Separable energy-dependent approximation to local potentials

An extension of the single-pole separable approximation of a two-body t-matrix in which the effects of several poles are included is made. The simple form for the t-matrix derived from a single separable potential is retained. However, the separable potential is constructed using an energy-dependent superposition of the states corresponding to the various poles. The energy dependence is chosen so as to obtain the correct residue of both the on-shell and off-shell t-matrices at each of these poles, while preserving unitarity. The formalism is specialized to the case of s-wave scattering from an attractive square well. Comparison to the exact s-wave cross section gives good results.     

Probing the pore wall structure of nanoporous carbons using adsorption

Hitherto, adsorption has been traditionally used to study only the porous structure in disordered materials, while the structure of the solid phase skeleton has been probed by crystallographic methods such as X-ray diffraction. Here we show that for carbons density functional theory, suitably adapted to consider heterogeneity of the pore walls, can be reliably used to probe features of the solid structure hitherto accessibly only approximately even by crystallographic methods. We investigate a range of carbons and determine pore wall thickness distributions using argon adsorption, with results corroborated by X-ray diffraction.     

Duality in nonlinear multiobjective programming using augmented Lagrangian functions

A vector-valued generalized Lagrangian is constructed for a nonlinear multiobjective programming problem. Using the Lagrangian, a multiobjective dual is considered. Without assuming differentiability, weak and strong duality theorems are established using Pareto efficiency.The research of the second author was partially supported a GTE/SLU grant while visiting St. Lawrence University in the summer of 1991.     

Norm inequalities related to the matrix geometric mean

Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.     

Reliability analysis of Polytube industry using supplementary variable technique

The purpose of this paper is to compute reliability of Polytube manufacturing plant having four units using supplementary variable technique. The failure and repair rates of the sub-systems are variable. The mathematical equations are derived using Chapman-Kolmogorov differential equations which are formed using mnemonic rule from the transition diagram of Polytube manufacturing plant. The system of partial differential equations obtained has been solved using Lagrange’s method and reliability of the system for the various choices of constant transition rates is solved numerically using Runge-Kutta fourth order. A sensitive analysis of subsystem is finally carried out to improve overall availability.     

Mehar’s method for solving fuzzy sensitivity analysis problems with LR flat fuzzy numbers

In published works on fuzzy linear programming there are only few papers dealing with stability or sensitivity analysis in fuzzy mathematical programming. To the best of our knowledge, till now there is no method in the literature to deal with the sensitivity analysis of such fuzzy linear programming problems in which all the parameters are represented by LR flat fuzzy numbers. In this paper, a new method, named as Mehar’s method, is proposed for the same. To show the advantages of proposed method over existing methods, some fuzzy sensitivity analysis problems which may or may not be solved by the existing methods are solved by using the proposed method.     

Quantum ω-Automata over Infinite Words and Their Relationships

Inspired by the results of finite automata working on infinite words, we studied the quantum ω-automata with Büchi, Muller, Rabin and Streett acceptance condition. Quantum finite automata play a pivotal part in quantum information and computational theory. Investigation of the power of quantum finite automata over infinite words is a natural goal. We have investigated the classes of quantum ω-automata from two aspects: the language recognition and their closure properties. It has been shown that quantum Muller automaton is more dominant than quantum Büchi automaton. Furthermore, we have demonstrated the languages recognized by one-way quantum finite automata with different quantum acceptance conditions. Finally, we have proved the closure properties of quantum ω-automata.

     

Quantum effect induced kinetic molecular sieving of hydrogen and deuterium in microporous materials

We report here our investigations using Monte Carlo and molecular dynamics (MD) simulations, as well as quasi-elastic neutron scattering experiments, to study the adsorption and diffusion of H₂ and D₂ in zeolite Rho. In the simulations, quantum effects are incorporated via the Feynman-Hibbs variational approach. At low temperatures, we observe a reversal of kinetic molecular sieving in which D₂ diffuses faster than H₂. Based on fits of bulk data, we suggest new set of potential parameters for hydrogen, with the Feynman-Hibbs variational approach used for quantum corrections. The transport properties obtained from MD simulations are in excellent agreement with the experimental results, with both showing significant quantum effects on the transport at low temperature. The MD simulation results on two different structures of zeolite Rho clearly demonstrate that the quantum effect is very sensitive to pore size. High transport flux selectivity is noted at low temperatures, suggesting feasibility of kinetic isotope separation.     

Pore accessibility of N2 and Ar in disordered nanoporous solids: theory and experiment

Recently (Nguyen and Bhatia, J. Phys. Chem. C 111:2212–2222, 2007) we have proposed a new algorithm utilising cluster analysis principles to determine pore network accessibility of a disordered material. The algorithm was applied to determine pore accessibility of the reconstructed molecular structure of a saccharose char, obtained in our recent work using hybrid reverse Monte Carlo simulation (Nguyen et al., Mol. Simul. 32:567–577, 2006). The method also identifies kinetically closed pores not accessed by adsorbate molecules at low temperature, when their low kinetic energy cannot overcome the potential barrier at the mouths of pores that can otherwise accommodate them. In the current work, the results are validated by transition state theory calculations for N₂ and Ar adsorption, showing that N₂ can equilibrate in narrow micropores at practical time scales at 300 K, but not at 77 K. Large differences between time scales for micropore entry and exit are predicted at low temperature for N₂, the latter being smaller by over three orders of magnitude. For N₂ at 77 K the time constant for pore entry exceeds 3 hr., while for exit it is 134 days. At 300 K these values are smaller than 1 μs, indicating good accessibility at this temperature. These results are verified by molecular dynamics simulations, which reveal that while N₂ molecules enter and leave all pores frequently at 300 K, entry and exit events for apparently inaccessible pores are absent at 77 K. For Ar at 87 K better accessibility is evident for the saccharose char compared to N₂ at 77 K. This finding is now experimentally shown in this work by comparison of pore size distributions obtained from experimental nitrogen adsorption isotherms of nitrogen and argon at 77 K and 87 K.     

Multiple dynamic regimes in colloid‐polymer dispersions: New insight using X‐ray photon correlation spectroscopy

We present an X‐ray photon correlation spectroscopy (XPCS) study of dynamic transitions in an anisotropic colloid‐polymer dispersion with multiple arrested states. The results provide insight into the mechanism for formation of repulsive glasses, attractive glasses, and networked gels of colloids with weakly adsorbing polymer chains. In the presence of adsorbing polymer chains, we observe three distinct regimes: a state with slow dynamics consisting of finite particles and clusters, for which interparticle interactions are predominantly repulsive; a second dynamic regime occurring above the saturation concentration of added polymer, in which small clusters of nanoparticles form via a short‐range depletion attraction; and a third regime above the overlap concentration in which dynamics of clusters are independent of polymer chain length. The observed complex dynamic state diagram is primarily governed by the structural reorganization of a nanoparticle cluster and polymer chains at the nanoparticle‐polymer surface and in the concentrated medium, which in turn controls the dynamics of the dispersion. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 752–760