Healthy longevity from incidence-based models: More kinds of health than stars in the sky

Background. Healthy longevity (HL) is an important measure of the prospects for quality of life in ageing societies. Incidence-based (cf. prevalence-based) models describe transitions among age classes and health stages. Despite the probabilistic nature of those transitions, analyses of healthy longevity have focused persistently on means ("health expectancy"), neglecting variances and higher moments. Objectives. Our goal is a comprehensive methodology to analyse HL in terms of any combination of health stages and age classes, or of transitions among health stages, or of values (e.g., quality of life) associated with health stages or transitions. Methods. We construct multistate Markov chains for individuals classified by age and health stage and use Markov chains with rewards to compute all moments of HL. Results. We present a new and straightforward algorithm to create the multistate reward matrices for occupancy, transitions, or values associated with occupancy or transitions. As an example, we analyse a published model for colorectal cancer. The possible definitions of HL in this simple model outnumber the stars in the visible universe. Our method can analyse any of them; we show four examples: longevity without abnormal cells, cancer-free longevity, and longevity with cancer before or after a critical age. Contribution. Our methods make it possible to analyse any incidence-based model, with any number of health stages, any pattern of transitions, and any kind of values assigned to stages. It is easily computable, requires no simulations, provides all the moments of healthy longevity, and solves the inhomogeneity problem.

Influence of Residual Stress Around Constituent Particles on Recrystallization and Grain Growth in Al-Mn-Based Alloy during Annealing

Effect of the residual stress on the recovery and recrystallization behaviors of the cold-rolled AA3003 aluminum alloy was investigated. The evolution of deformed microstructure and dislocation density characterized by TEM and Synchrotron X-ray measurements found that the change in the ratio between low angle grain boundaries (LAGBs) and high angle grain boundaries (HAGBs) during annealing is varied depending on the initial dislocation density, where the value of HAGB/LAGBs ratio is amounted to be about 0.8 at maximum. The nucleation and growth rate of the recrystallized grains are strongly dependent on the net driving pressure associated with dislocation density increased by the amount of reduction. EBSD analysis revealed that the deformed zone composed of the fine equi-axed grains with large misorientation angles would be formed in the vicinity of the constituent particles, which is consistent with the region of the large residual stress and total displacement predicted by Eshelby inhomogeneity problem under cold rolling condition.

Eshelby's problem of polygonal inclusions with polynomial eigenstrains in an anisotropic magneto-electro-elastic full plane

This paper presents a closed-form solution for the arbitrary polygonal inclusion problem with polynomial eigenstrains of arbitrary order in an anisotropic magneto-electro-elastic full plane. The additional displacements or eigendisplacements, instead of the eigenstrains, are assumed to be a polynomial with general terms of order M + N . By virtue of the extended Stroh formulism, the induced fields are expressed in terms of a group of basic functions which involve boundary integrals of the inclusion domain. For the special case of polygonal inclusions, the boundary integrals are carried out explicitly, and their averages over the inclusion are also obtained. The induced fields under quadratic eigenstrains are mostly analysed in terms of figures and tables, as well as those under the linear and cubic eigenstrains. The connection between the present solution and the solution via the Green's function method is established and numerically verified. The singularity at the vertices of the arbitrary polygon is further analysed via the basic functions. The general solution and the numerical results for the constant, linear, quadratic and cubic eigenstrains presented in this paper enable us to investigate the features of the inclusion and inhomogeneity problem concerning polynomial eigenstrains in semiconductors and advanced composites, while the results can further serve as benchmarks for future analyses of Eshelby's inclusion problem.

On the absence of the Eshelby property for slender non-ellipsoidal inhomogeneities

The method of matched asymptotic expansions is applied to construct an asymptotic model for the Eshelby inhomogeneity problem in the case of a slender sufficiently rigid inhomogeneity. On the basis of the obtained asymptotic model, it is shown that the only infinitesimal perturbations of the elongated ellipsoid that preserve constancy of stresses inside the inhomogeneity are those into another elongated ellipsoid.