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Abstract Gamma-ray bursts (GRBs) are among the most energetic events in the Universe, driven by relativistic jets launched from black holes (BHs) formed during the collapse of massive stars or after the merger of two neutron stars. The jet power depends on the BH spin and the magnetic flux accreted onto it. In the standard thin disk model, jet power is limited by insufficient magnetic flux, even when the spin approaches maximum possible value. In contrast, the magnetically arrested disk (MAD) state limits jet energy by extracting significant angular momentum, braking BH rotation. We propose a unified model incorporating both standard thin disk and MAD states, identifying a universal curve for jet power per accretion rate as a function of the magnetic flux ratio, ${\Delta }_{\mathrm{eq}}={({\Phi }_{\mathrm{BH}}/{\Phi }_{\mathrm{MAD}})}_{\mathrm{eq}}$, at spin equilibrium. For long GRBs (lGRBs), the model predicts a maximum jet energy of ∼1.5% of the accretion energy, occurring at Δ_eq ∼ 0.4, where the BH equilibrium spin isa ∼ 0.5. Both long and short GRBs are unlikely to be produced by a MAD: for short GRBs, this requires an accreted mass orders of magnitude smaller than that available, while for lGRBs, the narrow progenitor mass distribution challenges the ability to produce the observed broad distribution of jet energies. This framework provides a consistent explanation for both standard and luminous GRBs, emphasizing the critical role of magnetic flux. Both long and short GRBs require magnetic flux distributions that peak around 10²⁷G cm². 

Nowadays, non-volatile memory technologies have been widely applied in different areas. Of these memory technologies, non-volatile resistive random access memory (ReRAM) is attractive because of its simple device architecture and fabrication process, high scalability and data density, good performances in terms of switching speed, high power efficiency and reasonably wide memory window. In order to address the issues of disposable and degradation of electronic waste by typical ReRAM with the active layer made of inorganic oxide materials and fossil-fuel based polymeric materials, a green and sustainable strategy has been adopted in producing ReRAM by using natural organic-based materials based on protein and carbohydrate, such as honey, fructose, aloe vera, etc. Among these materials, pectin-polysaccharide thin film has demonstrated promising resistive switching characteristics. The two ranges of pectin concentrations that have been investigated are ³5 mg/ml and £1.5 mg/ml, and it showed that pectin with concentration <1.5 mg/ml reveals a higher ON/OFF ratio. However, the resistive switching characteristics with pectin concentration between 1.5 mg/ml and 5 mg/ml have yet been explored and reported. In this work, pectin with concentrations of 1.5~5 mg/ml were prepared from pectin-polysaccharide solution into the active switching layer, and ReRAM devices with such pectin resistive switching layer were fabricated. The pectin-polysaccharide solution, pectin resistive film, and ReRAM devices were systematically investigated. Surface tension and contact angle of pectin-polysaccharide precursor solutions as a function of pectin concentration on the substrate were measured by a goniometer. Surface topography of solidified thin films was characterized by an atomic force microscope (AFM) and a field-emission scanning electron microscope (FE-SEM). Chemical functional groups of the pectin-polysaccharide precursor solutions and solidified thin films were examined by a Fourier transform infrared (FTIR) spectroscopy. The resistive switching behaviors were characterized and compared by electrical measurement. The results show that 4 mg/ml recorded the highest ON/OFF ratio compared to ever reported values, as well as desirable memory window, non-volatility in retention, and stability over 100 cycles. This study proves that pectin-polysaccharide is a promising green and sustainable bio-organic material for non-volatile ReRAM for electronic applications such as in emerging neuromorphic computing systems.