24,167 research outputs found

    The prediction of nonlinear three dimensional combustion instability in liquid rockets with conventional nozzles

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    An analytical technique is developed to solve nonlinear three-dimensional, transverse and axial combustion instability problems associated with liquid-propellant rocket motors. The Method of Weighted Residuals is used to determine the nonlinear stability characteristics of a cylindrical combustor with uniform injection of propellants at one end and a conventional DeLaval nozzle at the other end. Crocco's pressure sensitive time-lag model is used to describe the unsteady combustion process. The developed model predicts the transient behavior and nonlinear wave shapes as well as limit-cycle amplitudes and frequencies typical of unstable motor operation. The limit-cycle amplitude increases with increasing sensitivity of the combustion process to pressure oscillations. For transverse instabilities, calculated pressure waveforms exhibit sharp peaks and shallow minima, and the frequency of oscillation is within a few percent of the pure acoustic mode frequency. For axial instabilities, the theory predicts a steep-fronted wave moving back and forth along the combustor

    The prediction of the nonlinear behavior of unstable liquid rockets

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    Analytical technique for solving nonlinear combustion problems associated with liquid propellant rocket engine

    Towards the parameterisation of the Hubbard model for salts of BEDT-TTF: A density functional study of isolated molecules

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    We calculate the effective Coulomb repulsion between electrons/holes, U, and site energy for an isolated BEDT-TTF [bis(ethylenedithio)tetrathiafulvalene] molecule in vacuo. U=4.2 \pm 0.1 eV for 44 experimental geometries taken from a broad range of conformations, polymorphs, anions, temperatures, and pressures (the quoted `error' is one standard deviation). Hence we conclude that U is essentially the same for all of the compounds studied. This shows that the strong (hydrostatic and chemical) pressure dependence observed in the phase diagrams of the BEDT-TTF salts is not due to U. Therefore, if the Hubbard model is sufficient to describe the phase diagram of the BEDT-TTF salts there must be significant pressure dependence on the intramolecular terms in the Hamiltonian and/or the reduction of the Hubbard U due to the interaction of the molecule with the polarisable crystal environment. The renormalised value of U is significantly smaller than the bare value of the Coulomb integral: F_0=5.2\pm0.1 eV across the same set of geometries, emphasising the importance of using the renormalised value of U. The site energy (for holes), xi=5.0\pm0.2 eV, varies only a little more than U across the same set of geometries. However, we argue that this plays a key role in understanding the role of disorder in ET salts in general and in explaining the difference between the beta_L and beta_H phases of beta-(BEDT-TTF)_2I_3 in particular.Comment: 13 pages, 6 figures, also see animations at http://www.youtube.com/watch?v=3K2kP8hWpZI, http://www.youtube.com/watch?v=wIz1cRsSdEs and http://www.youtube.com/watch?v=bNzUBAS6AFM, Expanded discussion of renormalisation effects. To appear in J. Chem. Phy

    Unified explanation of the Kadowaki-Woods ratio in strongly correlated materials

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    Discoveries of ratios whose values are constant within broad classes of materials have led to many deep physical insights. The Kadowaki-Woods ratio (KWR) compares the temperature dependence of a metal's resistivity to that of its heat capacity; thereby probing the relationship between the electron-electron scattering rate and the renormalisation of the electron mass. However, the KWR takes very different values in different materials. Here we introduce a ratio, closely related to the KWR, that includes the effects of carrier density and spatial dimensionality and takes the same (predicted) value in organic charge transfer salts, transition metal oxides, heavy fermions and transition metals - despite the numerator and denominator varying by ten orders of magnitude. Hence, in these materials, the same emergent physics is responsible for the mass enhancement and the quadratic temperature dependence of the resistivity and no exotic explanations of their KWRs are required.Comment: Final version accepted by Nature Phy

    Towards mechanomagnetics in elastic crystals: insights from [Cu(acac)2_2]

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    We predict that the magnetic properties of \cuacac, an elastically flexible crystal, change dramatically when the crystal is bent. We find that unbent \cuacac\ is an almost perfect Tomonaga-Luttinger liquid. Broken-symmetry density functional calculations reveal that the magnetic exchange interactions along the chains is an order of magnitude larger than the interchain exchange. The geometrically frustrated interchain interactions cannot magnetically order the material at any experimentally accessible temperature. The ordering temperature (TNT_N), calculated from the chain random phase approximation, increases by approximately 24 orders of magnitude when the material is bent. We demonstrate that geometric frustration both suppresses TNT_N and enhances the sensitivity of TNT_N to bending. In \cuacac, TNT_N is extremely sensitive to bending, but remains too low for practical applications, even when bent. Partially frustrated materials could achieve the balance of high TNT_N and good sensitivity to bending required for practical applications of mechanomagnetic elastic crystals

    Effects of anisotropy in spin molecular-orbital coupling on effective spin models of trinuclear organometallic complexes

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    We consider layered decorated honeycomb lattices at two-thirds filling, as realized in some trinuclear organometallic complexes. Localized S=1S=1 moments with a single-spin anisotropy emerge from the interplay of Coulomb repulsion and spin molecular-orbit coupling (SMOC). Magnetic anisotropies with bond dependent exchange couplings occur in the honeycomb layers when the direct intracluster exchange and the spin molecular-orbital coupling are both present. We find that the effective spin exchange model within the layers is an XXZ + 120∘^\circ honeycomb quantum compass model. The intrinsic non-spherical symmetry of the multinuclear complexes leads to very different transverse and longitudinal spin molecular-orbital couplings, which greatly enhances the single-spin and exchange coupling anisotropies. The interlayer coupling is described by a XXZ model with anisotropic biquadratic terms. As the correlation strength increases the systems becomes increasingly one-dimensional. Thus, if the ratio of SMOC to the interlayer hopping is small this stabilizes the Haldane phase. However, as the ratio increases there is a quantum phase transition to the topologically trivial `DD-phase'. We also predict a quantum phase transition from a Haldane phase to a magnetically ordered phase at sufficiently strong external magnetic fields.Comment: 22 pages, 11 figures. Final version of paper to be published in PRB. Important corrections to appendix

    Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in tri-nuclear organometallic clusters

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    Motivated by recent synthetic and theoretical progress we consider magnetism in crystals of multi-nuclear organometallic complexes. We calculate the Heisenberg symmetric exchange and the Dzyaloshinskii-Moriya antisymmetric exchange. We show how, in the absence of spin-orbit coupling, the interplay of electronic correlations and quantum interference leads to a quasi-one dimensional effective spin model in a typical tri-nuclear complex, Mo3_3S7_7(dmit)3_3, despite its underlying three dimensional band structure. We show that both intra- and inter-molecular spin-orbit coupling can cause an effective Dzyaloshinskii-Moriya interaction. Furthermore, we show that, even for an isolated pair of molecules the relative orientation of the molecules controls the nature of the Dzyaloshinskii-Moriya coupling. We show that interference effects also play a crucial role in determining the Dzyaloshinskii-Moriya interaction. Thus, we argue, that multi-nuclear organometallic complexes represent an ideal platform to investigate the effects of Dzyaloshinskii-Moriya interactions on quantum magnets.Comment: This update incorporates the corrections described in a recently submitted erratum. Changes are confined to sections IV.A and B. The conclusions of the paper are unchanged. 12 + 4 pages, 9 figure

    Spin-orbit coupling in {Mo3_3S7_7(dmit)3_3}

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    Spin-orbit coupling in crystals is known to lead to unusual direction dependent exchange interactions, however understanding of the consequeces of such effects in molecular crystals is incomplete. Here we perform four component relativistic density functional theory computations on the multi-nuclear molecular crystal {Mo3_3S7_7(dmit)3_3} and show that both intra- and inter-molecular spin-orbit coupling are significant. We determine a long-range relativistic single electron Hamiltonian from first principles by constructing Wannier spin-orbitals. We analyse the various contributions through the lens of group theory. Intermolecular spin-orbit couplings like those found here are known to lead to quantum spin-Hall and topological insulator phases on the 2D lattice formed by the tight-binding model predicted for a single layer of {Mo3_3S7_7(dmit)3_3}
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