An algorithm for the shallow water equations with body fitted meshes

An efficient algorithm based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations in a generalised coordinate system. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The scheme has good jump capturing properties and the advantage of using body-fitted meshes. Numerical results are shown for flow past a circular obstruction.

An isentropic flow algorithm with body fitted meshes

An efficient algorithm based on flux difference splitting is presented for the solution of the three-dimensional equations of isentropic flow in a generalised coordinate system, and with a general convex gas law. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The algorithm requires only one function evaluation of the gas law in each computational cell. The scheme has good shock capturing properties and the advantage of using body-fitted meshes. Numerical results are shown for Mach 3 flow of air past a circular cylinder. Furthermore, the algorithm also applies to shallow water flows by employing the familiar gas dynamics analogy.

A concept of approximated densities for efficient nonlinear estimation

This paper presents the theoretical development of a nonlinear adaptive filter based on a concept of filtering by approximated densities (FAD). The most common procedures for nonlinear estimation apply the extended Kalman filter. As opposed to conventional techniques, the proposed recursive algorithm does not require any linearisation. The prediction uses a maximum entropy principle subject to constraints. Thus, the densities created are of an exponential type and depend on a finite number of parameters. The filtering yields recursive equations involving these parameters. The update applies the Bayes theorem. Through simulation on a generic exponential model, the proposed nonlinear filter is implemented and the results prove to be superior to that of the extended Kalman filter and a class of nonlinear filters based on partitioning algorithms.

Motion estimation through approximated densities

Many techniques are currently used for motion estimation. In the block-based approaches the most common procedure applied is the block-matching based on various algorithms. To refine the motion estimates resulting from the full search or any coarse search algorithm, one can find few applications of Kalman filtering, mainly in the intraframe scheme. The Kalman filtering technique applicability for block-based motion estimation is rather limited due to discontinuities in the dynamic behaviour of the motion vectors. Therefore, we propose an application of the concept of the filtering by approximated densities (FAD). The FAD, originally introduced to alleviate limitations due to conventional Kalman modelling, is applied to interframe block-motion estimation. This application uses a simple form of FAD involving statistical characteristics of multi-modal distributions up to second order.

Retrieval of mesospheric electron densities using an optimal estimation inverse method

We present a new method to determine mesospheric electron densities from partially reflected medium frequency radar pulses. The technique uses an optimal estimation inverse method and retrieves both an electron density profile and a gradient electron density profile. As well as accounting for the absorption of the two magnetoionic modes formed by ionospheric birefringence of each radar pulse, the forward model of the retrieval parameterises possible Fresnel scatter of each mode by fine electronic structure, phase changes of each mode due to Faraday rotation and the dependence of the amplitudes of the backscattered modes upon pulse width. Validation results indicate that known profiles can be retrieved and that χ2 tests upon retrieval parameters satisfy validity criteria. Application to measurements shows that retrieved electron density profiles are consistent with accepted ideas about seasonal variability of electron densities and their dependence upon nitric oxide production and transport.

Tillage and herbicide treatments with inter-row cultivation influence weed densities and yield of three industrial crops

Field experiments were conducted in northern Greece in 2003 and 2004 to evaluate effects of tillage regimes (moldboard plowing, chisel plowing, and rotary tilling), cropping sequences(continuous cotton, cotton-sugar beet rotation,and continuous tobacco) and herbicide treatments with inter-row hand hoeing on weed population densities. Total weed densities were not affected by tillage treatment except that of barnyardgrass (Echinochloa crus-galli), which increased only in moldboard plowing treated plots during 2003. Redroot pigweed (Amaranthus retroflexus)and black nightshade (Solanum nigrum) densities were reduced in continuous cotton, while purple nutsedge (Cyperus rotundus), E. crus-galli, S. nigrum, and johnsongras(Sorghum halepense) densities were reduced in tobacco. A. retroflexus and S. nigrum were effectively controlled by all herbicide treatments with inter-row hand hoeing,whereas E. crus-galli was effectively reduced by herbicides applied to cotton and tobacco. S. halepense density reduction was a result of herbicide applied to tobacco with inter-row hand hoeing. Yield of all crops was higher under moldboard plowing and herbicide treatments. Pre-sowing and pre-emergence herbicide treatments in cotton and pre-transplant in tobacco integrated with inter-row cultivation resulted in efficient control of annual weed species and good crop yields. These observations are of practical relevance to crop selection by farmers in order to maintain weed populations at economically acceptable densities through the integration of various planting dates, sustainable herbicide use and inter-row cultivation; tools of great importance in integrated weed management systems. Keywords: cropping sequence, herbicide, integrated weed management, inter-row cultivation,tillage.

(Non)differentiability and asymptotics for potential densities of subordinators

For subordinators with positive drift we extend recent results on the structure of the potential measures and the renewal densities. Applying Fourier analysis a new representation of the potential densities is derived from which we deduce asymptotic results and show how the atoms of the Lévy measure translate into points of (non)differentiability of the potential densities.

The asymptotic behavior of densities related to the supremum of a stable process

If X is a stable process of index α∈(0, 2) whose Lévy measure has density cx−α−1 on (0, ∞), and S1=sup0x)∽Aα−1x−α as x→∞ and P(S1≤x)∽Bα−1ρ−1xαρ as x↓0. [Here ρ=P(X1>0) and A and B are known constants.] It is also known that S1 has a continuous density, m say. The main point of this note is to show that m(x)∽Ax−(α+1) as x→∞ and m(x)∽Bxαρ−1 as x↓0. Similar results are obtained for related densities.

Spatio-temporal variation in predation by urban domestic cats (Felis catus) and the acceptability of possible management actions in the UK

Urban domestic cat (Felis catus) populations can attain exceedingly high densities and are not limited by natural prey availability. This has generated concerns that they may negatively affect prey populations, leading to calls for management. We enlisted cat-owners to record prey returned home to estimate patterns of predation by free-roaming pets in different localities within the town of Reading, UK and questionnaire surveys were used to quantify attitudes to different possible management strategies. Prey return rates were highly variable: only 20% of cats returned ≥4 dead prey annually. Consequently, approximately 65% of owners received no prey in a given season, but this declined to 22% after eight seasons. The estimated mean predation rate was 18.3 prey cat−1 year−1 but this varied markedly both spatially and temporally: per capita predation rates declined with increasing cat density. Comparisons with estimates of the density of six common bird prey species indicated that cats killed numbers equivalent to adult density on c. 39% of occasions. Population modeling studies suggest that such predation rates could significantly reduce the size of local bird populations for common urban species. Conversely, most urban residents did not consider cat predation to be a significant problem. Collar-mounted anti-predation devices were the only management action acceptable to the majority of urban residents (65%), but were less acceptable to cat-owners because of perceived risks to their pets; only 24% of cats were fitted with such devices. Overall, cat predation did appear to be of sufficient magnitude to affect some prey populations, although further investigation of some key aspects of cat predation is warranted. Management of the predation behavior of urban cat populations in the UK is likely to be challenging and achieving this would require considerable engagement with cat owners.

Housing densities and consumer choice

From 2001, the construction of flats and high-density developments increased in England and the building of houses declined. Does this indicate a change in taste or is it a result of government planning policies? In this paper, an analysis is made of the long-term effects of the policy of constraint which has existed for the past 50 years but the increase in density is identified as occurring primarily after new, revised, planning guidance was issued in England in 2000 which discouraged low-density development. To substantiate this, it is pointed out that the change which occurred in England did not occur in Scotland where guidance was not changed to encourage high-density residential development. The conclusion that the change is the result of planning policies and not of a change in taste is confirmed by surveys of the occupants of new high-rise developments in Leeds. The new flat-dwellers were predominantly young and childless and expressed the intention, in the near future, when they could, of moving out of the city centre and into houses. From recent changes in guidance by the new coalition government, it is expected that the construction of flats in England will fall back to earlier levels over the next few years.

A depth-integrated 2D coastal and estuarine model with conformal boundary-fitted mesh generation

Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications

Ranging characteristics of the domestic cat (Felis catus) in an urban environment

In many countries, high densities of domestic cats (Felis catus) are found in urban habitats where they have the potential to exert considerable predation pressure on their prey. However, little is known of the ranging behaviour of cats in the UK. Twenty cats in suburban Reading, UK, were fitted with GPS trackers to quantify movement patterns. Cats were monitored during the summer and winter for an average of 6.8 24 h periods per season. Mean daily area ranged (95 % MCP) was 1.94 ha. Including all fixes, mean maximum area ranged was 6.88 ha. These are broadly comparable to those observed in urban areas in other countries. Daily area ranged was not affected by the cat’s sex or the season, but was significantly larger at night than during the day. There was no relationship between area ranged and habitat availability. Taking available habitat into account, cat ranging area contained significantly more garden and other green space than urban habitats. If cats were shown to be negatively affecting prey populations, one mitigation option for consideration in housing developments proposed near important wildlife sites would be to incorporate a ‘buffer zone’ in which cat ownership was not permitted. Absolute maximum daily area ranged by a cat in this study was 33.78 ha. This would correspond to an exclusory limit of approximately 300–400 m to minimise the negative effects of cat predation, but this may need to be larger if cat ranging behaviour is negatively affected by population density

Evaluating multivariate forecast densities: a comparison of two approaches

We consider methods of evaluating multivariate density forecasts. A recently proposed method is found to lack power when the correlation structure is mis-specified. Tests that have good power to detect mis-specifications of this sort are described. We also consider the properties of the tests in the presence of more general mis-specifications.