The effects of next-to-nearest-neighbour hopping on Bose-Einstein condensation in cubic lattices

In this paper, we present results of our calculations on the effects of next-to-nearest-neighbour boson hopping (t′) energy on Bose-Einstein condensation in cubic lattices. We consider both non-interacting and repulsively interacting bosons moving in the lowest Bloch band. The interacting bosons are studied using Bogoliubov method. We find that the Bose condensation temperature is enhanced by increasing t′ for bosons in a simple cubic (sc) lattice and decreases for bosons in body-centred cubic (bcc) and face-centred cubic (fcc) lattices. We also find that interaction-induced depletion of the condensate is reduced for bosons in an sc lattice while it is enhanced for bosons in bcc and fcc lattices.     

Development of ion chromatography and capillary electrophoresis methods for the determination of Li in Li–Al alloy

Two methods were developed for determination Li content in Li–Al alloy by employing ion chromatography (IC) and capillary electrophoresis (CE) without any prior separation of Al matrix. In absence of suitable certified reference material the two methods were used to validate each other. Using a high capacity column and a weaker eluent methane sulphonic acid, it was possible to separate Li in IC without eluting strongly retained Al. The method showed good precision and sensitivity and was extended for analysis of routine samples. In the case of CE using imidazole as co-ion, Li was detected in CE by indirect detection. In view of no interference from Al, samples were analyzed without any matrix separation. The CE method was used successfully for sample analysis and results were compared with IC results.     

Development of methodology for the determination of boron in ThO2 employing spectrophotometry

Boron was determined in ThO₂ employing spectrophotometry using curcumin as complexing agent after dissolution with 85 % ortho phosphoric acid and separation of boron with 10 % 2-ethyl hexane 1,3 diol in CHCl₃. The methodology was validated by employing ThO₂ standards made from inter laboratory comparison experiments DAE, India. Absolute detection limit of the methodology was found to be 30 ng. Precision and accuracy of the methodology were found to be 4.2 and 2 % respectively. The expanded uncertainty in measurement of boron (at coverage factor 2) was estimated as per ISO guidelines employing bottom-up approach and it was found to be 9.2 %.     

The free energy of a reaction coordinate at multiple constraints: a concise formulation

The free energy as a function of the reaction coordinate (rc) is the key quantity for the computation of equilibrium and kinetic quantities. When it is considered as the potential of mean force, the problem is the calculation of the mean force for given values of the rc. We reinvestigate the PMCF (potential of mean constraint force) method which applies a constraint to the rc to compute the mean force as the mean negative constraint force and a metric tensor correction. The latter allows for the constraint imposed to the rc and possible artefacts due to multiple constraints of other variables which for practical reasons are often used in numerical simulations. Two main results are obtained that are of theoretical and practical interest. First, the correction term is given a very concise and simple shape which facilitates its interpretation and evaluation. Secondly, a theorem describes various rcs and possible combinations with constraints that can be used without introducing any correction to the constraint force. The results facilitate the computation of free energy by molecular dynamics simulations.     

Studies on recovery of uranium from fluoride matrix employing sonochemistry

Application of power ultrasound in chemical processes is recognized as an effective tool to solve many industrial problems encountered in processes involved in nuclear industry, particularly, digestion and leaching steps. In addition, problems related to radiological safety are the most important factors to be considered, when handling radioactive materials. Sonochemical processes, due to relatively low temperature operations, are attractive in this regards. Further they are eco-friendly and economical as well. Hence, sonochemical studies were taken up for the removal of uranium from fluoride containing matrix. Dissolution studies were carried out in nitric acid medium, in a 5 L capacity tank type sono-reactor, operating at frequency and power of 22 ± 3 kHz and 150 W respectively. The parameters studied were concentration of HNO₃, temperature of water-bath, choice of purged gas (air/oxygen) and flow rate of purged gas passed. Experiments were also carried out to study the amount of fluoride matrix dissolved. Enhancement with US was 76 to 91 % for U removal from MgF₂ slag in 2 M HNO₃. The prime advantage achieved is the reduction in the reaction time. Other advantages are minimizing labor, remotisation of operations to reduce radiation exposure, use of less acid and accordingly lesser effluent for treatment before disposal.     

Lattice bosons in quartic confinement

We present a theoretical study of bose condensation of non-interacting bosons in finite lattices in quartic potentials in one, two, and three dimensions. We investigate dimensionality effects and quartic potential effects on single boson density of energy states, condensation temperature, condensate fraction, and specific heat. The results obtained are compared with corresponding results for lattice bosons in harmonic traps.