Bell Labs

About: Bell Labs is a based out in . It is known for research contribution in the topics: Laser & Optical fiber. The organization has 36499 authors who have published 59862 publications receiving 3190823 citations. The organization is also known as: Bell Laboratories & AT&T Bell Laboratories.

The Complexity of Flowshop and Jobshop Scheduling

Abstract: NP-complete problems form an extensive equivalence class of combinatorial problems for which no nonenumerative algorithms are known. Our first result shows that determining a shortest-length schedule in an m-machine flowshop is NP-complete for m ≥ 3. For m = 2, there is an efficient algorithm for finding such schedules. The second result shows that determining a minimum mean-flow-time schedule in an m-machine flowshop is NP-complete for every m ≥ 2. Finally we show that the shortest-length schedule problem for an m-machine jobshop is NP-complete for every m ≥ 2. Our results are strong in that they hold whether the problem size is measured by number of tasks, number of bits required to express the task lengths, or by the sum of the task lengths.

Behavior of the Electronic Dielectric Constant in Covalent and Ionic Materials

Abstract: Refractive-index dispersion data below the interband absorption edge in more than 100 widely different solids and liquids are analyzed using a single-effective-oscillator fit of the form ${n}^{2}\ensuremath{-}1=\frac{{E}_{d}{E}_{0}}{({E}_{0}^{2}\ensuremath{-}{\ensuremath{\hbar}}^{2}{\ensuremath{\omega}}^{2})}$, where $\ensuremath{\hbar}\ensuremath{\omega}$ is the photon energy, ${E}_{0}$ is the single oscillator energy, and ${E}_{d}$ is the dispersion energy. The parameter ${E}_{d}$, which is a measure of the strength of interband optical transitions, is found to obey the simple empirical relationship ${E}_{d}=\ensuremath{\beta}{N}_{c}{Z}_{a}{N}_{e}$, where ${N}_{c}$ is the coordination number of the cation nearest neighbor to the anion, ${Z}_{a}$ is the formal chemical valency of the anion, ${N}_{e}$ is the effective number of valence electrons per anion (usually ${N}_{e}=8$), and $\ensuremath{\beta}$ is essentially two-valued, taking on the "ionic" value ${\ensuremath{\beta}}_{i}=0.26\ifmmode\pm\else\textpm\fi{}0.04$ eV for halides and most oxides, and the "covalent" value ${\ensuremath{\beta}}_{c}=0.37\ifmmode\pm\else\textpm\fi{}0.05$ eV for the tetrahedrally bonded ${A}^{N}{B}^{8\ensuremath{-}N}$ zinc-blende- and diamond-type structures, as well as for scheelite-structure oxides and some iodates and carbonates. Wurtzite-structure crystals form a transitional group between ionic and covalent crystal classes. Experimentally, it is also found that ${E}_{d}$ does not depend significantly on either the bandgap or the volume density of valence electrons. The experimental results are related to the fundamental ${\ensuremath{\epsilon}}_{2}$ spectrum via appropriately defined moment integrals. It is found, using relationships between moment integrals, that for a particularly simple choice of a model ${\ensuremath{\epsilon}}_{2}$ spectrum, viz., constant optical-frequency conductivity with high- and low-frequency cutoffs, the bandgap parameter ${E}_{a}$ in the high-frequency sum rule introduced by Hopfield provides the connection between the single-oscillator parameters (${E}_{0},{E}_{d}$) and the Phillips static-dielectric-constant parameters (${E}_{g},\ensuremath{\hbar}{\ensuremath{\omega}}_{p}$), i.e., ${(\ensuremath{\hbar}{\ensuremath{\omega}}_{p})}^{2}={E}_{a}{E}_{d} \mathrm{and} {E}_{g}^{2}={E}_{a}{E}_{0}$. Finally, it is suggested that the observed dependence of ${E}_{d}$ on coordination number and valency implies that an understanding of refractive-index behavior may lie in a localized molecular theory of optical transitions.

Double exchange alone does not explain the resistivity of La1-xSrxMnO3.

Abstract: The ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{MnO}}_{3}$ system with $02\ensuremath{\lesssim}x\ensuremath{\lesssim}04$ has traditionally been modeled with a ``double-exchange'' Hamiltonian in which it is assumed that the only relevant physics is the tendency of carrier hopping to line up neighboring spins We present a solution of the double-exchange model, show it is incompatible with many aspects of the data, and propose that in addition to double-exchange physics a strong electron-phonon interaction arising from the Jahn-Teller splitting of the outer Mn $d$ level plays a crucial role