The Lidov-Kozai (LK) mechanism plays an important role in the secular evolution of many hierarchical triple systems. The standard LK mechanism consists of large-amplitude oscillations in eccentricity and inclination of a binary subject to the quadrupole potential from an outer perturber. Recent work has shown that when the octupole terms are included in the potential, the inner binary can reach more extreme eccentricities as well as undergo orientation flips. It is known that pericenter precessions due to short-range effects, such as General Relativity and tidal and rotational distortions, can limit the growth of eccentricity and even suppress standard (quadrupolar) LK oscillations, but their effect on the octupole-level LK mechanism has not been fully explored. In this paper, we systematically study how these short-range forces affect the extreme orbital behaviour found in octupole LK cycles. In general, the influence of the octupole potential is confined to a range of initial mutual inclinations i tot centered around 90• (when the inner binary mass ratio is 1), with this range expanding with increasing octupole strength. We find that, while the short-range forces do not change the width and location of this "window of influence", they impose a strict upper limit on the maximum achievable eccentricity. This limiting eccentricity can be calculated analytically, and its value holds even for strong octupole potential and for the general case of three comparable masses. Short-range forces also affect orbital flips, progressively reducing the range of i tot within which flips are possible as the intensity of these forces increases.

Black hole (BH) mergers driven by gravitational perturbations of external companions constitute an important class of formation channels for merging BH binaries detected by LIGO. We have studied the orbital and spin evolution of binary BHs in triple systems, where the tertiary companion excites large eccentricity in the inner binary through Lidov-Kozai oscillations, causing the binary to merge via gravitational radiation. Using the single-averaged and double-averaged secular dynamics of triples (where the equations of motion are averaged over the inner orbit and both orbits, respectively), we perform a large set of numerical integrations to determine the merger window (the range of companion inclinations that allows the inner binary to merge within ∼10 Gyrs) and the merger fraction as a function of various system parameters (e.g., the binary masses m 1 , m 2 and initial semi-major axis a 0 , the mass, semi-major axis and eccentricity e out of the outer companion). For typical BH binaries (m 1,2 20M − 30M and a 0 10 AU), the merger fraction increases rapidly with e out because of the octupole perturbation, ranging from ∼ 1% at e out = 0 to 10 − 20% at e out = 0.9. We derive the analytical expressions and approximate scaling relations for the merger window and merger fraction for systems with negligible octupole effect, and apply them to neutron star binary mergers in triples. We also follow the spin evolution of the BHs during the companion-induced orbital decay, where de-Sitter spin precession competes with Lidov-Kozai orbital precession/nutation. Starting from aligned spin axes (relative to the orbital angular momentum axis), a wide range of final spin-orbit misalignment angle θ f sl can be generated when the binary enters the LIGO sensitivity band. For systems where the octupole effect is small (such as those with m 1 m 2 or e out ∼ 0), the distribution of θ f sl peaks around 90 • . As the octuple effect increases, a more isotropic distribution of final spin axis is produced. Overall, merging BH binaries produced by Lidov-Kozai oscillations in triples exhibit a unique distribution of the effective (mass-weighted) spin parameter χ eff ; this may be used to distinguish this formation channel from other dynamical channels.

We study the effect of external companion on the orbital and spin evolution of merging blackhole (BH) binaries. An sufficiently close by and inclined companion can excite Lidov-Kozai (LK) eccentricity oscillations in the binary, thereby shortening its merger time. During such LK-enhanced orbital decay, the spin axis of the BH generally exhibits chaotic evolution, leading to a wide range (0• -180 • ) of final spin-orbit misalignment angle from an initially aligned configuration. For systems that do not experience eccentricity excitation, only modest ( 20• ) spin-orbit misalignment can be produced, and we derive an analytic expression for the final misalignment using the principle of adiabatic invariance. The spin-orbit misalignment directly impacts the gravitational waveform, and can be used to constrain the formation scenarios of BH binaries and dynamical influences of external companions.

We study the orbital evolution of black hole (BH) binaries in quadruple systems, where the tertiary binary excites large eccentricity in the BH binary through Lidov-Kozai (LK) oscillations, causing the binary BHs to merge via gravitational radiation. For typical BH binaries with masses m 1,2 20M − 30M and initial semimajor axis a 0 ∼ 100 AU (such that the binaries have no chance of merging by themselves within ∼ 10 10 yrs), we show that binary-binary interactions can significantly increase the LK window for mergers (the range of companion inclinations that allows the BH binary to merge within 10 Gyrs). This increase arises from a secular resonance between the LK oscillation of the BH binary and the nodal precession of the outer (binary-binary) orbit driven by the tertiary binary. Therefore, in the presence of tertiary binary, the BH merger fraction is increased to 10−30%, an order of magnitude larger than the merger fraction found in similar triple systems. Our analysis (with appropriate scalings) can be easily adapted to other configurations of systems, such as relatively compact BH binaries and moderately hierarchical triples, which may generate even higher merger fractions. Since the occurrence rate of stellar quadruples in the galactic fields is not much smaller than that of stellar triples, our result suggests that dynamically induced BH mergers in quadruple systems may be an important channel of producing BH mergers observed by LIGO/VIRGO.

We study the general relativitic (GR) effects induced by a supermassive black hole on the orbital and spin evolution of a merging black hole binary (BHB) in a hierarchical triple system. A sufficiently inclined outer orbit can excite Lidov-Kozai eccentricity oscillations in the BHB and induce its merger. These GR effects generate extra precessions on the BHB orbits and spins, significantly increasing the inclination window for mergers and producing a wide range of spin orientations when the BHB enters LIGO band. This "GR-enhanced" channel may play an important role in BHB mergers.

Phosphoglycerate mutase 1 (PGAM1) is a glycolytic enzyme that coordinates glycolysis and biosynthesis to promote cancer growth via its metabolic activity. Here, we report the discovery of a non-metabolic function of PGAM1 in promoting cancer metastasis. A proteomic study identified α-smooth muscle actin (ACTA2) as a PGAM1-associated protein. PGAM1 modulated actin filaments assembly, cell motility and cancer cell migration via directly interacting with ACTA2, which was independent of its metabolic activity. The enzymatically inactive H186R mutant retained its association with ACTA2, whereas 201-210 amino acids deleted PGAM1 mutant lost the interaction with ACTA2 regardless of intact metabolic activity. Importantly, PGAM1 knockdown decreased metastatic potential of breast cancer cells in vivo and PGAM1 and ACTA2 were jointly associated with the prognosis of breast cancer patients. Together, this study provided the first evidence revealing a non-metabolic function of PGAM1 in promoting cell migration, and gained new insights into the role of PGAM1 in cancer progression.

Lidov-Kozai oscillations of planets in stellar binaries, combined with tidal dissipation, can lead to the formation of hot Jupiters (HJs) or tidal disruption of planets. Recent population synthesis studies have found that the fraction of systems resulting in HJs (F HJ ) depends strongly on the planet mass, host stellar type and tidal dissipation strength, while the total migration fraction F mig = F HJ + F dis (including both HJ formation and tidal disruption) exhibits much weaker dependence. We present an analytical method for calculating F HJ and F mig in the Lidov-Kozai migration scenario. The key ingredient of our method is to determine the critical initial planet-binary inclination angle that drives the planet to reach sufficiently large eccentricity for efficient tidal dissipation or disruption. This calculation includes the effects of octupole potential and short-range forces on the planet. Our analytical method reproduces the resulting planet migration/disruption fractions from population synthesis, and can be easily implemented for various planet, stellar/companion types, and for different distributions of initial planetary semi-major axes, binary separations and eccentricities. We extend our calculations to planets in the super-Earth mass range and discuss the conditions for such planets to survive Lidov-Kozai migration and form close-in rocky planets.

Graphene sheets were obtained through solvothermal reduction of colloidal dispersion of graphene oxide in benzyl alcohol. The graphene/rod-shaped TiO(2) nanocomposite was synthesized by this novel and facile solvothermal method. During the solvothermal reaction, both the reduction of graphene oxide and the growth of rod-shaped TiO(2) nanocrystals as well as its deposition on graphene occur simultaneously. The photocatalytic activity of graphene/rod-shaped TiO(2) and graphene/spherical TiO(2) nanocomposites was compared. In the photocatalytic degradation of methyl orange (MO), the graphene/rod-shaped TiO(2) nanocomposite with the optimized graphene content of 0.48 wt% shows good stability and exhibits a significant enhancement of photocatalytic activity compared to the bare commercial TiO(2) (P25) and graphene/spherical TiO(2) nanocomposite with the same graphene content. Photocurrent experiments were performed, which demonstrate that the photocurrent of the graphene/rod-shaped TiO(2) nanocomposite electrode is about 1.2 times as high as that of the graphene/spherical TiO(2) nanocomposite electrode. The photocatalytic mechanism of graphene/rod-shaped TiO(2) nanocomposite was also discussed on the basis of the experimental results. This work is anticipated to open a possibility in the integration of graphene and TiO(2) with various morphologies for obtaining high-performance photocatalysts in addressing environmental protection issues.