Packing Non-Returning <Emphasis Type="Italic">A</Emphasis>-Paths*

Chudnovsky et al. gave a min-max formula for the maximum number of node-disjoint nonzero A-paths in group-labeled graphs [1], which is a generalization of Mader's theorem on node-disjoint A-paths [3]. Here we present a further generalization with a shorter proof. The main feature of Theorem 2.1 is that parity is “hidden” inside , which is given by an oracle for non-bipartite matching. * Research is supported by OTKA grants T 037547 and TS 049788, by European MCRTN Adonet, Contract Grant No. 504438 and by the Egerváry Research Group of the Hungarian Academy of Sciences. † The author is a member of the Egerváry Research Group (EGRES).     

Analysis of composition profiles to obtain interdiffusion coefficients in binary intermetallic compounds

Intermetallic compounds containing high concentrations of structural vacancies have made the determination of the interdiffusivity from the composition profile from a diffusion couple a confusing issue. In this paper, an exact procedure is formulated from fundamental principles. The only assumption made is the use of the Gibbs–Duhem relation. We show that the standard procedure for analysing composition profiles in diffusion couples slightly overestimates the interdiffusivity. We also show that the procedure put forward by Kim and Chang (Metall. Mater. Trans., 31A () 1519) to analyse the composition profiles in NiAl is incorrect near the stoichiometric composition where it seriously underestimates the interdiffusivity.     

Complete synchronization of symmetrically soupled sutonomous systems

In this article we derive conditions for complete synchronization of two symmetrically coupled identical systems of ordinary differential equations and differential-delay equations. Using Lyapunov function approach we give an estimate of the region of attraction of the synchronized solution. We also established that complete synchronization is robust with respect to small perturbations of the identical systems.     

Micros in mathematics education—Uses of spreadsheets in CAL

In this paper it is shown that teachers and students can study the mathematical problem through commercially available powerful spreadsheet software programs without being bogged down by the programming problem. It is illustrated by two examples. One is taken from a differentiable function the derivative of which is discontinuous at the origin. The other example uses Simpson's rule to find the area under the standard normal distribution.     

Interpretation of the stress dependence of creep by a mixed climb mechanism in TiAl

The behaviour of ordinary dislocations in TiAl alloy creep-deformed at 750°C has been investigated. Two alloys processed by the cast and powder metallurgy routes were crept under tensile stresses of 150 and 80?MPa, respectively. Transmission electron microscopy was performed on the crept samples to determine the characteristics of the dislocations. The stress dependence of the dislocation mechanisms was determined from stress jumps performed during creep deformation. Complementary in-situ heating experiments performed on previously crept samples are also presented. From these experimental investigations, it is shown that some ordinary dislocations move by a mixed climb mechanism for which the elementary process is the nucleation and the lateral propagation of a jog pair. The coherency between this mechanism and the determined activation parameters, as well as the driving force at its origin, are discussed.     

A dislocation-based model for creep recovery in ice

Creep recovery strain is significant in polycrystalline ice, and its stress dependence is strongly dependent on ice type and deformation history. Although it is generally recognized that creep recovery strain is largely attributable to dislocations, a dislocation-based model that rectifies the observed differences in two important ice types (freshwater and sea ice) has not previously emerged; and the development of such a model forms the goal of the present effort. The model considers basal dislocation distributions, employs a dislocation density–stress relationship from previous work, and uses an empirical expression for the decrease in slip-line spacing with increasing stress. The dislocation processes are taken to operate over a subgrain-sized domain, and the strain associated with the relative motion of neighbouring domains is considered. The model accounts for dislocation multiplication and the decrease in slip-line spacing if the applied stress is sufficiently high. The model explains the observed differences in creep recovery strain for freshwater and sea ice and adequately reproduces both the stress dependence and the limiting value of the experimentally observed behaviour. It also reproduces the shift from nonlinear to linear behaviour that has been observed in prestrain experiments on freshwater and sea ice cores.     

The stress-driven migration of point defects to a slowly moving crack

The migration kinetics of point defects near a slowly moving brittle crack are studied under the condition of pure drift. In the pure-drift approximation it is assumed that the point-defect flow in the vicinity of a crack tip is dominated by the elastic interaction between the stress field of the crack and a point defect and that concentration gradient effects can be neglected. While such a pure-drift approach has been shown to be useful to calculate the short-time diffusion kinetics of impurity-induced subcritical crack growth, previous applications are based on the drift solutions for a stationary crack. In the present paper, the first-order drift diffusion equation for a slowly moving crack at uniform velocity is solved. This yields the flow lines of the point defects and the impurity segregation rate directly in terms of the crack growth rate. The flow line patterns reveal important insights with respect to the point-defect migration kinetics near a steadily advancing crack. Although the calculation is entirely elastic, it is shown that the present drift model maintains some relevance also in the presence of a plastic zone ahead of the crack tip.