Poisson Cohomology of Del Pezzo surfaces

In this note, we compute the Poisson cohomology groups for any Poisson Del Pezzo surface

Integrated optimisation for production capacity, raw material ordering and production planning under time and quantity uncertainties based on two case studies

Abstract This paper develops a supply chain (SC) model by integrating raw material ordering and production planning, and production capacity decisions based upon two case studies in manufacturing firms. Multiple types of uncertainties are considered; including: time-related uncertainty (that exists in lead-time and delay) and quantity-related uncertainty (that exists in information and material flows). The SC model consists of several sub-models, which are first formulated mathematically. Simulation (simulation-based stochastic approximation) and genetic algorithm tools are then developed to evaluate several non-parameterised strategies and optimise two parameterised strategies. Experiments are conducted to contrast these strategies, quantify their relative performance, and illustrate the value of information and the impact of uncertainties. These case studies provide useful insights into understanding to what degree the integrated planning model including production capacity decisions could benefit economically in different scenarios, which types of data should be shared, and how these data could be utilised to achieve a better SC system. This study provides insights for small and middle-sized firm management to make better decisions regarding production capacity issues with respect to external uncertainty and/or disruptions; e.g. trade wars and pandemics.</jats:p

New constraints on cosmic polarization rotation from the ACTPol cosmic microwave background B-Mode polarization observation and the BICEP2 constraint update

Recently ACTPol has measured the cosmic microwave background (CMB) B-mode and E-mode polarizations and obtained TE, EE, BB, TB and EB power spectra in the multipole range 225-8725. In our previous paper (Ap. J. 792 (2014) 35 [Paper I]), we have analyzed jointly the results of three experiments on the CMB B-mode polarization -- SPTpol, POLARBEAR and BICEP2 to include in the model, in addition to the gravitational lensing and the inflationary gravitational waves components, also the fluctuation effects induced by the cosmic polarization rotation (CPR), if it exists within the upper limits at the time. In this paper, we fit both the mean CPR angle and its fluctuation from the new ACTPol data, and update our fitting of CPR fluctuations using BICEP2 data taking the new Planck dust measurement results into consideration. We follow the method of Paper I. The mean CPR angle is constrained from the EB correlation power spectra to || < 14 mrad (0.8{\deg}) and the fluctuation (rms) is constrained from the BB correlation power spectra to 1/2 < 29.3 mrad (1.68{\deg}). Assuming that the polarization angle of Tau A does not change from 89.2 to 146 GHz, the ACTPol data give = 1.0 {\pm} 0.63{\deg}. These results suggest that the inclusion of the present ACTPol data is consistent with no CPR detection. With the new Planck dust measurement, we update our fits of the BICEP2 CPR fluctuation constraint to be 32.8 mrad (1.88{\deg}). The joint ACTpol-BICEP2-POLARBEAR CPR fluctuation constraint is 23.7 mrad (1.36{\deg}).Comment: 15 pages, 2 figures, 2 tables, version to match the accepted submission to ApJ. Unfortunately there is a sign error in equation (6b). This propagated to equations (7b) and (8a) and to the results for \alpha_\beta. The errors in the last raw of Table 1 had been overestimated and correcte

Coherent transport on Apollonian networks and continuous-time quantum walks

We study the coherent exciton transport on Apollonian networks generated by simple iterative rules. The coherent exciton dynamics is modeled by continuous-time quantum walks and we calculate the transition probabilities between two nodes of the networks. We find that the transport depends on the initial nodes of the excitation. For networks less than the second generation the coherent transport shows perfect revivals when the initial excitation starts at the central node. For networks of higher generation, the transport only shows partial revivals. Moreover, we find that the excitation is most likely to be found at the initial nodes while the coherent transport to other nodes has a very low probability. In the long time limit, the transition probabilities show characteristic patterns with identical values of limiting probabilities. Finally, the dynamics of quantum transport are compared with the classical transport modeled by continuous-time random walks.Comment: 5 pages, 6 figues. Submitted to Phys. ReV.

The quantum solvation, adiabatic versus nonadiabatic, and Markovian versus non-Markovian nature of electron transfer rate processes

In this work, we revisit the electron transfer rate theory, with particular interests in the distinct quantum solvation effect, and the characterizations of adiabatic/nonadiabatic and Markovian/non-Markovian rate processes. We first present a full account for the quantum solvation effect on the electron transfer in Debye solvents, addressed previously in J. Theore. & Comput. Chem. {\bf 5}, 685 (2006). Distinct reaction mechanisms, including the quantum solvation-induced transitions from barrier-crossing to tunneling, and from barrierless to quantum barrier-crossing rate processes, are shown in the fast modulation or low viscosity regime. This regime is also found in favor of nonadiabatic rate processes. We further propose to use Kubo's motional narrowing line shape function to describe the Markovian character of the reaction. It is found that a non-Markovian rate process is most likely to occur in a symmetric system in the fast modulation regime, where the electron transfer is dominant by tunneling due to the Fermi resonance.Comment: 13 pages, 10 figures, submitted to J. Phys. Chem.

Is the late near-infrared bump in short-hard GRB 130603B due to the Li-Paczynski kilonova?

Short-hard gamma-ray bursts (GRBs) are widely believed to be produced by the merger of two binary compact objects, specifically by two neutron stars or by a neutron star orbiting a black hole. According to the Li-Paczynski kilonova model, the merger would launch sub-relativistic ejecta and a near-infrared/optical transient would then occur, lasting up to days, which is powered by the radioactive decay of heavy elements synthesized in the ejecta. The detection of a late bump using the {\em Hubble Space Telescope} ({\em HST}) in the near-infrared afterglow light curve of the short-hard GRB 130603B is indeed consistent with such a model. However, as shown in this Letter, the limited {\em HST} near-infrared lightcurve behavior can also be interpreted as the synchrotron radiation of the external shock driven by a wide mildly relativistic outflow. In such a scenario, the radio emission is expected to peak with a flux of $\sim 100 \mu$Jy, which is detectable for current radio arrays. Hence, the radio afterglow data can provide complementary evidence on the nature of the bump in GRB 130603B. It is worth noting that good spectroscopy during the bump phase in short-hard bursts can test validity of either model above, analogous to spectroscopy of broad-lined Type Ic supernova in long-soft GRBs.Comment: 4 pages, 2 figures, published in ApJ Lette

A supra-massive magnetar central engine for short GRB 130603B

We show that the peculiar early optical and in particular X-ray afterglow emission of the short duration burst GRB 130603B can be explained by continuous energy injection into the blastwave from a supra-massive magnetar central engine. The observed energetics and temporal/spectral properties of the late infrared bump (i.e., the "kilonova") are also found consistent with emission from the ejecta launched during an NS-NS merger and powered by a magnetar central engine. The isotropic-equivalent kinetic energies of both the GRB blastwave and the kilonova are about $E_{\rm k}\sim 10^{51}$ erg, consistent with being powered by a near-isotropic magnetar wind. However, this relatively small value demands that most of the initial rotational energy of the magnetar $(\sim {\rm a~ few \times 10^{52}~ erg})$ is carried away by gravitational wave radiation. Our results suggest that (i) the progenitor of GRB 130603B would be a NS-NS binary system, whose merger product would be a supra-massive neutron star that lasted for about $\sim 1000$ seconds; (ii) the equation-of-state of nuclear matter would be stiff enough to allow survival of a long-lived supra-massive neutron star, so that it is promising to detect bright electromagnetic counterparts of gravitational wave triggers without short GRB associations in the upcoming Advanced LIGO/Virgo era.Comment: Five pages including 1 Figure, to appear in ApJ

Generating Bell states and NN-partite WW states of long-distance qubits in superconducting waveguide QED

We show how to generate Bell states and $N$-partite $W$ states of long-distance superconducting (SC) qubits in a SC waveguide quantum electrodynamical (QED) system, where SC qubits are coupled to an open microwave transmission line. In the two-qubit case, the Bell state of two long-distance qubits can be a dark state of the system by choosing appropriate system parameters. If one proper microwave pulse drives one of two qubits, the two qubits will evolve from their ground states to a Bell state. Further, we extend this scheme to the multi-qubit case. We show that $W$ states of $N$ long-distance qubits can also be generated. Because both the Bell and $W$ states are decoupled from the waveguide (i.e., dark states of the system), they are steady and have very long lifetimes in the ideal case without decoherence of qubits. In contrast to the ideal case, the presence of decoherence of qubits limits the lifetimes of the Bell and $W$ states. Our study provides a novel scheme for generating Bell states and $N$-partite $W$ states in SC waveguide QED, which can be used to entangle long-distance nodes in waveguide quantum networks.Comment: 12 pages, 9 figure