Phytoplankton, and the zooplankton that graze upon them, play a crucial role in the dynamics observed at higher levels of the aquatic food web. Because of their small size, short lifespan, and large population size, plankton serve as an example system for theoretical ecology. In this presentation, we will (1) develop a piecewise-smooth dynamical system and (2) reformulate it as a fast-slow dynamical system to account for prey preference, flexible feeding behaviour or rapid evolution, and an ecological trade-off, all of which have been observed in plankton. We compare our model predictions with data and conclude that our model simulations capture the periodicity in the ratio between predator's preferred and alternative prey types exhibited by data on protozoan predator and two different phytoplankton prey groups collected in spring from Lake Constance on the German-Swiss-Austrian border.
Fissile material is relatively dense, and consequently will have an increased gravitational effect compared to most materials. We want to explore the possibility that a Tikhonov regularization approach can be used to identify such high density material. Since it is a largely parameter based method there are many different aspects of the problem to optimize, some of which may be dependent on others.
In this talk I will be going over the method I followed, which involves implementing a logarithmic barrier term in conjunction with the Newton method and conjugate gradient method. The Huber norm is also used to decrease the spreading in the recovered model, and other weighting functions are explored to improve on the penetration problems usually associated with gravity gradiometry. Accuracy is the main factor when analyzing the reconstructions. However the hope is that this method might be used to scan cargo containers, and so efficiency and ease of use must also be considered.
Abstract to appear here
The tubes carrying fluids around our bodies are flexible. When the flow through a flexible tube is sufficiently vigorous, a strong fluid-structure interaction can ensue, leading to vigorous self-excited oscillations (wheezing in lung airways is a familiar example). I will discuss recent attempts to understand some of the mechanisms of instability using simplified models.
Zombies pose a serious threat to our society, as well as providing a supply of fun mathematical problems. In this seminar, we will discuss the various strengths and weaknesses of modeling a zombie horde as a two-dimensional gas. The talk will be followed by a Matlab session in which zombie films will be played; don't expect much dialogue or character development!
We are concerned with the evolution of the unsteady axisymmetric boundary layer on a rotating sphere, where the sphere is located in an infinite expanse of fluid which is also rotating. The system is assumed to be initially undergoing a solid body rotation, after which the sphere is brought rapidly, but smoothly, to a new rotation rate. The special case of the system initially at rest has already received much attention, and it is known that the flow becomes eruptive and suffers a finite-time breakdown. A similar breakdown is seen for any case where the sphere is sped up from its initial rotation rate. When the sphere is slowed down, however, the flow no longer erupts. In this case we look at a travelling wave-like disturbance which develops near the sphere's pole for large time. Bi-directionality in the developing boundary layer leads to numerical breakdown due to the instability of the layer to short-wavelength disturbances propagating meridionally.
We are interested in a radially developing laminar free jet, which emanates from some orifice and propagates radially, being axisymmetric about the transverse (z) axis and reflectionally symmetric across its z = 0 centreline. The numerical solution of a superposed linear perturbation, whose temporal form is assumed to be driven by a periodic source pulsation, gives rise to a wave-like disturbance whose amplitude grows downstream as its local wavelength decreases. An asymptotic analysis of this linear perturbation captures the exact nature of the exponential spatial growth and also algebraic attenuation of the growth. The linear theory is only valid when solving for a small amplitude pulsation. When a nonlinear pulsation is applied, any linear theory which simplifies the solving of the system must be dropped. Solving the full nonlinear system of equations reveals a wave which steepens as it propagates downstream, becoming infinite at a critical location. When applying a linear pulsation to a turbulent radial free jet, similar behaviour may be observed, at least when considering an eddy viscosity model.
Combustion is essential to energy generation and transport needs, and will remain so for the foreseeable future. Mitigating its impact on the climate and human health, by reducing its associated emissions, is thus a priority. One suggested strategy to reduce NOx is to operate combustors at lean conditions. Unfortunately, combustion instability is more likely to occur in the lean regime, and may have catastrophic consequences on the components of combustion chambers, such as vibrations and structural fatigue. Ramjet engines, rocket engines and in general any type of gas turbine engines may be subject to this detrimental instability. The ability to predict and control the instability is crucial for implementing the lean burn strategy. In this talk, we will investigate the stability of premixed curved flames in a duct using an asymptotic formulation that is derived from first principles, based on high-activation-energy and low-Mach-number assumptions. Different types of instabilities will be studied and means of controlling such instabilities will be discussed.