An Expansion Term In Hamilton's Equations

For any given spacetime the choice of time coordinate is undetermined. A particular choice is the absolute time associated with a preferred vector field. Using the absolute time Hamilton's equations are $- (\delta H_{c})/(\delta q)=\dot{\pi}+\Theta\pi,$+ (\delta H_{c})/(\delta \pi)=\dot{q}$, where$\Theta = V^{a}_{.;a}$is the expansion of the vector field. Thus there is a hitherto unnoticed term in the expansion of the preferred vector field. Hamilton's equations can be used to describe fluid motion. In this case the absolute time is the time associated with the fluid's co-moving vector. As measured by this absolute time the expansion term is present. Similarly in cosmology, each observer has a co-moving vector and Hamilton's equations again have an expansion term. It is necessary to include the expansion term to quantize systems such as the above by the canonical method of replacing Dirac brackets by commutators. Hamilton's equations in this form do not have a corresponding sympletic form. Replacing the expansion by a particle number$N\equiv exp(-\int\Theta d \ta)$and introducing the particle numbers conjugate momentum$\pi^{N}$the standard sympletic form can be recovered with two extra fields N and$\pi^N$. Briefly the possibility of a non-standard sympletic form and the further possibility of there being a non-zero Finsler curvature corresponding to this are looked at.Comment: 10 page

Recent Developments in Fisheries Science and Their Prospects for Improving Fisheries Contributions to Food Security

Marine reserves, areas permanently closed to all fishing, are frequently proposed as a tool for managing fisheries. Fishery benefits claimed for reserves include increases in spawning stock size, animal body size, and reproductive output of exploited species. Reserves are predicted to augment catches through export of offspring to fishing grounds, and spillover of juveniles and adults from reserves to fisheries. Protection of stocks and development of extended age structures of populations in reserves are argued to offer insurance against environmental variability and management failure. Models also suggest reserves will reduce year-to-year variability in catches, and offer greater simplicity of management and enforcement. Reserves are predicted to lead to habitat recovery from fishing disturbance which can also enhance benefits to fisheries. Extensive field research confirms many of these predictions. Reserves worldwide have led to increases in abundance, body size, biomass and reproductive output of exploited species. Such measures often increase many times over, sometimes by an order of magnitude or more. Population build up is usually rapid with effects detectable within 2-3 years of protection. Increases are often sustained over extended periods, particularly for longer-lived species and for measures of habitat recovery. Reserves have benefitted species from a wide taxonomic spectrum that covers most economically important taxa, including many species of fish, crustaceans, mollusks and echinoderms. Encouraged by these results, many countries and states have embarked upon initiatives to establish networks of marine reserves. However, reserves remain highly controversial among fishers and fishing industry bodies who argue that fishery benefits remain unproven. In the last three years there has been rapid growth in the number of cases where fisheries have been shown to benefit from reserves. In this report, we critically analyze this body of evidence, drawing upon studies of reserves and fishery closures. Fishery managers have long used fishery closures, areas temporarily closed to fishing for one or more species or to specific fishing gears. They are employed to help rebuild depleted stocks, reduce gear conflicts, protect vulnerable life stages of exploited species or protect sensitive habitats from damaging gears. Such areas can tell us much about the potential effects of marine reserves. Fishery benefits from reserves and fishery closures typically develop quickly, in most cases within five years of their creation. Perhaps the most persuasive evidence of fishery effects of reserves comes from changing fishing patterns. In most places where well-respected reserves or fishery closures exist, fishers tend to move their fishing activities closer to their boundaries. Fishing-the-line, as it is called, allows fishers to benefit from spillover of animals from reserves to fishing grounds. There are now well-documented cases of spillover from more than a dozen countries and including a wide range of species. It is more technically demanding to prove fishery enhancement through export of offspring on ocean currents. Existing reserves are generally small, making it hard to detect increased recruitment to fisheries at a regional scale. However, there are now several cases in which export of eggs and larvae have been confirmed, including dramatic enhancement of scallop fisheries in Georges Bank and clam fisheries in Fiji. Small reserves have worked well and repeatedly produce local benefits. However, regional fisheries enhancement will require more extensive networks of reserves. Some of the most convincing success stories come from places in which between 10 and 35% of fishing grounds have been protected. In several cases there is evidence that yields with reserves have risen to higher levels than prior to protection, despite a reduction in the area of fishing grounds. In other cases, smaller reserves have stabilized catches from intensively exploited fisheries or slowed existing rates of decline. We describe experiences that prove that success of marine reserves is not contingent on habitat type, geographical location, the kind of fishery involved, or the technological sophistication of management. Reserve benefits are not restricted to habitats like coral reefs, or to artisanal fisheries, as some critics claim. Fishery benefits have been demonstrated from reserves established in tropical, warm- and cold-temperate waters, and in many habitats, including coral reefs, rocky reefs, kelp forests, seagrass beds, mangroves, estuaries, soft sediments, continental shelves and deep sea. Reserves and fishery closures have worked well for a wide range of fisheries, spanning recreational fisheries, artisanal fisheries like those of coral reefs, through small-scale nearshore fisheries for species like lobsters, up to industrial-scale fisheries for animals like flatfish and scallops. They have worked across a similarly broad spectrum of management sophistication, from self-policing by committed fishers, through warden patrols to satellite monitoring of distant fishing activities. We now have strong evidence that with the support of local communities, marine reserves offer a highly effective management tool. However, reserves will only rarely be adequate as a stand-alone management approach, although we describe cases where they have worked in the absence of other measures. They will be most effective when implemented as part of a package of limits on fishing effort and protect exploited species and their habitats

Developing future energy performance standards for UK housing: The St Nicholas Court project – Part 1

This paper (and Part 2, to appear in the next issue) set out the results of a housing field trial designed to evaluate the impact of an enhanced energy performance standard for dwellings. The project was designed to inform the next review of Part L of the Building Regulations for England and Wales, which, following the publication of the UK government's white paper on energy policy, is expected in 2005. The project explores the implications of an enhanced standard in the context of timber frame construction. Although for programming reasons it was necessary to terminate the research project at the end of the design phase, the results suggest that the standard investigated is well within the capacity of the industry but it was clear that the whole supply chain will need to take a positive approach to the development of new solutions. The secret to a smooth and cost optimised transition is for the necessary development work to begin immediately, not when regulation changes. © 2003, MCB UP Limite

The Transversal Relative Equilibria of a Hamiltonian System with Symmetry

We show that, given a certain transversality condition, the set of relative equilibria \mcl E near p_e\in\mcl E of a Hamiltonian system with symmetry is locally Whitney-stratified by the conjugacy classes of the isotropy subgroups (under the product of the coadjoint and adjoint actions) of the momentum-generator pairs $(\mu,\xi)$ of the relative equilibria. The dimension of the stratum of the conjugacy class (K) is $\dim G+2\dim Z(K)-\dim K$, where Z(K) is the center of K, and transverse to this stratum \mcl E is locally diffeomorphic to the commuting pairs of the Lie algebra of $K/Z(K)$. The stratum \mcl E_{(K)} is a symplectic submanifold of P near p_e\in\mcl E if and only if $p_e$ is nondegenerate and K is a maximal torus of G. We also show that there is a dense subset of G-invariant Hamiltonians on P for which all the relative equilibria are transversal. Thus, generically, the types of singularities that can be found in the set of relative equilibria of a Hamiltonian system with symmetry are those types found amongst the singularities at zero of the sets of commuting pairs of certain Lie subalgebras of the symmetry group.Comment: 18 page

Analytical stability and simulation response study for a coupled two-body system

An analytical stability study and a digital simulation response study of two connected rigid bodies are documented. Relative rotation of the bodies at the connection is allowed, thereby providing a model suitable for studying system stability and response during a soft-dock regime. Provisions are made of a docking port axes alignment torque and a despin torque capability for encountering spinning payloads. Although the stability analysis is based on linearized equations, the digital simulation is based on nonlinear models

Cryptoendolith colonization of diverse substrates (1): cultivation and characterization

We are investigating whether cryptoendolithic microorganisms are able to colonize diverse substrates through biogenic weathering. This first part of the study involves the cultivation and characterization of microbial consortia from Antarctic sandstone habitats