A nullstellensatz for sequences over F_p

Let p be a prime and let A=(a_1,...,a_l) be a sequence of nonzero elements in F_p. In this paper, we study the set of all 0-1 solutions to the equation a_1 x_1 + ... + a_l x_l = 0. We prove that whenever l >= p, this set actually characterizes A up to a nonzero multiplicative constant, which is no longer true for l < p. The critical case l=p is of particular interest. In this context, we prove that whenever l=p and A is nonconstant, the above equation has at least p-1 minimal 0-1 solutions, thus refining a theorem of Olson. The subcritical case l=p-1 is studied in detail also. Our approach is algebraic in nature and relies on the Combinatorial Nullstellensatz as well as on a Vosper type theorem.Comment: 23 page

Airborne Measurements of Gravity Wave Breaking at the Tropopause

2000 FLORIDA AVE NW, WASHINGTON, DC, 2000

Sensitivity of resolved and parameterized surface drag to changes in resolution and parameterization

The relative contribution of resolved and parameterized surface drag towards balancing the atmospheric angular momentum flux convergence (AMFC), and their sensitivity to horizontal resolution and parameterization, are investigated in an atmospheric model. This sensitivity can be difficult to elucidate in free-running climate models, in which the AMFC varies with changing climatologies and, as a result, the relative contributions of surface terms balancing the AMFC also vary. While the sensitivity question has previously been addressed using short-range forecasts, we demonstrate that a nudging framework is an effective method for constraining the AMFC. The Met Office Unified Model is integrated at three horizontal resolutions ranging from 130 km (N96) to 25 km (N512) while relaxing the model’s wind and temperature fields towards the ERAinterim reanalysis within the altitude regions of maximum AMFC. This method is validated against short range forecasts and good agreement is found. These experiments are then used to assess the fidelity of the exchange between parameterized and resolved orographic torques with changes in horizontal resolution. Although the parameterized orographic torque reduces substantially with increasing horizontal resolution, there is little change in resolved orographic torque over 20N to 50N. The tendencies produced by the nudging routine indicate that the additional drag at lower horizontal resolution is excessive. When parameterized orographic blocking is removed at the coarsest of these resolutions, there is a lack of compensation, and even compensation of the opposite sense, by the boundary layer and resolved torques which is particularly pronounced over 20N to 50N. This study demonstrates that there is strong sensitivity in the behaviour of the resolved and parameterized surface drag over this region

Sensitivity analysis of the dynamic CO2 storage capacity estimate for the Bunter Sandstone of the UK Southern North Sea

Carbon capture and storage (CCS) in subsurface reservoirs has been identified as a potentially cost-effective way to reduce CO2 emissions to the atmosphere. Global emissions reductions on the gigatonne scale using CCS will require regional or basin-scale deployment of CO2 storage in saline aquifers. Thus the evaluation of both the dynamic and ultimate CO2 storage capacity of formations is important for policy makers to determine the viability of CCS as a pillar of the greenhouse gas mitigation strategy in a particular region. We use a reservoir simulation model representing the large-scale Bunter Sandstone in the UK Southern North Sea to evaluate the dynamics and sensitivities of regional CO2 plume transport and storage. At the basin-scale, we predict hydrogeological changes in the storage reservoir in response to multiple regional carbon sequestration development scenarios. We test the sensitivity of injection capacity to a range of target CO2 injection rates and fluctuations in CO2 supply. Model sensitivities varying the target injection rates indicate that in the absence of pressure management up to 3.7 Gt of CO2 can be stored in the Bunter region over 50 years given the pressure constraints set to avoid fracturing the formation. Long-term (approx. 1000 years), our results show that up to 16 Gt of CO2 can be stored in the Bunter region without pressure management. With pressure management, the estimate rises to 32 Gt. However, consideration must be given to the additional operational and economic requirements of pressure management using brine production

Impacts of orography on large-scale atmospheric circulation

Some of the largest and most persistent circulation errors in global numerical weather prediction and climate models are attributable to the inadequate representation of the impacts of orography on the atmospheric flow. Existing parametrization approaches attempting to account for unresolved orographic processes, such as turbulent form drag, low-level flow blocking or mountain waves, have been successful to some extent. They capture the basic impacts of the unresolved orography on atmospheric circulation in a qualitatively correct way and have led to significant progress in both numerical weather prediction and climate modelling. These approaches, however, have apparent limitations and inadequacies due to poor observational evidence, insufficient fundamental knowledge and an ambiguous separation between resolved and unresolved orographic scales and between different orographic processes. Numerical weather prediction and climate modelling has advanced to a stage where these inadequacies have become critical and hamper progress by limiting predictive skill on a wide range of spatial and temporal scales. More physically-based approaches are needed to quantify the relative importance of apparently disparate orographic processes and to account for their combined effects in a rational and accurate way in numerical models. We argue that, thanks to recent advances, significant progress can be made by combining theoretical approaches with observations, inverse modelling techniques and high-resolution and idealized numerical simulations

On the critical pair theory in abelian groups : Beyond Chowla's Theorem

We obtain critical pair theorems for subsets S and T of an abelian group such that |S+T| < |S|+|T|+1. We generalize some results of Chowla, Vosper, Kemperman and a more recent result due to Rodseth and one of the authors.Comment: Submitted to Combinatorica, 23 pages, revised versio

Adopting the International Standard 'Becoming a human-centred organization (ISO 27500)' supports a strategic approach to internationalisation.

Educational development is increasingly focussed on quality assurance and enhancement. Individual states/countries have their own mechanisms for assuring the student experience, and this has been accompanied by development of tools (including the UK’s National Student Survey) for capturing student opinion of our efforts. Areas where more work is needed include equity and diversity and it is perhaps time for a fresh approach. In other sectors, International Standards ensure safety, reliability and quality of products and services. Such standards also represent a stakeholder-negotiated (and therefore shared) understanding of ‘good quality’, supporting organisations in accessing new markets and permitting a fair global trade, an approach relevant to higher education. Recent publication of ISO (The International Organization for Standardization) Standard 27500 (the International Standard describing the principles and rationales behind becoming a humancentred organization) seems timely. Encouraging educational institutions to adopt this Standard may offer a strategy for addressing several issues, including internationalisation

Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc

Interactions between the night time valley-wind system and a developing cold-air pool

This is a pre-copyedited, author-produced PDF of an article accepted for publication in Boundary-Layer Meteorology following peer review. The version of record [Arduini, G., Staquet, C & Chemel, C., ‘Interactions between the night time valley-wind system and a developing cold-air pool’, Boundary-Layer Meteorol (2016) 161:1 (49-72), first published online June 2, 2016, is available at Springer online at doi: 10.1007/s10546-016-0155-8The Weather Research and Forecast (WRF) numerical model is used to characterize the influence of a thermally-driven down-valley flow on a developing cold-air pool in an idealized alpine valley decoupled from the atmosphere above. Results for a three-dimensional (3D) valley, which allows for the formation of a down-valley flow, and for a two-dimensional (2D) valley, where the formation of a down-valley flow is inhibited, are analyzed and compared. A key result is that advection leads to a net cooling in the 2D valley and to a warming in the 3D valley, once the down-valley flow is fully developed. This difference stems from the suppression of the slope-flow induced upward motions over the valley centre in the 3D valley. As a result, the downslope flows develop a cross-valley circulation within the cold-air pool, the growth of the cold-air pool is reduced and the valley atmosphere is generally warmer than in the 2D valley. A quasi-steady state is reached for which the divergence of the down-valley flow along the valley is balanced by the convergence of the downslope flows at the top of the cold-air pool, with no net contribution of subsiding motions far from the slope layer. More precisely, the inflow of air at the top of the cold-air pool is found to be driven by an interplay between the return flow from the plain region and subsidence over the plateaux. Finally, the mechanisms that control the structure of the cold-air pool and its evolution are found to be independent of the valley length as soon as the quasi-steady state is reached and the down-valley flow is fully developed.Peer reviewedFinal Accepted Versio

Climate model biases in jet streams, blocking and storm tracks resulting from missing orographic drag

State-of-the art climate models generally struggle to represent important features of the large-scale circulation. Common model deficiencies include an equatorward bias in the location of the midlatitude westerlies and an overly zonal orientation of the North Atlantic storm track. Orography is known to strongly affect the atmospheric circulation and is notoriously difficult to represent in coarse-resolution climate models. Yet how the representation of orography affects circulation biases in current climate models is not understood. Here we show that the effects of switching off the parameterization of drag from low-level orographic blocking in one climate model resemble the biases of the Coupled Model Intercomparison Project Phase 5 ensemble: An overly zonal wintertime North Atlantic storm track and less European blocking events, and an equatorward shift in the Southern Hemispheric jet and increase in the Southern Annular Mode time scale. This suggests that typical circulation biases in coarse-resolution climate models may be alleviated by improved parameterizations of low-level drag