On the relationship between the entropy and enthalpy of interfacial segregation

The general relationship between the excess entropy and enthalpy of segregation is elucidated in terms of basic thermodynamical principles applied to the bulk-interface equilibrium. The linearity reported in several studies of different grain boundary or surface orientations in alloys is accounted for in case at some temperature, the excess entropy varies much more strongly than the ideal solution configurational contribution to the segregation entropy. The theoretical analysis done for monolayer segregation (e.g., of non-metal impurity), shows that the linear relationship can be explicitly quantified by means of a quasi-isotropic interfacial segregation level and the corresponding temperature, and without introducing significant error in case of multilayer segregation.     

On Varieties of Semilattice-Ordered Semigroups

We initiate here a systematic equational classification of semilattice-ordered semigroups. We start with various examples. Then we consider semilattice-ordered semigroups satisfying the identity x^r = x. Finally, we reduce the classification to finding certain operators on relatively free semigroups.     

An Outer Approximations Approach to Reliability-Based Optimal Design of Structures

We present a new formulation of the problem of minimizing the initial cost of a structure subject to a minimum reliability requirement, expressed in terms of the so-called design points of the first-order reliability theory, i.e., points on limit-state surfaces that are nearest to the origin in a transformed standard normal space, as well as other deterministic constraints. Our formulation makes it possible to use outer approximations algorithms for the solution of such optimal design problems, eliminating some of the major objections associated with treating them as bilevel optimization problems. A numerical example is presented that illustrates the reliability and efficiency of the algorithm.     

A quadratically convergent primal-dual algorithm with global convergence properties for solving optimization problems with equality constraints

This paper presents a globally convergent multiplier method which utilizes an explicit formula for the multiplier. The algorithm solves finite dimensional optimization problems with equality constraints. A unique feature of the algorithm is that it automatically calculates a value for the penalty coefficient, which, under certain assumptions, leads to global convergence.Research sponsored by the Joint Services Electronics Program, Contract F44620-71-C-0087 and the National Science Foundation, Grant GK-37672.     

Outer approximation algorithm for nondifferentiable optimization problems

Omissions from the list of references of Ref. 1 are corrected.     

A quadratically convergent algorithm for solving infinite dimensional inequalities

Many design algorithms can be formulated as determining a set of parameters to satisfy conventional and infinite dimensional constraints. An algorithm, with quadratic rate of convergence, for solving such inequalities, is presented.Research supported by the United Kingdom Science Research Council and the National Science Foundation ECS-79-13148.     

Feasible directions algorithms for optimization problems with equality and inequality constraints

In this paper two algorithms, of the feasible-directions and dual feasible-directions type, are presented for optimization problems with equality and inequality constraints. An associated problem, having only inequality constraints, is defined, and shown to be equivalent to the original problem if a certain parameter is sufficiently large. The algorithms solve the associated problem, but incorporate a method for automatically increasing this parameter in order to ensure global convergence to a solution to the original problem. Any feasible directions algorithm can be similarly modified to enable it to handle equality constraints.Research sponsored by the US Army Research Office — Durham, Contract DAHCO4-73-C-0025 and the National Science Foundation Grant GK-37572.