On Screening Induced Fluctuations in Ostwald Ripening

In this paper we derive a model for the evolution of the particle radius density for a system of many particles that evolve according to the Mullins–Sekerka problem. The derived model is a correction of the classical LSW theory that takes the effect of the fluctuations of the particle density into account. The main difference between the model derived in this paper and the classical LSW theory is the presence of a second order term which yields a boundary layer effect for large particles. In particular this model provides a possible solution for the so-called “selection problem” in the LSW theory.     

Strain-induced morphologies during homogeneous phase separation in alloys

When precipitates grow with a lattice misfit inside a matrix having cubic crystal symmetry, a transition may occur from an isotropic arrangement of the precipitates to an alignment along the cubic directions of the crystal. Furthermore, if a uniaxial external strain is applied, an additional transition towards tetragonal symmetry can occur by fusion of the precipitates into large plates perpendicular (or long rods parallel) to the direction of applied strain (“rafting”). Recent experiments on Ni-Al-Mo alloys as well as computer simulations relating to these two transitions are reviewed.     

Algebraic analysis of multigrid algorithms

We study the convergence rate of multilevel algorithms from an algebraic point of view. This requires a detailed analysis of the constant in the strengthened Cauchy–Schwarz inequality between the coarse‐grid space and a so‐called complementary space. This complementary space may be spanned by standard hierarchical basis functions, prewavelets or generalized prewavelets. Using generalized prewavelets, we are able to derive a constant in the strengthened Cauchy–Schwarz inequality which is less than 0.31 for the L² and H¹ bilinear form. This implies a convergence rate less than 0.15. So, we are able to prove fast multilevel convergence. Furthermore, we obtain robust estimations of the convergence rate for a large class of anisotropic ellipic equations, even for some that are not H¹‐elliptic. Copyright © 1999 John Wiley & Sons, Ltd.     

Monte Carlo simulation of antiphase boundaries and growth of antiphase domains in Al5Ti3 phase in Al-rich γ-TiAl intermetallics

Predominantly two kinds of antiphase boundaries (APBs) form in Al₅Ti₃, which is an Al-rich ordered derivative of the γ-TiAl (L1₀) phase. This phase can be viewed as a periodic arrangement of lean rhombs and squares on the Ti-rich (002) planes of the tetragonal L1₀. Energies of the two types of APBs were varied in a Monte Carlo simulation by suitably changing the pair interaction parameters. APBs of both types form boundaries of Al₅Ti₃ antiphase domains (APDs), which coarsen with time. An important observation in this regard is that mostly facetted APBs form at lower ageing temperatures, whereas curved APBs appear to form at relatively higher ageing temperatures. The findings of this work suggest that there exists a critical temperature, akin to the roughening transition temperature for crystals, that marks the transition from facetted to curved APBs.