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The Infinite Braid.
Anesth Analg
September 2021
From the Department of Anesthesia, Stanford Hospital, Stanford, California.
Transition to chaos of natural convection between two infinite differentially heated vertical plates.
Phys Rev E Stat Nonlin Soft Matter Phys
August 2013
CNRS, LIMSI, UPR3251, BP 133, 91403 Orsay Cedex, France and Universite Pierre et Marie Curie-Paris 6, 4, Place Jussieu, 75252 Paris, Cedex 05, France.
Natural convection of air between two infinite vertical differentially heated plates is studied analytically in two dimensions (2D) and numerically in two and three dimensions (3D) for Rayleigh numbers Ra up to 3 times the critical value Ra(c)=5708. The first instability is a supercritical circle pitchfork bifurcation leading to steady 2D corotating rolls. A Ginzburg-Landau equation is derived analytically for the flow around this first bifurcation and compared with results from direct numerical simulation (DNS).
View Article and Find Full Text PDFA triple helix of double helicates: three hierarchical levels of self-assembly in a single structure.
Chem Commun (Camb)
April 2012
Department of Chemistry, University of Sheffield, S3 7HF, UK.
The bis-bidentate bridging ligand L reacts with Ag(I) ions to form a conventional dinuclear [Ag(2)L(2)](2+) double helicate; individual double helicate units assemble via Ag···Ag interactions into infinite chains, three of which wrap around a central spine of anions to give a triple helical braid, which is therefore an infinite triple helix composed of molecular double helicate subunits.
View Article and Find Full Text PDFAn investigation of the self-assembly of neutral, interlaced, triple-stranded molecular braids.
Chemistry
August 2006
Department of Chemistry, Shaanxi Key Laboratory of Physico-Inorganic Chemistry, Northwest University, Xi'an, Shaanxi, 710069, P.R. China.
The synthesis and structures of six compounds prepared in two different systems have been explored with the purpose of isolating coordination polymers with interlaced triple-stranded molecular braid architectures. The dinuclear paddle-wheel units of [Cu(2)(maa)(4)2 H(2)O] can be rationally tuned to form three classes of isomorphous compounds, namely [Cu(2)(maa)(4)(bpp)] (1) (bpp=1,3-bis(4-pyridyl)propane, Hmaa=2-methylacrylic acid), [Cu(3)(maa)(6)(bpp)(2)] (2), and[Cu(4)(maa)(8)(bpp)(4)(H(2)O)(2)]2 H(2)O (3), with a bridging bpp ligand, at controlled ligand-to-metal molar ratios, and lead to three coordination polymers having similar one-dimensional characteristics but different mono- and dinuclear nodes. Compound 1, with a bpp:[Cu(2)(maa)(4)2 H(2)O] stoichiometry of 1:1, contains a zigzag chain containing dinuclear nodes, whereas polymer 2, with a bpp:[Cu(2)(maa)(4)2 H(2)O] stoichiometry of 1.
View Article and Find Full Text PDFFractional quantum hall effect in infinite-layer systems.
Phys Rev Lett
December 2000
Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
Stacked two dimensional electron systems in transverse magnetic fields exhibit three dimensional fractional quantum Hall phases. We analyze the simplest such phases and find novel bulk properties, e.g.
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