Randomly chosen chaotic maps can give rise to nearly ordered behavior

Parrondo’s paradox [J.M.R. Parrondo, G.P. Harmer, D. Abbott, New paradoxical games based on Brownian ratchets, Phys. Rev. Lett. 85 (2000), 5226–5229] (see also [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72]) states that two losing gambling games when combined one after the other (either deterministically or randomly) can result in a winning game: that is, a losing game followed by a losing game = a winning game. Inspired by this paradox, a recent study [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] asked an analogous question in discrete time dynamical system: can two chaotic systems give rise to order, namely can they be combined into another dynamical system which does not behave chaotically? Numerical evidence is provided in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] that two chaotic quadratic maps, when composed with each other, create a new dynamical system which has a stable period orbit. The question of what happens in the case of random composition of maps is posed in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] but left unanswered. In this note we present an example of a dynamical system where, at each iteration, a map is chosen in a probabilistic manner from a collection of chaotic maps. The resulting random map is proved to have an infinite absolutely continuous invariant measure (acim) with spikes at two points. From this we show that the dynamics behaves in a nearly ordered manner. When the foregoing maps are applied one after the other, deterministically as in [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72], the resulting composed map has a periodic orbit which is stable.     

Yang-Lee zeros of a planar Ising model with a boundary magnetic field

A planar Ising ferromagnet is investigated with a magnetic field acting on one surface. The Yang-Lee zeros associated with this field are located exactly on the imaginary axis and their limiting distribution is given. Above the critical temperature, this distribution has a gap, near which the pair correlation for spins in the surface exhibits cirtical behaviour. The zeros of certain antiferromagnets are located, in particular those for an antiferromagnetic ring coupled ferromagnetically to a planar Ising ferromagnet.On leave from: University of Oxford. Current Address: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712, USA     

Electric stress distribution in paper oil insulation due to sulphur corrosion of copper conductors

Failure of paper oil insulation due to formation of copper sulphide in transformer windings is a serious issue affecting the performance and life of large transformers. Though chemical effects leading to corrosion are well understood, quantification of electric stress and its correlation to formation and migration of copper sulphide has not been reported in literature. Hence electric stress distribution under copper corrosion using FEM simulation has been studied and discussed in this paper. The simulation results are compared and correlated to experimental findings. The study clearly points towards increase in electric stress in unaffected paper and non-uniform electric stress distribution in paper–oil insulation system. Implications of using enamel coating on copper conductor as a mitigation technique to combat copper corrosion is also discussed.     

Synthesis and characterization of chiral enantiopure bis-chromanones: a Baylis-Hillman approach

Enantiopure bis-chromanones were prepared from (S)-Binol and bromo esters via a Baylis-Hillman approach. Chiroptical studies indicate that the two-naphthyl units of the chromanone system are non-coplanar.     

Embracing the giant component

Consider a game in which edges of a graph are provided a pair at a time, and the player selects one edge from each pair, attempting to construct a graph with a component as large as possible. This game is in the spirit of recent papers on avoiding a giant component, but here we embrace it. We analyze this game in the offline and online setting, for arbitrary and random instances, which provides for interesting comparisons. For arbitrary instances, we find that the competitive ratio (the best possible solution value divided by best possible online solution value) is large. For “sparse” random instances the competitive ratio is also large, with high probability (whp); If the instance has ¼(1 + ε)n random edge pairs, with 0 < ε ≤ 0.003, then any online algorithm generates a component of size O((log n)^3/2) whp , while the optimal offline solution contains a component of size Ω(n) whp . For “dense” random instances, the average‐case competitive ratio is much smaller. If the instance has ½(1 ? ε)n random edge pairs, with 0 < ε ≤ 0.015, we give an online algorithm which finds a component of size Ω(n) whp . © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

A Web-Based Molecular-Level Inquiry Laboratory Activity

This paper presents a new computer-based atomic level simulation of an ideal gas. The simulation is written in Java and is accessed by students through a Web browser. This software is used in conjunction with a written laboratory experiment developed within the framework of an inquiry instructional strategy. This molecular-level laboratory experiment is used in combination with a parallel macroscopic laboratory experiment. We hypothesize that students exposed to these kinds of parallel activities will be better able to link the macroscopic, microscopic, and symbolic understanding of chemical concepts.Presented at the ACS Division of Chemical Education sponsored symposium on web-assisted learning in chemistry at its 221st national meeting in San Diego, CA April 1–5, 2001.     

Growth of single crystals of copper and their thermal profile estimation

Copper crystals have been grown by Czochralski technique in a 6-bar argon gas environment. X-ray analysis shows that these are single crystals and are strain-free. A slight pressure environment that is truly hydrostatic seems to improve the quality of the crystals. Thermal profile estimation results show that the values of temperature which decrease upto the neck region are same in magnitude as those measured during the experiments and that necking improves the thermal profile and, consequently, the crystal quality. No facet formation has been observed in these crystals.