A digital image correlation method for fatigue test experiments

In this paper, a method based on the digital image correlation (DIC) technique is proposed to monitor the crack growth process during a cyclic fatigue test. Stroboscopic illumination is used to acquire DIC speckle pattern images while the test sample is dynamically loaded. The proposed DIC algorithm uses the fact that the load is periodic to increase the accuracy of the displacement field estimates (a sinusoidal fitting method is introduced for this purpose). Using the appropriate post-processing both the crack lengths and the stress intensity factors can be estimated in function of the number of fatigue cycles. A validation test case on an aluminum U-profile will be presented in the paper.     

Hydroformylation of 1-Hexene Catalyzed by [Rh(COD)(2-Picoline)2]PF6 Immobilized on Poly(4-Vinylpyridine) Under Water Gas Shift Reaction Conditions

Reported here is the influence of the reaction conditions variation (1-hexene/rhodium content (S/C) = 16 - 105, temperature (T) = 70 - 110 °C and carbon monoxide pressure (P(CO)) = 0.6 - 1.8 atm) on the catalytic hydroformylation of 1-hexene to aldehydes (heptanal and 2-methyl-hexanal) by the rhodium(I) complex, [Rh(COD)(2-picoline)₂]PF₆ (COD = 1,5-cyclooctadiene)immobilized on poly(4-vinylpyridine) in contact with 10 mL of 80% aqueous 2-ethoxyethanol, under water gas shift reaction condition. This revised version was published online in June 2006 with corrections to the Cover Date.     

Biases of PIV measurement of turbulent flow and the masked correlation-based interrogation algorithm

Influences of evaluation bias of the correlation-based interrogation algorithm on particle image velocimetry (PIV) measurement of turbulent flow are investigated. Experimental tests in the Iowa Institute of Hydraulic Research towing tank with a towed PIV system and a surface-piercing flat plate and simulations demonstrate that the experimentally determined mean velocity and Reynolds stress components are affected by the evaluation bias and the gradient of the evaluation bias, respectively. The evaluation bias and gradient of the evaluation bias can both be minimized effectively by using Gaussian digital masks on the interrogation window, so that the measurement uncertainty can be reduced. Received: 16 September 1999/Accepted: 7 February 2000     

rac-[CH2(3-tert-butyl-1-indenyl)2]ZrCl2/MAO in the Copolymerization of Olefins and Dienes

Olefin-diene copolymerizations in the presence of C₂ symmetric zirconocene rac-[CH₂(3-tert-butyl-1-indenyl)₂]ZrCl₂/MAO catalytic system have been reported and rationalized by experimental and molecular modeling studies. Ethene gives 1,2-cyclopropane and 1,2-cyclopentane, 1,3-cyclobutane, and 1,3-cyclopentane units in copolymerization with 1,3-butadiene, 1,4-pentadiene, and 1,5-hexadiene, respectively. Propene-1,3-butadiene copolymerizations lead to 1,2 and 1,4 butadiene units and to a low amount of 1,2-cyclopropane units.     

Neural Networks Retrieving Boolean Patterns in a Sea of Gaussian Ones

Restricted Boltzmann machines are key tools in machine learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for associative memory. In this equivalence, weights in the former play as patterns in the latter. As Boltzmann machines usually require real weights to be trained with gradient-descent-like methods, while Hopfield networks typically store binary patterns to be able to retrieve, the investigation of a mixed Hebbian network, equipped with both real (e.g., Gaussian) and discrete (e.g., Boolean) patterns naturally arises. We prove that, in the challenging regime of a high storage of real patterns, where retrieval is forbidden, an additional load of Boolean patterns can still be retrieved, as long as the ratio between the overall load and the network size does not exceed a critical threshold, that turns out to be the same of the standard Amit–Gutfreund–Sompolinsky theory. Assuming replica symmetry, we study the case of a low load of Boolean patterns combining the stochastic stability and Hamilton-Jacobi interpolating techniques. The result can be extended to the high load by a non rigorous but standard replica computation argument.     

Equivalent Potential Functions to Calculate Thermodynamic Equilibria*

The present paper contains an analysis of alternative functions to describe chemical equilibrium. In particular we show the equivalence of equilibrium criteria based on pressure, volume and temperature, and corresponding constraints, with respect to those popularly used in thermodynamics, i.e. those based on the minimization of internal energy, enthalpy, Helmholtz and Gibbs potentials. The analysis emphasizes the role of mathematical virtual procedures in determining the equilibrium conditions and the irrelevance of physico-chemical transformations that bring the system into the equilibrium state. Different examples, including a new derivation of Saha’s equation, are dealt with to validate this conceptual approach. This paper is dedicated to the memory of one of the authors, Giuseppe Petrella, who unfortunately is not with us any more.