The effects of seed mix and management on the abundance of desirable and pernicious unsown species in arable buffer strip communities

Buffer strips are refuges for a variety of plants providing resources, such as pollen, nectar and seeds, for higher trophic levels, including invertebrates, mammals and birds. Margins can also harbour plant species that are potentially injurious to the adjacent arable crop (undesirable species). Sowing perennial species in non-cropped buffer strips can reduce weed incidence, but limits the abundance of annuals with the potential to support wider biodiversity (desirable species). We investigated the responses of unsown plant species present in buffer strips established with three different seed mixes managed annually with three contrasting management regimes (cutting, sward scarification and selective graminicide). Sward scarification had the strongest influence on the unsown desirable (e.g. Sonchus spp.) and unsown pernicious (e.g. Elytrigia repens) species, and was generally associated with higher cover values of these species. However, abundances of several desirable weed species, in particular Poa annua, were not promoted by scarification. The treatments of cutting and graminicide tended to have negative impacts on the unsown species, except for Cirsium vulgare, which increased with graminicide application. Differences in unsown species cover between seed mixes were minimal, although the grass-only mix was more susceptible to establishment by C. vulgare and Galium aparine than the two grass and forb mixes. Annual scarification can enable desirable annuals and sown perennials to co-exist, however, this practice can also promote pernicious species, and so is unlikely to be widely adopted as a management tool in its current form.

Soil disturbed using a strip tillage implement on a range of soil types and the effects on sugar beet establishment

The area of soil disturbed using a single tine is well documented. However, modern strip tillage implements using a tine and disc design have not been assessed in the UK or in mainland Europe. Using a strip tillage implement has potential benefits for European agriculture where economic returns and sustainability are key issues. Using a strip tillage system a narrow zone is cultivated leaving most of the straw residue on the soil surface. Small field plot experiments were undertaken on three soil types and the operating parameters of forward speed, tine depth and tine design were investigated together with measurements of seedbed tilth and crop emergence. The type of tine used was found to be the primary factor in achieving the required volume of disturbance within a narrow zone whilst maintaining an area of undisturbed soil with straw residue on the surface. The winged tine produced greater disturbance at a given depth compared with the knife tine. Increasing forward speed did not consistently increase the volume of disturbance. In a sandy clay loam the tilth created and emergence of sugar beet by strip tillage and ploughing were similar but on a sandy loam the strip tillage treatments generally gave a finer tilth but poorer emergence particularly at greater working depth.

Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.

Boundary value problems for the elliptic sine-Gordon equation in a semi-strip

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express the solution in terms of a 2 by 2 matrix Riemann-Hilbert problem whose \jump matrix" depends on both the Dirichlet and the Neumann boundary values. For a well posed problem one of these boundary values is an unknown function. This unknown function is characterised in terms of the so-called global relation, but in general this characterisation is nonlinear. We then concentrate on the case that the prescribed boundary conditions are zero along the unbounded sides of a semistrip and constant along the bounded side. This corresponds to a case of the so-called linearisable boundary conditions, however a major difficulty for this problem is the existence of non-integrable singularities of the function q_y at the two corners of the semistrip; these singularities are generated by the discontinuities of the boundary condition at these corners. Motivated by the recent solution of the analogous problem for the modified Helmholtz equation, we introduce an appropriate regularisation which overcomes this difficulty. Furthermore, by mapping the basic Riemann-Hilbert problem to an equivalent modified Riemann-Hilbert problem, we show that the solution can be expressed in terms of a 2 by 2 matrix Riemann-Hilbert problem whose jump matrix depends explicitly on the width of the semistrip L, on the constant value d of the solution along the bounded side, and on the residues at the given poles of a certain spectral function denoted by h. The determination of the function h remains open.

Planning autonomous vehicles in the absence of speed lanes using an elastic strip

Planning of autonomous vehicles in the absence of speed lanes is a less-researched problem. However, it is an important step toward extending the possibility of autonomous vehicles to countries where speed lanes are not followed. The advantages of having nonlane-oriented traffic include larger traffic bandwidth and more overtaking, which are features that are highlighted when vehicles vary in terms of speed and size. In the most general case, the road would be filled with a complex grid of static obstacles and vehicles of varying speeds. The optimal travel plan consists of a set of maneuvers that enables a vehicle to avoid obstacles and to overtake vehicles in an optimal manner and, in turn, enable other vehicles to overtake. The desired characteristics of this planning scenario include near completeness and near optimality in real time with an unstructured environment, with vehicles essentially displaying a high degree of cooperation and enabling every possible(safe) overtaking procedure to be completed as soon as possible. Challenges addressed in this paper include a (fast) method for initial path generation using an elastic strip, (re-)defining the notion of completeness specific to the problem, and inducing the notion of cooperation in the elastic strip. Using this approach, vehicular behaviors of overtaking, cooperation, vehicle following,obstacle avoidance, etc., are demonstrated.