177,404 research outputs found
Analogue black holes in relativistic BECs: Mimicking Killing and universal horizons
No full textRelativistic Bose-Einstein condensates (rBECs) have recently become a
well-established system for analogue gravity. Indeed, while such
relativistic systems cannot be yet realized experimentally, they provide
an interesting framework for mimicking metrics for which no analogue is
yet available, thus paving the way for further theoretical and numerical
explorations. In this vein, we here discuss black holes in rBECs and
explore how their features relate to the bulk properties of the system.
We then propose the coupling of external fields to the rBEC as a way to
mimic nonmetric features. In particular, we use a Proca field to
simulate an aether field, as found in Einstein-aether or Ho.
rava-Lifshitz gravity. This allows us to mimic a universal horizon, the
causal barrier relevant for superluminal modes in these modified
gravitational theories
Parameterising competing zooplankton for survival in plankton functional type models
No full textMarine plankton ecosystems are an important component of biogeochemical cycling in the oceans. Operational plankton functional type (PFT) models, that group plankton according to their biogeochemical properties, are currently being developed to resolve biogenic gas exchange between the ocean and atmosphere, and to model the lowest trophic levels in fisheries models. A fundamental problem with these models is that PFTs often go extinct in computer simulations, effectively removing the biogeochemical processes from the models. Cropp and Norbury [Cropp, R., Norbury, J., 2009a. Parameterizing plankton functional type models: insights from a dynamical systems perspective. J. Plankton Res. 31, 939-963] demonstrated that parameter combinations that allowed all PFTs to stay extant for all time in stable, homogeneous environments were rare in a PFT model with two competing phytoplankton and one zooplankton (NP1P2Z). In this paper, we examine the dynamical properties of a generic predator-predator-prey PFT model, and apply the analysis techniques developed by Cropp and Norbury to a simple example PFT model with one phytoplankton and two zooplankton (NPZ1Z2) in order to explore its properties and parameter space. We find that the properties of predator-predator-prey PFT systems are fundamentally different from those of predator-prey-prey PFT systems. The likelihood of parameter combinations for which all PFTs stay extant for all time in predator-predator-prey PFT systems depends critically on the process formulations used, and the properties of co-existing zooplankton (as defined by their parameter values) are quite different to those of co-existing phytoplankton.Griffith Sciences, Griffith School of EnvironmentFull Tex
Vorticity in analog gravity
No full textIn the analog gravity framework, the acoustic disturbances in a moving
fluid can be described by an equation of motion identical to a
relativistic scalar massless field propagating in curved space-time.
This description is possible only when the fluid under consideration is
barotropic, inviscid, and irrotational. In this case, the propagation of
the perturbations is governed by an acoustic metric that depends
algebrically on the local speed of sound, density, and the background
flow velocity, the latter assumed to be vorticity-free. In this work we
provide a straightforward extension in order to go beyond the
irrotational constraint. Using a charged-relativistic and
nonrelativistic-Bose- Einstein condensate as a physical system, we show
that in the low-momentum limit and performing the eikonal approximation
we can derive a d'Alembertian equation of motion for the charged phonons
where the emergent acoustic metric depends on flow velocity in the
presence of vorticity
Correction to: An eco-evolutionary system with naturally bounded traits
No full textCorrection to: Theoretical Ecology
https://doi.org/10.1007/s12080-019-0407-6
The original version of this article unfortunately contains an incorrect panel (b) in Fig. 1 introduced during the production process. The correct Fig. 1 is shown next page:
Ecospace diagrams illustrating the initial conditions (blue dots) and stable invasion outcomes (black dots) under ecological theory used for the four scenarios: a competitive exclusion—either x1 or x2 could survive depending on initial conditions, but for this initial condition x1 will survive and x2 will fail to invade; b competitive exclusion—R∗ theory predicts that x1 will win and x2 will go extinct; c competitive exclusion—R∗ theory predicts that x2 will win and x1 will go extinct; d competitive coexistence—both populations survive but x1 will dominate in non-adaptive scenarios. The lines are zero isoclines, the dots are stable (black) or unstable (white) equilibriums or initial conditions (blue). The vector field (blue arrows) show how the system changes in time. The initial population values have x1 set to its carrying capacity (i.e. x∗1=K1=r1/a11) and x∗2=0.05. Technically, R∗ is only relevant to panels b and c, but we will use the term generically to mean the outcome of non-evolutionary competition. (See Table 1 for parameter values)No Full Tex
A simple plankton model with complex behaviour
No full textIn this paper we extend the P1P2ZN model, introduced by Cropp and Norbury [5], to investigate the effects of specialist (or discriminate) and generalist (or indiscriminate) grazing (as parameterised by p) on a prey-prey-predator model for plankton, in the presence of a limiting nutrient. We also examine the influence of facultative and obligate omnivory on the survival of Z as a generalist predator, as we vary the linear mortality parameter oz • This leads to bifurcation transition diagrams, which also include steady state stability branches for certain critical points. For specialist grazing (p = 0) the bifurcation transition diagram shows steady states, periodic and chaotic dynamics, with very small windows of periodic behaviour, as az varies, while for generalist grazing (p = 1), we only find periodic or steady state behaviours. The dynamics is interpretable in terms of facultative/obligate omnivory of Z. Results suggest that green ocean plankton code in global climate change modelling might run more stably with generalist grazing terms and careful control of grazer mortality.Full Tex
Der Selbsteintritt des Kommissionärs und des Maklers. Inaugural-Dissertation... von Richard Cropp,...
No full text[Le droit du commissionnaire et du courtier à faire la contre-partie.].Diss
Obligate mutualism in a resource-based framework
No full textObligate mutualist interactions appear to be ubiquitous in nature but cannot be described by the simple models that have been so effective for developing the theory of other population interactions including competition, predation, mixotrophy, and facultative mutualism. We present a teaching framework that extends the standard Lotka--Volterra analysis of these interactions to the more complicated obligate mutualism. This provides a useful addition to applications of dynamical systems theory for mathematics students and an advanced course in population dynamics for ecology students.
The theoretical framework used in this work is based on explicitly accounted resources and per capita rates of change for populations that are negative when they have no resources and positive when they have maximal resources. We extend the Lotka--Volterra models by including terms that capture the “catalytic" effect of obligation, reflecting that while one population may be necessary for survival of another, the obligated population does not necessarily consume it. A key attribute of our consumer-resource approach is that the catalytic services provided by obligate mutualists are treated as pseudoresources for the purposes of determining these rates of change. This framework allows all major ecosystem population interactions to be modeled within a single, simple consumer-resource framework, and it reveals how populations can smoothly change their trophic status through a continuum of stable coexistence states.Full Tex
Pedogenesis and erosion history in a high rainfall, mountainous drainage basin - Cropp River, New Zealand
No full textCropp River drains a 28.5 km² drainage basin in the western Southern Alps. Extreme erosional modification of this formerly glaciated valley has occurred in response to high rainfall (10,800 mm a⁻¹) and rapid tectonic uplift (12 ± 2 mm a⁻¹). Studies of geomorphology, soil development and distribution, and contemporary forms of erosion provide the basis for interpreting the history of post-glacial erosion. During late Pleistocene (14 to 22,000 years BP) glacial advances Cropp basin was largely occupied by ice. Till dated at 10,250 ± 150 years BP, in the middle reaches of Cropp River, provides a maximum age for the post-glacial topography of the upper basin.
U-shaped cirques are present at the heads, of the larger tributaries. Elsewhere the glacial valley form has been largely destroyed by fluvial and mass movement erosion. This has produced a dominantly erosional landscape with extremely steep slopes (40 to 70° common), intense dissection, and steep V-shaped stream channels. Soil development sequences, independently dated by dendrochronology and radiocarbon dating, were examined on both gently and steeply sloping topography. Soil development is rapid and progressively forms recent soils (1000 years) are both podzolised and gleyed. Eluvial-illuvial coefficients, calculated from total element analyses, indicated the losses and gains of major elements during soil development.
Morphology of soils on steep slopes under both scrub-forest and grassland vegetation indicates most soils range in age from tens to a few thousand years. Soils are removed from steep slopes by episodic and progressive erosional processes, generally within 500 to 1000 years. Evidence of active erosion is widespread although largely concealed by dense vegetation cover. Natural revegetation of eroded sites is rapid despite low soil nutrient status. On steep slopes eroded sites have complete vegetation cover within 50 years, and within 500 to 1000 years have vegetation similar to uneroded areas. Obvious visual evidence of erosion is short-lived because of rapid revegetation and plant succession
Is maximizing resilience compatible with established ecological goal functions?
No full textCropp and Gabric [Ecosystem adaptation: do ecosystems maximise resilience? Ecology. In press] used a simple phytoplanktonzooplankton-nutrient model and a genetic algorithm to determine the parameter values that would maximize the value of certain goal functions. These goal functions were to maximize biomass, maximize flux, maximize flux to biomass ratio, and maximize resilience. It was found that maximizing goal functions maximized resilience. The objective of this study was to investigate whether the Cropp and Gabric [Ecosystem adaptation: do ecosystems maximise resilience? Ecology. In press] result was indicative of a general ecosystem principle, or peculiar to the model and parameter ranges used. This study successfully replicated the Cropp and Gabric [Ecosystem adaptation: do ecosystems maximise resilience? Ecology. In press] experiment for a number of different model types, however, a different interpretation of the results is made. A new metric, concordance, was devised to describe the agreement between goal functions. It was found that resilience has the highest concordance of all goal functions trialled. for most model types. This implies that resilience offers a compromise between the established ecological goal functions. The parameter value range used is found to affect the parameter versus goal function relationships. Local maxima and minima affected the relationship between parameters and goal functions, and between goal functions. (C) 2003 Elsevier B.V. All rights reserved
The dynamics of evolutionary branching in an ecological model
No full textEco-evolutionary modelling involves the coupling of ecological equations to evolutionary ones. The interaction between ecological dynamics and evolutionary processes is essential to simulating evolutionary branching, a precursor to speciation. The creation and maintenance of biodiversity in models depends upon their ability to capture the dynamics of evolutionary branching. Understanding these systems requires low-dimension models that are amenable to analysis. The rapid reproduction rates of marine plankton ecosystems and their importance in determining the fluxes of climatically important gases between the ocean and atmosphere suggest that the next generation of global climate models needs to incorporate eco-evolutionary models in the ocean. This requires simple population-level models, that can represent such eco-evolutionary processes with orders of magnitude fewer equations than models that follow the dynamics of individual phenotypes. We present a general framework for developing eco-evolutionary models and consider its general properties. This framework defines a fitness function and assumes a beta distribution of phenotype abundances within each population. It simulates the change in total population size, the mean trait value, and the trait differentiation, from which the variance of trait values in the population may be calculated. We test the efficacy of the eco-evolutionary modelling framework by comparing the dynamics of evolutionary branching in a six-equation eco-evolutionary model that has evolutionary branching, with that of an equivalent one-hundred equation model that simulates the dynamics of every phenotype in the population. The latter model does not involve a population fitness function, nor does it assume a distribution of phenotype abundance across trait values. The eco-evolutionary population model and the phenotype model produce similar evolutionary branching, both qualitatively and quantitatively, in both symmetric and asymmetric fitness landscapes. In order to better understand the six-equation model, we develop a heuristic three-equation eco-evolutionary model. We use the density-independent mortality parameter as a convenient bifurcation parameter, so that differences in evolutionary branching dynamics in symmetric and asymmetric fitness landscapes may be investigated. This model shows that evolutionary branching of a stable population is flagged by a zero in the local trait curvature; the trait curvature then changes sign from negative to positive and back to negative, along the solution. It suggests that evolutionary branching points may be generated differently, with different dynamical properties, depending upon, in this case, the symmetry of the system. It also suggests that a changing environment, that may change attributes such as mortality, could have profound effects on an ecosystem’s ability to adapt. Our results suggest that the properties of the three-dimensional model can provide useful insights into the properties of the higher-dimension models. In particular, the bifurcation properties of the simple model predict the processes by which the more complicated models produce evolutionary branching points. The corresponding bifurcation properties of the phenotype and population models, evident in the dynamics of the phenotype distributions they predict, suggest that our eco-evolutionary modelling framework captures the essential properties that underlie the evolution of phenotypes in populations
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