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.     

Weak solutions for a bi-fluid model for a mixture of two compressible non interacting fluids

Science China Mathematics - We investigate a version of one velocity Baer-Nunziato model with dissipation for the mixture of two compressible fluids with the goal to prove for it the existence of...     

Adsorptions de H2 et de O2 sur des alliages NiCu divisés supportés sur SiO2, etudiées par mesure d'aimantation á saturation

The linear combination of surface atom orbitals to which an adatom orbital will couple plays the important role of being the essential link between the adsorbate and the semi-infinite substrate. The group orbital (as it is called) is a function of the substrate character, the local adsorption geometry, and the adatom orbital. We present the spectral densities of states appropriate to the adsorption of a hydrogen or transition metal atom on a transition metal substrate for simple geometries, and comment upon some of the implications of the results for both past and future assumptions in chemisorption theory.     

Luminescence Study of Singlet Oxygen Production by Meso-Tetraphenylporphine

The research in the field of the photodynamic therapy of cancer (PDT) is focused on a development of photosensitizers exhibiting high quantum yield of singlet oxygen production. Direct time-resolved spectroscopic observation of singlet oxygen phosphorescence can provide time constants of its population and depopulation as well as photosensitizer phosphorescence lifetime and relative quantum yields. In our contribution, a study of time and spectral resolved phosphorescence of singlet oxygen photosensitized by meso-tetraphenylporphine in acetone together with the photosensitizer phosphorescence is presented. Time constants of singlet oxygen population and depopulation were determined at wide range of photosensitizer concentrations. The time constant of singlet oxygen generation (0.28 ± 0.01) s is slightly shorter then the lifetime of photosensitizer's triplet state (0.32 ± 0.01) s. It is caused by lower ability of TPP aggregates to transfer excitation energy to oxygen. The lifetime of singlet oxygen (50 s) decreases with increasing photosensitizer concentration. Therefore, the photosensitizer acts also as a quencher of oxygen singlet state, similarly to the effects observed in [A. A. Krasnovsky, P. Cheng, R. E. Blankenship, T. A. Moore, and D. Gust (1993). Photochem. Photobiol. 57, 324–330; H. Küpper, R. Ddic, A. Svoboda, J. Hála, and P. M. H. Kroneck (2002). Biochim. Biophys. Acta Gen. Subj. 1572, 107–113]. Moreover, the increasing concentraion of the photosensitizer causes a slight hypsochromic shift of the singlet oxygen luminescence maximum.     

A study of sulfur-free thiuram vulcanization using differential scanning calorimeter

A number of curative mixtures without rubber and with natural rubber or polybutadiene based on binary and tertiary combinations of zinc oxide, tetramethylthiuram disulfide, and 2-mercaptobenzothiazole were treated in a differential scanning calorimeter. From the shapes of exothermal curves a zinc-accelerator complex formation has been examined. Although the experimental results can give no direct evidence for the structure of the complexes, they do contribute to an elucidation of the complex formation in the vulcanization process.     

Metal-ion-coordinating properties of various phosphonate derivatives,including 9−[2−(phosphonylmethoxy)ethyl]adenine (PMEA) – an adenosine monophosphate (AMP) analogue with antiviral properties

The stability constants of the 1:1 complexes formed between Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺, Mn²⁺, Co²⁺, Ni²⁺, Cu²⁺, (in part) Zn²⁺, or Cd²⁺ and (phosphonylmethoxy)ethane (PME^2?) or 9?[2?(phosphonylmethoxy)ethyl]adenine (PMEA^2?) were determined by potentiometric pH titration in aqueous solution (I = 0.1M , NaNO₃; 25°). The experimental conditions were carefully selected such that self-association of the adenine derivative PMEA and of its complexes was negligibly small; i.e., it was made certain that the properties of the monomeric [M(PMEA)] complexes were studied. Recent measurements with simple phosphate monoesters, R–MP^2– (where R is a non-coordinating residue; S. S. Massoud, H. Sigel, Inorg. Chem. 1988 , 27, 1447), were used to show that analogously simple phosphonates (R? PO) – we studied now the complexes of methyl phosphonate and ethyl phosphonate – fit on the same log K/logK vs. pK/ pK straight-line plots. With these reference lines, it could be demonstrated that for all the [M(PME)] complexes with the mentioned metal ions an increased complex stability is measured; i.e., a stability higher than that expected for a sole phosphonate coordination of the metal ion. This increased stability is attributed to the formation of five-membered chelates involving the ether oxygen present in the ? O? CH₂? PO residue of PME^2? (and PMEA^2?); the formation degree of the five-membered [M(PME)] chelates varies between ca. 15 and 40% for the alkaline earth ions and ca. 35 to 65% for 3d ions and Zn²⁺ or Cd²⁺. Interestingly, for the [M(PMEA)] complexes within the error limits exactly the same observations are made indicating that the same five-membered chelates are formed, and that the adenine residue has no influence on the stability of these complexes, with the exception of those with Ni²⁺ and Cu²⁺. For these two metal ions, an additional stability increase is observed which has to be attributed to a metal ion-adenine interaction giving thus rise to equilibria between three different [M(PMEA)] isomers. These equilibria are analyzed, and for [Cu(PMEA)] it is calculated that 17(±3)% exist as an isomer with a sole Cu²⁺-phosphonate coordination, 34(±10)% form the mentioned five-membered chelate involving the ether oxygen, and the remaining 49(±10)% are due to an isomer containing also a Cu²⁺-adenine interaction. Based on various arguments, it is suggested that this latter isomer contains two chelate rings which result from a metal-ion coordination to the phosphonate group, the ether oxygen, and to N(3) of the adenine residue. For [Ni(PMEA)], the isomer with a Ni²⁺-adenine interaction is formed to only 22(±13)%; for [Cd(PMEA)] and the other [M(PMEA)] complexes if at all, only traces of such an isomer are occurring. In addition, the [M(PMEA)] complexes may be protonated leading to [M(H·PMEA)]⁺ species in which the proton is mainly at the phosphonate group, while the metal ion is bound in an adenosine-type fashion to the nucleic base residue. Finally, the properties of [M(PMEA)] and [M(AMP)] complexes are compared, and in this connection it should be emphasized that the ether oxygen which influences so much the stability and structure of the [M(PMEA)] complexes in solution is also crucial for the antiviral properties of PMEA.     

Some general remarks on hyperplasticity modelling and its extension to partially saturated soils

The essential ideas and equations of classic plasticity and hyperplasticity are successively recalled and compared, in order to highlight their differences and complementarities. The former is based on the mathematical framework proposed by Hill (The mathematical theory of plasticity. Oxford University Press, Oxford, 1950), whereas the latter is founded on the orthogonality hypothesis of Ziegler (An introduction to thermomechanics. Elsevier, North-Holland, 1983). The main drawback of classic plasticity is the possibility of violating the second principle of thermodynamics, while the relative ease to conjecture the yield function in order to approach experimental results is its main advantage. By opposition, the a priori satisfaction of thermodynamic principles constitutes the chief advantage of hyperplasticity theory. Noteworthy is also the fact that this latter approach allows a finer energy partition; in particular, the existence of frozen energy emerges as a natural consequence from its theoretical formulation. On the other hand, the relative difficulty to conjecture an efficient dissipation function to produce accurate predictions is its main drawback. The two theories are thus better viewed as two complementary approaches. Following this comparative study, a methodology to extend the hyperplasticity approach initially developed for dry or saturated materials to the case of partially saturated materials, accounting for interface energies and suction effects, is developed. A particular example based on the yield function of modified Cam–Clay model is then presented. It is shown that the approach developed leads to a model consistent with other existing works.     

Physically Reasonable Solutions to Steady Compressible Navier-Stokes Equations in 2d Exterior Domains with Nonzero Velocity at Infinity

In a previous paper, the present authors studied the asymptotic behaviour of solutions to steady compressible Navier-Stokes equations in barotropic and isothermal regime with sufficiently small external data, in particular, in the whole plane. Here, the same problem is investigated in a two dimensional exterior domain with the prescribed velocity at infinity v_￥ 1 0 v_{\infty}\ne 0 . Similar results as in Dutto and Novotny [DuNo] are found; in particular, it is proved that there exists a unique solution which possesses the similar pointwise decay and the wake structure as the fundamental Oseen tensor.