Optimization models for the single delay management problem in public transportation

Passengers travelling in public transportation networks often have to use different lines to cover the trip from their origin to the desired destination. As a consequence, the reliability of connections between vehicles is a key issue for the attractiveness of the intermodal transportation network and it is strongly affected by some unpredictable events like breakdowns or vehicle delays. In such cases, a decision is required to determine if the connected vehicles should wait for the delayed ones or keep their schedule. The delay management problem (DMP) consists in defining the wait/depart policy which minimizes the total delay on the network. In this work, we present two equivalent mixed integer linear programming models for the DMP with a single initial delay, able to reduce the number of variables with respect to the formulations proposed by the literature. The two models are solved by a branch and cut procedure and by a constraint generation approach respectively, and preliminary computational results are presented.     

Crystal Structure and Complexing Properties of p-tert-butylcalix[6]-1,4-2,5-bis(crown-4)

The X-ray structure of the alreadypublished p-tert-butylcalix[6]-1,4-2,5-bis(crown-4)1 is reported. Extraction of solid ammoniumpicrate in chloroform-d indicates thecation to be located outside of the calixcrown andforming a 1:2 (metal-ligand) complex.     

A one shot method for divertor target shape optimization

Shape optimization methods, as commonly applied in aerodynamic design applications, have recently been adapted for use in nuclear fusion divertor target design. The resulting algorithms are very efficient compared to the standard use of numerical edge plasma simulations as analysis tools only. In this paper, we highlight some numerical aspects of the underlying algorithm, focusing on a correct, nine-point discretization of the fluxes and the need for an adjoint pressure correction equation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Complex between C-Methylcalix[4]resorcinarene and Triethylammonium Nitrate

Abstract

The synthesis and crystal structure of the complex formed by the all-cis epimer of C-methylcalix[4]resorcinarene (1) and triethylammonium nitrate are reported. “1.(HNEt⁺ ₃)₄. (NO^? ₃)₄(2)”, crystallizes in the monoclinic space group P2₁/n, a=25.796(2), b=16.6048(11), c=29.5659(10) Å, β=94.636(4)°, V=12623(2) ų, Z=8. Refinement led to a final conventional R₁ value of 0.128 for 12428 reflections and 1473 parameters. The resorcinarene displays the usual bowl-type shape, with four hydroxyl protons involved in intramolecular hydrogen bonds, whereas the remaining four make hydrogen bonds with four bridging nitrate ions, which results in the formation of infinite chains. Those chains are arranged so as to form layers, between which the triethylammonium ions and the remaining nitrate ions are hydrogen-bonded one to another.     

Vibrational spectra of cyclopentadienyl chlorides of titanium,zirconium and hafnium. internal rotation and thermodynamic functions

The infrared and Raman spectra of some cyclopentadienyl compounds of the transition metals, namely Ti(C₅H₅)Cl₃ and M(C₅H₅)₂Cl₂ (M = Ti, Zr and Hf), are reported and discussed. The infrared spectra of the gaseous species isolated in argon matrices at 10 K provide structural information about the single molecules. Particular attention has been paid to the low-frequency region in order to achieve more reliable assignments for the internal-rotation modes. The structural data and the fundamental frequencies derived from the spectra are employed in a calculation of the thermodynamic functions for these compounds in the ideal gas state.     

Approximate inertial manifolds for reaction-diffusion equations in high space dimension

The concept of approximate inertial manifolds was introduced by Foiaset al. (1987) in the case of the two-dimensional Navier-Stokes equations. These manifolds are finite dimensional smooth manifolds such that the orbits enter a very thin neighborhood of the manifold after a transient time; this concept replaces the one of inertial manifold when either an inertial manifold does not exist or its existence is not known. Our aim in this paper is to prove that approximate inertial manifolds exist for reaction-diffusion equations in high space dimension by opposition with exact inertial manifolds whose existence has only been proved in low dimension and for which nonexistence results have been obtained in space dimensionn=4.     

Transient rheological behaviour of poly-para-henylenetherephthalamide (PpPTA) in sulphuric acid

Nearly all the available information on the transient flow behaviour of liquid crystalline polymers has been obtained on model systems, especially on solutions of polybenzylglutamate (PBG) and hydroxypropylcellulose (HPC). The assessment of rheological models has been based almost entirely on these model systems. It is not clear how much of the available theoretical and experimental knowledge can be applied to systems of industrial relevance, which have quite different molecular structures. Here, an industrial lyotropic system, poly(p-phenylenetherephthalamide) (PpPTA) in sulphuric acid (TWARON from AKZO), is investigated. Various techniques to study transient behaviour are used, these include measurements of transient shear and normal stresses after sudden changes in shear rate, dynamic moduli and stress relaxation after cessation of flow and elastic recoil. At all shear rates studied the PpPTA solution is shear thinning, and the first normal stress difference remains positive. For the stress transients a strain scaling applies reasonably well as it did in model systems. The moduli increase with time upon cessation of flow, indicating that the molecules become less oriented in the previous flow direction. This particular behaviour is similar to that of HPC. Transients also resemble more closely those of HPC rather than those of PBG. This latter difference might be attributed to the higher flexibility of HPC and PpPTA chains as compared with PBG molecules.     

Swelling instability of surface-attached gels as a model of soft tissue growth under geometric constraints

The purpose of this work is to provide a theoretical analysis of the mechanical behavior of the growth of soft materials under geometrical constraints. In particular, we focus on the swelling of a gel layer clamped to a substrate, which is still the subject of many experimental tests. Because the constrained swelling process induces compressive stresses, all these experiments exhibit surface instabilities, which ultimately lead to cusp formation. Our model is based on fixing a neo-Hookean constitutive energy together with the incompressibility requirement for a volumetric, homogeneous mass addition. Our approach is developed mostly, but not uniquely, in the plane strain configuration. We show how the standard equilibrium equations from continuum mechanics have a similarity with the two-dimensional Stokes flows, and we use a nonlinear stream function for the exact treatment of the incompressibility constraint. A free energy approach allows the extension both to arbitrary hyperelastic strain energies and to additional interactions, such as surface energies. We find that, at constant volumetric growth, the threshold for a wavy instability is completely governed by the amount of growth. Nevertheless, the determination of the wavelength at threshold, which scales with the initial thickness of the gel layer, requires the coupling with a surface effect. Our findings, which are valid in proximity of the threshold, are compared to experimental results. The proposed treatment can be extended to weakly nonlinearities within the aim of the theory of bifurcations.