On certain new exact solutions of a diffusive predator-prey system

We construct exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the G'/G expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained. © 2012 Elsevier B.V.

Grazing incidence pumped Zr x-ray laser for spectroscopy on Li-like ions

X-ray laser fluorescence spectroscopy of the 2s-2p transition in Li-like ions is promising to become a widely applicable tool to provide information on the nuclear charge radii of stable and radioactive isotopes. For performing such experiments at the Experimental Storage Ring ESR, and the future NESR within the FAIR Project, a grazing incidence pumped (GRIP) x-ray laser (XRL) was set up at GSI Darmstadt using PHELIX (Petawatt High Energy Laser for heavy Ions eXperiments). The experiments demonstrated that lasing using the GRIP geometry could be achieved with relatively low pump energy, a prerequisite for higher repetition rate. In the first chapter the need of a plasma XRL is motivated and a short history of the plasma XRL is presented. The distinctive characteristic of the GRIP method is the controlled deposition of the pump laser energy into the desired plasma density region. While up to now the analysis performed were mostly concerned with the plasma density at the turning point of the main pump pulse, in this thesis it is demonstrated that also the energy deposition is significantly modified for the GRIP method, being sensitive in different ways to a large number of parameters. In the second chapter, the theoretical description of the plasma evolution, active medium and XRL emission properties are reviewed. In addition an innovative analysis of the laser absorption in plasma which includes an inverse Bremsstrahlung (IB) correction factor is presented. The third chapter gives an overview of the experimental set-up and diagnostics, providing an analytical formula for the average and instantaneous traveling wave speed generated with a tilted, on-axis spherical mirror, the only focusing system used up to now in GRIP XRL. The fourth chapter describes the experimental optimization and results. The emphasis is on the effect of the incidence angle of the main pump pulse on the absorption in plasma and on output and gain in different lasing lines. This is compared to the theoretical results for two different incidence angles. Significant corrections for the temperature evolution during the main pump pulse due to the incidence angle are demonstrated in comparison to a simple analytical model which does not take into account the pumping geometry. A much better agreement is reached by the model developed in this thesis. An interesting result is also the appearance of a central dip in the spatially resolved keV emission which was observed in the XRL experiments for the first time and correlates well with previous near field imaging and plasma density profile measurements. In the conclusion also an outlook to the generation of shorter wavelength XRL’s is given.

IMEX finite volume methods for the shallow water equations

Die Flachwassergleichungen (SWE) sind ein hyperbolisches System von Bilanzgleichungen, die adäquate Approximationen an groß-skalige Strömungen der Ozeane, Flüsse und der Atmosphäre liefern. Dabei werden Masse und Impuls erhalten. Wir unterscheiden zwei charakteristische Geschwindigkeiten: die Advektionsgeschwindigkeit, d.h. die Geschwindigkeit des Massentransports, und die Geschwindigkeit von Schwerewellen, d.h. die Geschwindigkeit der Oberflächenwellen, die Energie und Impuls tragen. Die Froude-Zahl ist eine Kennzahl und ist durch das Verhältnis der Referenzadvektionsgeschwindigkeit zu der Referenzgeschwindigkeit der Schwerewellen gegeben. Für die oben genannten Anwendungen ist sie typischerweise sehr klein, z.B. 0.01. Zeit-explizite Finite-Volume-Verfahren werden am öftersten zur numerischen Berechnung hyperbolischer Bilanzgleichungen benutzt. Daher muss die CFL-Stabilitätsbedingung eingehalten werden und das Zeitinkrement ist ungefähr proportional zu der Froude-Zahl. Deswegen entsteht bei kleinen Froude-Zahlen, etwa kleiner als 0.2, ein hoher Rechenaufwand. Ferner sind die numerischen Lösungen dissipativ. Es ist allgemein bekannt, dass die Lösungen der SWE gegen die Lösungen der Seegleichungen/ Froude-Zahl Null SWE für Froude-Zahl gegen Null konvergieren, falls adäquate Bedingungen erfüllt sind. In diesem Grenzwertprozess ändern die Gleichungen ihren Typ von hyperbolisch zu hyperbolisch.-elliptisch. Ferner kann bei kleinen Froude-Zahlen die Konvergenzordnung sinken oder das numerische Verfahren zusammenbrechen. Insbesondere wurde bei zeit-expliziten Verfahren falsches asymptotisches Verhalten (bzgl. der Froude-Zahl) beobachtet, das diese Effekte verursachen könnte.Ozeanographische und atmosphärische Strömungen sind typischerweise kleine Störungen eines unterliegenden Equilibriumzustandes. Wir möchten, dass numerische Verfahren für Bilanzgleichungen gewisse Equilibriumzustände exakt erhalten, sonst können künstliche Strömungen vom Verfahren erzeugt werden. Daher ist die Quelltermapproximation essentiell. Numerische Verfahren die Equilibriumzustände erhalten heißen ausbalanciert.rnrnIn der vorliegenden Arbeit spalten wir die SWE in einen steifen, linearen und einen nicht-steifen Teil, um die starke Einschränkung der Zeitschritte durch die CFL-Bedingung zu umgehen. Der steife Teil wird implizit und der nicht-steife explizit approximiert. Dazu verwenden wir IMEX (implicit-explicit) Runge-Kutta und IMEX Mehrschritt-Zeitdiskretisierungen. Die Raumdiskretisierung erfolgt mittels der Finite-Volumen-Methode. Der steife Teil wird mit Hilfe von finiter Differenzen oder au eine acht mehrdimensional Art und Weise approximniert. Zur mehrdimensionalen Approximation verwenden wir approximative Evolutionsoperatoren, die alle unendlich viele Informationsausbreitungsrichtungen berücksichtigen. Die expliziten Terme werden mit gewöhnlichen numerischen Flüssen approximiert. Daher erhalten wir eine Stabilitätsbedingung analog zu einer rein advektiven Strömung, d.h. das Zeitinkrement vergrößert um den Faktor Kehrwert der Froude-Zahl. Die in dieser Arbeit hergeleiteten Verfahren sind asymptotisch erhaltend und ausbalanciert. Die asymptotischer Erhaltung stellt sicher, dass numerische Lösung das "korrekte" asymptotische Verhalten bezüglich kleiner Froude-Zahlen besitzt. Wir präsentieren Verfahren erster und zweiter Ordnung. Numerische Resultate bestätigen die Konvergenzordnung, so wie Stabilität, Ausbalanciertheit und die asymptotische Erhaltung. Insbesondere beobachten wir bei machen Verfahren, dass die Konvergenzordnung fast unabhängig von der Froude-Zahl ist.

Slowing down a pine invasion despite uncertainty in demography and dispersal

1. Management decisions regarding invasive plants often have to be made quickly and in the face of fragmentary knowledge of their population dynamics. However, recommendations are commonly made on the basis of only a restricted set of parameters. Without addressing uncertainty and variability in model parameters we risk ineffective management, resulting in wasted resources and an escalating problem if early chances to control spread are missed. 2. Using available data for Pinus nigra in ungrazed and grazed grassland and shrubland in New Zealand, we parameterized a stage-structured spread model to calculate invasion wave speed, population growth rate and their sensitivities and elasticities to population parameters. Uncertainty distributions of parameters were used with the model to generate confidence intervals (CI) about the model predictions. 3. Ungrazed grassland environments were most vulnerable to invasion and the highest elasticities and sensitivities of invasion speed were to long-distance dispersal parameters. However, there was overlap between the elasticity and sensitivity CI on juvenile survival, seedling establishment and long-distance dispersal parameters, indicating overlap in their effects on invasion speed. 4. While elasticity of invasion speed to long-distance dispersal was highest in shrubland environments, there was overlap with the CI of elasticity to juvenile survival. In shrubland invasion speed was most sensitive to the probability of establishment, especially when establishment was low. In the grazed environment elasticity and sensitivity of invasion speed to the severity of grazing were consistently highest. Management recommendations based on elasticities and sensitivities depend on the vulnerability of the habitat. 5. Synthesis and applications. Despite considerable uncertainty in demography and dispersal, robust management recommendations emerged from the model. Proportional or absolute reductions in long-distance dispersal, juvenile survival and seedling establishment parameters have the potential to reduce wave speed substantially. Plantations of wind-dispersed invasive conifers should not be sited on exposed sites vulnerable to long-distance dispersal events, and trees in these sites should be removed. Invasion speed can also be reduced by removing seedlings, establishing competitive shrubs and grazing. Incorporating uncertainty into the modelling process increases our confidence in the wide applicability of the management strategies recommended here.

A bidomain threshold model of propagating calcium waves

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travelling wave solutions to probe the dependence of Ca wave speed on physiologically important parameters such as the threshold for Ca release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca resequestration from the cytosol to the ER, and the total [Ca] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called "tango waves" and the dependence of Ca wave speed on the total [Ca]. The original publication is available at www.springerlink.com (Journal of Mathematical Biology)

Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitly construct stationary fronts and determine their stability using an Evans function approach. Our results show that a biologically motivated choice of a dynamic threshold, as opposed to a constant threshold, can pin stationary fronts that would otherwise be unstable. This illustrates a novel mechanism to stabilise pinned interfaces in continuous excitable systems. Our framework also allows us to compute travelling pulse solutions in closed form and systematically probe the wave speed as a function of physiologically important parameters. We find that the existence of travelling wave solutions depends on the time scale of the threshold dynamics, and that facilitating release by lowering the cytosolic threshold increases the wave speed. The construction of the Evans function for a travelling pulse shows that of the co-existing fast and slow solutions the slow one is always unstable.

Predicting wave glider speed from environmental measurements

In the ocean science community, researchers have begun employing novel sensor platforms as integral pieces in oceanographic data collection, which have significantly advanced the study and prediction of complex and dynamic ocean phenomena. These innovative tools are able to provide scientists with data at unprecedented spatiotemporal resolutions. This paper focuses on the newly developed Wave Glider platform from Liquid Robotics. This vehicle produces forward motion by harvesting abundant natural energy from ocean waves, and provides a persistent ocean presence for detailed ocean observation. This study is targeted at determining a kinematic model for offline planning that provides an accurate estimation of the vehicle speed for a desired heading and set of environmental parameters. Given the significant wave height, ocean surface and subsurface currents, wind speed and direction, we present the formulation of a system identification to provide the vehicle’s speed over a range of possible directions.

An analysis of regression models for predicting the speed of a wave glider autonomous surface vehicle

An important aspect of robotic path planning for is ensuring that the vehicle is in the best location to collect the data necessary for the problem at hand. Given that features of interest are dynamic and move with oceanic currents, vehicle speed is an important factor in any planning exercises to ensure vehicles are at the right place at the right time. Here, we examine different Gaussian process models to find a suitable predictive kinematic model that enable the speed of an underactuated, autonomous surface vehicle to be accurately predicted given a set of input environmental parameters.

Predicting the speed of a Wave Glider autonomous surface vehicle from wave model data

A key component of robotic path planning is ensuring that one can reliably navigate a vehicle to a desired location. In addition, when the features of interest are dynamic and move with oceanic currents, vehicle speed plays an important role in the planning exercise to ensure that vehicles are in the right place at the right time. Aquatic robot design is moving towards utilizing the environment for propulsion rather than traditional motors and propellers. These new vehicles are able to realize significantly increased endurance, however the mission planning problem, in turn, becomes more difficult as the vehicle velocity is not directly controllable. In this paper, we examine Gaussian process models applied to existing wave model data to predict the behavior, i.e., velocity, of a Wave Glider Autonomous Surface Vehicle. Using training data from an on-board sensor and forecasting with the WAVEWATCH III model, our probabilistic regression models created an effective method for forecasting WG velocity.

On the Analytical Approach to Present Engineering Problems: Photovoltaic Systems Behavior, Wind Speed Sensors Performance, and High-Speed Train Pressure Wave Effects in Tunnels

At present, engineering problems required quite a sophisticated calculation means. However, analytical models still can prove to be a useful tool for engineers and scientists when dealing with complex physical phenomena. The mathematical models developed to analyze three different engineering problems: photovoltaic devices analysis; cup anemometer performance; and high-speed train pressure wave effects in tunnels are described. In all cases, the results are quite accurate when compared to testing measurements.

In search of the Korean digital wave

This article sets the context for this special themed issue on the 'Korean digital wave' by considering the symbiotic relationship between digital technologies, their techniques and practices, their uses and the affordances they provide, and Korea's 'compressed modernity' and swift industrialisation. It underscores the importance of interrogating a range of groundbreaking developments and innovations within Korea's digital mediascapes, and its creative and cultural industries, in order to gain a complex understanding of one of Australia's most significant export markets and trading partners. Given the financial and political commitment in Australia to a high-speed broadband network that aims to stimulate economic and cultural activity, recent technological developments in Korea, and the double-edged role played by government policy in shaping the 'Korean digital wave', merit close attention from media and communications scholars.