Statistical approach of the irreversible entropy variation

The constructal theory is based on the thought that flow architecture is a consequence of a principle of maximization of flow access, in time, and in flow configuration that is free to be realised. The principle of maxima for the variation of the entropy due to irreversibility represents a general principle of investigation for the stability of open systems, by which it is possible to predict some macroscopic shapes, originated by the spatial organisation, in Nature, both in living and in non-living objects. Its statistical meaning has recently been introduced. Here a statistical and dynamical interpretation for the entropy due to irreversibility is proposed as a foundation of the constructal theory.     

Synergic Interplay Between Halogen Bonding and Hydrogen Bonding in the Activation of a Neutral Substrate in a Nanoconfined Space

The principle of amplified halogen bonding (XB) in a small space is exploited as a catalytic tool for the activation of an XB acceptor substrate in a nanoconfined environment. The inner cavity of the resorcinarene capsule has been equipped with an XB catalyst bearing an ammonium unit acting as a Trojan horse to drive the catalyst inside the capsule. In the presence of a specific XB catalyst, the capsule is able to catalyze a Michael reaction between N‐methylpyrrole and methyl vinyl ketone. In the bulk medium in absence of the resorcinarene capsule, the XB catalyst is catalytically ineffective. Quantum‐mechanical investigations highlight that the Michael reaction proceeds through the activation of the carbonyl group by synergistically enhanced halogen/hydrogen‐bonding interactions and takes place in an open pentameric capsule.     

The random energy model in a magnetic field and joint source-channel coding

We demonstrate that there is an intimate relationship between the magnetic properties of Derrida’s random energy model (REM) of spin glasses and the problem of joint source-channel coding in Information Theory. In particular, typical patterns of erroneously decoded messages in the coding problem have “magnetization” properties that are analogous to those of the REM in certain phases, where the non-uniformity of the distribution of the source in the coding problem plays the role of an external magnetic field applied to the REM. We also relate the ensemble performance (random coding exponents) of joint source-channel codes to the free energy of the REM in its different phases.     

Pulsed laser ablation of SiC in a nitrogen atmosphere: formation of CN

Optical emission lines from the plasma generated by a laser ablation process have been investigated to gather information on the nature of the chemical species present. In particular, the experiments were carried out during the laser ablation of a ceramic sintered SiC target, both in vacuum and in presence of controlled nitrogen atmosphere. Time integrated and spatially resolved emission spectra are dominated by the atomic emission lines from silicon and carbon species, either neutral, or singly ionized. When the ablation process was carried out in a nitrogen gas background direct evidence of the formation of the CN molecular specie was found. Fast photography imaging of the expanding plume revealed the formation of a shock wave at nitrogen pressure above 13.3 Pa, with the consequent heating of the shocked region and enhancement of the kinetics of ionization and excitation. Since the C₂ specie was absent, a CN formation mechanism involving atomic carbon and nitrogen in the presence of a shock wave is suggested. PACS 52.38.Mf; 52.50.Jm, 47.40.-x     

Multiple functional group cooperation in phosphate diester cleavage promoted by Zn(II) complexes

Zn(II) complexes bearing multiple auxiliary organic groups greatly accelerate the cleavage of a phosphate diester.     

Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation

We investigate the problem of falling paper by solving the two dimensional Navier-Stokes equations subject to the motion of a free-falling body at Reynolds numbers around 10(3). The aerodynamic lift on a tumbling plate is found to be dominated by the product of linear and angular velocities rather than velocity squared, as appropriate for an airfoil. This coupling between translation and rotation provides a mechanism for a brief elevation of center of mass near the cusplike turning points. The Navier-Stokes solutions further provide the missing quantity in the classical theory of lift, the instantaneous circulation, and suggest a revised model for the fluid forces.     

Some New Applications of the Subspace Theorem

We present some applications of the Subspace Theorem to the investigation of the arithmetic of the values of Laurent series f(z) at S-unit points. For instance we prove that if f(q ⁿ ) is an algebraic integer for infinitely many n, then h(f(q ⁿ )) must grow faster than n. By similar principles, we also prove diophantine results about power sums and transcendency results for lacunary series; these include as very special cases classical theorems of Mahler. Our arguments often appear to be independent of previous techniques in the context.     

Calderón algebras of smoothing operators

Summary Certain classes of integral operators between generalized Sobolev spaces are shown to form algebras, en lowed with an approximate functional calculus, having properties similar to those of pseudo-differential operators. This research was supported under National Science Foundation grant GP-12295 and was completed while the author was Visiting Professor at the University of Genoa under a grant from the Comitato Nazionale per la Matematica, Consiglio Nazionale Ricerche (C.N.R.), Italy. Entrata in Redazione il 1 giugno 1970.