Optimization in constrained crack problems

Following the optimization approach to brittle fracture, we consider the evolution of a crack in a domain as solution of the global problem of constrained minimization of the total potential energy with respect to both state variables (the displacement vector) and shape variables (parameters of the crack shape). This formulation describes the initiation of a crack in a homogeneous body and its stable as well as unstable propagation, which allows also a kink (topology change) of the crack during the evolution process. By this we assume that contact can occurs between the opposite crack faces. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence of solutions for motion equations for an objective model of viscoelastic medium

We consider the Dirichlet initial-boundary value problem for the equations of motion of incompressible viscoelastic medium with objective rheological constitutive laws of Maxwell and Jeffreys kind. Several types of existence results are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Core-Excited Molecules by Resonant Intense X-Ray Pulses Involving Electron-Rotation Coupling

It has been reported that electron-rotation coupling plays a significant role in diatomic nuclear dynamics induced by intense VUV pulses [Phys. Rev. A 102(2020) 033114; Phys. Rev. Res. 2(2020) 043348]. As a further step, we present here investigations of the electron-rotation coupling effect in the presence of Auger decay channel for core-excited molecules, based on theoretical modeling of the total electron yield(TEY), resonant Auger scattering(RAS) and x-ray absorption spectra(XAS) for two showcases of CO and CH~+ molecules excited by resonant intense x-ray pulses. The Wigner D-functions and the universal transition dipole operators are introduced to include the electron-rotation coupling for the core-excitation process. It is shown that with the pulse intensity up to 10~(16) W/cm~2, no sufficient influence of the electron-rotation coupling on the TEY and RAS spectra can be observed. This can be explained by a suppression of the induced electron-rotation dynamics due to the fast Auger decay channel, which does not allow for effective Rabi cycling even at extreme field intensities,contrary to transitions in optical or VUV range. For the case of XAS, however, relative errors of about 10% and 30% are observed for the case of CO and CH~+, respectively, when the electron-rotation coupling is neglected.It is concluded that conventional treatment of the photoexcitation, neglecting the electron-rotation coupling,can be safely and efficiently employed to study dynamics at the x-ray transitions by means of electron emission spectroscopy, yet the approximation breaks down for nonlinear processes as stimulated emission, especially for systems with light atoms.     

Quantitative Depth Profiling Using Online-Laser Ablation of Solid Samples in Liquid (LASIL) to Investigate the Oxidation Behavior of Transition Metal Borides

The increased demand for sustainability requires, among others, the development of new materials with enhanced corrosion resistance. Transition metal diborides are exceptional candidates, as they exhibit fascinating mechanical and thermal properties. However, at elevated temperatures and oxidizing atmospheres, their use is limited due to the fact of their inadequate oxidation resistance. Recently, it was found that chromium diboride doped with silicon can overcome this limitation. Further improvement of this protective coating requires detailed knowledge regarding the composition of the forming oxide layer and the change in the composition of the remaining thin film. In this work, an analytical method for the quantitative measurement of depth profiles without using matrix-matched reference materials was developed. Using this approach, based on the recently introduced online-LASIL technique, it was possible to achieve a depth resolution of 240 nm. A further decrease in the ablation rate is possible but demands a more sensitive detection of silicon. Two chromium diboride samples with different Si contents suffering an oxidation treatment were used to demonstrate the capabilities of this technique. The concentration profiles resembled the pathway of the formed oxidation layers as monitored with transmission electron microscopy. The stoichiometry of the oxidation layers differed strongly between the samples, suggesting different processes were taking place. The validity of the LASIL results was cross-checked with several other analytical techniques.     

Exploration of the Crystal Structure and Thermal and Spectroscopic Properties of Monoclinic Praseodymium Sulfate Pr2(SO4)3

Praseodymium sulfate was obtained by the precipitation method and the crystal structure was determined by Rietveld analysis. Pr₂(SO₄)₃ is crystallized in the monoclinic structure, space group C2/c, with cell parameters a = 21.6052 (4), b = 6.7237 (1) and c = 6.9777 (1) Å, β = 107.9148 (7)°, Z = 4, V = 964.48 (3) ų (T = 150 °C). The thermal expansion of Pr₂(SO₄)₃ is strongly anisotropic. As was obtained by XRD measurements, all cell parameters are increased on heating. However, due to a strong increase of the monoclinic angle β, there is a direction of negative thermal expansion. In the argon atmosphere, Pr₂(SO₄)₃ is stable in the temperature range of T = 30–870 °C. The kinetics of the thermal decomposition process of praseodymium sulfate octahydrate Pr₂(SO₄)₃·8H₂O was studied as well. The vibrational properties of Pr₂(SO₄)₃ were examined by Raman and Fourier-transform infrared absorption spectroscopy methods. The band gap structure of Pr₂(SO₄)₃ was evaluated by ab initio calculations, and it was found that the valence band top is dominated by the p electrons of oxygen ions, while the conduction band bottom is formed by the d electrons of Pr³⁺ ions. The exact position of ZPL is determined via PL and PLE spectra at 77 K to be at 481 nm, and that enabled a correct assignment of luminescent bands. The maximum luminescent band in Pr₂(SO₄)₃ belongs to the ³P₀ → ³F₂ transition at 640 nm.     

Physical Treatment Reduces Trypsin Inhibitor Activity and Modifies Chemical Composition of Marama Bean (Tylosema esculentum)

The utility of the marama bean (MB) as an alternative protein source to soybean (SB) can be limited by the high concentration of trypsin inhibitors (TI). The physical treatment of MB has the potential to ameliorate the antinutritional activities of TI and modify other chemical components. Thus, this study investigated the effects of physical treatments on the chemical components and trypsin inhibitor activity (TIA) of raw MB and SB. The bean substrates were subjected to each of the following treatment methods: (1) room temperature (20–22 °C) soaking for 24 h; (2) electric stove cooking at 100 °C for 10, 20, and 30 min; (3) steam autoclaving at a temperature of 110 °C and pressure of 7 pounds per square inch (psi), as well as a temperature of 121 °C and 7 psi for 5, 15, and 30 min; (4) pre-soaked autoclaving at 110 °C (7 psi) and 121 °C (17 psi) for 5, 15, and 30 min. Treated MB and SB had greater (p < 0.05) crude protein content than untreated samples. All the treatments (except 24 h soaking of MB) reduced (p < 0.05) the TIA and ash content. Marama and SB are similar in protein content, but their amino acids profile and TIA are quite different. Soaking for 24 h was less effective in reducing TIA in MB and SB, compared to the thermal methods, and it was detrimental to the ash and amino acids profile of the two beans. Soaking prior to autoclaving yielded beans with the lowest TI concentrations. In conclusion, thermal methods reduced the TI contents and modified the level of proximate components and amino acids profile of the beans.     

Use of spinning band distillation equipment for fractionation of volatile compounds of Copaifera oleoresins for developing a validated gas chromatographic method and evaluating antimicrobial activity

Copaifera is a tree that produces an oleoresin that has great historical and economic importance. These oleoresins display several pharmacological properties, such as anti‐inflammatory and antimicrobial, among others. The commercialization of Copaifera oleoresin occurs, in many cases, without any quality control, which facilitates its adulteration. Validated analytical methods can provide a safe quality control. In this work, the 800 Automatic Spinning Band Distillation equipment was used to perform the fractionation of the volatile oils obtained by hydrodistillation of Copaifera multijuga, C. paupera, C. Publifora and C. langsdorffii, aiming to isolate and purify the major compounds present in these oils. For purification, classical column chromatography was used, furnishing six isolated sesquiterpenes. The sesquiterpenes were used as standards in the development and validation of the method by GC–FID. The evaluated parameters were selectivity, linearity, precision, accuracy and robustness and they are all in accordance with ANVISA and International Conference on Harmonization guidelines. The developed method is reliable for the quantification of sesquiterpenes in Copaifera oleoresins. Both volatile oils and isolated sesquiterpenes had their minimum inhibitory concentration determined against strains of Gram‐negative and Gram‐positive bacteria and yeasts. Copaifera langsdorffi oleoresin was the only one active against all of the evaluated microorganisms, displaying good antimicrobial potential.