554 research outputs found
When does cyclic dominance lead to stable spiral waves?
Species diversity in ecosystems is often accompanied by characteristic spatio-temporal patterns. Here, we consider a generic two-dimensional population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species, mutation, pair-exchange and individual hopping. The dynamics is characterized by nonlinear mobility and a Hopf bifurcation around which the system's four-phase state diagram is inferred from a complex Ginzburg-Landau equation derived using a perturbative multiscale expansion. While the dynamics is generally characterized by spiraling patterns, we show that spiral waves are stable in only one of the four phases. Furthermore, we characterize a phase where nonlinearity leads to the annihilation of spirals and to the spatially uniform dominance of each species in turn. Away from the Hopf bifurcation, when the coexistence fixed point is unstable, the spiraling patterns are also affected by the nonlinear diffusion
Planktonic communities and chaotic advection in dynamical models of Langmuir circulation
A deterministic mechanism for the production of plankton patches within a typical medium scale oceanic structure is proposed and investigated. By direct numerical simulation of a simple model of Langmuir circulation we quantify the effects of unsteady flows on planktonic communities and demonstrate their importance. Two qualitatively different zones within the flow are identified: chaotic regions that help to spread plankton and locally coherent regions, that do not mix with the chaotic regions and which persist for long periods of time. The relative importance of these regions to both phytoplankton and zooplankton is investigated, taking into account variations in plankton buoyancy. In particular, species-specific retention zone structure is discussed in relation to variations in environmental forcing
Exact coherent structures in an asymptotically reduced description of parallel shear flows
A reduced description of shear flows motivated by the Reynolds number scaling of lower-branch exact coherent states in plane Couette flow (Wang J, Gibson J and Waleffe F 2007 Phys. Rev. Lett. 98 204501) is constructed. Exact time-independent nonlinear solutions of the reduced equations corresponding to both lower and upper branch states are found for a sinusoidal, body-forced shear flow. The lower branch solution is characterized by fluctuations that vary slowly along the critical layer while the upper branch solutions display a bimodal structure and are more strongly focused on the critical layer. The reduced equations provide a rational framework for investigations of subcritical spatiotemporal patterns in parallel shear flows
L\'evy flights as an emergent phenomenon in a spatially extended system
We provide an example of a stochastic partial differential equation (SPDE)
which, despite only driven by Gaussian white noise, exhibits superdiffusive
behaviour. The anomalous diffusion is an entirely emergent behaviour and
manifests itself in jumps in the location of a travelling front solution. Using
a collective coordinate approach we reduce the SPDE to a set of stochastic
differential equations (SDEs) driven by Gaussian white noise. This allows us to
identify the mechanism giving rise to the anomalous diffusion: We find that the
emergence of anomalous diffusion is induced by random widening events of the
front interface
Inertial Coupling Method for particles in an incompressible fluctuating fluid
We develop an inertial coupling method for modeling the dynamics of
point-like 'blob' particles immersed in an incompressible fluid, generalizing
previous work for compressible fluids. The coupling consistently includes
excess (positive or negative) inertia of the particles relative to the
displaced fluid, and accounts for thermal fluctuations in the fluid momentum
equation. The coupling between the fluid and the blob is based on a no-slip
constraint equating the particle velocity with the local average of the fluid
velocity, and conserves momentum and energy. We demonstrate that the
formulation obeys a fluctuation-dissipation balance, owing to the
non-dissipative nature of the no-slip coupling. We develop a spatio-temporal
discretization that preserves, as best as possible, these properties of the
continuum formulation. In the spatial discretization, the local averaging and
spreading operations are accomplished using compact kernels commonly used in
immersed boundary methods. We find that the special properties of these kernels
make the discrete blob a particle with surprisingly physically-consistent
volume, mass, and hydrodynamic properties. We develop a second-order
semi-implicit temporal integrator that maintains discrete
fluctuation-dissipation balance, and is not limited in stability by viscosity.
Furthermore, the temporal scheme requires only constant-coefficient Poisson and
Helmholtz linear solvers, enabling a very efficient and simple FFT-based
implementation on GPUs. We numerically investigate the performance of the
method on several standard test problems...Comment: Contains a number of corrections and an additional Figure 7 (and
associated discussion) relative to published versio
Modelling of surfactant-driven front instabilities in spreading bacterial colonies
The spreading of bacterial colonies at solid-air interfaces is determined by
the physico-chemical properties of the involved interfaces. The production of
surfactant molecules by bacteria is a widespread strategy that allows the
colony to efficiently expand over the substrate. On the one hand, surfactant
molecules lower the surface tension of the colony, effectively increasing the
wettability of the substrate, which facilitates spreading. On the other hand,
gradients in the surface concentration of surfactant molecules result in
Marangoni flows that drive spreading. These flows may cause an instability of
the circular colony shape and the subsequent formation of fingers. In this
work, we study the effect of bacterial surfactant production and substrate
wettability on colony growth and shape within the framework of a hydrodynamic
thin film model. We show that variations in the wettability and surfactant
production are sufficient to reproduce four different types of colony growth,
which have been described in the literature, namely, arrested and continuous
spreading of circular colonies, slightly modulated front lines and the
formation of pronounced fingers
- âŠ