Nematic - Isotropic Transition in Porous Media - a Monte Carlo Study

We propose a lattice model to simulate the influence of porous medium on the Nematic - Isotropic transition of liquid crystal confined to the pores. The effects of pore size and pore connectivity are modelled through a disorder parameter. Monte Carlo calculations based on the model leads to results that compare well with experiments.Comment: 11 pages; 4 figure

Column Flotation: Theory and Practice

Column flotation which employs a counter-current flow of slurry and air bubbles has proved to be better alternative to the conventional mechanical cells for separation of minerals. Because of the distince advantages of column flotation over mechanical cells, it is gaining wider acceptance in industry. Realizing the potentioal of column flotation, RRL Bhubaneswar also took initiative in the early ixties to develop column flotation technology for Indian ores. In the early stages, operation and design of columns wewe mainly based on experience. But with the increasing commercial installations, systematic investi-gations bave been carried out by several workers. In this paper an attempt is made to review the development of column flotation for concentration of law grade ores. The basic principles and applications of column flotation have been described. The salient results obtained at RRL, Bhubaneswar have been highlighted

Study of np-scattering for S, P and D Waves using Deng-Fan Potential by Phase Function Method

In this paper, the np - scattering phase shifts and cross section for S,P and D partial waves have been obtained for energies below the pion threshold, by considering Deng-Fan potential as model of interaction. The radial time independent Schr\"odinger equation has been analytically solved using Nikiforov - Uvarov method to obtain the energy expression for ground state of np system. Utilising this, the scattering phase shifts for $^3S_1$ have been obtained using phase function method. The phase equations for various scattering states $^1S_0$, $^1P_1$, $^3P_{0,1,2}$, $^1D_2$, and $^3D_{1,2,3}$ have been numerically solved for obtaining corresponding scattering phase shifts and their respective partial cross section. The total scattering cross sections computed at various energies are found to be closely matching with experimental data. The low energy scattering parameters determined from scattering phase shifts of $^3S_1$ and $^1S_0$ are reasonably close to experimental ones. Hence, Deng-Fan potential is a good phenomenological potential to understand the np - scattering system.Comment: 11 pages, 4 figures, 2 table

Comparative Study of alpha-alpha interaction potentials constructed using various phenomenological models

In this paper, we have made a comparative study of alpha-alpha scattering using different phenomenological models like Morse, double Gaussian, double Hulthen, Malfliet-Tjon and double exponential for the nuclear interaction and atomic Hulthen as screened coulomb potential. The phase equations for S, D and G channels have been numerically solved using 5th order Runge-Kutta Method to compute scattering phase shifts for elastic scattering region consisting of energies up to 25.5 MeV. The model parameters in each of the chosen potentials were varied in an iterative fashion to minimize the mean absolute percentage error between simulated and expected scattering phase shifts. A comparative analysis revealed that, all the phenomenological models result in exactly similar inverse potentials with closely matching mean absolute percentage error values for S, D and G state. One can conclude that any mathematical function that can capture the basic features of two body interaction would always guide correctly in construction of inverse potentials.Comment: 11 pages, 3 figures, 4 Table

Constructing Inverse Scattering Potentials for {\alpha}-{\alpha} System using Reference Potential Approach

Background: An accurate way to incorporate long range Coulomb interaction alongside short-range nuclear interaction has been a challenge for theoretical physicists. Purpose: In this paper, we propose a methodology based on the reference potential approach for constructing inverse potentials of alpha-alpha scattering. Methods: Two smoothly joined Morse potentials, regular for short-range nuclear interaction and inverted for long range Coulomb, are used in tandem as a reference potential in the phase function method to obtain the scattering phase shifts for the S, D and G states of alpha-alpha scattering. The model parameters are optimized by choosing to minimize the mean absolute percentage error between the obtained and experimental scattering phase shift values. Results: The constructed inverse potentials for S, D and G states have resulted in mean absolute percentage errors of 0.8, 0.5, and 0.4 respectively. The obtained resonances for D and G states closely match the experimental ones. Conclusion: The reference potential approach using a combination of smoothly joined Morse functions is successful in accurately accounting for the Coulomb interaction between charged particles in nuclear scattering studies.Comment: 10 pages, 4 figures, 2 Table

Neutron-Proton Scattering Phase Shifts in S-Channel using Phase Function Method for Various Two Term Potentials

The scattering phase shifts for n-p scattering have been modeled using various two term exponential type potentials such as Malfliet-Tjon, Manning-Rosen and Morse to study the phase shifts in the S-channels. As a first step, the model arameters for each of the potentials are determined by obtaining binding energy of the deuteron using matrix methods vis-a-vis Variational Monte-Carlo (VMC) technique to minimize the percentage error w.r.t. the experimental value. Then, the first order ODE as given by phase function method (PFM), is numerically solved using 5th order Runge-Kutta (RK-5) technique, by substituting the obtained potentials for calculating phase shifts for the bound 3S1 channel. Finally, the potential parameters are varied in least squares sense using VMC technique to obtain the scattering phase-shifts for each of the potentials in the 1S0 channel. The numerically obtained values are seen to be matching with those obtained using other analytical techniques and a comparative analysis with the experimental values up to 300 MeV is presented