A recursive-faulting model of distributed damage in confined brittle materials

We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177-182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579-584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155-158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141-159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement.     

Convergence analysis of time-point relaxation iterates for linear systems of differential equations

We study convergence properties of time-point relaxation (TR) Runge-Kutta methods for linear systems of ordinary differential equations. TR methods are implemented by decoupling systems in Gauss-Jacobi, Gauss-Seidel and successive overrelaxation modes (continuous-time iterations) and then solving the resulting subsystems by means of continuous extensions of Runge-Kutta (CRK) methods (discretized iterations). By iterating to convergence, these methods tend to the same limit called diagonally split Runge-Kutta (DSRK) method. We prove that TR methods are equivalent to decouple in the same modes the linear algebraic system obtained by applying DSRK limit method. This issue allows us to study the convergence of TR methods by using standard principles of convergence of iterative methods for linear algebraic systems. For a particular problem regions of convergence are plotted.     

Supramolecular adducts between macrocyclic Gd(iii) complexes and polyaromatic systems: a route to enhance the relaxivity through the formation of hydrophobic interactions

The set-up of reversible binding interactions between the hydrophobic region of macrocyclic GBCAs (Gadolinium Based Contrast Agents) and SO₃⁻/OH containing pyrene derivatives provides new insights for pursuing relaxivity enhancements of this class of MRI contrast agents. The strong binding affinity allows attaining relaxation enhancements up to 50% at pyrene/GBCA ratios of 3 : 1. High resolution NMR spectra of the Yb-HPDO3A/pyrene system fully support the formation of a supramolecular adduct based on the set-up of hydrophobic interactions. The relaxation enhancement may be accounted for in terms of the increase of the molecular reorientation time (τ_R) and the number of second sphere water molecules. This effect is maintained in blood serum and in vivo, as shown by the enhancement of contrast in T_1w-MR images obtained by simultaneous injection of GBCA and pyrene derivatives in mice.

The set-up of reversible binding interactions between the hydrophobic region of macrocyclic gadolinium based contrast agents and SO₃⁻/OH containing pyrene derivatives provides new insights for pursuing relaxivity enhancement of MRI contrast agents.     

A dominance-based rough set approach applied to evaluate the credit risk of sovereign bonds

4OR - Even though sovereign bonds represent low-risk alternatives that give investors a healthy income, the risk assessment process for these bonds is still considered subjective because of the...     

Ligand dynamics and reactivity in trimetallic clusters

The general relationships between trinuclear cluster reactivity and the ligand dynamical processes in these systems are explored. Three specific mechanistic studies are presented: (1) the rate and stereochemistry of ligand addition to ₃-imidoyl complexes, (2) the factors influencing the rate of carbon-hydrogen bond activation in ₃-alkyne complexes, and (3) the origin of anomalously large kinetic deuterium isotope effect in metal to ligand and ligand to metal hydrogen transfer in trinuclear and binuclear complexes. In all three cases, the current state of the mechanistic studies are summarized and the possible rate of specific ligand dynamical processes in controlling the mechanism are put forth.     

Structural investigation of 3,5‐disubstituted isoxazoles by 1H‐nuclear magnetic resonance

HIV‐1 integrase (IN) is a very promising and validated target for the development of therapeutic agents against AIDS. In an effort to design and synthesize biological isosteric analogs of β‐diketoacid‐containing inhibitors of IN, we prepared a series of substituted isoxazole carboxylic acids. Several of these compounds inhibited catalytic activities of purified IN at micromolar concentration range. With an aim to prepare a large number of analogues based on the isoxazole pharmacophore we focused our study on a series of 3,5‐disubstituted isoxazole isomers. For a rapid structural analysis we discovered a convenient ¹H‐nmr method for distinguishing between isomeric structures based on their H‐4 assignments. This “finger print” approach to isomer identification will be useful in combinatorial chemistry settings where a mixture can be further derivatized.     

Alkyl metal asymmetric reduction. 11. The reaction of α,β-unsaturated ketones with β-branched trialkylaluminium compounds.

The reduction of a series of α,β-unsaturated ketones has been studied under various experimental conditions, by using β-branched trialkylalanes. Asymmetric induction phenomena are observed when optically active trialkylalanes are used.     

Construction of a singular elliptic-harmonic measure

The authors study an example, suggested by E. De Giorgi, of a second-order uniformly elliptic partial differential operator in divergence form with continuous coefficients on a smooth domain in the plane such that the associated harmonic measure on the boundary is not absolutely continuous with respect to the ordinary surface measure.     

On the regulator problem for linear degenerate control systems

In this paper, we study the finite-time regulator problem for linear, autonomous, degenerate systems, i.e., systems described by the differential equation with det(K)=0. Two investigations of the regulator problem are presented, which depend on the quadratic cost associated with the differential equation.This work was performed under the auspices of the National Research Council of Italy, Gruppo Nazionale per l'Analisi Funzionale e le Sue Applicazioni, Rome, Italy.     

Transition metal-catalysed sequences of nucleophilic addition

Summary In presence of nickel or palladium catalysts, nucleophiles can attack vinylcyclopropanes with concomitant ring cleavage. With palladium catalysts in presence of appropriate substituents the terminal carbon atom of the resulting open chain is able to add to two molecules of a conjugated diene giving rise to long-chain unsaturated compounds.