Nonlocal effects in the continuum theory of shear localisation in 2d foams

Goyon et al. [J. Goyon, A. Colin, G. Ovarlez, A. Ajdari and L. Bocquet, Nature 454 (2008) p. 84] have shown that nonlocal effects in the rheology of foams may be accounted for by a modification of the standard (Herschel–Bulkley) model. Here we consider the effects of this modification on the continuum theory of 2d shear localisation. We compute results for various examples, showing that the localisation length is increased, and explore the limiting cases of zero and infinite nonlocality length ξ. Velocity profiles are shown to take an exponential form in the case where ξ is large. As the formulation of the nonlocal continuum model presented in this article is general, it may also be directly applicable to other complex fluids.     

Wentzel–Kramers–Brillouin solution of cut-off frequency for horizontal shear (SH) waves in various inhomogeneous thin films

The Wentzel–Kramers–Brillouin method is employed to study the cut-off frequencies of the horizontal shear waves in a freestanding functionally graded piezoelectric–piezomagnetic material film with the electrically and magnetically open boundary conditions. An analytical solution, which could be used in analyzing the problems of various functionally graded materials, is proven to have high precision by analytical analysis and a numerical example. The results reveal that the set of cut-off frequencies is a series of approximate arithmetic progressions. A theoretical foundation based on the relationship between the cut-off frequencies and the materials’ gradient property is established for nondestructive evaluation.     

Deformation twinning of Bi–Sb solid alloy formed under a strong gravitational field

We performed an ultracentrifuge experiment on Bi–Sb alloy. Deformation twins with misorientations of about 90° were observed in the low-gravitational region where grain refinement had not occurred. The twins were thicker than the conventional deformation twins and their thickness was proportional to the gravitational field. We found that the minimum gravitational field required for grain refinement was 0.17 × 10⁶ G at 240°C for periods <10 h.     

Twinning behaviour of TWIP steel studied by Taylor factor analysis

The twinning behaviour of Twinning-induced plasticity (TWIP) steel has been studied by analysing the grain orientation and the Taylor factor, based on microstructural and electron backscatter diffraction device observations. It is demonstrated that the Taylor factor can give an important guideline for determining the deformation mode of TWIP steel. The higher the Taylor factor, the easier the formation of twins and thus a tendency for the deformation mode to be mechanical twinning, while a low Taylor factor corresponds to a slip deformation mode. When the loading temperature is relatively low, the high Taylor factor regions increase and thus deformation twinning becomes easier while slip becomes more difficult, leading to increased tensile stress and decreased elongation.     

On the plasticity event in metallic glass

Based on a systematic molecular dynamics analysis, this study reveals that plastic deformation of metallic glass is not through a uniform configuration change but via many localized plasticity events. These events are manifested by the atomic clusters of high kinetic energy and high strain rate, emerging even in the elastic deformation regime. The life of such a plasticity event is on the order of 10^?12?s, during which the distribution of kinetic energy follows a power law. The study shows that yielding in metallic glass occurs at the sudden surge point of the number of plasticity events. In the steady plastic deformation regime, the continuous nucleation and annihilation of the plastic events lead to a steady flow stress and stabilized total potential energy.     

The relationship between dynamic strain aging and serrated flow behaviour in magnesium alloy

The relationship between dynamic strain ageing (DSA) and serrated flow has been investigated via alternately switching strain rates at various temperatures in a Mg–3Nd–1Zn alloy. The results reveal that serrated flow is enhanced with decreasing strain rate and increasing temperature and tends to vanish, while the DSA continually intensifies as revealed by a higher flow stress even after the serration flow disappears. A mechanism is proposed, which could explain some abnormal deformation behaviour, such as a negative strain rate sensitivity and thermal hardening.     

Two-matrix orthogonal rotation procedures

Examples are presented in which it is either desirable or necessary to transform two sets of orthogonal axes to simple structure positions by means of the same transformation matrix. A solution is then outlined which represents a two-matrix extension of the general orthomax orthogonal rotation criterion. In certain circumstances, oblique two-matrix solutions are possible using the procedure outlined and the Harris-Kaiser [1964] logic. Finally, an illustrative example is presented in which the preceding technique is applied in the context of an inter-battery factor analysis.The work reported herein was supported by Grant S72-1886 from the Canada Council. The author acknowledges the helpful contributions of Nancy Reid and Lawrence Ward to parts of this paper.     

Behavioral momentum: the effects of the temporal separation of rates of reinforcement.

In Part 1 of the experiment, rats responded under a variable-interval (VI) 30-s schedule and a VI 120-s schedule, with each in effect for a block of consecutive sessions. That is, the two VI schedules were presented in successive conditions. In Part 2 the VI schedules alternated each day, and in Part 3 the schedules alternated within the session as a multiple schedule. For half of the rats in Parts 1 and 2, the VI schedule alternated every few minutes within the session with a stimulus that signaled extinction. For each part, once response rates had stabilized, resistance to change was measured by prefeeding and extinction. When the schedules were examined in successive conditions (Part 1), resistance to extinction was greater under the VI 120-s schedule of reinforcement than under the VI 30-s schedule, but no consistent differences in resistance to prefeeding were observed between the two VI schedules. When the VI schedules alternated each day (Part 2), resistance to extinction was greater under the VI 120-s schedule. However, no consistent differences in resistance to prefeeding were observed between the VI schedules without extinction in Group A, but resistance to prefeeding was greater under the VI 30-s schedule for rats with the added extinction component in Group B. When the VI schedules alternated within the session as a multiple schedule (Part 3), resistance to extinction and resistance to prefeeding were greater under the VI 30-s schedule. The data suggest that different rates of reinforcement, and their accompanying discriminative stimuli, must be compared within the same session (or at least on alternate days) to produce data consistent with the behavioral momentum model.     

Estimation of interhemispheric dynamics from simple unimanual reaction time to extrafoveal stimuli

This essay reviews research on interhemispheric transfer time derived from simple unimanual reaction time to hemitachistoscopically presented visual stimuli. Part 1 reviews major theoretical themes including (a) the significance of the eccentricity effect on interhemispheric transfer time in the context of proposed underlying neurohistological constraints; (b) the significance of gender differences in interhemispheric transfer time and findings in dyslexics and left-handers in the context of a fetal brain testosterone model; and (c) the significance of complexity effects on interhemispheric transfer time in a context of dynamic vs. hard-wired concepts of the underlying interhemispheric communication systems. Part 2 consists of a meta-analysis of 49 published behavioral experiments, in view of drawing a portrait of the best set of experimental conditions apt to produce salient, reliable, and statistically significant measures of interhemispheric transfer time, namely (a) index rather than thumb response, (b) low rather than high target luminance, (c) short rather than prolonged target display, and (d) very eccentric rather than near-foveal stimulus location. Part 3 proposes a theoretical model of interhemispheric transfer time, postulating the measurable existence of fast and slow interhemispheric channels. The proposed mechanism's evolutionary adaptive value, the neurophysiological evidence in its support, and favorable functional evidence from studies of callosotomized patients are then presented followed by proposals for critical experimental tests of the model.