Curvature and geodesic instabilities in a geometrical approach to the planar three-body problem

The Maupertuis principle allows us to regard classical trajectories as reparametrized geodesics of the Jacobi-Maupertuis (JM) metric on configuration space. We study this geodesic reformulation of the planar three-body problem with both Newtonian and attractive inverse-square potentials. The associated JM metrics possess translation and rotation isometries in addition to scaling isometries for the inverse-square potential with zero energy E. The geodesic flow on the full configuration space $C^3$ (with collision points excluded) leads to corresponding flows on its Riemannian quotients: the center of mass configuration space $C^2$ and shape space $R^3$ (as well as $S^3$ and the shape sphere $S^2$ for the inverse-square potential when E = 0). The corresponding Riemannian submersions are described explicitly in `Hopf' coordinates which are particularly adapted to the isometries. For equal masses subject to inverse-square potentials, Montgomery shows that the zero-energy `pair of pants' JM metric on the shape sphere is geodesically complete and has negative gaussian curvature except at Lagrange points. We extend this to a proof of boundedness and strict negativity of scalar curvatures everywhere on $C^2, R^3$ & $S^3$ with collision points removed. Sectional curvatures are also found to be largely negative, indicating widespread geodesic instabilities. We obtain asymptotic metrics near collisions, show that scalar curvatures have finite limits and observe that the geodesic reformulation `regularizes' pairwise and triple collisions on $C^2$ and its quotients for arbitrary masses and allowed energies. For the Newtonian potential with equal masses and E=0, we find that the scalar curvature on $C^2$ is strictly negative though it could have either sign on $R^3$. However, unlike for the inverse-square potential, geodesics can encounter curvature singularities at collisions in finite geodesic time.Comment: 26 pages, 16 figures. Published version, typos corrected and references update

A Marketing-Oriented Inventory Model with Three-Component Demand Rate and Time-Dependent Partial Backlogging

This paper, an attempt has been made to extend the model of “An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging” with a view to making the model more flexible, realistic and applicable in practice. Here, objectives are to maximize the profit and minimize the total shortage cost. In this model, fuzzy goals are used by linear membership functions and after fuzzification, it is solved by weighted fuzzy non-linear programming technique. The model is illustrated with a numerical example adopted partially from “An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging”

Atomic structure, binding energy, and magnetic properties of iron atoms supported on a polyaromatic hydrocarbon

The atomic structure, energetics, and properties of gas-phase cluster complexes containing coronene (C24H12) molecule and up to two iron atoms are studied for the first time using density functional theory and generalized gradient approximation for exchange and correlation. The geometries of the neutral and cationic iron–coronene complexes are optimized without symmetry constraint and by examining the possibility that iron atoms could occupy various sites via individual π or bridging interactions. In both neutral and cationic complexes a single Fe atom is found to preferentially occupy the on-top site above the outer ring, while two Fe atoms dimerize and reside on the top of center of the outer rings. The binding energy of neutral Fe2–coronene defined with respect to dissociation into coronene and Fe2 is larger than that of Fe–coronene while reverse is true for the corresponding cations. Although the ionization potentials of these complexes are not very sensitive to the number of adsorbed Fe atoms, they are significantly reduced from those of the Fe atom or the coronene molecule. The photodecomposition of cationic (Fen–coronene)+ complexes proceeds through the ejection of either coronene+ or (Fe–coronene)+ cations while in the case of neutral Fe2–coronene, the ejection of Fe2 is energetically preferred. The coupling between the Fe atoms remains ferromagnetic although the magnetic moment/atom is reduced from the free-atom value. The results compare well with recent mass ion intensity and photofragmentation experiments

First-principles investigation of spin polarized conductance in atomic carbon wire

We analyze spin-dependent energetics and conductance for one dimensional (1D) atomic carbon wires consisting of terminal magnetic (Co) and interior nonmagnetic (C) atoms sandwiched between gold electrodes, obtained employing first-principles gradient corrected density functional theory and Landauer's formalism for conductance. Wires containing an even number of interior carbon atoms are found to be acetylenic with sigma-pi bonding patterns, while cumulene structures are seen in wires containing odd number of interior carbon atoms, as a result of strong pi-conjugation. Ground states of carbon wires containing up to 13 C atoms are found to have anti-parallel spin configurations of the two terminal Co atoms, while the 14 C wire has a parallel Co spin configuration in the ground state. The stability of the anti-ferromagnetic state in the wires is ascribed to a super-exchange effect. For the cumulenic wires this effect is constant for all wire lengths. For the acetylenic wires, the super-exchange effect diminishes as the wire length increases, going to zero for the atomic wire containing 14 carbon atoms. Conductance calculations at the zero bias limit show spin-valve behavior, with the parallel Co spin configuration state giving higher conductance than the corresponding anti-parallel state, and a non-monotonic variation of conductance with the length of the wires for both spin configurations.Comment: revtex, 6 pages, 5 figure

Effect of dietary supplementation of marigold oleoresin on growth, survival and total muscle carotenoid of Koi carp, Cyprinus carpio L.

The experiment was conducted to evaluate the effect of dietary supplementation of carotenoid (marigold oleoresin) on growth, survival and total body carotenoid of Koi carp (Cyprinus carpio). The experiment was carried out in 12 fiber aquarium tanks of size 12"×6"×6"(20l capacity). Each tank was stocked with15 fishes of uniform size. The marigold oleoresin were as dietary supplement at levels 60, 120, 180, 240, 300 ppm/kg of the feed and designated as treatment T1, T2, T3, T4 and T5 respectively and diet without marigold oleoresin supplementationserved as a control (T0). The result of the experiment showed that there was significant difference found in absolute growth rate and specific growth rate of the fish (P >0.05). However, 180ppm marigold oleoresin fed fishes showed higher mean weight gain of 3.98±0.22g and lower feed conversion ratio (FCR) of 2.81±0.04 than the other treatment groups. The body coloration and total carotenoid concentration of muscle tissue (30.16±0.60?g/g) was significantly higher in fish fed with 180 ppm marigold oleoresin diet. The study showed that incorporation of 180ppm of marigold oleoresin in diet was found better to enhance the growth and coloration in C. carpio

Superconducting and normal-state interlayer-exchange-coupling in La0.67_{0.67}Sr0.33_{0.33}MnO3{3}-YBa2_{2}Cu3_{3}O7−La_{7}-La_{0.67}SrSr_{0.33}MnO MnO{3}$ epitaxial trilayers

The issue of interlayer exchange coupling in magnetic multilayers with superconducting (SC) spacer is addressed in La$_{0.67}$Sr$_{0.33}$MnO$_{3}$ (LSMO) - YBa$_{2}$Cu$_{3}$O$_{7}$ (YBCO) - La$_{0.67}$Sr$_{0.33}$MnO$_{3}$ (LSMO) epitaxial trilayers through resistivity, ac-susceptibility and magnetization measurements. The ferromagnetic (FM) LSMO layers possessing in-plane magnetization suppress the critical temperature (T$_{c})$ of the c-axis oriented YBCO thin film spacer. The superconducting order, however, survives even in very thin layers (thickness d$_{Y} \sim$ 50 {\AA}, $\sim$ 4 unit cells) at T $<$ 25 K. A predominantly antiferromagnetic (AF) exchange coupling between the moments of the LSMO layers at fields $<$ 200 Oe is seen in the normal as well as the superconducting states of the YBCO spacer. The exchange energy J$_{1}$ ($\sim$ 0.08 erg/cm$^{2}$ at 150 K for d$_{Y}$ = 75 {\AA}) grows on cooling down to T$_{c}$, followed by truncation of this growth on entering the superconducting state. The coupling energy J$_{1}$ at a fixed temperature drops exponentially with the thickness of the YBCO layer. The temperature and d$_{Y}$ dependencies of this primarily non-oscillatory J$_{1}$ are consistent with the coupling theories for systems in which transport is controlled by tunneling. The truncation of the monotonic T dependence of J$_{1}$ below T$_{c}$ suggests inhibition of single electron tunneling across the CuO$_{2}$ planes as the in-plane gap parameter acquires a non-zero value.Comment: Accepted for publication in Phys. Rev.