The prediction of the nonlinear behavior of unstable liquid rockets

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

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

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 ($T_N$), 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 $T_N$ and enhances the sensitivity of $T_N$ to bending. In \cuacac, $T_N$ is extremely sensitive to bending, but remains too low for practical applications, even when bent. Partially frustrated materials could achieve the balance of high $T_N$ and good sensitivity to bending required for practical applications of mechanomagnetic elastic crystals

Sensitivity of the photo-physical properties of organometallic complexes to small chemical changes

We investigate an effective model Hamiltonian for organometallic complexes that are widely used in optoelectronic devices. The two most important parameters in the model are $J$, the effective exchange interaction between the $\pi$ and $\pi^*$ orbitals of the ligands, and $\epsilon^*$, the renormalized energy gap between the highest occupied orbitals on the metal and on the ligand. We find that the degree of metal-to-ligand charge transfer (MLCT) character of the lowest triplet state is strongly dependent on the ratio $\epsilon^*/J$. $\epsilon^*$ is purely a property of the complex and can be changed significantly by even small variations in the complex's chemistry, such as replacing substituents on the ligands. We find that that small changes in $\epsilon^*/J$ can cause large changes in the properties of the complex, including the lifetime of the triplet state and the probability of injected charges (electrons and holes) forming triplet excitations. These results give some insight into the observed large changes in the photophysical properties of organometallic complexes caused by small changes in the ligands.Comment: Accepted for publication in J. Chem. Phys. 14 pages, 9 figures, Supplementary Info: 15 pages, 17 figure

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

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

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

We consider layered decorated honeycomb lattices at two-thirds filling, as realized in some trinuclear organometallic complexes. Localized $S=1$ 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 `$D$-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

Emergence of quasi-one-dimensional physics in Mo3_3S7_7(dmit)3_3, a nearly-isotropic three-dimensional molecular crystal

We report density functional theory calculations for Mo$_3$S$_7$(dmit)$_3$. We derive an ab initio tight-binding model from overlaps of Wannier orbitals; finding a layered model with interlayer hopping terms $\sim3/4$ the size of the in-plane terms. The in-plane Hamiltonian interpolates the kagom\'e and honeycomb lattices. It supports states localized to dodecahedral rings within the plane, which populate one-dimensional (1D) bands and lead to a quasi-1D spin-one model on a layered honeycomb lattice once interactions are included. Two lines of Dirac cones also cross the Fermi energy.Comment: 5 pages, 3 figure

Development of a spinning wave heat engine

A theoretical analysis and an experimental investigation were conducted to assess the feasibility of developing a spinning wave heat engine. Such as engine would utilize a large amplitude traveling acoustic wave rotating around a cylindrica chamber, and it should not suffer from the inefficiency, noise, and intermittent thrust which characterizes pulse jet engines. The objective of this investigation was to determine whether an artificially driven large amplitude spinning transverse wave could induce a steady flow of air through the combustion chamber under cold flow conditions. In the theoretical analysis the Maslen and Moore perturbation technique was extended to study flat cylinders (pancake geometry) with completely open side walls and a central opening. In the parallel experimental study, a test moel was used to determine resonant frequencies and radial pressure distributions, as well as oscillatory and steady flow velocities at the inner and outer peripheries. The experimental frequency was nearly the same as the theoretical acoustic value for a model of the same outer diameter but without a central hole. Although the theoretical analysis did not predict a steady velocity component, simulaneous measurements of hotwire and microphone responses have shown that the spinning wave pumps a mean flow radially outward through the cavity

Determination of the effects of nozzle nonlinearities upon nonlinear stability of liquid propellant rocket motors

The research is reported concerning the development of a three-dimensional nonlinear nozzle admittance relation to be used as a boundary condition in the nonlinear combustion instability theories for liquid propellant rocket engines. The derivation of the nozzle wave equation and the application of the Galerkin method are discussed along with the nozzle response