Gamma-Ray Burst Jet Breaks Revisited

Gamma-ray Burst (GRB) collimation has been inferred with the observations of achromatic steepening in GRB light curves, known as jet breaks. Identifying a jet break from a GRB afterglow light curve allows a measurement of the jet opening angle and true energetics of GRBs. In this paper, we re-investigate this problem using a large sample of GRBs that have an optical jet break that is consistent with being achromatic in the X-ray band. Our sample includes 99 GRBs from 1997 February to 2015 March that have optical and, for Swift GRBs, X-ray light curves that are consistent with the jet break interpretation. Out of the 99 GRBs we have studied, 55 GRBs are found to have temporal and spectral behaviors both before and after the break, consistent with the theoretical predictions of the jet break models, respectively. These include 53 long/soft (Type II) and 2 short/hard (Type I) GRBs. Only 1 GRB is classified as the candidate of a jet break with energy injection. Another 41 and 3 GRBs are classified as the candidates with the lower and upper limits of the jet break time, respectively. Most jet breaks occur at 90 ks, with a typical opening angle θj = (2.5 ± 1.0)°. This gives a typical beaming correction factor ${f}_{b}^{-1}\sim 1000$ for Type II GRBs, suggesting an even higher total GRB event rate density in the universe. Both isotropic and jet-corrected energies have a wide span in their distributions: log(Eγ,iso/erg) = 53.11 with σ = 0.84; log(EK,iso/erg) = 54.82 with σ = 0.56; log(Eγ/erg) = 49.54 with σ = 1.29; and log(EK/erg) = 51.33 with σ = 0.58. We also investigate several empirical correlations (Amati, Frail, Ghirlanda, and Liang–Zhang) previously discussed in the literature. We find that in general most of these relations are less tight than before. The existence of early jet breaks and hence small opening angle jets, which were detected in the Swfit era, is most likely the source of scatter. If one limits the sample to jet breaks later than 104 s, the Liang–Zhang relation remains tight and the Ghirlanda relation still exists. These relations are derived from Type II GRBs, and Type I GRBs usually deviate from them

A STOCHASTIC SIMULATION-BASED HYBRID INTERVAL FUZZY PROGRAMMING APPROACH FOR OPTIMIZING THE TREATMENT OF RECOVERED OILY WATER

In this paper, a stochastic simulation-based hybrid interval fuzzy programming (SHIFP) approach is developed to aid the decision-making process by solving fuzzy linear optimization problems. Fuzzy set theory, probability theory, and interval analysis are integrated to take into account the effect of imprecise information, subjective judgment, and variable environmental conditions. A case study related to oily water treatment during offshore oil spill clean-up operations is conducted to demonstrate the applicability of the proposed approach. The results suggest that producing a random sequence of triangular fuzzy numbers in a given interval is equivalent to a normal distribution when using the centroid defuzzification method. It also shows that the defuzzified optimal solutions follow the normal distribution and range from 3,000-3,700 tons, given the budget constraint (CAD 110,000-150,000). The normality seems to be able to propagate throughout the optimization process, yet this interesting finding deserves more in-depth study and needs more rigorous mathematical proof to validate its applicability and feasibility. In addition, the optimal decision variables can be categorized into several groups with different probability such that decision makers can wisely allocate limited resources with higher confidence in a short period of time. This study is expected to advise the industries and authorities on how to distribute resources and maximize the treatment efficiency of oily water in a short period of time, particularly in the context of harsh environments

Fitting magnetic field gradient with Heisenberg-scaling accuracy

We propose a quantum fitting scheme to estimate the magnetic field gradient with $N$-atom spins preparing in W state, which attains the Heisenberg-scaling accuracy. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cram\'{e}r-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. In single parameter estimation with assumption that the magnetic field is strictly linear, two optimal measurements can achieve the identical Heisenberg-scaling accuracy. Proper interpretation of the super-Heisenberg-scaling accuracy is presented. The scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.Comment: 7 pages, 2 figure

Effect of Schisandra chinensis (Turcz) Schisandraceae seed extracts and cisplatin on cytotoxicity, genotoxicity and wound healing in MCF-7 cells

Purpose: Schisandra chinensis is a plant used in traditional Chinese and Russian medicine. An S. chinensis seed extract was tested for its ability to potentiate the effects of the anticancer agent cisplatin in MCF-7 breast cancer cells. Methods: S. chinensis seeds were extracted with ethanol and the ethanol was evaporated from the extracts to obtain an aqueous fraction of the S. chinensis seed extract (SCSE). MCF-7 cells were exposed to cisplatin alone or in combination with various concentrations of SCSE. The end points that were measured were cytotoxicity, genotoxicity, and wound healing. Results: The addition of 10 % SCSE increased the cytotoxicity of cisplatin by increasing MCF-7 cell death by 7 %. The combination of 20 % SCSE and cisplatin completely inhibited wound healing in MCF7 cells. SCSE alone did not induce DNA fragmentation in MCF-7 cells. Conclusion: Compounds from S. chinensis seed extracts may mitigate cancer cell proliferation and migration. Keywords: Schisandra chinensis, MCF-7 cells, Cytotoxicity, Genotoxicity, Wound healing, Cisplati

Architecture and engineering of a supramolecular functional material by manipulating the nano-structure of fiber network

Three-dimensional fiber networks were created from an organogel system consisting mainly of elongated fibrils by using a nonionic surfactant as an additive. The presence of the surfactant molecules manipulates the network structure by enhancing the mismatch nucleation on the growing fiber tips. Both the fiber network structure and the rheological properties of the material can be finely tuned by changing the surfactant concentration, which provides a robust approach to the engineering of supramolecular soft functional materials.<br /