A copula bi-level fractional programming (CBFP) method is developed for planning the water–food–energy–ecology (WFEE) nexus system. CBFP has advantages in (i) dealing with ratio-objective problems, (ii) balancing the conflicts between hierarchical decision levels, and (iii) reflecting joint risks of correlated uncertain variables. Then, a CBFP–WFEE model is formulated to the Ili-Balkhash basin in Central Asia, in which 108 scenarios associated with different irrigation efficiencies, ecological-flow demands (EBW), and water–land resources have been examined. Solutions of water allocation, hydropower generation, and land-use pattern are obtained. Our major findings are as follows: (i) from 2021 to 2050, water allocation to livestock in East Kazakhstan would remarkably increase (by 40.9%) when water allocation to food is satisfied; (ii) hydropower generation would increase with the rising ecological flows and arable land resources; (iii) EBW is the key factor influencing the water inflow to the Balkhash Lake; (iv) the share of ecosystem water allocation would exceed 17.5% by 2050, and grassland area would rank in the first place of the ecosystem. Compared with conventional bi-level stochastic programming and single-level fractional programming models, the CBFP–WFEE model can achieve a higher ecosystem service value and higher efficiency of water–land resources, which can provide more feasible and sustainable alternatives for the WFEE nexus system. The obtained results can help balance the contradictions among water shortage, economic development, and ecology protection, as well as provide synergic management strategies for regional sustainability.

Contact imaging based on MeV energy laser accelerated protons is studied in this paper. First, we show that both external structures and the internal organs of ants can be distinguished with micrometer spatial resolution by proton radiography. Then, we systematically study several specific influence factors and their coupled effects on the spatial resolution of proton radiography, i.e., the accumulated shot number, the proton irradiation dose, the different types of detectors, and the incident proton energy, using two specially designed resolution calibration targets. Under our experimental conditions with MeV protons, the best resolution obtained with the radiochromic film is 20 μm, and that with the solid-state nuclear-track detector (CR39) is 10 μm. In the end, we propose an image deblurring algorithm that uses deconvolution to eliminate the blurring caused by the nonzero spatial extent of the source and multiple Coulomb scattering. This work studies the comprehensive factors of laser accelerated proton radiography with resolution calibration targets and presents incremental additions to previous work on proton radiography.

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