The Tausk Controversy on the Foundations of Quantum Mechanics: Physics, Philosophy, and Politics

In 1966 the Brazilian physicist Klaus Tausk (b. 1927) circulated a preprint from the International Centre for Theoretical Physics in Trieste, Italy, criticizing Adriana Daneri,Angelo Loinger,and Giovanni Maria Prosperi’s theory of 1962 on the measurement problem in quantum mechanics. A heated controversy ensued between two opposing camps within the orthodox interpretation of quantum theory, represented by Léon Rosenfeld and Eugene P.Wigner. The controversy went well beyond the strictly scientific issues, however, reflecting philosophical and political commitments within the context of the Cold War, the relationship between science in developed and Third World countries, the importance of social skills, and personal idiosyncrasies.     

The mechanism of the gas-phase elimination kinetics of the β,γ-unsaturated aldehyde 2,2–dimethyl-3-butenal: a theoretical study

The study on the mechanism of the gas-phase elimination or thermal decomposition kinetics of 2, 2-dimethyl-3-butenal has been carried out by using theoretical calculation at MP2, combined ab initio CBSQB3 and DFT (B3LYP, B3PW91, MPW1PW91, PBEPBE, PBE1PBE, CAMB3LYP, M06, B97d) levels of theory. A good reasonable agreement between experimental and calculated parameters was obtained by using CAMB3LYP/6-311G(d,pd) calculations. The contrasted calculated parameters against experimental values suggested decarbonylation reaction to proceed through a concerted five-membered cyclic transition state type of mechanism, involving the hydrogen transfer from the carbonyl carbon to the gamma carbon, consistent with observed kinetic isotope effect. The breaking of alpha carbon–carbonyl carbon bond to produce carbon monoxide is 50% advanced in the transition state. The reaction mechanism may be described as a concerted moderately non-synchronous process. Examination of the Atoms in Molecules (AIM) analysis of electron density supports the suggested mechanism.     

Numerical spectral analysis of a grid: Application to strain measurements

We present a nondestructive and noncontact extensometry technique, which has been developed in order to study the behavior of different materials such as polycarbonate, araldite, urethane, etc. A spectral analysis of a crossed grating marked on the surface of a specimen and recorded by a charge coupled device camera is presented. The procedure is based on the use of a bidimensional fast Fourier transform algorithm coupled with an interpolation process. It leads to the accurate determination of frequencies. Numerical simulations have been made to evaluate the strain sensitivity; it depends on both the initial phase and the number of cycles characterizing the grid. Theoretically, the strain sensitivity can reach 10^-5 in best cases, but practically it is notbetter than 10^-4. Several applications on different materials are presented: polyurethane, paper and cloth.     

Tandem Michael addition–Claisen-type condensation of anions of O-ethyl carbonates of cyanohydrins to cyclohex-2-en-1-one

A one pot method for the synthesis of ethyl 2-acetoxy-6-aroylcyclohex-1-ene-1-carboxylates and ethyl 2-acetoxy-6-heterocarbonylcyclohex-1-ene-1-carboxylates through Michael addition of the anions of ethyl carbonates of cyanohydrins to cyclohex-2-en-1-one and subsequent reaction with acetic anhydride is described. These compounds are potential intermediates for the synthesis of 9,10-anthraquinone and heterofused 1,4-naphthoquinone derivatives.     

Liquid transport due to light scattering

Using experiments and theory, we show that light scattering by inhomogeneities in the index of refraction of a fluid can drive a large-scale flow. The experiment uses a near-critical, phase-separated liquid, which experiences large fluctuations in its index of refraction. A laser beam traversing the liquid produces a interface deformation on the scale of the experimental setup and can cause a liquid jet to form. We demonstrate that the deformation is produced by a scattering-induced flow by obtaining good agreements between the measured deformations and those calculated assuming this mechanism.     

Effect of excess methanol addition on the morphology of sonogel-derived silica

Sonochemical processing techniques may be used to create fully miscible sols without the initial addition of a solvent. However, by intentionally adding excess alcohol to a sol produced by sonication, it is possible to manipulate the porosity of the resulting sonogel. Sonogels of systematically varied methanol content were prepared using a two-step process with subsequent drying at 60°C. The as-prepared sol with no excess methanol produced a purely microporous solid. The addition of excess methanol to the sol resulted in the formation of mixed microporosity and mesoporosity as revealed by nitrogen gas adsorption and transmission electron microscopy.     

A new proof of partial regularity of solutions to Navier-Stokes equations

In this paper we give a new proof of the partial regularity of solutions to the incompressible Navier-Stokes equation in dimension 3 first proved by Caffarelli, Kohn and Nirenberg. The proof relies on a method introduced by De Giorgi for elliptic equations. This work was supported in part by NSF Grant DMS-0607953.     

Bilinear Sobolev–Poincaré Inequalities and Leibniz-Type Rules

The dual purpose of this article is to establish bilinear Poincaré-type estimates associated with an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type operators. The common underlying theme in both topics is their applications to Leibniz-type rules in Sobolev and Campanato–Morrey spaces under Sobolev scaling.