The stress intensity factor for non-smooth fractures in antiplane elasticity

Motivated by some questions arising in the study of quasistatic growth in brittle fracture, we investigate the asymptotic behavior of the energy of the solution u of a Neumann problem near a crack in dimension 2. We consider non smooth cracks K that are merely closed and connected. At any point of density 1/2 in K, we show that the blow-up limit of u is the usual “cracktip” function ${C\sqrt{r}\sin(\theta/2)}$ , with a well-defined coefficient (the “stress intensity factor” or SIF). The method relies on Bonnet’s monotonicity formula (Bonnet, Variational methods for discontinuous structures, pp. 93–103. Birkhäuser, Basel, 1996) together with Γ-convergence techniques.     

Nucleation of Polypropylene with Gold Nanoparticles. Part 1: Introduction of Sandwich Method for Evaluation of Very Weak Nucleation Activity

Although gold particles are known to nucleate isotactic polypropylene (PP), the nucleating effect of chemically pure 5 nm Au, prepared in vacuum sputter coater, was found to be hardly observable. In order to detect such a weak effect, we deposited a homogeneous layer of Au nanoparticles between thin PP films and evaluated the nucleation activity by a combination of three independent methods: polarized light microscopy (PLM), differential scanning calorimetry (DSC), and 2D wide-angle X-ray scattering (2D-WAXS). This new technique, which was called sandwich method, allowed us to demonstrate that gold nanoparticles were able to nucleate PP crystallization, although the effect was much weaker than that produced by commercial α-nucleant [1,2,3,4-bis(3,4-dimethylbenzylidene)sorbitol] and β-nucleant (N,N-Dicyclohexyl-2,6-naphthalene dicarboxamide). The sandwich method appeared to be quite universal and applicable for any micro-sized nucleants or nanonucleants.     

Unprecedented reaction course of 1-phenyl-2H,6H-imidazo[1,5-c]quinazoline-3,5-dione with 3-M excess of ethylene oxide

Structural Chemistry - The reaction of 1-phenyl-2H,6H-imidazo[1,5-c]quinazolino-3,5-dione (4) with 3-molar excess ethylene oxide was described. The resulting product was characterized by...     

Quantization of first-class constraints with structure functions

As part of a program to desuperize BRST symmetries, we show how to translate the BRST construction completely in terms of standard symplectic geometry in the case where the constraints are derived from a foliation on a configuration space. The consequences of this approach on quantization are investigated. As a corollary, we solve (in a restricted setting) the problem of how to deal in quantization with (globally independent) first-class constraints with structure functions rather than structure constants.     

Influence of the refractive index and dispersion of spectacle lens on its imaging properties

The paper shows an influence of the refractive index and dispersion of the spectacle lens on its imaging properties. Relations are presented for calculation of radii of curvature of anastigmatic spectacle lenses and their chromatic aberration. Moreover, the formulas are derived for calculation of the change of astigmatism of spectacle lens due to dispersion of spectacle lens material.     

Implementation of an adaptive finite-element approximation of the Mumford-Shah functional

Summary. We present and detail a method for the numerical solving of the Mumford-Shah problem, based on a finite element method and on adaptive meshes. We start with the formulation introduced in [13], detail its numerical implementation and then propose a variant which is proved to converge to the Mumford-Shah problem. A few experiments are illustrated. Received October 8, 1998 / Published online: April 20, 2000     

Revisiting Energy Release Rates in Brittle Fracture

We revisit in a 2d setting the notion of energy release rate, which plays a pivotal role in brittle fracture. Through a blow-up method, we extend that notion to crack patterns which are merely closed sets connected to the crack tip. As an application, we demonstrate that, modulo a simple meta-stability principle, a moving crack cannot generically kink while growing continuously in time. This last result potentially renders obsolete in our opinion a longstanding debate in fracture mechanics on the correct criterion for kinking.     

Impact dynamics for elastic membranes

We study the dynamic response of stretched thin polymeric films following an impact by a rigid sphere. We vary the sphere radius, the impact velocity, and the film tension, and measure the contact time and the maximum deflection of the film during the impact. The response is sensitive to nonlinearities associated with the additional tension provided by the deformation. A physical model at the scaling level is presented. This allows us (i) to understand qualitatively experimental and numerical results and (ii) to present a diagram mapping different possible impact dynamics for membrane systems, which accounts for the interplay between membrane tension, intrinsic modulus, and geometrical factors such as the frame size and the sphere radius.