physical parameters are calculated and thoroughly discussed in both models.