Functionalization of corroles: the nitration reaction

The reaction of meso-triarylcorroles with AgNO2 proceeds with concomitant metalation and peripheral substitution to give the corresponding nitro-substituted silverIII corrole complex. The substitution is highly regioselective, giving only the corresponding 3-nitro derivative, among the different possible isomers. The results obtained indicate that the reaction intermediate is the pi-cation radical of the complex, which is then attacked by nitrite ion. This was proven by the reaction of the copper corrole complexes with NaNO2: in this case, the nitration reaction proceeded without the addition of an oxidant, because of the pi-cation radical character of the copper complex. The reaction is also successful in the case of 2,3,17,18-tetraethyl-8,12-diacetoxymethyl-7,13-dimethylcorrole (AMCorH3), with the formation of the meso-substituted silver corrole derivative (NO2)3AMCorAg (fully characterized by X-ray crystallography), the first of its kind to be reported. Two of the corroles are characterized by cyclic voltammetry and spectroelectrochemistry in dichloromethane, and the site of electron transfer is elucidated.     

Sharp $$N^{3/4}$$ Law for the Minimizers of the Edge-Isoperimetric Problem on the Triangular Lattice

We investigate the edge-isoperimetric problem (EIP) for sets of n points in the triangular lattice by emphasizing its relation with the emergence of the Wulff shape in the crystallization problem. By introducing a suitable notion of perimeter and area, EIP minimizers are characterized as extremizers of an isoperimetric inequality: they attain maximal area and minimal perimeter among connected configurations. The maximal area and minimal perimeter are explicitly quantified in terms of n. In view of this isoperimetric characterizations, EIP minimizers \(M_n\) are seen to be given by hexagonal configurations with some extra points at their boundary. By a careful computation of the cardinality of these extra points, minimizers \(M_n\) are estimated to deviate from such hexagonal configurations by at most \(K_t\, n^{3/4}+\mathrm{o}(n^{3/4})\) points. The constant \(K_t\) is explicitly determined and shown to be sharp.     

Attractors for Gradient Flows of Nonconvex Functionals and Applications

This paper addresses the long-time behaviour of gradient flows of nonconvex functionals in Hilbert spaces. Exploiting the notion of generalized semiflows by J. M. Ball, we provide some sufficient conditions for the existence of a global attractor. The abstract results are applied to various classes of nonconvex evolution problems. In particular, we discuss the long-time behaviour of solutions of quasistationary phase field models and prove the existence of a global attractor.     

Crystallization in a One-Dimensional Periodic Landscape

Journal of Statistical Physics - We consider the crystallization problem for a finite one-dimensional collection of identical hard spheres in a periodic energy landscape. This issue arises in...     

Influence of some metal ions on oxidation of nadh and on formation of the superoxide anion radical (O(2)(-)), during enzymatic catalysis by E.C. 1.2.3.2 xanthine oxidase

The inhibitory effect of selected metal ions [Ag(I), Hg(II), Cu(II), Cr(VI), V(V), Au(III), T1(I) and Zn(II)], on the xanthine oxidase (XOD) catalysis of xanthine oxidation, has been investigated with reference to the XOD catalysis of oxidation of NADH. Hg(II), Ag(I), Zn(II) and Au(III) act as inhibitors, T1(I) has no effect and Cu(II), Cr(VI) and V(V) act as activators. The formation of O(2)(-) during XOD catalysis of oxidation of either xanthine or NADH has also been studied. All the metal ions considered act as inhibitors with respect to O(2)(-) production when the reducing substrate is xanthine, but only a few of them when the substrate is NADH, the others showing no effect whatsoever whether or not they activate NADH oxidation in the course of the same reaction. Vanadium (V) has an anomalous effect: it inhibits xanthine oxidation but considerably increases NADH oxidation, and thus appears to modify the catalytic properties of the enzyme. This behaviour appears promising as the basis for a kinetic method for determination of V(V).     

A variational characterization of rate‐independent evolution

Rate‐independent evolution driven by non‐convex potentials is by nature non‐smooth and some weak solvability notions have been recently advanced. This note is intended to contribute to this discussion by proposing a variational characterization of rate‐independent evolution based on a variational principle and a maximal dissipation criterion. The resulting novel solution notion is assessed in an elementary yet critical scalar case (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Long-time behavior for the full one-dimensional Frémond model for shape memory alloys

This note deals with a well-posed one-dimensional initial-boundary value problem related to the Frémond thermomechanical model of structural phase transitions in shape memory materials. The long-time behavior is investigated and it is proved that the limit set in a suitable topology only contains stationary states. Received July 06, 2000     

A New Minimum Principle for Lagrangian Mechanics

We present a novel variational view at Lagrangian mechanics based on the minimization of weighted inertia-energy functionals on trajectories. In particular, we introduce a family of parameter-dependent global-in-time minimization problems whose respective minimizers converge to solutions of the system of Lagrange’s equations. The interest in this approach is that of reformulating Lagrangian dynamics as a (class of) minimization problem(s) plus a limiting procedure. The theory may be extended in order to include dissipative effects thus providing a unified framework for both dissipative and nondissipative situations. In particular, it allows for a rigorous connection between these two regimes by means of Γ-convergence. Moreover, the variational principle may serve as a selection criterion in case of nonuniqueness of solutions. Finally, this variational approach can be localized on a finite time-horizon resulting in some sharper convergence statements and can be combined with time-discretization.     

Weighted energy-dissipation functionals for doubly nonlinear evolution

This paper is concerned with the Weighted Energy-Dissipation (WED) functional approach to doubly nonlinear evolutionary problems. This approach consists in minimizing (WED) functionals defined over entire trajectories. We present the features of the WED variational formalism and analyze the related Euler-Lagrange problems. Moreover, we check that minimizers of the WED functionals converge to the corresponding limiting doubly nonlinear evolution. Finally, we present a discussion on the functional convergence of sequences of WED functionals and present some application of the abstract theory to nonlinear PDEs.