Facets for the cut cone I

We study facets of the cut coneC _n , i.e., the cone of dimension 1/2n(n – 1) generated by the cuts of the complete graph onn vertices. Actually, the study of the facets of the cut cone is equivalent in some sense to the study of the facets of the cut polytope. We present several operations on facets and, in particular, a lifting procedure for constructing facets ofC _n+1 from given facets of the lower dimensional coneC _n . After reviewing hypermetric valid inequalities, we describe the new class of cycle inequalities and prove the facet property for several subclasses. The new class of parachute facets is developed and other known facets and valid inequalities are presented.     

Entropy-driven formation of the gyroid cubic phase

We show, by computer simulation, that tapered or pear-shaped particles, interacting through purely repulsive interactions, can freely self-assemble to form the three-dimensionally periodic, gyroid cubic phase. The Ia3d gyroid cubic phase is formed by these particles on both compression of an isotropic configuration and expansion of a smectic A bilayer arrangement. For the latter case, it is possible to identify the steps by which the topological transformation from nonintersecting planes to fully interpenetrating, periodic networks takes place.     

Topological and Steric Constraints to Stabilize Heteroleptic Copper(I) Complexes Combining Phenanthroline Ligands and Phosphines

Heteroleptic copper(I) complexes combining phenanthroline derivatives (NN) and chelating bisphosphine ligands (PP) are an important class of luminescent materials for various applications. Although thermodynamically stable, [Cu(NN)(PP)]⁺ derivatives are also kinetically unstable. As a result, a dynamic ligand-exchange reaction is often observed in solution, leading to a dynamic mixture of heteroleptic and homoleptic complexes. To prevent the formation of the homoleptic species, macrocyclic phenanthroline ligands have been used for the preparation of [Cu(NN)(PP)]⁺ pseudorotaxanes. The topological constraint resulting from the macrocyclic structure of the NN ligand drives the thermodynamic equilibrium towards the exclusive formation of the heteroleptic complex as long as the macrocycle is large and flexible enough to allow for the threading of the PP ligand. Conversely, when the threading is prevented by steric constraints, unprecedented copper(I) complexes with a trigonal coordination geometry are obtained. These results are summarized in the present concept article.     

In memoriam: Boris Dubrovin

Letters in Mathematical Physics -     

Initial interaction of oxygen with aluminium single crystal faces: A LEED,AES and work function study

Auger electron spectroscopy (AES), low energy electron diffraction (LEED) and work function (Kelvin probe) measurements have been used to study the initial interaction of clean Al(111), (100) and (110) surfaces with oxygen at room temperature. The oxidation process was found to be surface orientation dependent, but a common feature has been always observed on the three low-index surfaces: they show two distinct phases, i.e. a chemisorbed phase followed then by an oxidized phase. From analysis of AES, LEED and Kelvin probe results, an adsorption mechanism of O on Al for each surface orientation is proposed.     

Hydrodynamic modes in a gas of magnons

Density waves analogous to second sound are studied in a gas of magnons. Quasiparticle interaction is considered for both equilibrium and non equilibrium thermodynamics. The non equilibrium theory is based on a Boltzmann equation for magnon-magnon scattering. Contrary to the total energy and magnetization, (quasi)-momentum is not strictly conserved. In the hydrodynamic regime, the transport equation is reduced to a set of two coupled equations for the magnetization and the local temperature. For low temperatures these have diffusive and propagating solutions while for high temperatures, where momentum is dissipated by Umklapp processes, the solutions are only diffusive. The magnetization response function and the corresponding spectral function are discussed for various wavenumbers and temperatures.     

Etude de la structure magnetique et de la transition de typr “spin-flop” de Rb2FeF5

The nature of the magnetic interactions in the chain compound Rb₂FeF₅ has been investigated using neutron diffraction and magnetic measurements under high applied fields. Rb₂FeF₅ orders antiferromagnetically at T_N = 8.0 ± 0.5 K; the magnetic structure is of the A_Z + G_X mode and the moment of the Fe³⁺ ion extrapoled to 0K is 3.5 ± 0.2 μ_B, this low value being due to zero-point spin reduction. Within a chain the Fe³⁺ ions are antiferromagnetically coupled with an exchange constant of J/k = ?8.8 K. A spin-flop behavior has been observed and interpreted on the basis of the molecular field theory. The critical field was found to be H_C = 65 kOe at 1.7 K.     

Simulation of certain multivariate generalized Pareto distributions

The investigation of multivariate generalized Pareto distributions (GPDs) has begun only recently. For further progress with these distributions simulation methods are an important part. We describe several methods of simulating GPDs, beginning with an efficient method for the logistic GPD. The algorithm is based on the Shi transformation, which was already used for the simulation of multivariate extreme value distributions (EVDs) of logistic type. In the sequel another algorithm is presented simulating a broader class of GPDs. Due to its numerical complexity it is only practicably applicable in low dimensions. A method is given to generate unconditional GPD random vectors from conditionally GPD distributed random vectors. A short application of the simulation methods in the analysis of a real hydrological data set concludes the article. The simulation algorithms are available on the author’s home page .      

Path Relinking, Cycle-Based Neighbourhoods and Capacitated Multicommodity Network Design

In this paper, we propose a path relinking procedure for the fixed-charge capacitated multicommodity network design problem. Cycle-based neighbourhoods are used both to move along paths between elite solutions and to generate the elite candidate set by a tabu-like local search procedure. Several variants of the method are implemented and compared. Extensive computational experiments indicate that the path relinking procedure offers excellent results. It systematically outperforms the cycle-based tabu search method in both solution quality and computational effort and offers the best current meta-heuristic for this difficult class of problems.