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• The structure of urban multi-energy network is provided. • Three energy flows are generally defined and their convex relaxations are performed. • A mixed user equilibrium is applied to describe rational route and charging choices. • A two-stage bound-tightening algorithm is proposed to strengthen convex relaxations. The ever-growing interdependence among power distribution, natural gas networks and transportation infrastructure entails efficient and coordinated optimization techniques. This paper proposes an operational optimization model of urban multi-energy networks that encompasses the synergies among the above components, energy converters and electric vehicles. The proposed model defines and encapsulates three energy flows in a convex optimization problem. In the distribution network, the conic relaxation-based branch flow equation is employed to characterize the alternating current power flow. The static characteristics of gas flow are described via the Weymouth equation with convex envelop relaxations. In the transportation network, the traffic flow patterns associated with the interplay among routing and charging behaviors are studied. Since these behaviors are amenable to the Wardrop principle such that the travel cost cannot be reduced by unilaterally altering travel choice, a mixed user equilibrium model is established to describe the related traffic flows. Although the relaxation quality has been improved by deriving the tighter bounds of the variables, to date, bound-tightening approaches have not yet been effectively applied to multi-energy network problems. To strengthen convex relaxations, we enhance the proposed model with a two-stage approach. The first stage improves the variable bounds through sequential optimality-based bound contraction. The second stage iteratively and successively solves the model with a dynamic bound-tightening algorithm. Based on case studies, the interdependence among energy networks is discussed. In addition, the numerical experiments corroborate the solution quality and computational efficiency benefits of the proposed approach. [ABSTRACT FROM AUTHOR]

Rhizobia and arbuscular mycorrhizal fungi (AMF) are symbiotic microorganisms important for plants grown in nutrient-deficient and heavy metal-contaminated soils. However, it remains unclear how plants respond to the coupled stress by heavy metal and nitrogen (N) deficiency under co-inoculation. Here, we investigated the synergistic effect of Mesorhizobium huakuii QD9 and Funneliformis mosseae on the response of black locust (Robinia pseudoacacia L.) grown in sand culture to cadmium (Cd) under N deficiency conditions. The results showed that single inoculation of AMF improved the growth and Cd resistance of black locust, co-inoculation improved the most. Compared to non-inoculated controls, co-inoculation mediated higher biomass and antioxidant enzyme activity, reduced oxidative stress, and promoted nodulation, mycorrhizal colonization, photosynthetic capacity, and N, P, Fe and Mg acquisition when exposed to Cd. This increase was significantly higher under N deficiency compared to N sufficiency. In addition, the uptake of Cd by co-inoculated black locust roots increased, but Cd translocation to the above-ground decreased under both N deficiency and sufficiency. Thus, in the tripartite symbiotic system, not merely metabolic processes but also Cd uptake increased under N deficiency. However, enhanced Cd detoxification in the roots and reduced allocation to the shoot likely prevent Cd toxicity and rather stimulated growth under these conditions., (© 2024 Scandinavian Plant Physiology Society.)