On the possibility of elastic strain localisation in a fault

The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment-or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.

Post-Fordism, the welfare state and the personal social services: A comparison of Australia and Britain

The Post-Fordist welfare state thesis locates contemporary social welfare change within a wider analysis of the transformation of capitalist accumulation regimes. Whilst this analysis is useful in directing attention to macro socio-economic change, it has for the most part contained three shortcomings. First, the Post-Fordist thesis has overemphasized the role of historical 'breaks' in the development of social welfare as it purportedly passes from Fordism to Post-Fordism. Second, the thesis has assumed a degree of convergence between welfare states as a result of global economic forces. In doing so, it has underemphasized the mediating impact of existing institutional arrangements within nations. Third, the thesis has assumed, rather than demonstrated, the specific changes which are alleged to be taking place in various fields of social welfare. As a consequence, aspects of continuity in social welfare have been neglected. These three lacunae are addressed through a comparative analysis of developments in the personal social services in Australia and Britain. Services to older people are employed as the specific context of comparison in relation to three dimensions of measuring transformation along a Post-Fordist trajectory: a shift from a unitary economy to a mixed economy of service provision; changes in the model of service delivery and consumption; and strengthening the governance function of the central state. This comparative analysis suggests the need for refinement of the Post-Fordist welfare state thesis concerning the restructuring of social welfare and its impact on the personal social services.

The Debreu Gap Lemma and some generalizations

In this paper we study the Debreu Gap Lemma and its generalizations to totally ordered sets more general than (R, less than or equal to). We explain why it is important in economics to study utility functions which may not be real-valued and we build the foundations of a theory of continuity of such generalized utility functions. (C) 2004 Published by Elsevier B.V.