High-pressure access to the Δ9-cis- and Δ9-trans-tetrahydrocannabinols family

Diels-Alder reactions of a range of 1-(alkoxy/alkyl-substituted phenyl)buta-1,3-dienes with methyl vinyl ketone and methyl acrylate carried out in ethanol as the reaction medium under 9 kbar pressure were investigated. The use of high pressure as the activating method of the Diels-Alder reactions allows the efficient and endodiastereoselective generation of a series of cis-cyclohexenyl-benzene cycloadducts, which are selectively converted into their trans-epimers. The cis-cyclohexenyl-benzenes and trans-cyclohexenyl-benzenes produced are useful precursors for accessing substituted privileged cis-6a,7,8,10a-tetrahydro-6H-benzo[c]chromene and trans-6a,7,8,10a-tetrahydro-6H-benzo[c]chromene skeletons. The total syntheses of Δ(9)-cis-tetrahydrocannabinol (THC) and Δ(9)-trans-THC, through the use of selected Diels-Alder adducts, are described. Finally, a route for obtaining Δ(9)-trans-THC in both enantiomeric pure forms based on the (S)-(-)-1-amino-2-(methoxymethyl)pyrrolidine (SAMP)-hydrazone method is also reported.     

“Zero” temperature stochastic 3D ising model and dimer covering fluctuations: A first step towards interface mean curvature motion

We consider the Glauber dynamics for the Ising model with “+” boundary conditions, at zero temperature or at a temperature that goes to zero with the system size (hence the quotation marks in the title). In dimension d = 3 we prove that an initial domain of linear size L of “−” spins disappears within a time τ₊, which is at most L²(log L)^c and at least L²/(c log L) for some c > 0. The proof of the upper bound proceeds via comparison with an auxiliary dynamics which mimics the motion by mean curvature that is expected to describe, on large time scales, the evolution of the interface between “+” and “−” domains. The analysis of the auxiliary dynamics requires recent results on the fluctuations of the height function associated to dimmer coverings of the infinite honeycomb lattice. Our result, apart from the spurious logarithmic factors, is the first rigorous confirmation of the Lifshitz law τ₊ ≃ const × L², conjectured on heuristic grounds [8, 13]. In dimension d = 2, τ₊ can be shown to be of order L² without logarithmic corrections: the upper bound was proven in [6], and here we provide the lower bound. For d = 2, we also prove that the spectral gap of the generator behaves like for L large, as conjectured in [2]. © 2011 Wiley Periodicals, Inc.     

The Thermodynamic Limit in Mean Field Spin Glass Models

 We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and the Derrida p-spin model. The main argument is based on a smooth interpolation between a large system, made of N spin sites, and two similar but independent subsystems, made of N ₁ and N ₂ sites, respectively, with N ₁ +N ₂ =N. The quenched average of the free energy turns out to be subadditive with respect to the size of the system. This gives immediately convergence of the free energy per site, in the infinite volume limit. Moreover, a simple argument, based on concentration of measure, gives the almost sure convergence, with respect to the external noise. Similar results hold also for the ground state energy per site. Received: 19 April 2002 / Accepted: 22 April 2002 Published online: 6 August 2002     

Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs

A theoretical model of disorder for the etched holes or pillars in a generic two-dimensional photonic crystal slab is presented. This model is employed to calculate the effects of size disorder on propagation losses in linear photonic crystal waveguides as well as on quality (Q)-factors in photonic crystal nano-cavities. The main results obtained by the present theory and shown in this work are: (a) large single-mode bandwidth and low-loss (<0.1 dB/mm) propagation of light is predicted for increased-width membrane-type photonic crystal waveguides, (b) pillar-based lattices show reduced sensitivity to size fluctuations than hole-based ones, (c) the effects of disorder on cavity Q-factors are quantitatively evaluated. An extension of the model is also introduced in order to take into account the side-wall micro-roughness of the perfectly vertical holes, and preliminary results of this more general approach are discussed.     

Crystallography of vitamin B12 proteins

This review deals with results from crystallographic studies on proteins that interact with the essential micronutrient cobalamin (vitamin B12). Both B12-dependent enzymes and B12-transport proteins are described with an emphasis on structural aspects of cobalamin and its protein environment.     

Linear stability of the spatially homogeneous equilibria of the Vlasov-Poisson system with collisions

In this work we study the stability of the spatially homogeneous solutions of the Vlasov-Poisson system (Vlasov equilibria) when a collision term, in the form of a BGK operator with velocity-dependent collision frequency, is added to the Vlasov equation. Generalizing earlier results, obtained for the same collision model with a constant collision frequency, we find the spectrum and the eigenfunctions of the linear transport operator and derive a new linear dispersion relation for the linearized kinetic equations. Finally, we present some numerical results.     

Algebraic spinors and SUSY

Using the Dirac-Kaehler formalism, we formulate the supersymmetric Wess-Zumino model. Special attention is paid to the proper definition of a two-dimensional spinor, its adjoint, and its generalization to other dimensions.