Convective shutdown in a porous medium at high Rayleigh number

Convection in a closed domain driven by a dense buoyancy source along the upper boundary soon starts to wane owing to the increase of the average interior density. In this paper, theoretical and numerical models are developed of the subsequent long period of shutdown of convection in a two-dimensional porous medium at high Rayleigh number Ra\mathit{Ra}. The aims of this paper are twofold. Firstly, the relationship between this slowly evolving ‘one-sided’ shutdown system and the statistically steady ‘two-sided’ Rayleigh–Bénard (RB) cell is investigated. Numerical measurements of the Nusselt number Nu\mathit{Nu} from an RB cell (Hewitt et al., Phys. Rev. Lett., vol. 108, 2012, 224503) are very well described by the simple parametrization Nu=2.75+0.0069Ra\mathit{Nu}= 2. 75+ 0. 0069\mathit{Ra}. This parametrization is used in theoretical box models of the one-sided shutdown system and found to give excellent agreement with high-resolution numerical simulations of this system. The dynamical structure of shutdown can also be accurately predicted by measurements from an RB cell. Results are presented for a general power-law equation of state. Secondly, these ideas are extended to model more complex physical systems, which comprise two fluid layers with an equation of state such that the solution that forms at the (moving) interface is more dense than either layer. The two fluids are either immiscible or miscible. Theoretical box models compare well with numerical simulations in the case of a flat interface between the fluids. Experimental results from a Hele-Shaw cell and numerical simulations both show that interfacial deformation can dramatically enhance the convective flux. The applicability of these results to the convective dissolution of geologically sequestered CO2{\mathrm{CO} }_{2} in a saline aquifer is discussed

High resolution imaging at large telescopes

Image recovery at a resolution limited only by diffraction is now possible at large telescopes. The theory of speckle image reconstruction is explained and the current status of a video recording and digitization system for the reconstruction procedure is described. Potential applications of the process when used with very large telescopes are discussed. The constraints on telescope design imposed by these techniques are listed

A dynamical systems approach to the tilted Bianchi models of solvable type

We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VI$_h$ and VII$_h$) with a perfect fluid and a linear barotropic $\gamma$-law equation of state. In particular, we study the late-time behaviour of tilted Bianchi models, with an emphasis on the existence of equilibrium points and their stability properties. We briefly discuss the tilting Bianchi type V models and the late-time asymptotic behaviour of irrotational Bianchi VII$_0$ models. We prove the important result that for non-inflationary Bianchi type VII$_h$ models vacuum plane-wave solutions are the only future attracting equilibrium points in the Bianchi type VII$_h$ invariant set. We then investigate the dynamics close to the plane-wave solutions in more detail, and discover some new features that arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of tilt. We point out that in a tiny open set of parameter space in the type IV model (the loophole) there exists closed curves which act as attracting limit cycles. More interestingly, in the Bianchi type VII$_h$ models there is a bifurcation in which a set of equilibrium points turn into closed orbits. There is a region in which both sets of closed curves coexist, and it appears that for the type VII$_h$ models in this region the solution curves approach a compact surface which is topologically a torus.Comment: 29 page

Understanding the Drivers of Urban Expansion: Case Study of Seville Province

Urban development has accelerated across the globe in recent decades. Much of this development has not been concentrated in cities, but has occurred as dispersed, low-density development outside of major centers but within their area of economic influence, along transport networks, in coastal areas, or close to areas of high natural value. This research focuses on the case study of the province of Seville, Spain, which has experienced notable urban expansion in recent years. We present a systems approach to model dependence between economic development and distribution of urban and non-urban land in this region from data collection to model validation. An extensive search of available indicators of socioeconomic development in this region has been carried out. We apply this data to create a generic statistical model of urban expansion, which links land-use patterns with population density and other indicators of economic growth. The model is tested across the whole Seville region and in its sub-regions to derive drivers of urban expansion in this territory

Self-similar Bianchi models: II. Class B models

In a companion article (referred hearafter as paper I) a detailed study of the simply transitive Spatially Homogeneous (SH) models of class A concerning the existence of a simply transitive similarity group has been given. The present work (paper II) continues and completes the above study by considering the remaining set of class B models. Following the procedure of paper I we find all SH models of class B subjected only to the minimal geometric assumption to admit a proper Homothetic Vector Field (HVF). The physical implications of the obtained geometric results are studied by specialising our considerations to the case of vacuum and $\gamma -$law perfect fluid models. As a result we regain all the known exact solutions regarding vacuum and non-tilted perfect fluid models. In the case of tilted fluids we find the \emph{general }self-similar solution for the exceptional type VI$_{-1/9}$ model and we identify it as equilibrium point in the corresponding dynamical state space. It is found that this \emph{new} exact solution belongs to the subclass of models $n_\alpha ^\alpha =0$, is defined for $\gamma \in (\frac 43,\frac 32)$ and although has a five dimensional stable manifold there exist always two unstable modes in the restricted state space. Furthermore the analysis of the remaining types, guarantees that tilted perfect fluid models of types III, IV, V and VII$_h$ cannot admit a proper HVF strongly suggesting that these models either may not be asymptotically self-similar (type V) or may be extreme tilted at late times. Finally for each Bianchi type, we give the extreme tilted equilibrium points of their state space.Comment: Latex, 15 pages, no figures; to appear in Classical Quantum Gravity (uses iopart style/class files); (v2) minor corrections to match published versio

Dispersal Dynamics in a Wind-Driven Benthic System

Bedload and water column traps were used with simultaneous wind and water velocity measurements to study postlarval macrofaunal dispersal dynamics in Manukau Harbour, New Zealand. A 12-fold range in mean wind condition resulted in large differences in water flow (12-fold), sediment flux (285-fold), and trap collection of total number of individuals (95-fold), number of the dominant infaunal organism (84-fold for the bivalve Macomona liliana), and number of species (4-fold). There were very strong, positive relationships among wind condition, water velocity, sediment flux, and postlarval dispersal, especially in the bedload. Local density in the ambient sediment was not a good predictor of dispersal. Results indicate that postlarval dispersal may influence benthic abundance pat- terns over a range of spatial scales

Convective shutdown in a porous medium at high Rayleigh number

Convection in a closed domain driven by a dense buoyancy source along the upper boundary soon starts to wane owing to the increase of the average interior density. In this paper, theoretical and numerical models are developed of the subsequent long period of shutdown of convection in a two-dimensional porous medium at high Rayleigh number Ra\mathit{Ra}. The aims of this paper are twofold. Firstly, the relationship between this slowly evolving ‘one-sided’ shutdown system and the statistically steady ‘two-sided’ Rayleigh–Bénard (RB) cell is investigated. Numerical measurements of the Nusselt number Nu\mathit{Nu} from an RB cell (Hewitt et al., Phys. Rev. Lett., vol. 108, 2012, 224503) are very well described by the simple parametrization Nu=2.75+0.0069Ra\mathit{Nu}= 2. 75+ 0. 0069\mathit{Ra}. This parametrization is used in theoretical box models of the one-sided shutdown system and found to give excellent agreement with high-resolution numerical simulations of this system. The dynamical structure of shutdown can also be accurately predicted by measurements from an RB cell. Results are presented for a general power-law equation of state. Secondly, these ideas are extended to model more complex physical systems, which comprise two fluid layers with an equation of state such that the solution that forms at the (moving) interface is more dense than either layer. The two fluids are either immiscible or miscible. Theoretical box models compare well with numerical simulations in the case of a flat interface between the fluids. Experimental results from a Hele-Shaw cell and numerical simulations both show that interfacial deformation can dramatically enhance the convective flux. The applicability of these results to the convective dissolution of geologically sequestered CO2{\mathrm{CO} }_{2} in a saline aquifer is discussed

Ames collaborative study of cosmic-ray neutrons. 2: Low- and mid-latitude flights

Progress of the study of cosmic ray neutrons is described. Data obtained aboard flights from Hawaii at altitudes of 41,000 and 45,000 feet, and in the range of geomagnetic latitude 17 N less than or equal to lambda less than or equal to 21 N are reported. Preliminary estimates of neutron spectra are made

Integrability and explicit solutions in some Bianchi cosmological dynamical systems

The Einstein field equations for several cosmological models reduce to polynomial systems of ordinary differential equations. In this paper we shall concentrate our attention to the spatially homogeneous diagonal G_2 cosmologies. By using Darboux's theory in order to study ordinary differential equations in the complex projective plane CP^2 we solve the Bianchi V models totally. Moreover, we carry out a study of Bianchi VI models and first integrals are given in particular cases

The Asymptotic Behaviour of Tilted Bianchi type VI0_0 Universes

We study the asymptotic behaviour of the Bianchi type VI$_0$ universes with a tilted $\gamma$-law perfect fluid. The late-time attractors are found for the full 7-dimensional state space and for several interesting invariant subspaces. In particular, it is found that for the particular value of the equation of state parameter, $\gamma=6/5$, there exists a bifurcation line which signals a transition of stability between a non-tilted equilibrium point to an extremely tilted equilibrium point. The initial singular regime is also discussed and we argue that the initial behaviour is chaotic for $\gamma<2$.Comment: 22 pages, 4 figures, to appear in CQ