Impact of the Monthly Variability of the Trent River on the Hydrodynamical Conditions of the Bay of Quinte, Ontario: A Case Study 2016–2019

The spatial and temporal (monthly) variability of river discharge has a significant effect on circulation and transport pathways within shallow embayments whose dynamics are largely controlled by wind and riverine inputs. This study illustrates the effects of the monthly variation in Trent River discharge on simulated particle transport and settling destination in the Bay of Quinte, Lake Ontario for the years 2016–2019. Observations of Lagrangian surface drifter data were used to derive Trent River discharge forcing for a three-dimensional hydrodynamic numerical model of the Bay of Quinte. Peak monthly flushing was up to three times as much as the lowest monthly flushing in any year, with the Trent River responsible for up to 95% of the flushing in low runoff years. Particle transport simulations showed that particles could be trapped along shorelines, which extended residence times, and Trent River releases suggest that researchers should look for delayed peaks in Total Phosphorous (TP) load measurements in observations between Trenton and Belleville as particles move downstream. Particles with constant settling velocities originating from the Trent River did not move downstream past Big Bay, and particles from the Napanee River were the primary source for Longreach.

The Landau-Zener Transition and the Surface Hopping Method for the 2D Dirac Equation for Graphene

A Lagrangian surface hopping algorithm is implemented to study the two dimensional massless Dirac equation for Graphene with an electrostatic potential, in the semiclassical regime. In this problem, the crossing of the energy levels of the system at Dirac points requires a particular treatment in the algorithm in order to describe the quantum transition—characterized by the Landau-Zener probability— between different energy levels. We first derive the Landau-Zener probability for the underlying problem, then incorporate it into the surface hopping algorithm. We also show that different asymptotic models for this problem derived in [O. Morandi, F. Schurrer, J. Phys. A:Math. Theor. 44 (2011) 265301]may give different transition probabilities. We conduct numerical experiments to compare the solutions to the Dirac equation, the surface hopping algorithm, and the asymptotic models of [O. Morandi, F. Schurrer, J. Phys. A: Math. Theor. 44 (2011) 265301].

Annual and Interannual Variability of the Tropical Instability Vortices in the Equatorial Eastern Pacific Observed from Lagrangian Surface Drifters

This study documents the spatial distributions and temporal variations of anticyclonic eddies with identified radii ≥100 km in the equatorial eastern tropical Pacific Ocean [viz., tropical instability vortices (TIVs)] using Lagrangian surface drifters. The TIVs identified from Lagrangian surface drifters are distributed in a band along 5°N and are closely associated with latitudinal barotropically unstable shear between the westward South Equatorial Current (SEC) and the eastward North Equatorial Countercurrent (NECC). Fewer TIVs are identified from February to June when the shear between the SEC and NECC is weak, whereas more TIVs are found from July to January when the shear is enhanced. The number of identified TIVs also exhibits substantial interannual variability, with fewer TIVs identified during El Niño events and more TIVs found during La Niña events. This relationship is likely associated with the interannual variations of the zonal circulation in the equatorial Pacific modulated by El Niño–Southern Oscillation (ENSO).

Elastic Theory of Nanomaterials Based on Surface-Energy Density

Recent investigations into surface-energy density of nanomaterials lead to a ripe chance to propose, within the framework of continuum mechanics, a new theory for nanomaterials based on surface-energy density. In contrast to the previous theories, the linearly elastic constitutive relationship that is usually adopted to describe the surface layer of nanomaterials is not invoked and the surface elastic constants are no longer needed in the new theory. Instead, a surface-induced traction to characterize the surface effect in nanomaterials is derived, which depends only on the Eulerian surface-energy density. By considering sample-size effects, residual surface strain, and external loading, an explicit expression for the Lagrangian surface-energy density is achieved and the relationship between the Eulerian surface-energy density and the Lagrangian surface-energy density yields a conclusion that only two material constants—the bulk surface-energy density and the surface-relaxation parameter—are needed in the new elastic theory. The new theory is further used to characterize the elastic properties of several fcc metallic nanofilms under biaxial tension, and the theoretical results agree very well with existing numerical results. Due to the nonlinear surface effect, nanomaterials may exhibit a nonlinearly elastic property though the inside of nanomaterials or the corresponding bulk one is linearly elastic. Moreover, it is found that externally applied loading should be responsible for the softening of the elastic modulus of a nanofilm. In contrast to the surface elastic constants required by existing theories, the bulk surface-energy density and the surface-relaxation parameter are much easy to obtain, which makes the new theory more convenient for practical applications.