Relaxation Height in Energy Landscapes: An Application to Multiple Metastable States

The study of systems with multiple (not necessarily degenerate) metastable states presents subtle difficulties from the mathematical point of view related to the variational problem that has to be solved in these cases. We prove sufficient conditions to identify multiple metastable states. Since this analysis typically involves non-trivial technical issues, we give different conditions that can be chosen appropriately depending on the specific model under study. We show how these results can be used to attack the problem of multiple metastable states via the use of the modern approaches to metastability. We finally apply these general results to the Blume–Capel model for a particular choice of the parameters for which the model happens to have two multiple not degenerate in energy metastable states. We estimate in probability the time for the transition from the metastable states to the stable state. Moreover we identify the set of critical configurations that represent the minimal gate for the transition.     

A new facile synthesis of d₄-pterosin B and d₄-bromopterosin, deuterated analogues of ptaquiloside

Ptaquiloside (Pta) is a potent carcinogen present in bracken fern and in soil matrices, that can potentially leach to the aquatic environment. More recently its presence in the milk of different farm animals has been reported. Pterosin B (Ptb) and bromopterosin (BrPt) represent the most convenient analogues in the detection of ptaquiloside by mass spectrometry. Pterosin sesquiterpenes are also involved in many patented biomedical protocols. In this work we introduce a new and convenient approach to the synthesis in three steps and more than 80% yield of d?-pterosin B (d?-Ptb) and d?-bromopterosin (d?-BrPt), useful as internal standards in the quantification of ptaquiloside.     

QCD saturation and deuteron–nucleus collisions

We make quantitative predictions for the rapidity and centrality dependencies of hadron multiplicities in dA collisions at RHIC basing on the ideas of parton saturation in the color glass condensate.     

Triazolylbenzimidazolthiones and derivatives of the new 1,2,3‐triazolo[ 1,5‐a][ 1,3,5]benzotriazepine heterocycle

Four new triazolylbenzimidazolthione derivatives (2a‐d), analogous to triazolylbenzimidazolone derivatives previously tested as activators of the BK_Ca potassium channels, were prepared and assayed without success. Some derivatives of a new tricyclic nitrogen heterocycle, 1,2,3‐triazolo[1,5‐a][1,3,5]benzo‐triazepine, bearing a carboxamido group in the 3 position, other substituents in the 8 position and a carbonyl (5a‐d) or thione (6a‐c) or methylthio (7a‐c) function in the 5 position were synthesised. The nucleophilic displacement of the methylthio substituent with morpholine or cyclopentylamine provided the 5‐amino‐substituted tricyclic derivatives 8a‐d. Starting from the l‐(2‐nitrophenyl)‐4‐cyano‐5‐amino‐1,2,3‐triazole (9), the 3‐cyano‐triazolobenzotriazepin‐5‐one derivative 12 was also obtained. The majority of the new compounds were tested towards the BK_Ca potassium channels, the benzodiazepine and adenosine A₁ and A_2a receptors, but no remarkable activity was detected.     

Heterocyclic compounds from 3,3-dimercapto-1-aryl-2-propen-1-ones. Note 3. Condensation with N-methyl-o-phenylenediamine and N-benzyl-o-phenylenediamine

Two seven-membered ring compounds and three five-membered ring compounds were obtained by reaction in hot xylene of 3,3-dimercapto-l-phenyl-2-propen-1-one (1) with N-alkyl-o-phenylenediamines (2) . Compounds isolated were the 4-phenyl-5-alkyl-1,5-dihydro-2H-1,5-benzodiazepine-2-thiones (3) the 1-alkyl-4-phenyl-1,3-dihydro-2H-1,5-benzodiazepine-2-thiones (4) , the 1-alkyl-2-phenacylbenzimidazoles (5) , the 1-alkyl-2-phenylbenzimidazoles (6) and the 1-alkyl-2-methylbenzimidazoles (7) . The structures of these compounds were elucidated from their chemical reactivity and their nmr and ir spectra.     

Use of cyclodextrins for the enantioselective separation of ergot alkaloids by capillary zone electrophoresis.

Ergot alkaloid enantiomer derivatives were resolved using capillary zone electrophoresis. The effect of cyclodextrins, added to the background electrolyte, on the migration time and the resolution was studied. Good separation for epimeric ergot alkaloid derivatives was also obtained using phosphate buffer at pH 2.5. Separation was improved by supplementing the background electrolyte with 30 mM of gamma-cyclodextrin. Good resolution of racemic ergot alkaloid derivatives in their enantiomers was achieved in a background electrolyte containing either beta-cyclodextrin or its derivative, or gamma-cyclodextrin.     

Sharp Asymptotics for Stochastic Dynamics with Parallel Updating Rule

In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a finite volume Probabilistic Cellular Automaton (PCA) in a small external field at low temperature regime. We are interested in the nucleation of the system, i.e., the typical excursion from the metastable phase (the configuration with all minuses) to the stable phase (the configuration with all pluses), triggered by the formation of a critical droplet. The main result of the paper is the sharp estimate of the nucleation time: we show that the nucleation time divided by its average converges to an exponential random variable and that the rate of the exponential random variable is an exponential function of the inverse temperature β times a prefactor that does not scale with β. Our approach combines geometric and potential theoretic arguments.