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High-Pressure Synthesis and Structural Behavior of Sodium OrthonitrateNa3NO4. -The title compound is synthesized in high yield by high-pressure reaction of a 3:1 mixture of Na2O and NaNO3 (4 GPa, 500°C, 2 d). The product is characterized by powder XRD and Raman spectroscopy. The obtained sample is likely a high-pressure polymorph, containing groups. The high-pressure behavior of Na3NO4 is investigated up to 61 GPa. No evidence for coordination changes or polymerization of the groups exists. -(CABRERA, R. Q.; SELLA, A.; BAILEY, E.; LEYNAUD, O.; MCMILLAN*, P. F.; J. Solid State Chem. 184 (2011) 4, 915-920, http://dx.

In this work we study a modification of the Monge-Kantorovich problem taking into account path dependence and interaction effects between particles. We prove existence of solutions under mild conditions on the data, and after imposing stronger conditions, we characterize the minimizers by relating them to an auxiliary Monge-Kantorovich problem of the more standard kind. With this notion of how particles interact and travel along paths, we produce a dual problem. The main novelty here is to incorporate an interaction effect to the optimal path transport problem. This covers for instance, N -body dynamics when the underlying measures are discrete. Lastly, our results include an extension of Brenier's theorem on optimal transport maps.