Twist points of planar domains

We establish a potential theoretic approach to the study of twist points in the boundary of simply connected planar domains.

     

A kinetic Monte Carlo method on super-lattices for the study of the defect formation in the growth of close packed structures

A modified Kinetic Lattice Monte Carlo model has been developed to predict growth rate regimes and defect formation in the case of the homo-epitaxial growth of close packed crystalline structures. The model is an improvement over standard Monte Carlo algorithms, which usually retain fixed atom positions and bond partners indicative of perfect crystal lattices. Indeed, we extend the concepts of Monte Carlo growth simulations on super-lattices containing additional sites (defect sites) with respect to those of the reference material. This extension implies a reconsideration of the energetic mapping, which is extensively presented, and allows to describe a complex phenomenology that is out of accessibility of standard stochastic approaches. Results obtained using the Kawasaki and the Bond-Counting rules for the transition probability of the Monte Carlo event are discussed in details. These results demonstrate how the defect types (local or extended), the formation mechanisms and the defect generation regimes can be characterized using our approach.     

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

The CeCl3·7H2O-NaI system as promoter in the synthesis of functionalized trisubstituted alkenes via Knoevenagel condensation

The arylidene malonates with two different geminal carboxylate functions, a suitable class of substrates of several synthetic and pharmacological studies, are easily available through Knoevenagel condensation of ethyl tert-butyl malonate and different aromatic aldehydes. The results have increased the potentialities of CeCl₃·7H₂O-NaI system as a type of water-tolerant green Lewis acid promoter for carbon-carbon bond forming procedures.     

Free-radical reactions of diazonium salts with α,β-unsaturated carbonyl compounds. A new synthesis of 1,4-diarylpyrazole derivatives

Free-radical decomposition of diazonium salts catalyzed by titanous or titanous and ferrous salts in the presence of β-substituted α,β-unsaturated carbonyl compounds leads to 1,4-diarylpyrazole derivatives. The reaction occurs via an intermediate azo compound ( 1 ), which can be reduced by the metal salt or can be isolated and hydrogenated to pyrazole derivatives.     

A simple model for the structure of fractal aggregates

Structural properties of small aggregates containing up to 100 particles have been studied through detailed Monte Carlo cluster-cluster aggregation simulations in both diffusion-limited and reaction-limited conditions. First, the radius of gyration, the radius of the smallest sphere encompassing the cluster, and the particle-particle correlation function, g(r), have been computed based on the positions of all the particles in the cluster, and their fractal scaling has been analyzed. Then, an empirical model has been developed to simulate the g(r) function for aggregates of any size and used to determine the corresponding structural properties and scattering structure factors. Finally, in order to illustrate the application of the structural properties thus computed, two experiments on diffusion-limited aggregation have been performed, and the average scattering structure factors have been measured as a function of time using a small-angle light-scattering device. The obtained average scattering structure factors have been simulated using the Smoluchowski population balance equations, using the single aggregate structural properties and scattering structure factor predicted by the developed empirical g(r) model.