Yield functions for porous materials with cubic symmetry using different definitions of yield

Plastic yield criteria for porous ductile materials are explored numerically using the finite-element technique. The cases of spherical voids arranged in simple cubic, body-centred cubic and face-centred cubic arrays are investigated with void volume fractions ranging from 2 % through to the percolation limit (over 90 %). Arbitrary triaxial macroscopic stress states and two definitions of yield are explored. The numerical data demonstrates that the yield criteria depend linearly on the determinant of the macroscopic stress tensor for the case of simple-cubic and body-centred cubic arrays - in contrast to the famous Gurson-Tvergaard-Needleman (GTN) formula - while there is no such dependence for face-centred cubic arrays within the accuracy of the finite-element discretisation. The data are well fit by a simple extension of the GTN formula which is valid for all void volume fractions, with yield-function convexity constraining the form of the extension in terms of parameters in the original formula. Simple cubic structures are more resistant to shear, while body-centred and face-centred structures are more resistant to hydrostatic pressure. The two yield surfaces corresponding to the two definitions of yield are not related by a simple scaling.

Mixed order parameters, accidental nodes and broken time reversal symmetry in organic superconductors: a group theoretical analysis

We present a group theoretical analysis of several classes of organic superconductor. We predict that highly frustrated organic superconductors, such as K-(ET)(2)Cu-2(CN)(3) (where ET is BEDT-TTF, bis(ethylenedithio) tetrathiafulvalene) and beta'-[Pd(dmit)(2)](2)X, undergo two superconducting phase transitions, the first from the normal state to a d-wave superconductor and the second to a d + id state. We show that the monoclinic distortion of K-(ET)(2)Cu(NCS)(2) means that the symmetry of its superconducting order parameter is different from that of orthorhombic-K-(ET)(2)Cu[N(CN)(2)] Br. We propose that beta'' and theta phase organic superconductors have d(xy) + s order parameters.

On the modelling of wave breaking and set-up on coral reefs

An extended refraction-diffraction equation [Massel, S.R., 1993. Extended refraction-diffraction equation for surface waves. Coastal Eng. 19, 97-126] has been applied to predict wave transformation and breaking as well as wave-induced set-up on two-dimensional reef profiles of various shapes. A free empirical coefficient alpha in a formula for the average rate of energy dissipation [epsilon(b)] = (alpha rho g omega/8 pi)(root gh/C)(H-3/h) in the modified periodic bore model was found to be a function of the dimensionless parameter F-c0 = (g(1.25)H(0)(0.5)T(2.5))/h(r)(1.75), proposed by Gourlay [Gourlayl M.R., 1994. Wave transformation on a coral reef. Coastal Eng. 23, 17-42]. The applicability of the developed model has been demonstrated for reefs of various shapes subjected to various incident wave conditions. Assuming proposed relationships of the coefficient alpha and F-c0, the model provides results on wave height attenuation and set-up elevation which compare well with experimental data. (C) 2000 Elsevier Science B.V. All rights reserved.

Dynamics of a transient wave group breaking on a beach

New experimental data are presented on the dynamics of a transient wave group breaking on a beach. The transient group is tracked during shoaling and wave breaking, together with the long waves forced during those processes. High spatial sampling enables novel resolution of the evolution of the wave envelope during breaking and the correlation between the envelope and the long waves. The data show a strong dynamic long wave setup in front of the group in shallow water. The amplitude of the dynamic setup is likely to be a function of beach slope, and larger on steeper beaches.

Adaptive back-propagation in on-line learning of multilayer networks

An adaptive back-propagation algorithm is studied and compared with gradient descent (standard back-propagation) for on-line learning in two-layer neural networks with an arbitrary number of hidden units. Within a statistical mechanics framework, both numerical studies and a rigorous analysis show that the adaptive back-propagation method results in faster training by breaking the symmetry between hidden units more efficiently and by providing faster convergence to optimal generalization than gradient descent.

On-line learning with adaptive back-propagation in two-layer networks

An adaptive back-propagation algorithm parameterized by an inverse temperature 1/T is studied and compared with gradient descent (standard back-propagation) for on-line learning in two-layer neural networks with an arbitrary number of hidden units. Within a statistical mechanics framework, we analyse these learning algorithms in both the symmetric and the convergence phase for finite learning rates in the case of uncorrelated teachers of similar but arbitrary length T. These analyses show that adaptive back-propagation results generally in faster training by breaking the symmetry between hidden units more efficiently and by providing faster convergence to optimal generalization than gradient descent.

Lobe interactions within the thallus margin and the maintenance of symmetry in the lichen Parmelia conspersa (Ehrh. ex Ach.)Ach.

This study determined whether the radial growth of lobes of the foliose lichen Parmelia conspersa (Ehrh. ex Ach.)Ach. was influenced by the radial growth and morphology of their closest neighbours and whether such interactions influence thallus symmetry. The radial growth and morphology of a sample of adjacent lobes from six thalli was measured. Positive correlations were observed between radial growth and lobe width in three thalli and with the degree of bifurcation of the lobe in two thalli. Negative correlations between the radial growth of adjacent lobes were observed in four thalli suggesting that faster growing lobes may inhibit the growth of their neighbours.Lobes glued next to individual lobes had no signifiacnt effect on the radial growth of wide or narrow lobes. Lobes glued 1-2 mm in front of their neighbours exhibited an intital phase of increased radial growth and then a phase of slower growth. Radial growth decreased when the lobes were glued 2 mm behind their neighbours and these lobes were essentially eliminated by the growth of the adjacent lobes. The data suggest that lobe interactions may incresae lobe growth variation within a thallus. However, the decrease in radial growth of lobes which protrude from the margin and the elimination of slower growing lobes may help to maintain thallus symmetry.

Lobe growth variation and the maintenance of symmetry in foliose lichen thalli

The aim of this study was to determine how thallus symmetry could be maintained in foliose lichens when variation in the growth of individual lobes may be high. Hence, the radial growth of a sample of lobes was studied monthly, over 22 months, in 7 thalli of Parmelia conspersa (Ehrh. Ex Ach.) Ach. And 5 thalli of P. glabratula ssp fuliginosa (fr. ex Duby) Laund. The degree of variation in the total radial growth of different lobes within a thallus over 22 months varied between thalli. Individual lobes showed a fluctuating pattern of radial growth from month to month with alternating periods of fast and slow growth. Monthly variations in radial growth of different lobes were synchronized in some but not in all thalli. Few significant correlations were found between the radial growth of individual lobes and total monthly rainfall or shortwave radiation. The levels of ribitol, arabitol and mannitol were measured in individual lobes. All three polyols varied significantly between lobes within a thallus suggesting that variations in algal phostosynthesis and in the partitioning of fungal polyols may contribute to lobe growth variation. The effect on thallus symmetry of lobes which grew radially either consistently faster or slower than average was studied. Slow growing lobes were overgrown, and gaps in the perimeter were eliminated by the growth of neighbouring lobes, in approximately 7 to 9 months. However, a rapidly growing lobe, with its neighbours removed on either side, continued to grow radially at the same rate as rapidly growing control lobes. The results suggested that lobe growth variation results from a combination of factors which may include the origin of the lobes, lobe morphology and the patterns of algal cell division and hyphal elongation in different lobes. No convincing evidence was found to suggest that exchange of carbohydrate occurred between lobes which would tend to equalize their radial growth. Hence, the fluctuating pattern of lobe growth observed may be sufficient to maintain a degree of symmetry in most thalli. In addition, slow growing lobes would tend to be overgrown by faster growing neighbours thus preventing the formation of indentations in the thallus perimeter.