The determinants of a cross market arbitrage opportunity: theory and evidence for the European bond market

This paper examines the determinants of cross-platform arbitrage profits. We develop a structural model that enables us to decompose the likelihood of an arbitrage opportunity into three distinct factors: the fixed cost to trade the opportunity, the level at which one of the platforms delays a price update and the impact of the order flow on the quoted prices (inventory and asymmetric information effects). We then investigate the predictions from the theoretical model for the European Bond market with the estimation of a probit model. Our main finding is that the results found in the empirical part corroborate strongly the predictions from the structural model. The event of a cross market arbitrage opportunity has a certain degree of predictability where an optimal ex ante scenario is represented by a low level of spreads on both platforms, a time of the day close to the end of trading hours and a high volume of trade.

Structure of turbulent flow over arrays of cubical roughness

The structure of turbulent flow over large roughness consisting of regular arrays of cubical obstacles is investigated numerically under constant pressure gradient conditions. Results are analysed in terms of first- and second-order statistics, by visualization of instantaneous flow fields and by conditional averaging. The accuracy of the simulations is established by detailed comparisons of first- and second-order statistics with wind-tunnel measurements. Coherent structures in the log region are investigated. Structure angles are computed from two-point correlations, and quadrant analysis is performed to determine the relative importance of Q2 and Q4 events (ejections and sweeps) as a function of height above the roughness. Flow visualization shows the existence of low-momentum regions (LMRs) as well as vortical structures throughout the log layer. Filtering techniques are used to reveal instantaneous examples of the association of the vortices with the LMRs, and linear stochastic estimation and conditional averaging are employed to deduce their statistical properties. The conditional averaging results reveal the presence of LMRs and regions of Q2 and Q4 events that appear to be associated with hairpin-like vortices, but a quantitative correspondence between the sizes of the vortices and those of the LMRs is difficult to establish; a simple estimate of the ratio of the vortex width to the LMR width gives a value that is several times larger than the corresponding ratio over smooth walls. The shape and inclination of the vortices and their spatial organization are compared to recent findings over smooth walls. Characteristic length scales are shown to scale linearly with height in the log region. Whilst there are striking qualitative similarities with smooth walls, there are also important differences in detail regarding: (i) structure angles and sizes and their dependence on distance from the rough surface; (ii) the flow structure close to the roughness; (iii) the roles of inflows into and outflows from cavities within the roughness; (iv) larger vortices on the rough wall compared to the smooth wall; (v) the effect of the different generation mechanism at the wall in setting the scales of structures.

A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

Evidence for global circuit current flow through water droplet layers

Abstract Foggy air and clear air have appreciably different electrical conductivities. The conductivity gradient at horizontal droplet boundaries causes droplet charging, as a result of vertical current flow in the global atmospheric electrical circuit. The charging is poorly known, as both the current flow through atmospheric water droplet layers and the air conductivity are poorly characterised experimentally. Surface measurements during three days of continuous fog using new instrument techniques show that a shallow (of order 100 m deep) fog layer still permits the vertical conduction current to pass. Further, the conductivity in the fog is estimated to be approximately 20% lower than in clear air. Assuming a fog transition thickness of one metre, this implies a vertical conductivity gradient of order 10 fS m−2 at the boundary. The actual vertical conductivity gradient at a cloud boundary would probably be greater, due to the presence of larger droplets in clouds compared to fog, and cleaner, more conductive clear air aloft.

The acoustic signature of fluid flow in complex porous media

Effective medium approximations for the frequency-dependent and complex-valued effective stiffness tensors of cracked/ porous rocks with multiple solid constituents are developed on the basis of the T-matrix approach (based on integral equation methods for quasi-static composites), the elastic - viscoelastic correspondence principle, and a unified treatment of the local and global flow mechanisms, which is consistent with the principle of fluid mass conservation. The main advantage of using the T-matrix approach, rather than the first-order approach of Eshelby or the second-order approach of Hudson, is that it produces physically plausible results even when the volume concentrations of inclusions or cavities are no longer small. The new formulae, which operates with an arbitrary homogeneous (anisotropic) reference medium and contains terms of all order in the volume concentrations of solid particles and communicating cavities, take explicitly account of inclusion shape and spatial distribution independently. We show analytically that an expansion of the T-matrix formulae to first order in the volume concentration of cavities (in agreement with the dilute estimate of Eshelby) has the correct dependence on the properties of the saturating fluid, in the sense that it is consistent with the Brown-Korringa relation, when the frequency is sufficiently low. We present numerical results for the (anisotropic) effective viscoelastic properties of a cracked permeable medium with finite storage porosity, indicating that the complete T-matrix formulae (including the higher-order terms) are generally consistent with the Brown-Korringa relation, at least if we assume the spatial distribution of cavities to be the same for all cavity pairs. We have found an efficient way to treat statistical correlations in the shapes and orientations of the communicating cavities, and also obtained a reasonable match between theoretical predictions (based on a dual porosity model for quartz-clay mixtures, involving relatively flat clay-related pores and more rounded quartz-related pores) and laboratory results for the ultrasonic velocity and attenuation spectra of a suite of typical reservoir rocks. (C) 2003 Elsevier B.V. All rights reserved.

Use of a portable topographic mapping millimetre wave radar at an active lava flow

A ground-based millimetre wave radar, AVTIS (All-weather Volcano Topography Imaging Sensor), has been developed for topographic monitoring. The instrument is portable and capable of measurements over ranges up to similar to 7 km through cloud and at night. In April and May 2005, AVTIS was deployed at Arenal Volcano, Costa Rica, in order to determine topographic changes associated with the advance of a lava flow. This is the first reported application of mm-wave radar technology to the measurement of lava flux rates. Three topographic data sets of the flow were acquired from observation distances of similar to 3 km over an eight day period, during which the flow front was detected to have advanced similar to 200 m. Topographic differences between the data sets indicated a flow thickness of similar to 10 m, and a dense rock equivalent lava flux of similar to 0.20 +/- 0.08 m(3) s(-1).

Landscape gene flow, coexistence and threshold effect: The case of genetically modified herbicide tolerant oilseed rape (Brassica napus)

Globally there have been a number of concerns about the development of genetically modified crops many of which relate to the implications of gene flow at various levels. In Europe these concerns have led the European Union (EU) to promote the concept of 'coexistence' to allow the freedom to plant conventional and genetically modified (GM) varieties but to minimise the presence of transgenic material within conventional crops. Should a premium for non-GM varieties emerge on the market, the presence of transgenes would generate a 'negative externality' to conventional growers. The establishment of maximum tolerance level for the adventitious presence of GM material in conventional crops produces a threshold effect in the external costs. The existing literature suggests that apart from the biological characteristics of the plant under consideration (e.g. self-pollination rates, entomophilous species, anemophilous species, etc.), gene flow at the landscape level is affected by the relative size of the source and sink populations and the spatial arrangement of the fields in the landscape. In this paper, we take genetically modified herbicide tolerant oilseed rape (GM HT OSR) as a model crop. Starting from an individual pollen dispersal function, we develop a spatially explicit numerical model in order to assess the effect of the size of the source/sink populations and the degree of spatial aggregation on the extent of gene flow into conventional OSR varieties under two alternative settings. We find that when the transgene presence in conventional produce is detected at the field level, the external cost will increase with the size of the source area and with the level of spatial disaggregation. on the other hand when the transgene presence is averaged among all conventional fields in the landscape (e.g. because of grain mixing before detection), the external cost will only depend on the relative size of the source area. The model could readily be incorporated into an economic evaluation of policies to regulate adoption of GM HT OSR. (c) 2007 Elsevier B.V. All rights reserved.

A rheological and SAXS study of the lamellar order in a side-on liquid crystalline block copolymer

We study the structure and shear flow behavior of a side-on liquid crystalline triblock copolymer, named PBA-b-PA444-b-PBA (PBA is poly(butyl acrylate) and PA444 is a poly(acrylate) with a nematic liquid crystal side-on mesogen), in the self-assembled lamellar phase and in the disordered phase. Simultaneous oscillatory shear and small-angle X-ray scattering experiments show that shearing PBA-b-PA444-b-PBA at high frequency and strain amplitudes leads to the alignment of the lamellae with normals perpendicular to the shear direction and to the velocity gradient direction, i.e., in the perpendicular orientation. The order-to-disorder transition temperature (T-ODT) is independent of the applied strain, in contrast to results reported in the literature for coil-coil diblock copolymers, which show an increase in T-ODT with shear rate. It is possible that in our system, T-ODT does not depend on the applied strain because the fluctuations are weaker than those present in coil-coil diblock copolymer systems.

A SAXS study of flow alignment of thermotropic liquid crystal mixtures

We report on the capillary flow behaviour of thermotropic liquid crystal mixtures containing 4-n-octyl-4'-cyanobiphenyl (8CB) and 4-n-pentyl-4'-cyanobiphenyl (5CB). The liquid crystal mixtures are studied in the Nematic (N) and Smectic (SA) phases at room temperature. Polarised optical microscopy (POM), rheology and simultaneous X-ray diffraction (XRD)/capillary flow experiments are performed to characterise the system. Polarised optical microscopy reveals a dramatic change in optical texture when the 5CB content is increased from 20 to 30% in the mixtures. X-ray diffraction results show that the system goes through a SA-N phase transition, such that the mixtures are smectic for 10-20% 5CB and nematic for 30-90% 5CB. Smectic mixtures flow with the layers aligned along the flow direction (mesogens perpendicular to flow) while nematic mixtures flow with the mesogens aligned in the flow direction. Simultaneous XRD/shear flow experiments show that the SA-N transition is independent of the flow rate in the range 1-6 ml min-1. The correlation length of the liquid crystal order decreases with increasing 5CB content. Rheology is used to prove that the correlation length behaviour is related to a reduction in the viscosity of the mixture.

Investigation into the performance of an algorithm for deriving concise descriptions of optic flow fields for real-time control

This paper describes a region-based algorithm for deriving a concise description of a first order optical flow field. The algorithm described achieves performance improvements over existing algorithms without compromising the accuracy of the flow field values calculated. These improvements are brought about by not computing the entire flow field between two consecutive images, but by considering only the flow vectors of a selected subset of the images. The algorithm is presented in the context of a project to balance a bipedal robot using visual information.

Prediction of supercritical flow in open channels

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow water equations in open channels. A linearised problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

State estimation using model order reduction for unstable systems

The problem of state estimation occurs in many applications of fluid flow. For example, to produce a reliable weather forecast it is essential to find the best possible estimate of the true state of the atmosphere. To find this best estimate a nonlinear least squares problem has to be solved subject to dynamical system constraints. Usually this is solved iteratively by an approximate Gauss–Newton method where the underlying discrete linear system is in general unstable. In this paper we propose a new method for deriving low order approximations to the problem based on a recently developed model reduction method for unstable systems. To illustrate the theoretical results, numerical experiments are performed using a two-dimensional Eady model – a simple model of baroclinic instability, which is the dominant mechanism for the growth of storms at mid-latitudes. It is a suitable test model to show the benefit that may be obtained by using model reduction techniques to approximate unstable systems within the state estimation problem.

A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountains

An analytical model of orographic gravity wave drag due to sheared flow past elliptical mountains is developed. The model extends the domain of applicability of the well-known Phillips model to wind profiles that vary relatively slowly in the vertical, so that they may be treated using a WKB approximation. The model illustrates how linear processes associated with wind profile shear and curvature affect the drag force exerted by the airflow on mountains, and how it is crucial to extend the WKB approximation to second order in the small perturbation parameter for these effects to be taken into account. For the simplest wind profiles, the normalized drag depends only on the Richardson number, Ri, of the flow at the surface and on the aspect ratio, γ, of the mountain. For a linear wind profile, the drag decreases as Ri decreases, and this variation is faster when the wind is across the mountain than when it is along the mountain. For a wind that rotates with height maintaining its magnitude, the drag generally increases as Ri decreases, by an amount depending on γ and on the incidence angle. The results from WKB theory are compared with exact linear results and also with results from a non-hydrostatic nonlinear numerical model, showing in general encouraging agreement, down to values of Ri of order one.

Pulsatory andesite lava flow at Bagana Volcano

Using a time series of TerraSAR-X spaceborne radar images we have measured the pulsatory motion of an andesite lava flow over a 14-month period at Bagana volcano, Papua New Guinea. Between October 2010 and December 2011, lava flowed continuously down the western flank of the volcano forming a 3 km-long blocky lava flow with a channel, levees, overflows and branches. We captured four successive pulses of lava advancing down the channel system, the first such behaviour of an andesite flow to be recorded using radar. Each pulse had a volume of the order of 107 m3 emplaced over many weeks. The average extrusion rate estimated from the radar data was 0.92 ± 0.35 m3 s-1 , and varied between 0.3 and 1.8 m3 s-1, with higher rates occurring earlier in each pulse. This, together with observations of sulphur dioxide emissions, explosions and incandescence suggest a variable supply rate of magma through Bagana’s conduit as the most likely source of the pulsatory behaviour.

The unsteady flow of a weakly compressible fluid in a thin porous layer II: three-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a three-dimensional layer, composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Numerical solution of this three-dimensional evolution problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l, a situation which occurs frequently in the application to oil and gas reservoir recovery and which leads to significant stiffness in the numerical problem. Under the assumption that $\epsilon\propto h/l\ll 1$, we show that, to leading order in $\epsilon$, the pressure field varies only in the horizontal directions away from the wells (the outer region). We construct asymptotic expansions in $\epsilon$ in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive expressions for all significant process quantities. The only computations required are for the solution of non-stiff linear, elliptic, two-dimensional boundary-value, and eigenvalue problems. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the layer, $\epsilon$, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighbourhood of wells and away from wells.