Jordan-Kronecker invariants of finite-dimensional Lie algebras

For any finite-dimensional Lie algebra we introduce the notion of Jordan-Kronecker invariants, study their properties and discuss examples. These invariants naturally appear in the framework of the bi-Hamiltonian approach to integrable systems on Lie algebras and are closely related to Mischenko-Fomenko's argument shift method

A note about integrable systems on low-dimensional Lie groups and Lie algebras

The goal of the paper is to explain why any left-invariant Hamiltonian system on (the cotangent bundle of) a 3-dimensonal Lie group G is Liouville integrable. We derive this property from the fact that the coadjoint orbits of G are two-dimensional so that the integrability of left-invariant systems is a common property of all such groups regardless their dimension. We also give normal forms for left-invariant Riemannian and sub-Riemannian metrics on 3-dimensional Lie groups focusing on the case of solvable groups, as the cases of SO(3) and SL(2) have been already extensively studied. Our description is explicit and is given in global coordinates on G which allows one to easily obtain parametric equations of geodesics in quadratures

Single and dual stage closed-loop pressure retarded osmosis for power generation: Feasibility and performance

© 2017 Elsevier Ltd This work proposes an analysis of conventional (single stage) and dual stage Closed-Loop Pressure Retarded Osmosis (CLPRO) for power generation from a salinity gradient resource. Model calculations were performed taking into account the influence of operating parameters such as the draw solution concentration, membrane area, and draw solution pressure on the performance of the CLPRO process. Modeling results showed that the dual stage CLPRO process outperformed the conventional CLPRO process and power generation increased 18% by adding a second stage of PRO membrane. Multi-Effect Distillation (MED) was selected for the regeneration of the draw solution taking advantage of an available source of waste heat energy. The performance of MED process has been assessed by investigating two key parameters: the specific thermal consumption and the specific heat transfer area. The model calculations showed that the power generation by the single and dual stage CLPRO was higher than the electrical power consumption by the MED plant. In the case of the power generation obtained by the dual stage CLPRO, it was 95% higher than the electrical power consumption by the MED plant, proving the possibility of using low-grade heat for producing electricity from a salinity gradient resource