Generalized Stabilizing Conditions for Model Predictive Control

© 2015, The Author(s).This note addresses the tracking problem for model predictive control. It presents simple procedures for both linear and nonlinear constrained model predictive control when the desired equilibrium state is any point in a specified set. The resultant region of attraction is the union of the regions of attraction for each equilibrium state in the specified set and is therefore larger than that obtained when conventional model predictive control is employed

Using the UM dynamical cores to reproduce idealised 3D flows

We demonstrate that both the current (New Dynamics), and next generation (ENDGame) dynamical cores of the UK Met Office global circulation model, the UM, reproduce consistently, the long-term, large-scale flows found in several published idealised tests. The cases presented are the Held-Suarez test, a simplified model of Earth (including a stratosphere), and a hypothetical tidally locked Earth. Furthermore, we show that using simplifications to the dynamical equations, which are expected to be justified for the physical domains and flow regimes we have studied, and which are supported by the ENDGame dynamical core, also produces matching long-term, large-scale flows. Finally, we present evidence for differences in the detail of the planetary flows and circulations resulting from improvements in the ENDGame formulation over New Dynamics.Comment: 34 Pages, 23 Figures. Accepted for publication in Geoscientific Model Development (pre-proof version

Results from a set of three-dimensional numerical experiments of a hot Jupiter atmosphere

We present highlights from a large set of simulations of a hot Jupiter atmosphere, nominally based on HD 209458b, aimed at exploring both the evolution of the deep atmosphere, and the acceleration of the zonal flow or jet. We find the occurrence of a super-rotating equatorial jet is robust to changes in various parameters, and over long timescales, even in the absence of strong inner or bottom boundary drag. This jet is diminished in one simulation only, where we strongly force the deep atmosphere equator-to-pole temperature gradient over long timescales. Finally, although the eddy momentum fluxes in our atmosphere show similarities with the proposed mechanism for accelerating jets on tidally-locked planets, the picture appears more complex. We present tentative evidence for a jet driven by a combination of eddy momentum transport and mean flow.Comment: 26 pages, 22 Figures. Accepted for publication in Astronomy and Astrophysic

ADAPTIVE MULTILEVEL SPLITTING IN MOLECULAR DYNAMICS SIMULATIONS

Adaptive Multilevel Splitting (AMS) is a replica-based rare event sampling method that has been used successfully in high-dimensional stochastic simulations to identify trajectories across a high potential barrier separating one metastable state from another, and to estimate the probability of observing such a trajectory. An attractive feature of AMS is that, in the limit of a large number of replicas, it remains valid regardless of the choice of reaction coordinate used to characterize the trajectories. Previous studies have shown AMS to be accurate in Monte Carlo simulations. In this study, we extend the application of AMS to molecular dynamics simulations and demonstrate its effectiveness using a simple test system. Our conclusion paves the way for useful applications, such as molecular dynamics calculations of the characteristic time of drug dissociation from a protein target

Alignment and Design of a 73-Km Long Coastal Road in the South-Central Segment of the Niger Delta, Nigeria

A 73-km East-West Coastal Highway that traverses six major rivers within the Mangrove and Coastal Hydro-meteorological Zones of the Niger Delta is to be built. The total number of river crossings along the five intervening sections of this road is 36.The Niger Delta Sub-region lies at the southern-most portion of Nigeria. Geotechnical investigations along the road profiles showed between 10-18 meters of thick Organic Clays (OH) underlain by 2.50-4.50m thick Silty-clays (OL) along the first three Sections (A,B,&C) of the road. These have saturated densities (γsat) of 10-15.40 kN/m2; PI ~15.00-35.00%; cohesion (c) ≤24.50-68.50kPa, low strength (qult ≤ 12.00 kPa) and relatively high settlement values of δult ~ 0.056m-0.072m. Poorly-graded sands (SP) and well-graded sands with high bearing capacity values (482 – 4,250kPa) lie beneath these at depths of 20m and 30m, respectively. Most of the road alignments were submerged, with few points lying 0.30m above water level during the time of the investigations (December – March). Sections D &E of the road have relatively thinner soft layers (2.00 – 2.50m thick) underlain by sands (SP and SW) with relatively high bearing values of 582-4,250kPa. The large thicknesses of compressible layers underlying most portions of the road alignment require special pavement construction techniques such as: (i) Excavation of 2.50m of the soft layer materials; (ii) Emplacement of vertical pre-fabricated Geo-drains; (iii) Emplacement of woven geotextiles atop the pre-fabricated Geo-drains, (iv) Emplacement of about 4.50m high sand-dump on top of the woven geotextiles, (v) Allow for settlement of the underlying soft layer corresponding to t50, in this case ~1.14 years. Settlement computations obtained prior to- and after pre-loading phases were 0.0608m and 0.670m, respectively. Geosynthetic reinforcements were to be used in the pavement construction of the highway in order to attain a four-fold pavement structure consisting of: (a) Bound layers made up of (i) Overlay, (ii) Surface layer and (iii) Binder layer course; (b) Either bound or Unbound made up of (i) Base; (c) Unbound layers made up of (i) Sub-base, (ii) capping and (iii) Protection layer; (d) Sub-grades made up of (i) Stabilized sub-grades and (ii) Sub-grade proper. For most portions of the remaining Sections D and E, where the thin upper soft layers are less than 1.25m these are to be scraped off before emplacement of the Bound layer directly on top of Sub-grades. This paper describes the geotechnical characteristics of the sub-soils along the entire 73-km of the road alignment and the pavement design considerations adopted