The K-SAT Problem in a Simple Limit

In this work we compute the thermodynamic properties of the 3-satisfiability problem in the infinite connectivity limit. In this limit the computation can be strongly simplified and the thermodynamic properties can be obtained with a high accuracy. We find evidence for a continuous replica symmetry breaking in the region of high number of clauses, >_c.     

Lars, the Oracle

Lars Onsager was known for his obscure but correct predictions in several fields of science. Some scientific events, particularly in the field of superfluidity, are recollected here by one of his old friends.     

Nickel nanostructured materials from liquid phase photodeposition

Liquid Phase Photo-Deposition (LPPD) technique has been used to obtain both colloidal particles and thin films of metallic and chloride nickel from solutions of only precursor Ni(acac)₂ (acac=2,4-pentandionato). Metallic nickel was obtained from ethanol solutions by direct nickel(II) photoreduction at 254 nm and by acetone sensitised reaction at 300 nm. In this latter process the rate was higher than in the first one. NiCl₂ was formed from CCl₄ solution by a solvent-initiated reaction. TEM analysis, performed on colloidal particles of nickel, showed that their dimensions are in the range 2–4 nm. The films did not present carbon contamination and were characterized by AFM, XPS and GIXRD. Metallic films consisted of particles of 20–40 nm that are the result of the aggregation of smaller crystallites (4–5 nm). Larger agglomerations (around 200 nm) have been observed for NiCl₂ films.     

Spin glass theory: Numerical and experimental results in three-dimensional systems

Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental verifications.     

Direct and inverse computation of Jacobi matrices of infinite iterated function systems

We introduce a new set of algorithms to compute the Jacobi matrices associated with invariant measures of infinite iterated function systems, composed of one–dimensional, homogeneous affine maps. We demonstrate their utility in the study of theoretical problems, like the conjectured almost periodicity of such Jacobi matrices, the singularity of the measures, and the logarithmic capacity of their support. Since our technique is based on a reversible transformation between pairs of Jacobi matrices, it can also be applied to solve an inverse/approximation problem. The proposed algorithms are tested in significant, highly sensitive cases: they perform in a stable fashion, and can reliably compute Jacobi matrices of large order.     

Metal complexes of C2-symmetric chiral bipyridine ligands. X-ray structure of [bis(nitrato)(4S,5S)-2,2-dimethyl-4,5-bis(2-pyridyl)-1,3-dioxolane cobalt(II)]

Chelating properties of C₂-symmetric chiral bipyridine ligands are discussed. In particular we report the syntheses of the cobalt(II), nickel(II), zinc(II) and copper(II) complexes of (4S,5S)-2,2-dimethyl-4,5-bis(2-pyridyl)-1,3-dioxolane. All compounds have been characterized by IR spectroscopy, and an X-ray diffraction analysis has been carried out on one of them: Co(L)(NO₃)₂. The ligand coordinates the cobalt atom by the two nitrogen donors N(1) and N(2). A seven-membered chelation ring is formed, presenting a remarkable non-crystallographic twofold pseudosymmetry around the axis connecting Co and the midpoint of the C(6)–C(7) bond. The metal also binds two monodentate nitrates, thus completing a distorted coordination tetrahedron.