Supersymmetric quantum mechanics in one,two and three dimensions

We discuss a few supersymmetric quantum mechanical models in one, two and three dimensions. In the case of one particle in both two and three dimensions we present some examples where supersymmetry is unbroken and the ground state is many-fold degenerate. Further, we consider the supersymmetric generalization of the nearest neighbour XY model and show that supersymmetry remains unbroken in this case.     

Summability of Laguerre series at the pointx=0

In this paper, the authors prove a theorem on matrix summability of Laguerre series at the point x=0. Various results on Casàro, Nörlund and generalized Nörlund summability method have been deduced.     

Forward scattering in systems with non-central potentials: an analysis of the infinite order sudden approximation

The l-labelled version of the IOS is re-examined in detail. It is shown that recent severe criticism of the method, based on studies of a system with a long-range attractive anisotropy and spherically symmetric hard core and assuming a weak anisotropy and straight-line Trajectories, is unjustified.     

Quantum interference effect in laser patterned BSCCO thick film

DC SQUID structure consisting of two microbridges and a circular hole was patterned on BSCCO thick film using laser ablation technique. Quantum interference effects on these patterned films were studied at fixed biasing current by applying changing magnetic field. The SQUID with 100 μm × 70 μm microbridges showed noisy and irregular V-B behaviour whereas the SQUID containing smaller microbridges showed better V-B characteristic. Temperature dependence of the I-V and V-B characteristics of the SQUID is also reported.     

Effect of three-body interactions on electronic polarizabilities and photoelastic behaviour of partially covalent crystals

Summary We have investigated the effect of three-body interactions on the photoelastic behaviour and the electronic polarization of silver, thallium and copper halides, which are partially covalent in character and possess three different crystall structures. The cation, anion and molecular polarizabilities calculated in their crystalline state seem to be reliable as they follow a systematic trend. Our calculated values of the strain derivatives of the electronic dielectric constants are much closer to their experimental data than those obtained by earlier workers. To speed up publication, the authors of this paper have agreed to not rceive the proofs for correction.     

An exactly solvable quarkonium model and lower bounds on 3 p J decay rates

The exact 1P-state wavefunction R _1P (r) is obtained for the potential     

Switching liquid morphologies on linear grooves

The morphology of liquids confined to linear micrometer-sized grooves of triangular and rectangular cross section is studied for different substrate wettabilities. Depending on the wettability and exact geometry, either droplike morphologies or elongated liquid filaments represent the generic equilibrium structures on the substrate. Upon changing the apparent contact angle of aqueous drops by electrowetting, we are able to trigger the transition between elongated filaments and droplets. In the case of rectangular grooves, this transition allows us to advance liquid reversibly into the grooves while crossing a certain threshold contact angle. In triangular grooves, however, these elongated filaments undergo a dynamic instability when the contact angle returns to a value above the filling threshold. The different filling and drainage behavior is explained by specific aspects of the triangular and rectangular groove geometry.     

Mathematical Modeling of Nylon 6/6,6 Copolymerization: Beneficial Influence of Comonomers on Degree of Polymerization in Batch Reactor

A model is developed for hydrolytic copolymerization of caprolactam with hexamethylene diamine (HMD) and adipic acid (ADA) in a batch reactor to produce nylon 6/6,6 copolymer. The reaction mechanism includes hydrolysis of caprolactam and cyclic dimer, polycondensation, polyaddition, transamidation, and ring formation via end biting and back biting. The catalyzing effect of carboxyl groups is accounted for using kinetic parameters from the literature. Model predictions are compared with low‐temperature literature data before simulating reactor conditions of industrial interest. The model predicts a higher degree of polymerization (DP) for nylon 6/6,6 copolymer compared to nylon 6 and 6,6 homopolymers produced using the same reactor conditions. Dynamic changes in concentrations of water, caprolactam, HMD, ADA, and end groups are tracked and used to explain the positive influence of comonomers on reaction rates and DP. Insights gained from this model will form a useful basis to build future models of continuous industrial reactors.

     

Radiolysis of ferrous ammonium sulphate in alkali nitrate and alkali halide matrices

Radiolysis of ferrous ammonium sulphate (FAS) dispersed in (a) alkali nitrates [KNO₃, NaNO₃, Ba(NO₃)₂, CO(NH₃)₆(NO₃)₃] (b) alkali halides [KCl, KBr] and (c) binary mixtures of above [KNO₃ + KCl, Ba(NO³)₂ + BaCl₂) has been extensively investigated. FAS becomes oxidized and Fe³⁺ formation seems to depend upon the nitrate concentration and gamma dose but is independent of halide concentration. Mossbauer studies confirm these findings and it appears that basic ferric sulphate may be formed during the oxidation process.