Quasi Two-dimensional Network Research Articles

Optimized two-dimensional networks with edge-crossing cost: Frustrated antiferromagnetic spin system.

We consider a quasi-two-dimensional network connection growth model that minimizes the wiring cost while maximizing the network connections, but at the same time edge crossings are penalized or forbidden. This model is mapped to a dilute antiferromagnetic Ising spin system with frustrations. We obtain analytic results for the order-parameter or mean degree of the optimized network using mean-field theories. The cost landscape is analyzed in detail showing complex structures due to frustration as the crossing penalty increases. For the case of strictly no edge crossing is allowed, the mean-field equations lead to a new algorithm that can effectively find the (near) optimal solution even for this strongly frustrated system. All these results are also verified by Monte Carlo simulations and numerical solution of the mean-field equations. Possible applications and relation to the planar triangulation problem is also discussed.

Spin quantum Hall effect and plateau transitions in multilayer network models

We study the spin quantum Hall effect and transitions between Hall plateaus in quasi two-dimensional network models consisting of several coupled layers. Systems exhibiting the spin quantum Hall effect belong to class C in the symmetry classification for Anderson localisation, and for network models in this class there is an established mapping between the quantum problem and a classical one involving random walks. This mapping permits numerical studies of plateau transitions in much larger samples than for other symmetry classes, and we use it to examine localisation in systems consisting of $n$ weakly coupled layers. Standard scaling ideas lead one to expect $n$ distinct plateau transitions, but in the case of the unitary symmetry class this conclusion has been questioned. Focussing on a two-layer model, we demonstrate that there are two separate plateau transitions, with the same critical properties as in a single-layer model, even for very weak interlayer coupling.

New silver(I) complexes of Schiff base with hydrogen-bonding interactions: effects of anions on the framework formations of complexes

Two new one-dimensional Ag I complexes, [Ag L(NO 3)] ∞ ( 1) and {[Ag L](ClO 4)} ∞ ( 2) ( L= N, N′-bis(2-hydroxyethy)- p-phenylenedimethyleneamine), have been synthesized and their structures were determined by single-crystal X-ray diffraction analysis. 1 crystallizes in the monoclinic system, space group Cc, with a=13.305(5), b=14.107(5), c=7.608(3) Å, β=97.226(6)° and Z=4, while 2 crystallizes in the monoclinic space group C2/c, with a=12.902(5), b=8.671(3), c=27.776(11) Å, β=97.796(6)° and Z=8. In 1, the Ag I atom adopts distorted N 2O 2 tetrahedral coordination geometry, while in 2, the Ag I center is coordinated by two nitrogen atoms from two different L ligands. The structural differences of 1 and 2 suggest that counter anions have a profound effect upon the framework formations of Ag I complexes with the ligand L. The strong and weak hydrogen-bonding interactions in 1 and 2 extend two one-dimensional complexes into two quasi two-dimensional networks, and such weak interactions further stabilized two complexes.

New Silver(I) Complexes of Pyridyl Dithioether Ligands with Ag–Ag Interactions: Effects of Anions and Ligand Spacers on the Framework Formations of Complexes

Three new silver(I) complexes existing Ag–Ag interactions, a trinuclear cluster complex [Ag3(L1)2(NO3)2](NO3) 1, a dinuclear complex [Ag2(L1)2](PF6)22 and a one-dimensional chain complex [Ag2L2(NO3)2]∞3, where L1 and L2 are two structurally related pyridyl dithioether ligands, bis(2-pyridylthio)methane (L1) and 1,3-bis(2-pyridylthio)-propane (L2), have been synthesized and their structures were determined by single-crystal X-ray diffraction analysis. The striking structural differences of 1 and 2 suggest that counter anions have a profound effect upon the framework formations of silver complexes with pyridyl dithioether ligands, and the differences of 1 and 3 indicate that the subtle changes of the space groups have great influence on the coordination modes of the terminal pyridylsulfanyl groups and the geometries of AgI ion and therefore greatly influence the structures of their complexes. The weak Ag⋅⋅⋅O interactions in the trinuclear complex 1 and the one-dimensinoal chain complex 3 extend them into quasi two-dimensional networks, and the Ag⋅⋅⋅S weak interactions in the dinuclear complex 2 into one-dimensinoal chains, and such weak interactions further stabilized these complexes.

Percolation threshold and interface optimization in a HUP/C doublelayer supercapacitor

Energy consumption of electronic devices has decreased gradually with progress in integrated circuits; thus, the durable voltage required for a capacitor has become lower and use of the electric double layer developed at a highly polarizable blocking electrode/electrolyte interface is possible. The demand for miniaturized high energy density and low leakage current capacitors as, for example, a stand-by power source for RAM devices or for actuators offers new opportunities for these devices. The first attempts to achieve such a device were made in the seventies [1], but electrical performances were poor and potential applications were restricted. More recently, a double layer capacitor using a liquid electrolyte (H2SO4) and a carbon electrode was developed and commercialized by NEC [2]. Use of a solid electrolyte opens new possibilities: (i) manufacture of microdevices using a collective process, (ii) a better long-time stability and, owing to the use of pure ionic conductor as separator, a high charge capability, (iii) the slow rate of electrochemical reactions in the solid state prevents degradation due to transient overvoltages. All these potential advantages require a high interface area between the electrolyte and the electrode. The double layer capacity of a typical electrode/electrolyte interface falls into the 10 to 40/~F cm 2 range per effective interface area, indeed. Use of a liquid electrolyte facilitates: contacts with area of carbon. On the other hand, a double percolation (between the solid electrolyte itself and the carbon particulates itself) it necessary to combine in the all solid system a high interface area and a (relatively) low serial resistance [3]. Here we present results concerning the optimization of percolation conditions for two kinds of black activated carbon in the case of an all solid HUP (H3OUO2PO 4. 3H20)/C double layer capacitor. H 3 O U O z P O 4 ° 3H20 is among the best known-fast proton solid conductors [4] and is used in microionic devices such as electrochromic displays [5], sensors [6] or batteries [7]. The HUP structure consists in a quasitwo-dimensional network of water molecules and H3 O+ ions, alternately with layers of uranyl and phosphate ions. The high protonic conductivity occurs via the formation of a quasi-liquid state of H30 + and H20 species between the ( U O z P O 4 ) n slabs [81. Fig. 1 shows a schematic representation of the *To whom all correspondence should be addressed.