Food Quality in Producer-Grazer Models: A Generalized Analysis

Stoichiometric constraints play a role in the dynamics of natural populations, but are not explicitly considered in most mathematical models. Recent theoretical works suggest that these constraints can have a significant impact and should not be neglected. However, it is not yet resolved how stoichiometry should be integrated in population dynamical models, as different modeling approaches are found to yield qualitatively different results. Here we investigate a unifying framework that reveals the differences and commonalities between previously proposed models for producer-grazer systems. Our analysis reveals that stoichiometric constraints affect the dynamics mainly by increasing the intraspecific competition between producers and by introducing a variable biomass conversion efficiency. The intraspecific competition has a strongly stabilizing effect on the system, whereas the variable conversion efficiency resulting from a variable food quality is the main determinant for the nature of the instability once destabilization occurs. Only if the food quality is high an oscillatory instability, as in the classical paradox of enrichment, can occur. While the generalized model reveals that the generic insights remain valid in a large class of models, we show that other details such as the specific sequence of bifurcations encountered in enrichment scenarios can depend sensitively on assumptions made in modeling stoichiometric constraints.Comment: Online appendixes include

Shallow BF2 implants in Xe-bombardment-preamorphized Si: the interaction between Xe and F

Si(100) samples, preamorphized to a depth of ~30 nm using 20 keV Xe ions to a nominal fluence of 2×1014 cm-2 were implanted with 1 and 3 keV BF2 ions to fluences of 7×1014 cm-2. Following annealing over a range of temperatures (from 600 to 1130 °C) and times the implant redistribution was investigated using medium-energy ion scattering (MEIS), secondary ion mass spectrometry (SIMS), and energy filtered transmission electron microscopy (EFTEM). MEIS studies showed that for all annealing conditions leading to solid phase epitaxial regrowth, approximately half of the Xe had accumulated at depths of 7 nm for the 1 keV and at 13 nm for the 3 keV BF2 implant. These depths correspond to the end of range of the B and F within the amorphous Si. SIMS showed that in the preamorphized samples, approximately 10% of the F migrates into the bulk and is trapped at the same depths in a ~1:1 ratio to Xe. These observations indicate an interaction between the Xe and F implants and a damage structure that becomes a trapping site. A small fraction of the implanted B is also trapped at this depth. EXTEM micrographs suggest the development of Xe agglomerates at the depths determined by MEIS. The effect is interpreted in terms of the formation of a volume defect structure within the amorphized Si, leading to F stabilized Xe agglomerates or XeF precipitates

Singular continuous spectra in a pseudo-integrable billiard

The pseudo-integrable barrier billiard invented by Hannay and McCraw [J. Phys. A 23, 887 (1990)] -- rectangular billiard with line-segment barrier placed on a symmetry axis -- is generalized. It is proven that the flow on invariant surfaces of genus two exhibits a singular continuous spectral component.Comment: 4 pages, 2 figure

Dissipative chaotic scattering

We show that weak dissipation, typical in realistic situations, can have a metamorphic consequence on nonhyperbolic chaotic scattering in the sense that the physically important particle-decay law is altered, no matter how small the amount of dissipation. As a result, the previous conclusion about the unity of the fractal dimension of the set of singularities in scattering functions, a major claim about nonhyperbolic chaotic scattering, may not be observable.Comment: 4 pages, 2 figures, revte

Edge anisotropy and the geometric perspective on flow networks

ACKNOWLEDGMENTS This work was financially supported by the German Research Foundation (DFG) via the DFG Graduate School 1536 (“Visibility and Visualization”), the European Commission via the Marie-Curie ITN LINC (P7-PEOPLE-2011-ITN, Grant No. 289447), the German Federal Ministry for Education and Research (BMBF) via the BMBF Young Investigator's Group CoSy-CC2 (“Complex Systems Approaches to Understanding Causes and Consequences of Past, Present and Future Climate Change, Grant No. 01LN1306A”) and the project GLUES, the Stordalen Foundation (via the Planetary Boundary Research Network PB.net), the Earth League's EarthDoc program, and the Volkswagen Foundation via the project “Recurrent extreme events in spatially extended excitable systems: Mechanism of their generation and termination” (Grant No. 85391). The presented research has greatly benefited from discussions with Emilio Hernández-Garcia and Cristóbal López. Parts of the network calculations have been performed using the Python package pyunicorn56 (see http://tocsy.pik-potsdam.de/pyunicorn.php). pyunicorn is freely available for download at https://github.com/pik-copan/pyunicornPeer reviewedPublisher PD

Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow

Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent wall-bounded shear flows, these states have been hypothesized to be saddle points organizing the trajectories within a chaotic attractor. These states must be computed with Newton's method or one of its generalizations, since time-integration cannot converge to unstable equilibria. The bottleneck is the solution of linear systems involving the Jacobian of the Navier-Stokes or Boussinesq equations. Originally such computations were carried out by constructing and directly inverting the Jacobian, but this is unfeasible for the matrices arising from three-dimensional hydrodynamic configurations in large domains. A popular method is to seek states that are invariant under numerical time integration. Surprisingly, equilibria may also be found by seeking flows that are invariant under a single very large Backwards-Euler Forwards-Euler timestep. We show that this method, called Stokes preconditioning, is 10 to 50 times faster at computing steady states in plane Couette flow and traveling waves in pipe flow. Moreover, it can be carried out using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes to these popular spectral codes. We explain the convergence rate as a function of the integration period and Reynolds number by computing the full spectra of the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, ed. Alexander Gelfgat (Springer, 2018

Coagulation and fragmentation dynamics of inertial particles

Inertial particles suspended in many natural and industrial flows undergo coagulation upon collisions and fragmentation if their size becomes too large or if they experience large shear. Here we study this coagulation-fragmentation process in time-periodic incompressible flows. We find that this process approaches an asymptotic, dynamical steady state where the average number of particles of each size is roughly constant. We compare the steady-state size distributions corresponding to two fragmentation mechanisms and for different flows and find that the steady state is mostly independent of the coagulation process. While collision rates determine the transient behavior, fragmentation determines the steady state. For example, for fragmentation due to shear, flows that have very different local particle concentrations can result in similar particle size distributions if the temporal or spatial variation of shear forces is similar.Comment: 8 pages, 7 figure

Intermittency transitions to strange nonchaotic attractors in a quasiperiodically driven Duffing oscillator

Different mechanisms for the creation of strange nonchaotic attractors (SNAs) are studied in a two-frequency parametrically driven Duffing oscillator. We focus on intermittency transitions in particular, and show that SNAs in this system are created through quasiperiodic saddle-node bifurcations (Type-I intermittency) as well as through a quasiperiodic subharmonic bifurcation (Type-III intermittency). The intermittent attractors are characterized via a number of Lyapunov measures including the behavior of the largest nontrivial Lyapunov exponent and its variance as well as through distributions of finite-time Lyapunov exponents. These attractors are ubiquitous in quasiperiodically driven systems; the regions of occurrence of various SNAs are identified in a phase diagram of the Duffing system.Comment: 24 pages, RevTeX 4, 12 EPS figure