A new look at energy release rates for quasistatically propagating cracks in inelastic materials

A mapping technique is used to derive an integral expression for the energy release rate for a quasistatically propagating crack. The derivation does not depend on any assumptions in regard to the contitutive behavior of the material. It leads to a contour integral around the crack tip, plus an area integral over the region enclosed by this contour. Only the stress and displacement fields appear in the integrands. Although for stationary crack solutions known to the authors the area integral is not convergent, for propagating crack solutions in elastoplastic material, the integrals are convergent, and lead to zero energy release rate. This confirms conclusions by Rice from an independent point of view.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42773/1/10704_2004_Article_BF00012388.pd

Funding approaches for mental health services : Is there still a role for clustering?

Funding for mental health services in England faces many challenges including operating under financial constraints where it is not easy to demonstrate the link between activity and funding. Mental health services need to operate alongside and collaborate with acute hospital services where there is a well-established system for paying for activity. The funding landscape is shifting at a rapid pace and we outline the distinctions between the three main options – block contracts, episodic payment and capitation. Classification of treatment episodes via clustering presents an opportunity to demonstrate activity and reward it within these payment approaches. We have been engaged in research to assess how well the clustering system is performing against a number of fundamental criteria. Clusters need to be reliably recorded, to correspond to health needs, and to treatments that require roughly similar resources. We find that according to these criteria, clusters are falling short of providing a sound basis for measuring and financing services. Yet, we argue, it is the best available option and is essential for a more transparent funding approach for mental health to demonstrate its claim on resources, and that, as such, clusters should be a starting point for evolving a better funding system

Simple deterministic dynamical systems with fractal diffusion coefficients

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic scattering process of the map can be changed by a control parameter. This induces a parameter dependence for the macroscopic diffusion coefficient. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match to the ones of the simple phenomenological diffusion equation. Our main result is that the difffusion coefficient exhibits a fractal structure by varying the system parameter. To understand the origin of this fractal structure, we give qualitative and quantitative arguments. These arguments relate the sequence of oscillations in the strength of the parameter-dependent diffusion coefficient to the microscopic coupling of the single scatterers which changes by varying the control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.

Statistical Theory of Spin Relaxation and Diffusion in Solids

A comprehensive theoretical description is given for the spin relaxation and diffusion in solids. The formulation is made in a general statistical-mechanical way. The method of the nonequilibrium statistical operator (NSO) developed by D. N. Zubarev is employed to analyze a relaxation dynamics of a spin subsystem. Perturbation of this subsystem in solids may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between the particles or with a thermal bath (lattice). The generalized kinetic equations were derived previously for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. In this paper, these results are used to describe the relaxation and diffusion of nuclear spins in solids. The aim is to formulate a successive and coherent microscopic description of the nuclear magnetic relaxation and diffusion in solids. The nuclear spin-lattice relaxation is considered and the Gorter relation is derived. As an example, a theory of spin diffusion of the nuclear magnetic moment in dilute alloys (like Cu-Mn) is developed. It is shown that due to the dipolar interaction between host nuclear spins and impurity spins, a nonuniform distribution in the host nuclear spin system will occur and consequently the macroscopic relaxation time will be strongly determined by the spin diffusion. The explicit expressions for the relaxation time in certain physically relevant cases are given.Comment: 41 pages, 119 Refs. Corrected typos, added reference

Synthetic control over orientational degeneracy of spacer cations enhances solar cell efficiency in two-dimensional perovskites

Two-dimensional perovskites have emerged as more intrinsically stable materials for solar cells. Chemical tuning of spacer organic cations has attracted great interest due to their additional functionalities. However, how the chemical nature of the organic cations affects the properties of two-dimensional perovskites and devices is rarely reported. Here we demonstrate that the selection of spacer cations (i.e., selective fluorination of phenethylammonium) affects the film properties of two-dimensional perovskites, leading to different device performance of two-dimensional perovskite solar cells (average n = 4). Structural analysis reveals that different packing arrangements and orientational disorder of the spacer cations result in orientational degeneracy and different formation energies, largely explaining the difference in film properties. This work provides key missing information on how spacer cations exert influence on desirable electronic properties and device performance of two-dimensional perovskites via the weak and cooperative interactions of these cations in the crystal lattice