Phase Equilibria in the System $Al_{2}O_{3}-CaO-CoO$ and Gibbs Energy of Formation of $Ca_{3}CoAl_{4}O_{10}$

The floating-zone method with different growth ambiences has been used to selectively obtain hexagonal or orthorhombic DyMnO3 single crystals. The crystals were characterized by x-ray powder diffraction of ground specimens and a structure refinement as well as electron diffraction. We report magnetic susceptibility, magnetization and specific heat studies of this multiferroic compound in both the hexagonal and the orthorhombic structure. The hexagonal DyMnO3 shows magnetic ordering of Mn3+ (S = 2) spins on a triangular Mn lattice at T-N(Mn) = 57 K characterized by a cusp in the specific heat. This transition is not apparent in the magnetic susceptibility due to the frustration on the Mn triangular lattice and the dominating paramagnetic susceptibility of the Dy3+ (S = 9/2) spins. At T-N(Dy) = 3 K, a partial antiferromagnetic order of Dy moments has been observed. In comparison, the magnetic data for orthorhombic DyMnO3 display three transitions. The data broadly agree with results from earlier neutron diffraction experiments, which allows for the following assignment: a transition from an incommensurate antiferromagnetic ordering of Mn3+ spins at T-N(Mn) = 39 K, a lock-in transition at Tlock-in = 16 K and a second antiferromagnetic transition at T-N(Dy) = 5 K due to the ordering of Dy moments. Both the hexagonal and the orthorhombic crystals show magnetic anisotropy and complex magnetic properties due to 4f-4f and 4f-3d couplings.

Different phenomenological theories and their abilities to describe the interdiffusion process in a binary system during multiphase growth

There are essentially two different phenomenological models available to describe the interdiffusion process in binary systems in the olid state. The first of these, which is used more frequently, is based on the theory of flux partitioning. The second model, developed much more recently, uses the theory of dissociation and reaction. Although the theory of flux partitioning has been widely used, we found that this theory does not account for the mobility of both species and therefore is not suitable for use in most interdiffusion systems. We have first modified this theory to take into account the mobility of both species and then further extended it to develop relations or the integrated diffusion coefficient and the ratio of diffusivities of the species. The versatility of these two different models is examined in the Co-Si system with respect to different end-member compositions. From our analysis, we found that the applicability of the theory of flux partitioning is rather limited but the theory of dissociation and reaction can be used in any binary system.

Free energy landscape of a dense hard-sphere system

The topography of the free energy landscape in phase space of a dense hard-sphere system characterized by a discretized free energy functional of the Ramakishnan-Yussouff form is investigated numerically using a specially devised Monte Carlo procedure. We locate a considerable number of glassy local minima of the free energy and analyze the distributions of the free energy at a minimum and an appropriately defined phase-space "distance" between different minima. We find evidence for the existence of pairs of closely related glassy minima("two-level systems"). We also investigate the way the system makes transitions as it moves from the basin of attraction of a minimum to that of another one after a start under nonequilibrium conditions. This allows us to determine the effective height of free energy barriers that separate a glassy minimum from the others. The dependence of the height of free energy barriers on the density is investigated in detail. The general appearance of the free energy landscape resembles that of a putting green: relatively deep minima separated by a fairly flat structure. We discuss the connection of our results with the Vogel-Fulcher law and relate our observations to other work on the glass transition.

Solution of a System of Generalized Abel Integral Equations Using Fractional Calculus

A method is presented for obtaining useful closed form solution of a system of generalized Abel integral equations by using the ideas of fractional integral operators and their applications. This system appears in solving certain mixed boundary value problems arising in the classical theory of elasticity.

Fuzzy optimization model for water quality management of a river system - Closure

A fuzzy waste-load allocation model, FWLAM, is developed for water quality management of a river system using fuzzy multiple-objective optimization. An important feature of this model is its capability to incorporate the aspirations and conflicting objectives of the pollution control agency and dischargers. The vagueness associated with specifying the water quality criteria and fraction removal levels is modeled in a fuzzy framework. The goals related to the pollution control agency and dischargers are expressed as fuzzy sets. The membership functions of these fuzzy sets are considered to represent the variation of satisfaction levels of the pollution control agency and dischargers in attaining their respective goals. Two formulations—namely, the MAX-MIN and MAX-BIAS formulations—are proposed for FWLAM. The MAX-MIN formulation maximizes the minimum satisfaction level in the system. The MAX-BIAS formulation maximizes a bias measure, giving a solution that favors the dischargers. Maximization of the bias measure attempts to keep the satisfaction levels of the dischargers away from the minimum satisfaction level and that of the pollution control agency close to the minimum satisfaction level. Most of the conventional water quality management models use waste treatment cost curves that are uncertain and nonlinear. Unlike such models, FWLAM avoids the use of cost curves. Further, the model provides the flexibility for the pollution control agency and dischargers to specify their aspirations independently.

Fuzzy Logic-Based Approaches in Water Resource System Modelling

Recent research in modelling uncertainty in water resource systems has highlighted the use of fuzzy logic-based approaches. A number of research contributions exist in the literature that deal with uncertainty in water resource systems including fuzziness, subjectivity, imprecision and lack of adequate data. This chapter presents a broad overview of the fuzzy logic-based approaches adopted in addressing uncertainty in water resource systems modelling. Applications of fuzzy rule-based systems and fuzzy optimisation are then discussed. Perspectives on the scope for further research are presented.