The Origin of Chaos in the Outer Solar System

Classical analytic theories of the solar system indicate that it is stable, but numerical integrations suggest that it is chaotic. This disagreement is resolved by a new analytic theory. The theory shows that the chaos among the Jovian planets results from the overlap of the components of a mean motion resonance among Jupiter, Saturn, and Uranus, and provides rough estimates of the Lyapunov time (10 million years) and the dynamical lifetime of Uranus (10^{18} years). The Jovian planets must have entered the resonance after all the gas and most of the planetesimals in the protoplanetary disk were removed.Comment: 19 pages, 3 figures, to appear in Scienc

Eccentricity Excitation and Apsidal Resonance Capture in the Planetary System Upsilon Andromedae

The orbits of the outer two known planets orbiting Upsilon Andromedae are remarkably eccentric. Planet C possesses an orbital eccentricity of e1 = 0.253. For the more distant planet D, e2 = 0.308. Previous dynamical analyses strongly suggest that the two orbits are nearly co-planar and are trapped in an apsidal resonance in which the difference between their longitudes of periastron undergoes a bounded oscillation about 0 degrees. Here we elucidate the origin of these large eccentricities and of the apsidal alignment. Resonant interactions between a remnant circumstellar disk of gas lying exterior to the orbits of both planets can smoothly grow e2. Secular interactions between planets D and C can siphon off the eccentricity of the former to grow that of the latter. Externally amplifying e2 during the phase of the apsidal oscillation when e2/e1 is smallest drives the oscillation amplitude towards zero. Thus, the substantial eccentricity of planet C and the locking of orbital apsides are both consequences of externally pumping the eccentricity of planet D over timescales exceeding apsidal precession periods of order 1e4 yr. We explain why the recently detected stellar companion to Upsilon Andromedae is largely dynamically decoupled from the planetary system.Comment: accepted to Ap

A virtual environment for the design and simulated construction of prefabricated buildings

The construction industry has acknowledged that its current working practices are in need of substantial improvements in quality and efficiency and has identified that computer modelling techniques and the use of prefabricated components can help reduce times, costs, and minimise defects and problems of on-site construction. This paper describes a virtual environment to support the design and construction processes of buildings from prefabricated components and the simulation of their construction sequence according to a project schedule. The design environment can import a library of 3-D models of prefabricated modules that can be used to interactively design a building. Using Microsoft Project, the construction schedule of the designed building can be altered, with this information feeding back to the construction simulation environment. Within this environment the order of construction can be visualised using virtual machines. Novel aspects of the system are that it provides a single 3-D environment where the user can construct their design with minimal user interaction through automatic constraint recognition and view the real-time simulation of the construction process within the environment. This takes this area of research a step forward from other systems that only allow the planner to view the construction at certain stages, and do not provide an animated view of the construction process

Symetric Monopoles

We discuss $SU(2)$ Bogomolny monopoles of arbitrary charge $k$ invariant under various symmetry groups. The analysis is largely in terms of the spectral curves, the rational maps, and the Nahm equations associated with monopoles. We consider monopoles invariant under inversion in a plane, monopoles with cyclic symmetry, and monopoles having the symmetry of a regular solid. We introduce the notion of a strongly centred monopole and show that the space of such monopoles is a geodesic submanifold of the monopole moduli space. By solving Nahm's equations we prove the existence of a tetrahedrally symmetric monopole of charge $3$ and an octahedrally symmetric monopole of charge $4$, and determine their spectral curves. Using the geodesic approximation to analyse the scattering of monopoles with cyclic symmetry, we discover a novel type of non-planar $k$-monopole scattering process

Soil biota in grassland, its ecosystem services and the impact of management

In the search for sustainable grassland systems, self-regulating processes in the soil become increasingly important. Soil biota play an important role in these processes and in the provision of various ecosystem services. For grassland systems important ecosystem services are supply of nutrients, soil structure maintenance and water retention. For developing and optimising sustainable grassland systems, insight is needed into the mechanisms by which soil biota are influenced by management and what it means for the functioning of the soil-plant system. Interactions between soil and plants can be represented by a cyclic conceptual framework including plant/roots, soil biota and soil properties. The challenge for sustainable grassland is to allow this cycle to function optimally with a minimum of external inputs. In these systems the soil food web is probably bacterial-based with a high density of earthworms. The impacts of grassland management on soil biota are discussed on the basis of two cases: use of grass-clover mixtures and a ley-arable crop rotation versus permanent grassland and continuous arable land