Computation of energy release rate using material differentiation of elastic BIE for 3-D elastic fracture

This paper deals with a novel approach, based on material differentiation of elastic BIE formulations, for the numerical computation of the energy release rate G along a crack front in 3-D elastic fracture problems. It is based upon the definition of G in terms of the material derivative of the potential energy at equilibrium W with respect to all possible regular virtual crack extensions. W can be formulated in terms of surface integrals; this fact in turn allows for a boundary-only formulation of its material derivative with respect to virtual crack extensions. The necessary step of computing the shape sensitivities of the boundary elastic variables is done by means of a derivative BIE. The latter results from a material differentiation of the primary elastic BIE, which is performed on a regularized (weakly singular) displacement BIE so that the process is mathematically sound. The unknowns of both primary and derivative BIEs are governed by the same integral operator, with obvious computational advantages. The present approach thus does not resort to any finite-difference evaluation of derivatives with respect to crack front perturbations. The implementation of the present method, including the key technical step of constructing appropriate vector interpolation functions for the transformation velocity associated with a virtual crack extension, is discussed. Finally, in order to demonstrate the potential of the proposed approach, numerical results are presented for two mode I examples where reference results are available for comparison: the round bar with a circular internal crack and the semielliptical surface crack, in both cases under uniform tension

Income composition and propensities to consume

So as to better understand households' consumption behaviour, the composition of incomes was not as regarded as wealth structure. Since the 80s in France, the former has dramatically changed though, retirement and unemployment transfers taking a heavier weight. Various reasons can justify that the income composition influences consumption. Aggregation of behaviours of different households with different propensity to consume is a first reason. A second one is that some incomes are more persistent and are consequently more consumed: a positive shock for these incomes is translated into a higher increase of permanent income. An illustration is proposed within the life-cycle model framework for both these justifications. Econometric estimations, with data from the national accounts at 1995 constant prices, show that the propensity to consume dependent wages, social transfers and self-employed incomes is higher that for other incomes. In comparison with other specifications which insist on wealth effects or interest rate effects, we find this result challenging. But, a future research using micro data would be most welcome to confirm it. Above all, the high propensity to consume self-employed incomes should be studied more precisely. And new national accounts will also bring another test of robustness for this result.propensity to consume, income composition, forecasting

Stability Analysis of Cell Dynamics in Leukemia

Cataloged from PDF version of article.In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized system around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations

Stability analysis of cell dynamics in leukemia

In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized system around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations. © 2012 EDP Sciences

PID controller design for fractional-order systems with time delays

Cataloged from PDF version of article.Classical proper PID controllers are designed for linear time invariant plants whose transfer functions are rational functions of s(alpha), where 0 < alpha < 1, and s is the Laplace transform variable. Effect of input-output time delay on the range of allowable controller parameters is investigated. The allowable PID controller parameters are determined from a small gain type of argument used earlier for finite dimensional plants. (C) 2011 Elsevier B.V. All rights reserved

Scaling behavior of the overlap quark propagator in Landau gauge

The properties of the momentum space quark propagator in Landau gauge are examined for the overlap quark action in quenched lattice QCD. Numerical calculations are done on three lattices with different lattice spacings and similar physical volumes to explore the approach of the quark propagator toward the continuum limit. We have calculated the nonperturbative momentum-dependent wave function renormalization function Z(p) and the nonperturbative mass function M(p) for a variety of bare quark masses and perform an extrapolation to the chiral limit. We find the behavior of Z(p) and M(p) are in reasonable agreement between the two finer lattices in the chiral limit, however the data suggest that an even finer lattice is desirable. The large momentum behavior is examined to determine the quark condensate.Comment: 9 pages, 5 figures, Revtex 4. Streamlined presentation, additional data. Final versio

On the Invariant Theory of Weingarten Surfaces in Euclidean Space

We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural functions and the normal curvature function satisfying a geometric differential equation. We apply these results to the special Weingarten surfaces: minimal surfaces, surfaces of constant mean curvature and surfaces of constant Gauss curvature.Comment: 16 page

Impaired musculoskeletal response to age and exercise in PPARβ(-/-) diabetic mice.

Fragility fractures are recognized complication of diabetes, but yet the underlying mechanisms remain poorly understood. This is particularly pronounced in type 2 diabetes in which the propensity to fall is increased but bone mass is not necessarily low. Thus, whether factors implicated in the development of insulin resistance and diabetes directly impact on the musculoskeletal system remains to be investigated. PPARβ(-/-) mice have reduced metabolic activity and are glucose intolerant. We examined changes in bone and muscle in PPARβ(-/-) mice and investigated both the mechanism behind those changes with age as well as their response to exercise. Compared with their wild type, PPARβ(-/-) mice had an accelerated and parallel decline in both muscle and bone strength with age. These changes were accompanied by increased myostatin expression, low bone formation, and increased resorption. In addition, mesenchymal cells from PPARβ(-/-) had a reduced proliferation capacity and appeared to differentiate into more of an adipogenic phenotype. Concomitantly we observed an increased expression of PPARγ, characteristic of adipocytes. The anabolic responses of muscle and bone to exercise were also diminished in PPARβ(-/-) mice. The periosteal bone formation response to direct bone compression was, however, maintained, indicating that PPARβ controls periosteal bone formation through muscle contraction and/or metabolism. Taken together, these data indicate that PPARβ deficiency leads to glucose intolerance, decreased muscle function, and reduced bone strength. On a molecular level, PPARβ appears to regulate myostatin and PPARγ expression in muscle and bone, thereby providing potential new targets to reverse bone fragility in patients with metabolic disturbances