A savings based method for real-life vehicle routing problems

This paper describes a Savings Based algorithm for the Extended Vehicle Routing Problem. This algorithm is compared with a Sequential Insertion algorithm on real-life data. Besides the traditional quality measures such as total distance traveled and total workload, we compare the routing plans of both algorithms according to non-standard quality measures that help to evaluate the "visual attractiveness" of the plan. Computational results show that, in general, the Savings Based algorithm not only performs better with respect to these non-standard quality measures, but also with respect to the traditional measures.distribution;vehicle routing;road transport

Magnetic susceptibility of the frustrated spinels ZnCr2O4, MgCr2O4 and CdCr2O4

We analyzed the magnetic susceptibilities of several Cr spinels using two recent models for the geometrically frustrated pyrochlore lattice, the Quantum Tetrahedral Mean Field model and a Generalized Constant Coupling model. Both models can describe the experimental data for ACr2 O4 (with A = Zn, Mg, and Cd) satisfactorily, with the former yielding a somewhat better agreement with experiment for A = Zn, Mg. The obtained exchange constants for nearest and next-nearest neighbors are discussed.Comment: 4 pages, 1 figure, 1 table, conferenc

Spin-phonon coupling in antiferromagnetic chromium spinels

The temperature dependence of eigenfrequencies and intensities of the IR active modes has been investigated for the antiferromagnetic chromium spinel compounds CdCr2O4, ZnCr2O4, ZnCr2S4, ZnCr2Se4, and HgCr2S4 by IR spectroscopy for temperatures from 5 K to 300 K. At the transition into the magnetically ordered phases, and driven by spin-phonon coupling, most compounds reveal significant splittings of the phonon modes. This is true for geometrically frustrated CdCr2O4, and ZnCr2O4, for bond frustrated ZnCr2S4 and for ZnCr2Se4, which also is bond frustrated, but dominated by ferromagnetic exchange. The pattern of splitting is different for the different compounds and crucially depends on the nature of frustration and of the resulting spin order. HgCr2S4, which is almost ferromagnetic, exhibits no splitting of the eigenfrequencies, but shows significant shifts due to ferromagnetic spin fluctuations.Comment: 15 pages, 6 figure

A finite element model for a higher-order shear-deformable beam theory

The theory for a higher order shear-deformable beam model is first developed. It is based on a higher order displacement model and incorporates linear and quadratic variation of transverse normal strain and transverse shearing strain respectively through the beam thickness. The effects of the transverse normal and shear stresses are included in the definition of the material's constitutive law. The warping of the transverse normal cross-section of the beam is automatically incorporated in the mathematical model. The question of selecting a shear correction coefficient as in a first-order shear deformable Timoshenko theory does not arise. A linear two-noded finite element model of this theory is introduced and developed next. Both static and free vibration results of this theory are presented and compared with those of Euler and Timoshenko theories for various boundary and loading conditions

Broadband dielectric response of CaCu3Ti4O12: From dc to the electronic transition regime

We report on phonon properties and electronic transitions in CaCu3Ti4O12, a material which reveals a colossal dielectric constant at room temperature without any ferroelectric transition. The results of far- and mid-infrared measurements are compared to those obtained by broadband dielectric and millimeter-wave spectroscopy on the same single crystal. The unusual temperature dependence of phonon eigenfrequencies, dampings and ionic plasma frequencies of low lying phonon modes are analyzed and discussed in detail. Electronic excitations below 4 eV are identified as transitions between full and empty hybridized oxygen-copper bands and between oxygen-copper and unoccupied Ti 3d bands. The unusually small band gap determined from the dc-conductivity (~200 meV) compares well with the optical results.Comment: 7 pages, 8 figure

Polar phonons and spin-phonon coupling in HgCr2S4 and CdCr2S4

Polar phonons of HgCr2S4 and CdCr2S4 are studied by far-infrared spectroscopy as a function of temperature and external magnetic field. Eigenfrequencies, damping constants, effective plasma frequencies and Lyddane-Sachs-Teller relations, and effective charges are determined. Ferromagnetic CdCr2S4 and antiferromagnetic HgCr2S4 behave rather similar. Both compounds are dominated by ferromagnetic exchange and although HgCr2S4 is an antiferromagnet, no phonon splitting can be observed at the magnetic phase transition. Temperature and magnetic field dependence of the eigenfrequencies show no anomalies indicating displacive polar soft mode behavior. However, significant effects are detected in the temperature dependence of the plasma frequencies indicating changes in the nature of the bonds and significant charge transfer. In HgCr2S4 we provide experimental evidence that the magnetic field dependence of specific polar modes reveal shifts exactly correlated with the magnetization showing significant magneto-dielectric effects even at infrared frequencies.Comment: 8 pages, 8 figure

Exciton-magnon transitions in the frustrated chromium antiferromagnets CuCrO2, alpha-CaCr2O4, CdCr2O4, and ZnCr2O4

We report on optical transmission spectroscopy of the Cr-based frustrated triangular antiferromagnets CuCrO2 and alpha-CaCr2O4, and the spinels CdCr2O4 and ZnCr2O4 in the near-infrared to visible-light frequency range. We explore the possibility to search for spin correlations far above the magnetic ordering temperature and for anomalies in the magnon lifetime in the magnetically ordered state by probing exciton-magnon sidebands of the spin-forbidden crystal-field transitions of the Cr3+ ions (spin S = 3/2). In CuCrO2 and alpha-CaCr2O4 the appearance of fine structures below T_N is assigned to magnon sidebands by comparison with neutron scattering results. The temperature dependence of the line width of the most intense sidebands in both compounds can be described by an Arrhenius law. For CuCrO2 the sideband associated with the 4A2 -> 2T2 transition can be observed even above T_N. Its line width does not show a kink at the magnetic ordering temperature and can alternatively be described by a Z2 vortex scenario proposed previously for similar materials. The exciton-magnon features in alpha-CaCr2O4 are more complex due to the orthorhombic distortion. While for CdCr2O4 magnon sidebands are identified below T_N and one sideband excitation is found to persist across the magnetic ordering transition, only a weak fine structure related to magnetic ordering has been observed in ZnCr2O4.Comment: 14 pages, 10 figures, all comments are welcome and appreciated, accepted for publication in PR