Bifurcation in growth patterns for arrays of parallel Griffith, edge and sliding cracks

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the dipole asymptotic or pseudo-traction method. The nonlinear parameter for the problem is the crack length/ spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if lambda is larger than a critical value lambda(cr) (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of lambda(cr) decreases monotonically from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The critical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of lambda(cr) for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium. The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton-Rogers-Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton-Rogers-Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton-Rogers-Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. (C) 1997 by John Wiley & Sons, Ltd.

The intersection problem for star designs

We determine those triples (m, II, k) of integers for which there are two m-star designs on the same n-set having exactly k stars in common.

The meeting place problem: Salience and search.

The notion of salience was developed by Schelling in the context of the meeting-place problem of locating a partner in the absence of a pre-agreed meeting place. In this paper, we argue that a realistic specification of the meeting place problem involves allowing a strategy of active search over a range of possible meeting places. We solve this extended problem, allowing for extensions such as repeated play, search costs and asymmetric payoffs. The result is a considerably richer, but more complex, notion of salience. (C) 1998 Elsevier Science B.V.

Adjustment to a low-control situation: Reexamining the role of coping responses

The aim of the study was to test a revised conceptualization of the role of coping in adjustment to a low-control stressor-women's adjustment to a failed in vitro fertilization (NF) attempt. Data were collected prior to the IVF treatment (Time I) and twice after the failed NF attempt (1 to 2 weeks after finding out the results, n = 171, and fi weeks later, n = 139). Initial adjustment was assessed at Time I, whereas measures of coping and both self-report and partner ratings of adjustment were obtained at Times ? and 3. As predicted, escapist strategies and problem-management strategies (mainly at Time ?) were associated with poor adjustment, whereas problem-appraisal coping was associated with better adjustment., There was also support for the proposed positive relationship between adjustment and emotional approach coping (on self-report adjustment).

Evolution of three-dimensional folds for a non-Newtonian plate in a viscous medium

We derive analytical solutions for the three-dimensional time-dependent buckling of a non-Newtonian viscous plate in a less viscous medium. For the plate we assume a power-law rheology. The principal, axes of the stretching D-ij in the homogeneously deformed ground state are parallel and orthogonal to the bounding surfaces of the plate in the flat state. In the model formulation the action of the less viscous medium is replaced by equivalent reaction forces. The reaction forces are assumed to be parallel to the normal vector of the deformed plate surfaces. As a consequence, the buckling process is driven by the differences between the in-plane stresses and out of plane stress, and not by the in-plane stresses alone as assumed in previous models. The governing differential equation is essentially an orthotropic plate equation for rate dependent material, under biaxial pre-stress, supported by a viscous medium. The differential problem is solved by means of Fourier transformation and largest growth coefficients and corresponding wavenumbers are evaluated. We discuss in detail fold evolutions for isotropic in-plane stretching (D-11 = D-22), uniaxial plane straining (D-22 = 0) and in-plane flattening (D-11 = -2D(22)). Three-dimensional plots illustrate the stages of fold evolution for random initial perturbations or initial embryonic folds with axes non-parallel to the maximum compression axis. For all situations, one dominant set of folds develops normal to D-11, although the dominant wavelength differs from the Biot dominant wavelength except when the plate has a purely Newtonian viscosity. However, in the direction parallel to D-22, there exist infinitely many modes in the vicinity of the dominant wavelength which grow only marginally slower than the one corresponding to the dominant wavelength. This means that, except for very special initial conditions, the appearance of a three-dimensional fold will always be governed by at least two wavelengths. The wavelength in the direction parallel to D-11 is the dominant wavelength, and the wavelength(s) in the direction parallel to D-22 is determined essentially by the statistics of the initial state. A comparable sensitivity to the initial geometry does not exist in the classic two-dimensional folding models. In conformity with tradition we have applied Kirchhoff's hypothesis to constrain the cross-sectional rotations of the plate. We investigate the validity of this hypothesis within the framework of Reissner's plate theory. We also include a discussion of the effects of adding elasticity into the constitutive relations and show that there exist critical ratios of the relaxation times of the plate and the embedding medium for which two dominant wavelengths develop, one at ca. 2.5 of the classical Biot dominant wavelength and the other at ca. 0.45 of this wavelength. We propose that herein lies the origin of parasitic folds well known in natural examples.

Some new examples for nonuniqueness of the evolution problem of harmonic maps

We find some new examples to show nonuniquence for the heat flow of harmonic maps where weak solutions satisfy the same monotonicity property.

Bioimpedance: Is it a predictor of true water volume?

Bioelectrical impedance analysis (BIA) has been reported to be insensitive to changes in water volumes in individual subjects, This study was designed to investigate the effect on the intra- and extracellular resistances (Ri and Re) of the segments of subjects for whom body water was changed without significant change to the total amount of electrolyte in the respective fluids, Twelve healthy adult subjects were recruited. Ri and Re of the leg, trunk, and arm of the subjects were determined from BIA measures prior to commencement of two separate studies that involved intervention, resulting in a loss/gain of body water effected either bt a sauna followed by water intake (study 1) or by ingestion (study 2). Ri and Re of the segments were also determined at a number of times following these interventions, The mean change in body water, expressed as a percentage of body weight, was 0.9% in study 1 and 1.25% in study 2. For each study, the results for each subject were normalized for each limb to the initial (prestudy) value and then the normalized results for each segment were pooled for all subjects, ANOVA of these pooled results failed to demonstrate any significant differences between the normalized mean values of Ri or Re of the segments measured through the course of each study, The failure to detect a change in Ri or Re is explained in terms of the basic theory of BIA.

Protein sequence threading, the alignment problem, and a two-step strategy

Conventionally, protein structure prediction via threading relies on some nonoptimal method to align a protein sequence to each member of a library of known structures. We show how a score function (force field) can be modified so as to allow the direct application of a dynamic programming algorithm to the problem. This involves an approximation whose damage can be minimized by an optimization process during score function parameter determination. The method is compared to sequence to structure alignments using a more conventional pair-wise score function and the frozen approximation. The new method produces results comparable to the frozen approximation, but is faster and has fewer adjustable parameters. It is also free of memory of the template's original amino acid sequence, and does not suffer from a problem of nonconvergence, which can be shown to occur with the frozen approximation. Alignments generated by the simplified score function can then be ranked using a second score function with the approximations removed. (C) 1999 John Wiley & Sons, Inc.

Percolative fragmentation of char particles during gasification

Percolative fragmentation was confirmed to occur during gasification of three microporous coal chars. Indirect evidence obtained by the variation of electrical resistivity (ER) with conversion was supported by direct observation of numerous fragments during gasification. The resistivity increases slowly at low conversions and then sharply after a certain conversion value, which is a typical percolation phenomenon suggesting the occurrence of internal fragmentation at high conversion. Two percolation models are applied to interpret the experimental data and determine the percolation threshold. A percolation threshold of 0.02-0.07 was found, corresponding to a critical conversion of 92-96% for fragmentation. The electrical resistivity variation at high conversions is found to be very sensitive to diffusional effects during gasification. Partially burnt samples with a narrow initial particle size range were also observed microscopically, and found to yield a large number of small fragments even when the particles showed no disintegration and chemical control prevailed. It is proposed that this is due to the separation of isolated clusters from the particle surface. The particle size distribution of the fragments was essentially independent of the reaction conditions and the char type, and supported the prediction by percolation theory that the number fraction distribution varies linearly with mass in a log-log plot. The results imply that perimeter fragmentation would occur in practical combustion systems in which the reactions are strongly diffusion affected.

The clinical value compass: Achieving benchmarking and quality improvement in aged care

Quality measurement and benchmarking in aged cave presents several challenges. A model which addresses this by linking four dimensions of outcomes has been developed - the Clinical Value Compass (CVC). A CVC was developed for stroke rehabilitation and measured across four sites. The CVC teas well accepted by the treatment teams and proved practical to measure. The results revealed differences in practices and client groups that led to a closer analysis of process and subsequent changes in these processes. Remeasuring of the CVC is required to demonstrate improved outcomes arising from these process changes.

Soil carbon determination by high temperature combustion - A comparison with dichromate oxidation procedures and the influence of charcoal and carbonate carbon on the measured value

The measurement of organic carbon in soils has traditionally used dichromate oxidation procedures including the Wakley and Black and the Heanes methods. The measurement of carbon in soils by high temperature combustion is now widely used providing a rapid automated procedure without the use of toxic chemicals. This procedure however measures total carbon thus requiring some means of correction for soil samples containing carbonate and charcoal forms of carbon. This paper examines the effects of known additions of charcoal to a range of soil types on the results obtained by the Walkley and Black, Heanes and combustion methods. The results show, that while the charcoal carbon does not react under Walkley and Black conditions, some proportion does so with the Heanes method. A comparison of six Australian Soil and Plant Analysis Council reference soil samples by the three methods showed good agreement between the Heanes method, the combustion method and only slightly lower recoveries by the Walkley and Black procedure. Carbonate carbon will cause an overestimation of soil organic carbon by the combustion method thus requiring a separate determination of carbonate carbon to be applied as a correction. This work shows that a suitable acid pre-treatment of alkaline soils in the sample boats followed by a drying step eliminates the carbonate carbon prior to combustion and the need for an additional measurement. The measurement of carbon in soils by high temperature combustion in an oxygen atmosphere has been shown to be a rapid and reliable method capable of producing results in good agreement with one of the established dichromate oxidation procedures.

Numerical modelling of single-layer folding: clarification of an issue regarding the possible effect of computer codes and the influence of initial irregularities

The influence of initial perturbation geometry and material propel-ties on final fold geometry has been investigated using finite-difference (FLAC) and finite-element (MARC) numerical models. Previous studies using these two different codes reported very different folding behaviour although the material properties, boundary conditions and initial perturbation geometries were similar. The current results establish that the discrepancy was not due to the different computer codes but due to the different strain rates employed in the two previous studies (i.e. 10(-6) s(-1) in the FLAC models and 10(-14) s(-1) in the MARC models). As a result, different parts of the elasto-viscous rheological field were bring investigated. For the same material properties, strain rate and boundary conditions, the present results using the two different codes are consistent. A transition in Folding behaviour, from a situation where the geometry of initial perturbation determines final fold shape to a situation where material properties control the final geometry, is produced using both models. This transition takes place with increasing strain rate, decreasing elastic moduli or increasing viscosity (reflecting in each case the increasing influence of the elastic component in the Maxwell elastoviscous rheology). The transition described here is mechanically feasible but is associated with very high stresses in the competent layer (on the order of GPa), which is improbable under natural conditions. (C) 2000 Elsevier Science Ltd. All rights reserved.