Composites of poly(ε‐caprolactone) and Mo6S3I6 Nanowires

Composites of poly(ε‐caprolactone) (PCL) and molybdenum sulfur iodine (MoSI) nanowires were prepared using twin‐screw extrusion. Extensive microscopic examination of the composites revealed the nanowires were well dispersed in the PCL matrix, although bundles of Mo₆S₃I₆ ropes were evident at higher loadings. Secondary electron imaging (SEI) showed the nanowires had formed an extensive network throughout the PCL matrix, resulting in increased electrical conductivity of PCL, by eight orders of magnitude, and an electrical percolation threshold of 6.5 × 10^?3 vol%. Thermal analysis (DSC), WAXD, and hot stage polarized optical microscopy (HSPOM) experiments revealed Mo₆S₃I₆ addition altered PCL crystallization kinetics, nucleation density, and crystalline content. A greater number of smaller spherulites were formed via heterogeneous nucleation. The onset of thermal decomposition (TGA) of PCL decreased by 70°C, a consequence of the thermal degradation of Mo₆S₃I₆ to MoO₃, which in turn accelerates the formation of volatile gases during the first stage of PCL decomposition. Copyright © 2010 John Wiley & Sons, Ltd.     

Classical and quantum effects in spatially modulated optical parametric oscillators

We study the effects of transverse spatial modulations in a multimode degenerate optical parametric oscillator. Intracavity photonic crystals allow us to tune the instability threshold and improve entanglement above threshold. Here we compare such results with the case in which the modulation is in the injected field profile.     

Algorithmic boundedness-from-below conditions for generic scalar potentials

Checking that a scalar potential is bounded from below (BFB) is an ubiquitous and notoriously difficult task in many models with extended scalar sectors. Exact analytic BFB conditions are known only in simple cases. In this work, we present a novel approach to algorithmically establish the BFB conditions for any polynomial scalar potential. The method relies on elements of multivariate algebra, in particular, on resultants and on the spectral theory of tensors, which is being developed by the mathematical community. We give first a pedagogical introduction to this approach, illustrate it with elementary examples, and then present the working Mathematica implementation publicly available at GitHub. Due to the rapidly increasing complexity of the problem, we have not yet produced ready-to-use analytical BFB conditions for new multi-scalar cases. But we are confident that the present implementation can be dramatically improved and may eventually lead to such results.     

The shadow of a collapsing dark star

The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it has existed for all time. Here we ask the question of how this shadow comes about in the course of time when a black hole is formed by gravitational collapse. To that end we consider a star that is spherically symmetric, dark and non-transparent and we assume that it begins, at some instant of time, to collapse in free fall like a ball of dust. We analytically calculate the dependence on time of the angular radius of the shadow, first for a static observer who is watching the collapse from a certain distance and then for an observer who is falling towards the centre following the collapsing star.     

Colour rearrangement for dipole showers

We present an algorithm to rearrange the colour chains of dipole showers in the shower process according to the colour amplitudes of a simple matrix element. We implement the procedure in the dipole shower of Herwig and show comparisons to data.     

Reconstruction of physics objects at the Circular Electron Positron Collider with Arbor

After the Higgs discovery, precise measurements of the Higgs properties and the electroweak observables become vital for the experimental particle physics. A powerful Higgs/Z factory, the Circular Electron Positron Collider (CEPC) is proposed. The Particle Flow oriented detector design is proposed to the CEPC and a Particle Flow algorithm, Arbor is optimized accordingly. We summarize the physics object reconstruction performance of the Particle Flow oriented detector design with Arbor algorithm and conclude that this combination fulfills the physics requirement of CEPC.     

Solitary wave solutions for some nonlinear time-fractional partial differential equations

In this paper, we have studied the hybrid projective synchronisation for incommensurate, integer and commensurate fractional-order financial systems with unknown disturbance. To tackle the problem of unknown bounded disturbance, fractional-order disturbance observer is designed to approximate the unknown disturbance. Further, we have introduced simple sliding mode surface and designed adaptive sliding mode controllers incorporating with the designed fractional-order disturbance observer to achieve a bounded hybrid projective synchronisation between two identical fractional-order financial model with different initial conditions. It is shown that the slave system with disturbance can be synchronised with the projection of the master system generated through state transformation. Simulation results are presented to ensure the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. Also, synchronisation error for commensurate, integer and incommensurate fractional-order financial systems is studied in numerical simulation.