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For millennia, societies have tried to find ways to sustain people’s livelihoods by setting rules to equitably and sustainably access, harvest and manage common pools of resources (CPR) that are productive and rich in species. But what are the elements that explain historical successes and failures? Elinor Ostrom suggested that it depends on at least eight axiomatic principles of good governance, whereas empirical results suggest that these principles are not sufficient to describe them, especially when applied to CPRs that possess great social and ecological diversity. The aim of this article is to explore the behavior of a mathematical model of multi-species forest dynamics that respects the foundations of ecology and Ostrom’s governance theory, in order to detect possible constraints inherent to the functioning of these complex systems. The model reveals that fundamental structural laws of compatibilities between species life-history traits are indeed constraining the level of co-existence (average and variance) between a diversity of co-vulnerable timber resource users (RU) and of competing tree species. These structural constraints can also lead to unexpected outcomes. For instance in wetter forest commons, opening up the access to as many diverse RUs as there are competing tree species, produces a diversity of independently-controlled disturbances on species, collectively improving the chances of coexistence between species with different life-history traits. Similar benefits are observed on forest carbon and on profits from timber harvesting. However in drier forest commons, the same benefits cannot be observed, as predicted on the basis of the constraining laws. The results show that the successes and failures of certain management strategies can be reasonably explained by simple mechanistic theories from ecology and the social-ecological sciences, which are themselves constrained by fundamental ecological invariants. If corroborated, the results could be used, in conjunction with Ostrom’s CPR theory, to understand and solve various human-nature coexistence dilemmas in complex social-ecological systems.

A calculation model of activity for CaO–SiO2–MgO–Al2O3–TiO2 slag is established according to molecular-ion coexistence theory of slag structure to calculate the activities of Al2O3, SiO2, and TiO2 in the slag. The possibility of TiO2 reduction in the slag during refining is analyzed by thermodynamics and verified by laboratory and industrial experiments. Both theoretical analysis and laboratory experimental results show that the content of TiO2 in the ladle slag significantly influences the Ti content in molten steel. When the content of the dissolved aluminum in molten steel is 0.030–0.050%, the TiO2 content in the ladle slag should be controlled below 0.3% to prevent TiO2 reduction. The critical content of TiO2 decreases with an increasing amount of the dissolved aluminum in molten steel. In addition, silicon should be used as a deoxidizer during diffused deoxidization because aluminum as a deoxidizer would lead to the reduction of TiO2. The industrial experiments confirm the results of the laboratory experiments and thermodynamics analysis.

The effect of alkaline oxide content,optical basicity,total iron content in slag and temperature on the measured slag phosphate capacity was investigated through the calculation and analysis of the slag phosphate capacity during the converter dephosphorization process combined with previous study. The relationship between phosphate capacity and composition of slag was fitted according to the production data. In addition,different prediction models of phosphate capacity were compared and analyzed from previous studies. Based on the coexistence theory,the prediction model of phosphate capacity in slag system was established,and the error analysis shows that the prediction model is accurate and credible,which can provide a theoretical guidance for the field production.

A thermodynamic model is proposed for calculating the mass action concentration of structural units in the Al-Ti binary melt system based on the atom-molecule coexistence theory. The standard equilibrium constants of reactions for forming three associated molecules as Al3Ti,Al Ti,and Al11Ti5 in the Al-Ti binary melt system at the temperature of 2073 to 2273 K are calculated based on the activity reported in the literature,and the expressions of the standard molar Gibbs free energy change of reactions are obtained.Meanwhile,the calculated mass action concentrations NAl and NTi of Al and Ti are compared with the reported activities of both Al and Ti in the full composition range of the Al-Ti binary melt system at different temperatures from the literature. The results show that the calculated mass action concentrations NAl and NTi are in agreement with the activities aAl and aTi in the reported literature. The relationship between the calculated mass action concentration Ni and the calculated equilibrium amount of substance ni of Al3Ti and Al11Ti5 in the Al-Ti binary melt system is rod-type. However,the relationship between the calculated mass action concertation NAlTi and the calculated equilibrium amount of substance nAlTi in this binary melt system is spindle-type.

According to the ion and molecule coexistence theory (IMCT) for molten slags and corresponding phase diagrams, a thermodynamic model for the evaluation of mass action concentrations (designated by Ni for structure unit i) for La2O3-Al2O3, La2O3-Al2O3-CaF2, La2O3-Al2O3-CaF2-CaO, La2O3-Al2O3-CaF2-MgO and La2O3-Al2O3-CaF2-CaO-MgO slag systems for electroslag remelting (ESR) has been formulated. The influencing factors for the mass action concentration of La2O3, such as mass fraction of Al2O3, CaF2, CaO and MgO and temperature, were investigated. The results show that when the mole fraction of La2O3 is at 0.495, the mass action concentration of La2O3 · Al2O3 achieves its maximum value 0.946 in the La2O3-Al2O3 binary slag. In a composition area of La2O3: 10wt% ∼ 45wt%, Al2O3: 0wt% ∼ 50wt% and CaF2: 20wt% ∼ 70wt% of the La2O3-Al2O3-CaF2 ternary slag at 1873 K, the results show that the calculated values of NLa2O3 are in good agreement with the reported measured values of aLa2O3. The iso-curves of NLa2O3 is also drawn from the calculated results, which reveals that the mass action concentration of La2O3 decreases with the increasing of the Al2O3 and CaF2 content, and Al2O3 is stronger than CaF2 in decreasing the mass action concentration of La2O3. However, in La2O3-Al2O3-CaF2-CaO, La2O3-Al2O3-CaF2-MgO and La2O3-Al2O3-CaF2-CaO-MgO slag systems, the mass action concentration of La2O3 increases with the increasing of the MgO and CaO content, and CaO is stronger than MgO in increasing the mass action concentration of La2O3. In addition, the mass action concentration of La2O3 increases with the increasing temperature at the composition of 30wt%La2O3, 10wt%Al2O3, 40wt%CaF2, 10wt%MgO and 10wt%CaO.

According to the ion and molecule coexistence theory (IMCT) for molten slags and corresponding phase diagrams, a thermodynamic model for the evaluation of mass action concentrations (designated by Ni for structure unit i) for Ce2O3-Al2O3, CaO-Al2O3-Ce2O3 and CaO-Al2O3-SiO2-Ce2O3 slag systems has been formulated. The results show that when the mole fraction of Ce2O3 is at 0.49 in the binary slag, the mass action concentration of Ce2O3·Al2O3 achieves its maximum value 0.90. In a composition area of CaO/Al2O3 (mass fraction ratio) from 0.7 to 1.5 and Ce2O3 content (mass fraction) from 0 to 45% of the ternary slag at 1773 K, the results show that trends of calculated NAl2O3 are in good agreement with reported measured trends of aAl2O3. The iso-curves of NCe2O3 and NCaO are also drawn from the calculated results. A thermodynamic model of the equilibrium between 55.83%CaO-23%Al2O3-11.17%SiO2-10%Ce2O3 quaternary slag and molten steel containing aluminum has been further discussed. Results indicate that certain content of Ce would be dissolved in steel, which increases with the increasing of temperature and aluminum content, and when the aluminum content is 0.02%, the corresponding cerium content is in the range of 1.87 to 13.30 ppm at 1873 K. In summary, using Ce2O3 to replace Al2O3 can effectively reduce NAl2O3, certain content of Ce can dissolved in steel.