Recursive definition for elements of reality

Elements of reality are defined as in the work of Einstein, Podolsky, and Rosen. It is further assumed that the sum or product of twocommuting elements of reality also is an element of reality. An algebra contradiction ensues.Dedicated to Sir Karl Popper, on the occasion of his 90th birthday.     

Growth Rates and Explosions in Sandpiles

We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in ? ^d . Any site with at least 2d particles then topples by sending one particle to each neighbor. We find that with constant background height h≤2d?2, the diameter of the set of sites that topple has order n ^1/d . This was previously known only for h<d. Our proof uses a strong form of the least action principle for sandpiles, and a novel method of background modification. We can extend this diameter bound to certain backgrounds in which an arbitrarily high fraction of sites have height 2d?1. On the other hand, we show that if the background height 2d?2 is augmented by 1 at an arbitrarily small fraction of sites chosen independently at random, then adding finitely many particles creates an explosion (a sandpile that never stabilizes).     

Interaction effects in single layer and multi-layer graphene

We discuss the excitation spectrum, electronic susceptibilities, and possible electronic instabilities in graphene and graphene stacks. The corrections due interactions of Landau levels in graphene are analyzed. At low dopings, and for sufficiently low couplings, single layer graphene is stable against ferromagnetism. On the other hand, a graphene bilayer, and infinite graphite, are unstable towards ferromagnetism and antiferromagnetism.     

Biased bilayer graphene: semiconductor with a gap tunable by the electric field effect

We demonstrate that the electronic gap of a graphene bilayer can be controlled externally by applying a gate bias. From the magnetotransport data (Shubnikov-de Haas measurements of the cyclotron mass), and using a tight-binding model, we extract the value of the gap as a function of the electronic density. We show that the gap can be changed from zero to midinfrared energies by using fields of less, approximately < 1 V/nm, below the electric breakdown of SiO2. The opening of a gap is clearly seen in the quantum Hall regime.     

Structural and optical spectroscopy of LiNbO3:Tm nanocrystals embedded in a SiO2 glass matrix

Transparent SiO₂:Li₂O:Nb₂O₅ glass doped with Tm³⁺ has been prepared by the sol–gel method, and heat-treated in air (HT) at temperatures between 500 and 800 °C. X-ray diffraction (XRD) patterns and Raman spectroscopy show SiO₂ and LiNbO₃ phases in samples HT above 650 °C, and a NbTmO₄ phase for T > 750 °C. The XRD SEM analysis show increasing particle size and number with the increase of HT temperature. Intra-4f¹² transitions due to Tm³⁺ ion dispersed in the matrix are observed in samples with T > 650 °C. The luminescence is dominated by the ¹G₄ → ³F₄ (～650 nm), ¹D₂ → ³F₃ (～780 nm), ³H₄ → ³H₆ (～800 nm), ³H₅ → ³H₆ (～1200 nm) and ³H₄ → ³F₄ (～1500 nm) transitions under resonant excitation to the ion levels.     

Evaluation of healthy and sensory indexes of sweetened beverages using an electronic tongue

Overconsumption of sugar-sweetened beverages may increase the risk of health problems and so, the evaluation of their glycemic load and fructose-intolerance level is essential since it may allow establishing possible relations between physiologic effects of sugar-rich beverages and health. In this work, an electronic tongue was used to accurately classify beverages according to glycemic load (low, medium or high load) as well to their adequacy for people suffering from fructose malabsorption syndrome (tolerable or not): 100% of correct classifications (leave-one-out cross-validation) using linear discriminant models based on potentiomentric signals selected by a meta-heuristic simulated annealing algorithm. These results may be partially explained by the electronic tongue’s capability to mimic the human sweetness perception and total acid flavor of beverages, which can be related with glycemic load and fructose-intolerance index. Finally, the E-tongue was also applied to quantify, accurately, healthy and sensory indexes using multiple linear regression models (leave-one-out cross-validation: R_adj > 0.99) in the following dynamic ranges: 4.7 < glycemic load ≤ 30; 0.4 < fructose intolerance index ≤ 1.5; 32 < sweetness perception < 155; 1.3 < total acid flavor, g L⁻¹ < 8.3; and, 5.8 < well-balanced flavor ≤ 74. So, the proposed electronic tongue could be used as a practical, fast, low-cost and green tool for beverage’s healthy and sensory evaluation.     

Irradiated UAmO2 transmutation discs analyses: from dissolution to isotopic analyses

Journal of Radioanalytical and Nuclear Chemistry - This paper details the different steps for the isotopic determination of UAmO2 discs from analytical irradiation. MARIOS and DIAMINO irradiations...     

Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our earlier work (Levine and Peres, Indiana Univ Math J 57(1):431–450, 2008). For the shape consisting of sites, where ω _d is the volume of the unit ball in , we show that the inradius of the set of occupied sites is at least r − O(logr), while the outradius is at most r + O(r ^α ) for any α > 1 − 1/d. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total mass. For the classical abelian sandpile model in two dimensions, with n = πr ² particles, we show that the inradius is at least , and the outradius is at most . This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions, improving on bounds of Fey and Redig. Yuval Peres is partially supported by NSF grant DMS-0605166.