Delta Self-Consistent Field as a method to obtain potential energy surfaces of excited molecules on surfaces

We present a modification of the $\Delta$SCF method of calculating energies of excited states, in order to make it applicable to resonance calculations of molecules adsorbed on metal surfaces, where the molecular orbitals are highly hybridized. The $\Delta$SCF approximation is a density functional method closely resembling standard density functional theory (DFT), the only difference being that in $\Delta$SCF one or more electrons are placed in higher lying Kohn-Sham orbitals, instead of placing all electrons in the lowest possible orbitals as one does when calculating the ground state energy within standard DFT. We extend the $\Delta$SCF method by allowing excited electrons to occupy orbitals which are linear combinations of Kohn-Sham orbitals. With this extra freedom it is possible to place charge locally on adsorbed molecules in the calculations, such that resonance energies can be estimated. The method is applied to N$_2$, CO and NO adsorbed on different metallic surfaces and compared to ordinary $\Delta$SCF without our modification, spatially constrained DFT and inverse-photoemission spectroscopy (IPES) measurements. This comparison shows that the modified $\Delta$SCF method gives results in close agreement with experiment, significantly closer than the comparable methods. For N$_2$ adsorbed on ruthenium (0001) we map out a 2-dimensional part of the potential energy surfaces in the ground state and the 2$\pi$-resonance. Finally we compare the $\Delta$SCF approach on gas-phase N$_2$ and CO, to higher accuracy methods. Excitation energies are approximated with accuracy close to that of time-dependent density functional theory, and we see very good agreement in the minimum shift of the potential energy surfaces in the excited state compared to the ground state.Comment: 11 pages, 7 figure

Interaction between lateral sorting in river bends and vertical sorting in dunes

Sediment is sorted in river bends under the influence of gravity that pulls the heavier grains downslope and secondary flow that drags the finer grains upslope. Furthermore, when dunes are present, sediment is also sorted vertically at the dune lee side. However, sorting functions are poorly defined, since the relation to transverse bed slope and the interaction between lateral and vertical sorting is not yet understood for lack of data under controlled conditions. The objective of this study is to describe lateral sorting as a function of transverse bed slope and to gain an understanding of the interaction between lateral and vertical sorting in river bends. To this end, experiments were conducted with a poorly sorted sediment mixture in a rotating annular flume in which secondary flow intensity can be controlled separately from the main flow velocity, and therefore transverse bed slope towards the inner bend and dune dimensions can be systematically varied. Sediment samples were taken along cross‐sections at the surface of dune troughs and dune crests, and over the entire depth at the location of dune crests (bulk samples), which enabled comparison of the relative contribution of vertical sorting by dunes to lateral sorting by the transverse bed slope. The data show that lateral sorting is always the dominant sorting mechanism in bends, and bulk samples showed minor effects of vertical sorting by dunes as long as all grain‐size fractions are mobile. An empirical bend sorting model was fitted that redistributes the available sediment fractions over the cross‐section as a function of transverse bed slope. Comparison with field data showed that the model accurately reproduces spatially‐averaged trends in sorting at the bend apex in single‐thread channels. The bend sorting model therefore provides a better definition of bend sorting with conservation of mass by size fraction and adds to current understanding of bend sorting. The implication for numerical modelling is that bend sorting mechanisms can be modelled independently of dunes, allowing the application of the active layer concept

The fluctuation energy balance in non-suspended fluid-mediated particle transport

Here we compare two extreme regimes of non-suspended fluid-mediated particle transport, transport in light and heavy fluids ("saltation" and "bedload", respectively), regarding their particle fluctuation energy balance. From direct numerical simulations, we surprisingly find that the ratio between collisional and fluid drag dissipation of fluctuation energy is significantly larger in saltation than in bedload, even though the contribution of interparticle collisions to transport of momentum and energy is much smaller in saltation due to the low concentration of particles in the transport layer. We conclude that the much higher frequency of high-energy particle-bed impacts ("splash") in saltation is the cause for this counter-intuitive behavior. Moreover, from a comparison of these simulations to Particle Tracking Velocimetry measurements which we performed in a wind tunnel under steady transport of fine and coarse sand, we find that turbulent fluctuations of the flow produce particle fluctuation energy at an unexpectedly high rate in saltation even under conditions for which the effects of turbulence are usually believed to be small

Data protection, safeguarding and the protection of children's privacy: exploring local authority guidance on parental photography at school events

Should parents be allowed to take photographs at school events? Media reports suggest that increasingly schools are answering no to this question, either prohibiting or imposing stringent restrictions upon such photography. The legal justifications for such restrictions are, however, unclear. Accordingly, in 2013 freedom of information requests were sent to local education authorities across England, Scotland and Wales, the aim being to determine what advice local education authorities provide to schools in relation to parental photography at school events, and to identify how education authorities’ understandings of the law influence the advice they offer. That research reveals that local education authorities’ understandings of the law vary significantly and that where authorities do not fully appreciate the extent of the legal obligations arising this may have significant repercussions for the children concerned

The Dynamics of a Meandering River

We present a statistical model of a meandering river on an alluvial plane which is motivated by the physical non-linear dynamics of the river channel migration and by describing heterogeneity of the terrain by noise. We study the dynamics analytically and numerically. The motion of the river channel is unstable and we show that by inclusion of the formation of ox-bow lakes, the system may be stabilised. We then calculate the steady state and show that it is in agreement with simulations and measurements of field data.Comment: Revtex, 12 pages, 2 postscript figure

Effects of Density‐Driven Flows on the Long‐Term Morphodynamic Evolution of Funnel‐Shaped Estuaries

Subtidal flows driven by density gradients affect the tide‐averaged sediment transport in estuaries and, therefore, can influence their long‐term morphodynamic evolution. The three‐dimensional Coupled Ocean‐Atmosphere‐Wave‐Sediment Transport modeling system is applied to numerically analyze the effects of baroclinicity and Earth\u27s rotation on the long‐term morphodynamic evolution of idealized funnel‐shaped estuaries. The morphodynamic evolution in all the analyzed cases reproduced structures identified in many tide‐dominated estuaries: a meandering region in the fluvial‐tidal transition zone, a tidal maximum area close to the head, and a turbidity maxima region in the brackish zone. As the morphology of the estuaries evolved, the tidal propagation (including its asymmetry), the salinity gradient, and the strength of subtidal flows changed, which reflects the strong bathymetric control of these systems. The comparison with barotropic simulations showed that the three‐dimensional structure of the flow (induced by density gradients) has leading order effects on the morphodynamic evolution. Density gradient‐driven subtidal flows (1) promote near‐bed flood dominance and, consequently, the import of sediment into the estuary, (2) accelerate the morphodynamic evolution of the upper/middle estuary, (3) promote a more concave shape of the upper estuary and reduce the ebb‐tidal delta volume, and (4) produce an asymmetric bathymetry and inhibit the formation of alternate bars that would form under barotropic conditions. This latter effect is the consequence of the combined effect of Earth\u27s rotation and baroclinicity

Interplay between spatially explicit sediment sourcing, hierarchical river-network structure, and in-channel bed material sediment transport and storage dynamics

Understanding how sediment moves along source to sink pathways through watersheds„from hillslopes to channels and in and out of floodplains„is a fundamental problem in geomorphology. We contribute to advancing this understanding by modeling the transport and in-channel storage dynamics of bed material sediment on a river network over a 600æyear time period. Specifically, we present spatiotemporal changes in bed sediment thickness along an entire river network to elucidate how river networks organize and process sediment supply. We apply our model to sand transport in the agricultural Greater Blue Earth River Basin in Minnesota. By casting the arrival of sediment to links of the network as a Poisson process, we derive analytically (under supply-limited conditions) the time-averaged probability distribution function of bed sediment thickness for each link of the river network for any spatial distribution of inputs. Under transport-limited conditions, the analytical assumptions of the Poisson arrival process are violated (due to in-channel storage dynamics) where we find large fluctuations and periodicity in the time series of bed sediment thickness. The time series of bed sediment thickness is the result of dynamics on a network in propagating, altering, and amalgamating sediment inputs in sometimes unexpected ways. One key insight gleaned from the model is that there can be a small fraction of reaches with relatively low-transport capacity within a nonequilibrium river network acting as ñbottlenecksî that control sediment to downstream reaches, whereby fluctuations in bed elevation can dissociate from signals in sediment supply. ©2017. American Geophysical Union. All Rights Reserved

Field evidence for the upwind velocity shift at the crest of low dunes

Wind topographically forced by hills and sand dunes accelerates on the upwind (stoss) slopes and reduces on the downwind (lee) slopes. This secondary wind regime, however, possesses a subtle effect, reported here for the first time from field measurements of near-surface wind velocity over a low dune: the wind velocity close to the surface reaches its maximum upwind of the crest. Our field-measured data show that this upwind phase shift of velocity with respect to topography is found to be in quantitative agreement with the prediction of hydrodynamical linear analysis for turbulent flows with first order closures. This effect, together with sand transport spatial relaxation, is at the origin of the mechanisms of dune initiation, instability and growth.Comment: 13 pages, 6 figures. Version accepted for publication in Boundary-Layer Meteorolog

Sediment Transport of Fine Sand to Fine Gravel on Transverse Bed Slopes in Rotating Annular Flume Experiments

Large‐scale morphology, in particular meander bend depth, bar dimensions, and bifurcation dynamics, are greatly affected by the deflection of sediment transport on transverse bed slopes due to gravity and by secondary flows. Overestimating the transverse bed slope effect in morphodynamic models leads to flattening of the morphology, while underestimating leads to unrealistically steep bars and banks and a higher braiding index downstream. However, existing transverse bed slope predictors are based on a small set of experiments with a minor range of flow conditions and sediment sizes, and in practice models are calibrated on measured morphology. The objective of this research is to experimentally quantify the transverse bed slope effect for a large range of near‐bed flow conditions with varying secondary flow intensity, sediment sizes (0.17–4 mm), sediment transport mode, and bed state to test existing predictors. We conducted over 200 experiments in a rotating annular flume with counterrotating floor, which allows control of the secondary flow intensity separate from the streamwise flow velocity. Flow velocity vectors were determined with a calibrated analytical model accounting for rough bed conditions. We isolated separate effects of all important parameters on the transverse slope. Resulting equilibrium transverse slopes show a clear trend with varying sediment mobilities and secondary flow intensities that deviate from known predictors depending on Shields number, and strongly depend on bed state and sediment transport mode. Fitted functions are provided for application in morphodynamic modelin