Abstract: A particular type of order-to-chaos transition mediated by an infinite set of coexisting neutrally stable limit cycles of different periods is studied in the Varley-Gradwell-Hassell population model. We prove by an algebraic method that this kind of transition can only happen for a particular bifurcation parameter value. Previous results on the structure of the attractor at the transition point are here simplified and extended.

Abstract: We extend previous results in spherically symmetric gravitational systems coupled with a massless scalar field within the loop quantum gravity framework. As a starting point, we take the Schwarzschild spacetime. The results presented here rely on the uniform discretization method. We are able to minimize the associated discrete master constraint using a variational method. The trial state for the vacuum consists of a direct product of a Fock vacuum for the matter part and a Gaussian centered around the classical Schwarzschild solution. This paper follows the line of research presented by Gambini et al (2009 Class. Quantum Grav. 26 215011 (arXiv: 0906.1774v1)) and a comparison between their result and the one given in this work is made.

Abstract: Two metallacyclic complexes of general formula Na-8[(M2L3)-L-II]center dot xH(2)O [M = Ni (4) and Co (5) with x = 15 (4) and 17 (5)] have been self-assembled in aqueous solution from N,N'-1,3-phenylenebis(oxamic acid) (H4L) and M2+ ions in a ligand/metal molar ratio of 3 : 2 in the presence of NaOH acting as base. X-Ray structural analyses of 4 and 5 show triple-stranded, dinuclear anions of the meso-helicate-type (so-called mesocates) with C-3h molecular symmetry. The two octahedral metal-tris(oxamate) moieties of opposite chiralities (Delta, Lambda form) are connected by three m-phenylene spacers at intermetallic distances of 6.822(2) (4) and 6.868(2) angstrom (5) to give a metallacryptand core. In the crystal lattice, the binding of these heterochiral dinickel(II) and dicobalt(II) triple mesocates to sodium(I) ions leads to oxamato-bridged heterobimetallic three-dimensional open-frameworks with a hexagonal diamond architecture having small pores of 17.566(4) (4) and 17.640(2) angstrom (5) in diameter where the crystallization water molecules and the sodium(I) countercations are hosted. Variable temperature (2.0-300 K) magnetic susceptibility measurements reveal relatively anisotropic S = 2 Ni-2(II) (4) and S = 3 Co-2(II) (5) ground states resulting from the moderate to weak intramolecular ferromagnetic coupling between the two high-spin Ni-II (S-Ni = 1) or Co-II (S-Co = 3/2) ions across the m-phenylenediamidate bridges [J = +3.6 (4) and +1.1 cm(-1) (5); H = -JS(1)center dot S-2]. A simple molecular orbital analysis of the electron exchange interaction identifies the p-type pathways of the meta-substituted phenylene spacers involving the d(z2) and d(x2-y2) pairs of magnetic orbitals of the two trigonally distorted octahedral high-spin M-II ions (M = Ni and Co) as responsible for the overall ferromagnetic coupling observed in 4 and 5 in agreement with a spin polarization mechanism. The decrease of the overall ferromagnetic coupling from 4 to 5 is in turn explained by the additional antiferromagnetic exchange contribution involving the d(xy) pair of magnetic orbitals of the two trigonally distorted octahedral high-spin Co-II ions across the sigma-type pathway of the meta-substituted phenylene spacers.