Structural dimorphism of N-(3-hydroxysalicylidene)-2,4,6-trimethylaniline

The title compound N-(3-hydroxysalicylidene)-2,4,6-trimethylaniline exhibits dimorphism. The structure of (I) is orthorhombic Pbca with a = 22.222(3), b = 16.200(2), c = 7.596(2) Å, V = 2735(1) ų, and Z = 8. The structure of (II) is monoclinic P2₁/c with a = 11.734(1), b = 15.734(1), c = 7.432(2) Å, = 100.97(1)°, V = 1347.0(5)ų, and Z = 4. The two structures are analyzed in relation with the possibility of an equilibrium between two tautomeric phenol and quinone forms by rapid hydrogen transfer. The molecules associated by intermolecular hydrogen bonds form centrosymmetric dimers. The compounds are thermochromic. The results are compared with the photochromic analog N-(hydroxysalicylidene)-2,4,6-trimethylaniline (compound III) and with the thermochromic one N-(5-hydroxysalicylidene)-2,4,6-trimethylaniline (compound IV). It is concluded that the 3-hydroxyl substituent of the salicylidene moiety enables the intermolecular hydrogen transfer from oxygen to nitrogen.     

Corrigendum to "Virtual experimentation through 3D full-loop simulation of a circulating fluidized bed" [Particuology 6 (2008) 529-539]

The authors regret that the below errors were present in the above-mentioned article when originally published.     

Convex decomposition of games and axiomatizations of the core and the D-core

This paper provides an axiomatic framework to compare the D-core (the set of undominated imputations) and the core of a cooperative game with transferable utility. Theorem 1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity. Moreover, these axioms also characterize the core on the domain of convex games, totally balanced games, balanced games, and superadditive games.      

Minimal large sets for cooperative games

We analyze the concept of large set for a coalitional game v introduced by Martínez-de-Albéniz and Rafels (Int. J. Game Theory 33(1):107–114, 2004). We give some examples and identify some of these sets. The existence of such sets for any game is proved, and several properties of largeness are provided. We focus on the minimality of such sets and prove its existence using Zorn’s lemma. Institutional support from research grants (Generalitat de Catalunya) 2005SGR00984 and (Spanish Government and FEDER) SEJ2005-02443/ECON is gratefully acknowledged, and the support of the Barcelona Economics Program of CREA.     

Magnetic anisotropy engineering in square magnetic elements

Square magnetic elements with side in the 100–500 nm range have been fabricated using the focused ion beam (FIB) milling technique from a 10 nm thick, single-crystal Fe film, epitaxially grown on MgO(0 0 1). Thanks to the good crystal quality of the film, magnetic elements with well-defined magnetocrystalline anisotropy have been prepared, while the fine control of the size and shape of the magnets allows for the effective engineering of the anisotropic behavior of the magnetostatic energy that determines the so-called configurational anisotropy. Micromagnetic calculations and experiments show that the angular dependence of the transverse susceptibility has a strong dependence on the material parameters as well as on the static applied field. This allows the effective engineering of the total anisotropy of the magnets.     

WKB Analysis for Nonlinear Schrödinger Equations with Potential

We justify the WKB analysis for the semiclassical nonlinear Schrödinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the supercritical case, this extends a previous result by E. Grenier; we also have to restrict to nonlinearities which are defocusing and cubic at the origin, but besides subquadratic potentials, we consider initial phases which may be unbounded. For this, we construct solutions for some compressible Euler equations with unbounded source term and unbounded initial velocity.     

Polyoxometalates in solution: Molecular dynamics simulations on the alpha-PW12O40(3-) Keggin anion in aqueous media

The Keggin anion, PW12O40(3-), is one of the most representative polyoxometalates (POMs). In recent years increasing theoretical work focused on this family of compounds has explained or even predicted some of their properties using quantum mechanics methods. In this report we applied for the first time molecular dynamics (MD) to the title compound to analyze its interactions with water. We used three atomic charge definitions (Mulliken, ChelpG, and formal charges) to carry out MD simulations. The results show that the terminal oxygens of the cluster are invariably most effectively solvated by water because of their prominent position within the framework. On the other hand, bridging oxygens, which are confined in more internal positions, concentrate a smaller portion of the whole solvation. We investigated the hydrogen bonds existing between water and the cluster, confirming that the terminal positions form more contacts with H2O than any other site of the cluster. In the end, the lifetime of such contacts is longer with bridging oxygens, presumably due to their higher atomic charge.     

Effective dissipation and turbulence in spectrally truncated euler flows

A new transient regime in the relaxation towards absolute equilibrium of the conservative and time-reversible 3D Euler equation with a high-wave-number spectral truncation is characterized. Large-scale dissipative effects, caused by the thermalized modes that spontaneously appear between a transition wave number and the maximum wave number, are calculated using fluctuation dissipation relations. The large-scale dynamics is found to be similar to that of high-Reynolds number Navier-Stokes equations and thus obeys (at least approximately) Kolmogorov scaling.