Efficient Regular Polygon Dissections

We study the minimum number g(m,n) (respectively, p(m,n)) of pieces needed to dissect a regular m-gon into a regular n-gon of the same area using glass-cuts (respectively, polygonal cuts). First we study regular polygon-square dissections and show that n/2 -2 g(4,n) (n/2) + o(n) and n/4 g(n,4) (n/2) + o(n) hold for sufficiently large n. We also consider polygonal cuts, i.e., the minimum number p(4,n) of pieces needed to dissect a square into a regular n-gon of the same area using polygonal cuts and show that n/4 p(4,n) (n/2) + o(n) holds for sufficiently large n. We also consider regular polygon-polygon dissections and obtain similar bounds for g(m,n) and p(m,n).     

Constant memory routing in quasi-planar and quasi-polyhedral graphs

We address the problem of online route discovery for a class of graphs that can be embedded either in two or in three-dimensional space. In two dimensions we propose the class of quasi-planar graphs and in three dimensions the class of quasi-polyhedral graphs. In the former case such graphs are geometrically embedded in R² and have an underlying backbone that is planar with convex faces; however within each face arbitrary edges (with arbitrary crossings) are allowed. In the latter case, these graphs are geometrically embedded in R³ and consist of a backbone of convex polyhedra and arbitrary edges within each polyhedron. In both cases we provide a routing algorithm that guarantees delivery. Our algorithms need only “remember” the source and destination nodes and one (respectively, two) reference nodes used to store information about the underlying face (respectively, polyhedron) currently being traversed. The existence of the backbone is used only in proofs of correctness of the routing algorithm; the particular choice is irrelevant and does not affect the behaviour of the algorithm.     

Double-wall carbon nanotubes: The outer shell may pattern the structure of the inner one

An existing model [L. Bellarosa, E. Bakalis, M. Melle-Franco, F. Zerbetto, Nano Lett. 6 (2006) 1950] predicts that the structures of the seven double-wall carbon nanotubes, DWCNTs, identified by high-resolution transmission electron microscopy [L. Guan, K. Suenaga, S. Iijima, Nano Lett. 8 (2008) 459] are the most stable. Since the samples were obtained from single-wall carbon nanotubes, SWCNTs, filled with ferrocene molecules that were annealed at 1273 K for 24 h, it is concluded that under proper conditions the host SWCNT patterns the formation of the inner one to form the most stable pair.     

Modelling the use of lanthanides(III) as probes at calcium(II) binding sites in biological systems: Preparation and characterization of neodymium(III) and calcium(II) malonamato(-1) complexes

A bioinorganic approach into the problem of the isomorphous substitution of calcium(II) by lanthanide(III) ions in biological systems is discussed. Reactions of malonamic acid (H₂malm) with Ca^II and Nd^III sources under similar conditions yielded the compounds [Ca(Hmalm)₂]_n (1), [Nd(Hmalm)₂(H₂O)₂]_n(NO₃)_n (2) and [Nd(Hmalm)₂(H₂O)₂]_nCl_n·2nH₂O (3·2nH₂O). Their X-ray crystal structure data show that the malonamate(-1) ligand presents two different ligation modes and coordinates through the two carboxylate and the amide-O atoms, thus bridging three Ca^II ions in 1 and two Nd^III ions in 2 and 3·2nH₂O. Complex 1 is a 3D coordination polymer based on neutral repeating units, whereas 2 and 3·2nH₂O are 1D coordination polymers based on the same cationic repeating unit. Hydrogen bonding interactions further stabilize the 3D framework structure of 1 and assemble the 1D chains of 2 and 3·2nH₂O into 3D networks. The three complexes were characterized spectroscopically (IR, far-IR, and Raman) and the thermal decomposition of 2 and 3·2nH₂O was monitored by TG/DTA and TG/DTG measurements. Variable-temperature magnetic susceptibility data for 2 are also reported. The bioinorganic chemistry relevance of our results is discussed.     

Continuous symmetry reduction and return maps for high-dimensional flows

We present two continuous symmetry reduction methods for reducing high-dimensional dissipative flows to local return maps. In the Hilbert polynomial basis approach, the equivariant dynamics is rewritten in terms of invariant coordinates. In the method of moving frames (or method of slices) the state space is sliced locally in such a way that each group orbit of symmetry-equivalent points is represented by a single point. In either approach, numerical computations can be performed in the original state space representation, and the solutions are then projected onto the symmetry-reduced state space. The two methods are illustrated by reduction of the complex Lorenz system, a five-dimensional dissipative flow with rotational symmetry. While the Hilbert polynomial basis approach appears unfeasible for high-dimensional flows, symmetry reduction by the method of moving frames offers hope.     

Transient gas flow simulation using an Adaptive Method of LinesSimulation d'écoulements dans un gazoduc par la méthode adaptative de lignes

Designing natural gas pipelines to safely and efficiently handle unsteady flows, requires knowledge of pressure drop, flowrate and temperature distribution throughout the system. The accurate prediction of these parameters is essential in order to achieve optimum cumulative deliverability, and safe and reliable operation. An Adaptive Method of Lines algorithm is formulated for the solution of Euler system of equations, which fully simulates slow and fast transients. Two test cases present the improvement of the numerical solution from grid adaptation. Good results are obtained both for slow and fast transients simulations proving that the suggested numerical procedure is appropriate for such predictions. To cite this article: E. Tentis et al., C. R. Mecanique 331 (2003).     

Phenanthriporphyrin: An Antiaromatic Aceneporphyrinoid as a Ligand for a Hypervalent Organophosphorus(V) Moiety

The incorporation of a phenanthrene moiety into a porphyrin framework results in the formation of a hybrid macrocycle—phenanthriporphyrin—merging the structural features of polycyclic aromatic hydrocarbons and porphyrins. An antiaromatic aceneporphyrinoid, adopting the trianionic {CCNN} core, is suitable for the incorporation of a phosphorus(V) center to form a hypervalent organophosphorus(V) derivative.     

Monte Carlo simulations of a coarse grained model for an athermal all-polystyrene nanocomposite system

The structure of a polystyrene matrix filled with tightly cross-linked polystyrene nanoparticles, forming an athermal nanocomposite system, is investigated by means of a Monte Carlo sampling formalism. The polymer chains are represented as random walks and the system is described through a coarse grained Hamiltonian. This approach is related to self-consistent-field theory but does not invoke a saddle point approximation and is suitable for treating large three-dimensional systems. The local structure of the polymer matrix in the vicinity of the nanoparticles is found to be different in many ways from that of the corresponding bulk, both at the segment and the chain level. The local polymer density profile near to the particle displays a maximum and the bonds develop considerable orientation parallel to the nanoparticle surface. The depletion layer thickness is also analyzed. The chains orient with their longest dimension parallel to the surface of the particles. Their intrinsic shape, as characterized by spans and principal moments of inertia, is found to be a strong function of position relative to the interface. The dispersion of many nanoparticles in the polymeric matrix leads to extension of the chains when their size is similar to the radius of the dispersed particles.     

Interfacial thermodynamics of gallic acid adsorption on a chargeable hydrophobic surface

The thermodynamics of adsorption of gallic acid (GA, 3,4,5-trihydroxylbenzoic acid) on the hanging mercury drop electrode (HMDE) surface was studied by temperature-dependent stripping voltammetry (TD-SV), at physiological pH 7.4. The thermodynamic parameters, e.g., Gibbs free energy, ΔG(ADS), enthalpy, ΔΗ(ADS) and entropy, ΔS(ADS), of adsorption have been determined at physiological temperatures 2-40 °C. Chemisorption of the radical species ≡[GA(OH)(2)(O(-))]* is the energetically important reaction. The thermodynamic data show a complex mechanism of adsorption of GA on the electrode surface, which is strongly dependent on temperature. At low-temperatures T<12 °C, adsorption is controlled by enthalpy, while at T>22 °C, adsorption is entropy driven. In the temperature range 12 °C and 22 °C, a combined enthalpy-entropy stabilization occurs. A mechanism is proposed which analyses the implication of thermodynamics to the interfacial adsorption of polyphenols with cell membranes under physiological conditions.