River Basin Export Reduction Optimization Support Tool; a tool to screen options for reducing nutrient loads while minimizing cost

Excess loading of nitrogen and phosphorus to river networks causes environmental harm, but reducing loads from large river basins is difficult and expensive. We develop a new tool, the River Basin Export Reduction Optimization Support Tool (RBEROST) to identify least-cost combinations of management practices that will reduce nutrient loading to target levels in downstream and mid-network waterbodies. We demonstrate the utility of the tool in a case study in the Upper Connecticut River basin in New England, USA. The total project cost of optimized lowest-cost plans ranged from $18.0 million to $41.0 million per year over 15 years depending on user specifications. Plans include both point source and non-point source management practices, and most costs are associated with urban stormwater practices. Adding a 2% margin of safety to loading targets improved estimated probability of success from 37.5% to 99%. The large spatial scale of RBEROST, and the consideration of both point and non-point source contributions of nutrients, makes it well suited as an initial screening tool in watershed planning.

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method, in general, only captures the ultrashort time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.