Studies in the application of recurrence relations to special perturbation methods

The numerical integration of the differential equations describing dynamical systems has been shown in previous papers of this series to be most effectively accomplished by an explicit Taylor series method.In this paper we show that one explicit Taylor series method, developed earlier in this series and which appears to possess a high degree of versatility, yields considerable gains in efficiency over classical single-step and multi-step methods. (In this context efficiency is a measure of the time taken to carry out a calculation of a specific accuracy).For a given accuracy criterion governing the local truncation error (LTE) it is found that the Taylor series method is generallytwice as fast as the classical multi-step method and up totwenty times faster than the classical single-step method.     

Bayesian geological and geophysical data fusion for the construction and uncertainty quantification of 3D geological models

Traditional approaches to develop 3D geological models employ a mix of quantitative and qualitative scientific techniques,which do not fully provide quantification of uncertainty in the constructed models and fail to optimally weight geological field observations against constraints from geophysical data.Here,using the Bayesian Obsidian software package,we develop a methodology to fuse lithostratigraphic field observations with aeromagnetic and gravity data to build a 3D model in a small(13.5 km×13.5 km)region of the Gascoyne Province,Western Australia.Our approach is validated by comparing 3D model results to independently-constrained geological maps and cross-sections produced by the Geological Survey of Western Australia.By fusing geological field data with aeromagnetic and gravity surveys,we show that 89%of the modelled region has>95%certainty for a particular geological unit for the given model and data.The boundaries between geological units are characterized by narrow regions with<95%certainty,which are typically 400-1000 m wide at the Earth's surface and 500-2000 m wide at depth.Beyond~4 km depth,the model requires geophysical survey data with longer wavelengths(e.g.,active seismic)to constrain the deeper subsurface.Although Obsidian was originally built for sedimentary basin problems,there is reasonable applicability to deformed terranes such as the Gascoyne Province.Ultimately,modification of the Bayesian engine to incorporate structural data will aid in developing more robust 3D models.Nevertheless,our results show that surface geological observations fused with geophysical survey data can yield reasonable 3D geological models with narrow uncertainty regions at the surface and shallow subsurface,which will be especially valuable for mineral exploration and the development of 3D geological models under cover.     

Benthic species as mud patrol - modelled effects of bioturbators and biofilms on large-scale estuarine mud and morphology

Sediment-stabilizing and -destabilizing organisms, i.e. microphytobenthos (biofilms) and macrozoobenthos (bioturbators), affect the erodibility of muddy sediments, potentially altering large-scale estuarine morphology. Using a novel eco-morphodynamic model of an idealized estuary, we investigate eco-engineering effects of microphytobenthos and two macrozoobenthic bioturbators. Local mud erodibility is based on species pattern predicted through hydrodynamics, soil mud content, competition and grazing. Mud resuspension and export is enhanced under bioturbation and prevented under biostabilization through respective exposure and protection of the supra- and intertidal. Bioturbation decreases mud thickness and bed elevations, which increases net mud fluxes. Microphytobenthos reduces erosion, leading to a local mud increase of intertidal sediments. In multi-species scenarios, an effective mud-prone bioturbator strongly alters morphology, exceeding that of a more abundant sand-prone moderate species, showing that morphological change depends on species traits as opposed to abundance. Altering their habitat, the effective mud-prone bioturbator facilitates expansion of the sand-prone moderate bioturbator. Grazing and species competition favor species distributions of dominant bioturbators. Consequently, eco-engineering affects habitat conditions while species interactions determine species dominance. Our results show that eco-engineering species determine the mud content of the estuary, which suggests large effects on the morphology of estuaries with aggravating habitat degradation.     

Exchange orbits: an interesting case of co-orbital motion

In this investigation we treat a special configuration of two celestial bodies in 1:1 mean motion resonance namely the so-called exchange orbits. There exist—at least—theoretically—two different types: the exchange-a orbits and the exchange-e orbits. The first one is the following: two celestial bodies are in orbit around a central body with almost the same semi-major axes on circular orbits. Because of the relatively small differences in semi-major axes they meet from time to time and exchange their semi-major axes. The inner one then moves outside the other planet and vice versa. The second configuration one is the following: two planets are moving on nearly the same orbit with respect to the semi-major axes, one on a circular orbit and the other one on an eccentric one. During their dynamical evolution they change the characteristics of the orbit, the circular one becomes an elliptic one whereas the elliptic one changes its shape to a circle. This ‘game’ repeats periodically. In this new study we extend the numerical computations for both of these exchange orbits to the three dimensional case and in another extension treat also the problem when these orbits are perturbed from a fourth body. Our results in form of graphs show quite well that for a large variety of initial conditions both configurations are stable and stay in these exchange orbits.     

Microstructure characteristics during hydrate formation and dissociation revealed by X-ray tomographic microscopy

Despite much progress over the past years in fundamental gas hydrate research, frontiers to the unknown are the early beginning and early decomposition of gas hydrates in their natural, submarine environment: gas bubbles meeting ocean water and forming hydrate, and gas starting to escape from the surface of a hydrate grain. In this paper we report on both of these topics, and present three-dimensional microstructure results obtained by synchrotron radiation X-ray cryo-tomographic microscopy (SRXCTM). Hydrates can precipitate when hydrate-forming molecules such as methane exceed solubility, and combine with water within the gas hydrate stability zone. Here we show hydrate formation on surfaces of bubbles from different gas mixtures and seawater, based on underwater robotic in situ experiments in the deep Monterey Canyon, offshore California. Hydrate begins to form from the surrounding water on the bubble surfaces, and subsequently grows inward into the bubble, evidenced by distinct edges. Over time, the bubbles become smaller while gas is being incorporated into newly formed hydrate. In contrast, current understanding has been that hydrate decomposition starts on the outer surface of hydrate aggregates and grains. It is shown that in an early stage of decomposition, newly found tube structures connect well-preserved gas hydrate patches to areas that are dissociating, demonstrating how dissociating areas in a hydrate grain are linked through hydrate that is still intact and will likely decompose at a later stage.

Contribution of photosynthetic gains during tidal emersion to production of Zostera capricorni in a North Island,New Zealand estuary

Photosynthetic characteristics of intertidal Zostera capricorni were measured under different tidal conditions in Whangapoua Harbour on the eastern Coromandel Peninsula, New Zealand, and compared with permanently submerged seagrass beds. Photosynthetic characteristics were measured using pulse amplitude modulated (PAM) fluorom‐etry and oxygen (O2) electrode techniques. Gross light saturated photosynthesis measured as oxygen exchange averaged 5.74 and 5.36 mg O₂ g^–1 dry weight (DW) h^–1 and leaf respiration rates averaged 1.22 and 1.38 mg O₂ g^–1 DW h^–1, for intertidal and subtidal plants respectively. Photosynthesis of both intertidal and shallow subtidal plants was light saturated at between 195 and 242 μmol photons m ^–2 s^–1, suggestive of acclimation to a high light environment. Despite the period of exposure at low tide clearly being an important time for photosynthetic gains for intertidal plants, when water clarity was sufficiently high, maximum rates of photosynthesis were also possible when the beds were submerged. If average water clarity was at the clearer end of a range measured for this site (K_d = 0.85 m^–1) then it was calculated that for intertidal seagrass beds growing at mean sea level in Whangapoua, c. 50% of above‐ground production could occur while plants were submerged.     

Willingness to pay among households to prevent coastal resources from polluting by oil spills: A pilot survey

In many coastal regions oil spills can be considered to be one of the most important risks for the coastal environment. Efficient contingency management in responding to oil spills is critically important. Strategic priorities in contingency management highly depend upon the importance attributed to different economic and ecological resources such as beaches or birds. Due to the lack of a market for natural resources in the real world, these resources cannot be directly measured in monetary terms. This increases the risk that natural resources and their services are neglected in contingency decision making. This paper evaluates these natural resources in a hypothetical market by using the methodology of stated choice experiments. Results from a pilot survey show that according to the perspective of individuals, an oil spill combat process should focus on the protection of coastal waters, beaches and eider ducks.     

CFD-based modelling of bubble-particle collision efficiency with mobile bubble surface in a turbulent environment

Flotation modelling to date has concentrated either on macroscale processes or on ideal microscale processes — there has been no attempt to integrate detailed models at different scales. In this paper, bubble-particle collision efficiency with mobile bubble surfaces in a turbulent flow is investigated from a multiscale modelling viewpoint and a general methodology for modelling is present. Comparisons are carried out to illustrate the method. Turbulence effects on bubble-particle collision efficiency are systematically studied using a 3D k–ε turbulence model.