An Evaluation of Nutrient Trading Options in Virginia: A Role for Agriculture?

Water Quality Trading, offsets, nutrients, agriculture, BMPs, Environmental Economics and Policy,

A novel, structure-preserving, second-order-in-time relaxation scheme for Schrödinger-Poisson systems

The authors acknowledge the support from The Carnegie Trust Research Incentive Grant RIG008215 . I.K. would also like to acknowledge the support from London Mathematical Society through an Emmy Noether Fellowship . In addition, Th. K. and I.K. thank the Edinburgh Mathematical Society for the Covid Recovery Fund that allowed for the completion and the submission of this paper.We introduce a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schrödinger-Poisson system. More specifically, we use the Crank-Nicolson scheme as a time stepping mechanism, whilst the nonlinearity is handled by means of a relaxation approach in the spirit of [10,11,34] for the nonlinear Schrödinger equation. For the spatial discretisation we use the standard conforming finite element scheme. The resulting scheme is explicit with respect to the nonlinearity, i.e. it requires the solution of a linear system for each time-step, and satisfies discrete versions of the system's mass conservation and energy balance laws for constant meshes. The scheme is seen to be second order in time. We conclude by presenting some numerical experiments, including an example from cosmology and an example with variable time-steps which demonstrate the effectiveness and robustness of the new scheme.Peer reviewe

A novel, structure-preserving, second-order-in-time relaxation scheme for Schrödinger-Poisson systems

We introduce a new second order in time relaxation-type scheme for approximating solutions of the Schr\"odinger-Poisson system. More specifically, we use the Crank-Nicolson scheme as a time stepping mechanism, whilst the nonlinearity is handled by means of a relaxation approach in the spirit of \cite{Besse, KK} for the nonlinear Schr\"odinger equation. For the spatial discretisation we use the standard conforming finite element scheme. The resulting scheme is explicit with respect to the nonlinearity, satisfies discrete versions of the system's conservation laws, and is seen to be second order in time. We conclude by presenting some numerical experiments, including an example from cosmology, that demonstrate the effectiveness and robustness of the new scheme.Comment: 17pages, 10 figure

Influence of wheel size on muscle activity and tri-axial accelerations during Cross-Country mountain biking

This study aimed to investigate the influence of different mountain bike wheel diameters on muscle activity and whether larger diameter wheels attenuate muscle vibrations during cross-country riding. Nine male competitive mountain bikers (age 34.7 ± 10.7 years; stature 177.7 ± 5.6 cm; body mass 73.2 ± 8.6 kg) participated in the study. Riders performed one lap at race pace on 26, 27.5 and 29 inch wheeled mountain bikes. sEMG and acceleration (RMS) were recorded for the full lap and during ascent and descent phases at the gastrocnemius, vastus lateralis, biceps brachii and triceps brachii. No significant main effects were found by wheel size for each of the four muscle groups for sEMG or acceleration during the full lap and for ascent and descent (P > .05). When data were analysed between muscle groups, significant differences were found between biceps brachii and triceps brachii (P < .05) for all wheel sizes and all phases of the lap with the exception of for the 26 inch wheel during the descent. Findings suggest wheel diameter has no influence on muscle activity and vibration during mountain biking. However, more activity was observed in the biceps brachii during 26 inch wheel descending. This is possibly due to an increased need to manoeuvre the front wheel over obstacles