Global Hopf bifurcation in the ZIP regulatory system

Regulation of zinc uptake in roots of Arabidopsis thaliana has recently been modeled by a system of ordinary differential equations based on the uptake of zinc, expression of a transporter protein and the interaction between an activator and inhibitor. For certain parameter choices the steady state of this model becomes unstable upon variation in the external zinc concentration. Numerical results show periodic orbits emerging between two critical values of the external zinc concentration. Here we show the existence of a global Hopf bifurcation with a continuous family of stable periodic orbits between two Hopf bifurcation points. The stability of the orbits in a neighborhood of the bifurcation points is analyzed by deriving the normal form, while the stability of the orbits in the global continuation is shown by calculation of the Floquet multipliers. From a biological point of view, stable periodic orbits lead to potentially toxic zinc peaks in plant cells. Buffering is believed to be an efficient way to deal with strong transient variations in zinc supply. We extend the model by a buffer reaction and analyze the stability of the steady state in dependence of the properties of this reaction. We find that a large enough equilibrium constant of the buffering reaction stabilizes the steady state and prevents the development of oscillations. Hence, our results suggest that buffering has a key role in the dynamics of zinc homeostasis in plant cells.Comment: 22 pages, 5 figures, uses svjour3.cl

Phenotypic and Genetic Divergence among Poison Frog Populations in a Mimetic Radiation

The evolution of Müllerian mimicry is, paradoxically, associated with high levels of diversity in color and pattern. In a mimetic radiation, different populations of a species evolve to resemble different models, which can lead to speciation. Yet there are circumstances under which initial selection for divergence under mimicry may be reversed. Here we provide evidence for the evolution of extensive phenotypic divergence in a mimetic radiation in Ranitomeya imitator, the mimic poison frog, in Peru. Analyses of color hue (spectral reflectance) and pattern reveal substantial divergence between morphs. However, we also report that there is a “transition-zone� with mixed phenotypes. Analyses of genetic structure using microsatellite variation reveals some differentiation between populations, but this does not strictly correspond to color pattern divergence. Analyses of gene flow between populations suggest that, while historical levels of gene flow were low, recent levels are high in some cases, including substantial gene flow between some color pattern morphs. We discuss possible explanations for these observations

The Radial Dependence of Proton-scale Magnetic Spectral Break in Slow Solar Wind during PSP Encounter 2

International audienceMagnetic field fluctuations in the solar wind are commonly observed to follow a power-law spectrum. Near proton-kinetic scales, a spectral break occurs that is commonly interpreted as a transition to kinetic turbulence. However, this transition is not yet entirely understood. By studying the scaling of the break with various plasma properties, it may be possible to constrain the processes leading to the onset of kinetic turbulence. Using data from the Parker Solar Probe, we measure the proton-scale break over a range of heliocentric distances, enabling a measurement of the transition from inertial to kinetic-scale turbulence under various plasma conditions. We find that the break frequency f(b) increases as the heliocentric distance r decreases in the slow solar wind following a power law of f(b) similar to r(-1.11). We also compare this to the characteristic plasma ion scales to relate the break to the possible physical mechanisms occurring at this scale. The ratio f(b)/f(c) (f(c) for Doppler-shifted ion cyclotron resonance scale) is close to unity and almost independent of plasma beta(p). While f(b)/f(p) (f(p) for Doppler-shifted proton thermal gyroradius) increases with beta(p) approaching to unity at larger beta(p), f(b)/f(d) (f(d) for Doppler-shifted proton inertial length) decreases with beta(p) from unity at small beta(p). Due to the large comparable Alfven and solar wind speeds, we analyze these results using both the standard and modified Taylor hypotheses, demonstrating the robust statistical results

Cross Helicity Reversals in Magnetic Switchbacks

International audienceWe consider 2D joint distributions of normalized residual energy, sigma(r)(s, t), and cross helicity, sigma(c)(s, t), during one day of Parker Solar Probe's (PSP's) first encounter as a function of wavelet scale s. The broad features of the distributions are similar to previous observations made by Helios in slow solar wind, namely well-correlated and fairly Alfvenic wind, except for a population with negative cross helicity that is seen at shorter wavelet scales. We show that this population is due to the presence of magnetic switchbacks, or brief periods where the magnetic field polarity reverses. Such switchbacks have been observed before, both in Helios data and in Ulysses data in the polar solar wind. Their abundance and short timescales as seen by PSP in its first encounter is a new observation, and their precise origin is still unknown. By analyzing these MHD invariants as a function of the wavelet scale, we show that magnetohydrodynamic (MHD) waves do indeed follow the local mean magnetic field through switchbacks, with a net Elsasser flux propagating inward during the field reversal and that they, therefore, must be local kinks in the magnetic field and not due to small regions of opposite polarity on the surface of the Sun. Such observations are important to keep in mind as computing cross helicity without taking into account the effect of switchbacks may result in spurious underestimation of sigma(c) as PSP gets closer to the Sun in later orbits

Secondary contact and admixture between independently invading populations of the Western corn rootworm, diabrotica virgifera virgifera in Europe

The western corn rootworm, Diabrotica virgifera virgifera (Coleoptera: Chrysomelidae), is one of the most destructive pests of corn in North America and is currently invading Europe. The two major invasive outbreaks of rootworm in Europe have occurred, in North-West Italy and in Central and South-Eastern Europe. These two outbreaks originated from independent introductions from North America. Secondary contact probably occurred in North Italy between these two outbreaks, in 2008. We used 13 microsatellite markers to conduct a population genetics study, to demonstrate that this geographic contact resulted in a zone of admixture in the Italian region of Veneto. We show that i) genetic variation is greater in the contact zone than in the parental outbreaks; ii) several signs of admixture were detected in some Venetian samples, in a Bayesian analysis of the population structure and in an approximate Bayesian computation analysis of historical scenarios and, finally, iii) allelic frequency clines were observed at microsatellite loci. The contact between the invasive outbreaks in North-West Italy and Central and South-Eastern Europe resulted in a zone of admixture, with particular characteristics. The evolutionary implications of the existence of a zone of admixture in Northern Italy and their possible impact on the invasion success of the western corn rootworm are discussed

Constraining Ion-Scale Heating and Spectral Energy Transfer in Observations of Plasma Turbulence

International audienceWe perform a statistical study of the turbulent power spectrum at inertial and kinetic scales observed during the first perihelion encounter of the Parker Solar Probe. We find that often there is an extremely steep scaling range of the power spectrum just above the ion-kinetic scales, similar to prior observations at 1 A.U., with a power-law index of around −4. Based on our measurements, we demonstrate that either a significant (>50%) fraction of the total turbulent energy flux is dissipated in this range of scales, or the characteristic nonlinear interaction time of the turbulence decreases dramatically from the expectation based solely on the dispersive nature of nonlinearly interacting kinetic Alfvén waves

Ion-scale Electromagnetic Waves in the Inner Heliosphere

International audienceUnderstanding the physical processes in the solar wind and corona that actively contribute to heating, acceleration, and dissipation is a primary objective of NASA's Parker Solar Probe (PSP) mission. Observations of circularly polarized electromagnetic waves at ion scales suggest that cyclotron resonance and wave-particle interactions are dynamically relevant in the inner heliosphere. A wavelet-based statistical study of circularly polarized events in the first perihelion encounter of PSP demonstrates that transverse electromagnetic waves at ion resonant scales are observed in 30-50% of radial field intervals. Average wave amplitudes of approximately 4 nT are measured, while the mean duration of wave events is on the order of 20 s; however, long-duration wave events can exist without interruption on hour-long timescales. Determination of wave vectors suggests propagation parallel/antiparallel to the mean magnetic field. Though ion-scale waves are preferentially observed during intervals with a radial mean magnetic field, we show that measurement constraints, associated with single spacecraft sampling of quasi-parallel waves superposed with anisotropic turbulence, render the measured coherent ion-wave spectrum unobservable when the mean magnetic field is oblique to the solar wind flow; these results imply that the occurrence of coherent ion-scale waves is not limited to a radial field configuration. The lack of radial scaling of characteristic wave amplitudes and duration suggests that the waves are generated in situ through plasma instabilities. Additionally, observations of proton distribution functions indicate that temperature anisotropy may drive the observed ion-scale

[Plasma 2020 Decadal] Disentangling the Spatiotemporal Structure of Turbulence Using Multi-Spacecraft Data

This white paper submitted for 2020 Decadal Assessment of Plasma Science concerns the importance of multi-spacecraft missions to address fundamental questions concerning plasma turbulence. Plasma turbulence is ubiquitous in the universe, and it is responsible for the transport of mass, momentum, and energy in such diverse systems as the solar corona and wind, accretion discs, planet formation, and laboratory fusion devices. Turbulence is an inherently multi-scale and multi-process phenomenon, coupling the largest scales of a system to sub-electron scales via a cascade of energy, while simultaneously generating reconnecting current layers, shocks, and a myriad of instabilities and waves. The solar wind is humankind's best resource for studying the naturally occurring turbulent plasmas that permeate the universe. Since launching our first major scientific spacecraft mission, Explorer 1, in 1958, we have made significant progress characterizing solar wind turbulence. Yet, due to the severe limitations imposed by single point measurements, we are unable to characterize sufficiently the spatial and temporal properties of the solar wind, leaving many fundamental questions about plasma turbulence unanswered. Therefore, the time has now come wherein making significant additional progress to determine the dynamical nature of solar wind turbulence requires multi-spacecraft missions spanning a wide range of scales simultaneously. A dedicated multi-spacecraft mission concurrently covering a wide range of scales in the solar wind would not only allow us to directly determine the spatial and temporal structure of plasma turbulence, but it would also mitigate the limitations that current multi-spacecraft missions face, such as non-ideal orbits for observing solar wind turbulence. Some of the fundamentally important questions that can only be addressed by in situ multipoint measurements are discussed

Kinetic‐Scale Turbulence in the Venusian Magnetosheath

While not specifically designed as a planetary mission, NASA's Parker Solar Probe (PSP) mission uses a series of Venus gravity assists (VGAs) in order to reduce its perihelion distance. These orbital maneuvers provide the opportunity for direct measurements of the Venus plasma environment at high cadence. We present first observations of kinetic scale turbulence in the Venus magnetosheath from the first two VGAs. In VGA1, PSP observed a quasi‐parallel shock, β ∼ 1 magnetosheath plasma, and a kinetic range scaling of k−2.9. VGA2 was characterized by a quasi‐perpendicular shock with β ∼ 10, and a steep k−3.4 spectral scaling. Temperature anisotropy measurements from VGA2 suggest an active mirror mode instability. Significant coherent waves are present in both encounters at sub‐ion and electron scales. Using conditioning techniques to exclude these electromagnetic wave events suggests the presence of developed sub‐ion kinetic turbulence in both magnetosheath encounters