The singularity in weakly nonlinear fracture mechanics

Material failure by crack propagation essentially involves a concentration of large displacement-gradients near a crack's tip, even at scales where no irreversible deformation and energy dissipation occurs. This physical situation provides the motivation for a systematic gradient expansion of general nonlinear elastic constitutive laws that goes beyond the first order displacement-gradient expansion that is the basis for linear elastic fracture mechanics (LEFM). A weakly nonlinear fracture mechanics theory was recently developed by considering displacement-gradients up to second order. The theory predicts that, at scales within a dynamic lengthscale ℓ from a crack's tip, significant logr displacements and 1/r displacement-gradient contributions arise. Whereas in LEFM the 1/r singularity generates an unbalanced force and must be discarded, we show that this singularity not only exists but is also necessary in the weakly nonlinear theory. The theory generates no spurious forces and is consistent with the notion of the autonomy of the near-tip nonlinear region. The J-integral in the weakly nonlinear theory is also shown to be path-independent, taking the same value as the linear elastic J-integral. Thus, the weakly nonlinear theory retains the key tenets of fracture mechanics, while providing excellent quantitative agreement with measurements near the tip of single propagating cracks. As ℓ is consistent with lengthscales that appear in crack tip instabilities, we suggest that this theory may serve as a promising starting point for resolving open questions in fracture dynamics.     

Pore Space Microstructure Evolution of Regular Sphere Packings Undergoing Compaction and Cementation

We examine the pore space structure evolution of ordered uniform sphere packs: simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC), undergoing simple diagenetic processes that reduce their pore spaces. Focus is on the occurrence of pore space microstructure changes or transitions, which are followed through their characteristic or critical pore lengths (l _c). For almost all the cubic packings undergoing either compaction or cementation there are no singularities in l _c. This is a consequence of having a single pore shape controlling flow at all stages of the process. However, this is not so for the BCC packing under cementation, for which l _c is non-monotonic exhibiting a kink at ${\phi \approx 0.1452}$ , the porosity at which the pore shape controlling flow switches to a different form and position. These results for uniform compaction/cementation complement our previous works on pore networks under random shrinkage. Kinks in l _c as porosity decreases signal pore space microstructure transitions that anticipate sudden changes in the permeability?Cporosity relation as porosity decreases. The consequences are great; clearly l _c is not a constant unless the diagenetic process is mild. A l _c function of compaction/cementation advancement should be used above a transition and a different l _c function below. For the sphere packs here, once the diagenetic process has reduced the pore space substantially, a l _c function of compaction/cementation advancement is mandatory if we are to capture all significant flow features.     

Two new polyketides from Hawaiian endophytic fungus Pestalotiopsis sp. FT172

Two new polyketides, pestalotiotones A (1) and B (2) were isolated from the cultured broth of Pestalotiopsis sp. FT172. The structures of compounds 1 and 2 were determined by analysis of HRMS and NMR spectroscopic data. The absolute configurations of compound 1 were assigned by Mosher reaction, J-based configuration analysis, and DP4 NMR calculations. Both compounds were tested against cancer cell lines, pathogenic fungi and bacteria.     

Solvation phenomena in dilute multicomponent solutions I. Formal results and molecular outlook

We derive second-order thermodynamically consistent truncated composition expansions for the species residual partial molar properties--including volume, enthalpy, entropy, and Gibbs free energy--of dilute ternary systems aimed at the molecular account of solvation phenomena in compressible media. Then, we provide explicit microscopic interpretation of the expansion coefficients in terms of direct and total correlation function integrals over the microstructure of the corresponding infinite dilution reference system, as well as their pressure and temperature derivatives, allowing for the direct prediction of the species partial molar properties from the knowledge of the effective intermolecular interactions. Finally, we apply these formal results (a) to derive consistent expressions for the corresponding properties of the binary system counterparts, (b) to illustrate how the formal expressions converge, at the zero density limit, to those for multicomponent mixtures of imperfect gases obeying the virial equation of state Z = 1 + BPkT, and (c) to discuss, and highlight with examples from the literature, the thermodynamic inconsistencies encountered in the currently available first-order truncated expansions, by pinpointing the mathematical origin and physical meaning of the inconsistencies that render the first-order truncated expansions invalid.     

Harmonic functions of linear growth on solvable groups

We answer a question posed by Bonilla and Grosse-Erdmann by showing that the operators P(D) on the space of entire functions H(C), where D is the differentiation operator and P is a polynomial, do not possess a frequently hypercyclic subspace.     

A new ruthenium nitrosyl species based on a pendant-arm 1,4,8,11-tetraazacyclotetradecane (cyclam) derivative: An experimental and theoretical study

The complex cis-[Ru(L^py)NO]³⁺ (I) (L^py = N-(2-methylpyridyl)1,4,8,11-tetraazacyclotetradecane) was prepared by the stoichiometric reaction between Ru(dmso)₄Cl₂ and L^py and an excess of NaNO₂ in ethanolic medium, followed by acidification of the solution. The diamagnetic species was isolated as its hexafluorophosphate salt, and fully characterized by IR (ν_NO = 1917 cm⁻¹) and diverse NMR techniques in combination with theoretical computations based on the density functional theory (DFT). The compound displays strong electronic transitions below 300 nm and weak ones in the visible region of the spectrum, all of them solvent insensitive. The reaction of cis-[Ru(L^py)NO]³⁺ with OH⁻ generates the strongly colored nitro compound cis-[Ru(L^py)NO₂]⁺ (II) The {RuNO}⁶ compound can be interconverted into the one-electron reduced {RuNO}⁷ species cis-[Ru(L^py)NO]²⁺ (III). The reduction process is completely reversible in the cyclic voltammetry timescale with E⁰ (versus Ag/AgCl, 3 M Cl⁻) = −0.02 V and 0.18 V in water and acetonitrile, respectively. Controlled potential reduction in both solvents yields to the quantitative formation of III, a process which involves significant changes in the electronic spectroscopy. The {RuNO}⁷ species proved to be inert against ligand loss, and electrogenerated solutions remained unchanged for several hours if protected from atmospheric oxygen. Electrochemical reoxidation or exposure to air lead to the complete recovery of the starting cis-[Ru(L^py)NO]³⁺ material, without signs of secondary reactions. The robustness of the coordination sphere appears as a consequence of the multidentate nature of L^py.     

Anodic stripping voltammetry in a flow-through cell with a fixed mercury film glassy carbon disc electrode. Part I

Anodic stripping voltammetry at a glassy carbon disc electrode covered by a thin mercury film was adapted for use in a flow-through cell. The resulting system is characterized by extreme simplicity of set-up and operation, high sensitivity and excellent precision and stability. Its performance was tested via the determination of hydrated or labile complex ions of heavy metal ions in sea water, using short (2–10 min) deposition periods. The dependence of the stripping peak charge on metal ion concentration, length of deposition period, solution flow rate and other variables was examined and the reliability of the results obtained were evaluated under conditions resembling continuous monitoring.     

Determination of polybrominated diphenyl ethers in water and soil samples by cloud point extraction-ultrasound-assisted back-extraction-gas chromatography–mass spectrometry

A novel and efficient analytical methodology is proposed for extracting and preconcentrating polybrominated diphenyl ethers (PBDEs) from samples of environmental interest prior gas chromatography–mass spectrometry (GC–MS) analysis. It is based on the induction of micellar organized medium by using a non-ionic surfactant (Triton X-114) to extract the target PBDEs. To enable coupling the efficient extracting technique with GC analysis, ultrasound-assisted back-extraction (UABE) into an organic solvent was required. Several factors, including surfactant type and concentration, equilibration temperature and time, ionic strength, pH and buffers nature and concentration were studied and optimized over the extraction efficiency of the proposed technique. Under optimal experimental conditions, the target analytes were quantitatively extracted achieving an enrichment factor of 250 when 10 mL aliquot of ultrapure water spiked with PBDE-standard mixture (10 pg mL⁻¹ each PBDE) was extracted. Method detection limits (MDLs) calculated with aqueous PBDEs solutions as three times the signal-to-noise ratio (S/N), ranged from 1 to 2 pg mL⁻¹ with RSDs values ≤8.5% (n = 5). The coefficients of estimation of the calibration curves obtained following the proposed methodology were ≥0.9987 and linear range of all PBDEs was 4–150 pg mL⁻¹. The proposed methodology was validated by carrying out a recovery study by spiking the samples at two different concentration levels of PBDEs (10 and 50 pg mL⁻¹ for waters samples). Recoveries values in the range of 96–106% for water samples were obtained showing satisfactory robustness of the method for analyzing PBDEs in water samples. The proposed methodology was applied for the analysis of PBDEs: 2,2′,4,4′-tetraBDE (BDE-47), 2,2′,4,4,5-pentaBDE (BDE-99), 2,2′,4,4,6-pentaBDE (BDE-100) and 2,2,4,4′,5,5′-hexaBDE (BDE-153) in water samples, including drinking, lake, river water and soil samples. Significant quantities of PBDEs were not found in the analyzed samples.     

Simulated water adsorption in chemically heterogeneous carbon nanotubes

Grand canonical Monte Carlo simulations are used to study the adsorption of water in single-walled (10:10), (12:12), and (20:20) carbon nanotubes at 298 K. Water is represented by the extended simple point charge model and the carbon atoms as Lennard-Jones spheres. The nanotubes are decorated with different amounts of oxygenated sites, represented as carbonyl groups. In the absence of carbonyl groups the simulated isotherms are characterized by negligible amounts of water uptake at low pressures, sudden and complete pore filling once a threshold pressure is reached, and wide adsorption-desorption hysteresis loops. In the presence of a few carbonyl groups the simulated adsorption isotherms are characterized by pore filling at lower pressures and by narrower adsorption-desorption hysteresis loops compared to the results obtained in the absence of carbonyl groups. Our results show that the distribution of the carbonyl groups has a strong effect on the adsorption isotherms. For carbonyl groups localized in a narrow section the adsorption of water may be gradual because a cluster of adsorbed water forms at low pressures and grows as the pressure increases. For carbonyl groups distributed along the nanotube the adsorption isotherm is of type V.