Comparison of different plasticity criteria for trabecular bone failure modelling

Different plasticity criteria applied to failure analysis of trabecular bone are compared. A cylindrical sample of bovine trabecular bone is mechanically tested in uniaxial compression/tension with 2% applied strain. Obtained response in compared to responses obtained using finite element model of trabecular bone inner structure subjected to the same loading conditions. FE model is reconstructed from micro–CT images. Elastic material properties at the level of trabecula are determined using nanoindentation. Compared plasticity criteria are based on these elastic material properties, i.e. on Young's modulus of elasticity from nanoindentation. The objective of the paper is to demonstrate the importance to reflect the anisotropic plasticity and to evaluate variation in obtained response when the anisotropy is neglected. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The discrete Prüfer transformation

The classical Prüfer transformation has proved to be a useful tool in the study of Sturm-Liouville theory. In this paper we introduce the Prüfer transformation for self-adjoint difference equations and use it to obtain oscillation criteria and other results. We then offer an extension of this approach to the case of general symplectic systems on time scales. Time scales have been introduced in order to unify discrete and continuous analysis, and indeed our results cover as special cases both the Prüfer transformation for differential and for difference equations.

     

Weak Solutions to Stochastic Wave Equations with Values in Riemannian Manifolds

Let M be a compact Riemannian manifold. We prove existence of a global weak solution of the stochastic wave equation D _t u _t  = D _x u _x  + (X _u  + λ₀(u)u _t  + λ₁(u)u _x )[Wdot] where X is a continuous vector field on M, λ₀ and λ₁ are continuous vector bundles homomorphisms from TM to TM, and W is a spatially homogeneous Wiener process on ? with finite spectral measure. We use recently introduced general method of constructing weak solutions of SPDEs that does not rely on any martingale representation theorem.     

On weighted strong type inequalities for the generalized weighted mean operator

The generalized weighted mean operator ${\mathbf{M}^{g}_{w}}$ is given by $$[\mathbf{M}^{g}_{w}f](x) = g^{-1} \left( \frac{1}{W(x)} \int \limits_{0}^{x}w(t)g(f(t))\,{\rm d}t \right),$$ with $$W(x) = \int \limits_{0}^{x} w(s) {\rm d}s, \quad {\rm for} \, x \in (0, + \infty),$$ where w is a positive measurable function on (0, + ∞) and g is a real continuous strictly monotone function with its inverse g ^?1. We give some sufficient conditions on weights u, v on (0, + ∞) for which there exists a positive constant C such that the weighted strong type (p, q) inequality $$\left( \int \limits_{0}^{\infty} u(x) \Bigl( [\mathbf{M}^{g}_{w}f](x) \Bigr)^{q} {\rm d}x \right)^{1 \over q} \leq C \left( \int \limits_{0}^{\infty}v(x)f(x)^{p} {\rm d}x \right)^{1 \over p}$$ holds for every measurable non-negative function f, where the positive reals p,q satisfy certain restrictions.     

Configurational Entropy Relaxation of Silica Glass—Molecular Dynamics Simulations

Vitreous silica was modelled using molecular dynamics (MD). The glass structure was transferred into an undirected graph and decomposed into disjoint structural units that were ideally mixed to calculate the configurational entropy. The Debye relaxation model was suggested to simulate the evolution of entropy during the cooling of the system. It was found that the relaxation of the configurational entropy of MD corresponds to the effective cooling rate of 6.3 × 10⁶ Ks⁻¹ and its extrapolation to 0.33 Ks⁻¹ mimics the glass transition with T_g; close to the experimental value. Debye relaxation correctly describes the observed MD evolution of configurational entropy and explains the existence of freezing-in temperature and the shape of the curve in the transition region.     

Sensoric potential of gold�Csilver core�Cshell nanoparticles

The sensitivities of five different core-shell nanostructures were investigated towards changes in the refractive index of the surrounding medium. The shift of the localized surface plasmon resonance (LSPR) maximum served as a measure of the (respective) sensitivity. Thus, gold-silver core-shell nanoparticles (NPs) were prepared with different shell thicknesses in a two-step chemical process without the use of any (possibly disturbing) surfactants. The measurements were supported by ultramicroscopic images in order to size the resulting core-shell structures. When compared to sensitivities of nanostructures reported in the literature with those of the (roughly spherical) gold-silver core-shell NPs, the latter showed comparable (or even higher) sensitivities than gold nanorods. The experimental finding is supported by theoretical calculation of optical properties of such core-shell NP. Extinction spectra of ideal spherical and deformed core-shell NPs with various core/shell sizes were calculated, and the presence of an optimal silver shell thickness with increased sensitivity was confirmed. This effect is explained by the existence of two overlapping plasmon bands in the NP, which change their relative intensity upon change of refractive index. Results of this research show a possibility of improving LSPR sensor by adding an extra metallic layer of certain thickness.     

S-alkylation of thiacalixarenes: a long-neglected possibility in the calixarene family

Despite the high nucleophilicity of sulfur atoms, thiacalixarenes have been alkylated only on oxygen atoms thus far. Using strong alkylating agents (triflates, trialkyloxonium salts), the substitution of the sulfur bridges has been successfully accomplished. The corresponding sulfonium salts of thiacalix[4]arene are formed regio- and stereoselectively as a completely new type of substitution pattern in thiacalixarene chemistry. These compounds possess interesting conformational behavior and could be used as unusual alkylating agents with uncommon selectivity.     

The use of high performance liquid chromatography-quadrupole time-of-flight mass spectrometry coupled to advanced data mining and chemometric tools for discrimination and classification of red wines according to their variety

In this study, the potential of high performance liquid chromatography coupled to quadrupole time-of-flight mass spectrometry (HPLC–QTOFMS) for metabolomic profiling of red wine samples was examined. Fifty one wines representing three varieties (Cabernet Sauvignon, Merlot, and Pinot Noir) of various geographical origins were sourced from the European and US retail market. To find compounds detected in analyzed samples, an automated compound (feature) extraction algorithm was employed for processing background subtracted single MS data. Stepwise reduction of the data dimensionality was followed by principal component analysis (PCA) and partial least square-discriminant analysis (PLS-DA) which were employed to explore the structure of the data and construct classification models. The validated PLS-DA model based on data recorded in positive ionization mode enabled correct classification of 96% of samples. Determination of molecular formula and tentative identification of marker compound was carried out using accurate mass measurement of full single MS spectra. Additional information was obtained by correlating the fragments obtained by MS/MS accurate mass spectra using the QTOF with collision induced dissociation (CID) of precursor ions.     

Interaction of metal ions with biomolecular ligands: how accurate are calculated free energies associated with metal ion complexation?

To address fundamental questions in bioinorganic chemistry, such as metal ion selectivity, accurate computational protocols for both the gas-phase association of metal-ligand complexes and solvation/desolvation energies of the species involved are needed. In this work, we attempt to critically evaluate the performance of the ab initio and DFT electronic structure methods available and recent solvation models in calculations of the energetics associated with metal ion complexation. On the example of five model complexes ([M(II)(CH(3)S)(H(2)O)](+), [M(II)(H(2)O)(2)(H(2)S)(NH(3))](2+), [M(II)(CH(3)S)(NH(3))(H(2)O)(CH(3)COO)], [M(II)(H(2)O)(3)(SH)(CH(3)COO)(Im)], [M(II)(H(2)S)(H(2)O)(CH(3)COO)(PhOH)(Im)](+) in typical coordination geometries) and four metal ions (Fe(2+), Cu(2+), Zn(2+), and Cd(2+); representing open- and closed-shell and the first- and second-row transition metal elements), we provide reference values for the gas-phase complexation energies, as presumably obtained using the CCSD(T)/aug-cc-pVTZ method, and compare them with cheaper methods, such as DFT and RI-MP2, that can be used for large-scale calculations. We also discuss two possible definitions of interaction energies underlying the theoretically predicted metal-ion selectivity and the effect of geometry optimization on these values. Finally, popular solvation models, such as COSMO-RS and SMD, are used to demonstrate whether quantum chemical calculations can provide the overall free enthalpy (ΔG) changes in the range of the expected experimental values for the model complexes or match the experimental stability constants in the case of three complexes for which the experimental data exist. The data presented highlight several intricacies in the theoretical predictions of the experimental stability constants: the covalent character of some metal-ligand bonds (e.g., Cu(II)-thiolate) causing larger errors in the gas-phase complexation energies, inaccuracies in the treatment of solvation of the charged species, and difficulties in the definition of the reference state for Jahn-Teller unstable systems (e.g., [Cu(H(2)O)(6)](2+)). Although the agreement between the experimental (as derived from the stability constants) and calculated values is often within 5 kcal·mol(-1), in more complicated cases, it may exceed 15 kcal·mol(-1). Therefore, extreme caution must be exercised in assessing the subtle issues of metal ion selectivity quantitatively.