The influence of solute atoms on point-defect properties and defect generation by radiation damage in alloys is known to be important, and hence it is desirable to understand their effect on the basic mecha- nisms involved. Most computer modeling of these phenomena has only considered pure metals, but as part of a project to investigate displacement cascades in alloys, we have simulated dilute solutions of gold (Au) in copper (Cu), treating this as a "model" for a heavy, oversized solute alloy system. In the present paper, modified many-body interatomic potentials for the Cu-Au system are described that are suitable for modeling high-energy atomic collisions. The properties of point defects in pure copper and the dilute alloy, including solute-defect binding energies, are presented. The oversized solute has a larger binding energy with an interstitial atom than with a vacancy. The displacement threshold energy, Ea, of a Cu atom and a Au atom in the copper matrix has been investigated as a function of primary recoil direction, and the difference between the two species is found to be substantial. Furthermore, the pres- ence of a Au solute has a significant effect on the formation of Frenkel pairs by the replacement- collision-sequence mechanism. These results are discussed in terms of the mass and size difference of Cu and Au atoms.

Considered in this paper are the two-person zerosumlinear quadratic differential games. It is shown that thevalue of the game exists if and only if both the upper value andlower value exist. As an consequence, we prove that anothernecessary and sufficient condition for the existence of the valueof the game is the existence of an open loop-open loop saddlepoint. An example is also given where lower value exists butupper value does not exist.

In this paper, a novel waiting-time distribution function (WTDF), ψ(t), which is not purely ex- ponential and is universally valid for explaining recently the low-frequency (say, w<10GHz) fluc- tuation, dissipation, and relaxation properties of condensed matter, is used to discuss asymptotic solutions of the continuous-time random-walk (CTRW) problems. Many results of theoretical and experimental interest are obtained. These results include the mean displacement, the dispersive mobility, the mean-squared displacement, the dispersive diffusion coefficient, the Nernst-Einstein relation, the variance and the standard variance, the lattice statistics, the initial-site occupation probability, the dispersive conductivity, the dispersive electrical transport, and the memory func- tion. All results show that the CTRW process described by the WTDF (t) appears to be non- Markovian over the very broad time domain and is Markovian only in the long-time limit; in oth- er words, all results contain a single parameter n, the infrared divergence exponent, which depends on the microscopic structure of condensed matter and governs the degree of dispersion. The larger the value of n, the stronger the dispersion. When n=0, the dispersion disappears and all results reduce immediately to the classical Markovian forms. This is in agreement with some ex- perimental facts.

A soluble, but nontrivial, model of a dilute Ising ferromagnet is studied, with infinite-range in- teractions but finite average connectivity c. The density of (Yang-Lee) zeros of the partition func- tion in the complex z=exp(-2H) plane (where H is the external magnetic field in units of the tem- perature) is calculated explicitly in the high-temperature phase for large but finite c and small ]H]. The density of zeros on the unit circle H=iO has the form p(θ)～exp{-[cf(K)/]θ]ln( 1/[θ]for [01 >0. The function f(K) (K=J/73 vanishes at the critical coupling Kc(c). Heuristic arguments are given for the form of p(θ) expected for systems with short-range interactions.

On the basis of a new physical picture universally valid for all condensed matter of the infrared-divergence theory and starting from a non-Markovian process, the author investigates electronic excited-state or exciton transfer in disordered systems. The obtained results indicate that the present picture, which differs from the traditional Markovian-transport picture, is more reasonable and more universal than other existing theories. The theoretical predictions are in good agreement with the experimental investigation.