The structure and dynamics of the near-sun solar wind

The solar wind is a collisionless plasma that flows at hundreds of km/s away from the Sun into interplanetary space. Despite over half a century of solar wind research many questions remain unanswered. To address these questions, in situ data from small heliocentric distances is required. To date, Parker Solar Probe (PSP) is the only spacecraft to measure data within 0.29 au. Therefore, the PSP data set offers a unique opportunity to study the near-Sun solar wind. The data from the Solar Probe Cup instrument are fitted to extract bulk solar wind parameters. These parameters are used in conjunction with data from the SPAN and MAG instruments to analyse three structures found in the solar wind: switchbacks, patches and quiet periods. The ion velocity distribution functions within full-reversal switchbacks are shown to be consistent with a velocity-space rotation of the background plasma. This suggests that the proton core parallel temperature is the same inside and outside of full-reversal switchbacks despite the enhanced plasma velocity above the background. The solar wind associated with two switchback patches is found to be consistent with slow Alfv\'enic solar wind from near the boundary of the southern polar coronal hole. A patch is also found to have a particularly low $\alpha-$particle abundance which is in contrast to a subsequent study, suggesting that $\alpha-$particle abundance within patches is variable. Quiet periods are found to be consistent with longitudinal solar wind streams in close proximity to the heliospheric current sheet (HCS). The typical longitudinal scale size of these quiet periods is $\sim$2$^{\circ}$. However, most quiet period durations are not consistent with this scale, as they are modulated by PSP's orbital trajectory and the HCS dynamics.Open Acces

Pattern production through a chiral chasing mechanism

Recent experiments on zebrafish pigmentation suggests that their typical black and white striped skin pattern is made up of a number of interacting chromatophore families. Specifically, two of these cell families have been shown to interact through a nonlocal chasing mechanism, which has previously been modeled using integro-differential equations. We extend this framework to include the experimentally observed fact that the cells often exhibit chiral movement, in that the cells chase, and run away, at angles different to the line connecting their centers. This framework is simplified through the use of multiple small limits leading to a coupled set of partial differential equations which are amenable to Fourier analysis. This analysis results in the production of dispersion relations and necessary conditions for a patterning instability to occur. Beyond the theoretical development and the production of new pattern planiforms we are able to corroborate the experimental hypothesis that the global pigmentation patterns can be dependent on the chirality of the chromatophores

Graph-Facilitated Resonant Mode Counting in Stochastic Interaction Networks

Oscillations in a stochastic dynamical system, whose deterministic counterpart has a stable steady state, are a widely reported phenomenon. Traditional methods of finding parameter regimes for stochastically-driven resonances are, however, cumbersome for any but the smallest networks. In this letter we show by example of the Brusselator how to use real root counting algorithms and graph theoretic tools to efficiently determine the number of resonant modes and parameter ranges for stochastic oscillations. We argue that stochastic resonance is a network property by showing that resonant modes only depend on the squared Jacobian matrix $J^2$ , unlike deterministic oscillations which are determined by $J$. By using graph theoretic tools, analysis of stochastic behaviour for larger networks is simplified and chemical reaction networks with multiple resonant modes can be identified easily.Comment: 5 pages, 4 figure

Likely equilibria of stochastic hyperelastic spherical shells and tubes

In large deformations, internally pressurised elastic spherical shells and tubes may undergo a limit-point, or inflation, instability manifested by a rapid transition in which their radii suddenly increase. The possible existence of such an instability depends on the material constitutive model. Here, we revisit this problem in the context of stochastic incompressible hyperelastic materials, and ask the question: what is the probability distribution of stable radially symmetric inflation, such that the internal pressure always increases as the radial stretch increases? For the classic elastic problem, involving isotropic incompressible materials, there is a critical parameter value that strictly separates the cases where inflation instability can occur or not. By contrast, for the stochastic problem, we show that the inherent variability of the probabilistic parameters implies that there is always competition between the two cases. To illustrate this, we draw on published experimental data for rubber, and derive the probability distribution of the corresponding random shear modulus to predict the inflation responses for a spherical shell and a cylindrical tube made of a material characterised by this parameter.Comment: arXiv admin note: text overlap with arXiv:1808.0126

Likely oscillatory motions of stochastic hyperelastic solids

Stochastic homogeneous hyperelastic solids are characterised by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input data to output quantities of interest. To investigate the effect of probabilistic parameters on predicted mechanical responses, we study radial oscillations of cylindrical and spherical shells of stochastic incompressible isotropic hyperelastic material, formulated as quasi-equilibrated motions where the system is in equilibrium at every time instant. Additionally, we study finite shear oscillations of a cuboid, which are not quasi-equilibrated. We find that, for hyperelastic bodies of stochastic neo-Hookean or Mooney-Rivlin material, the amplitude and period of the oscillations follow probability distributions that can be characterised. Further, for cylindrical tubes and spherical shells, when an impulse surface traction is applied, there is a parameter interval where the oscillatory and non-oscillatory motions compete, in the sense that both have a chance to occur with a given probability. We refer to the dynamic evolution of these elastic systems, which exhibit inherent uncertainties due to the material properties, as `likely oscillatory motions'

Boundary conditions cause different generic bifurcation structures in Turing systems

Turing’s theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still able to generate new results by returning to common dogmas. One such widely reported belief is that the Turing bifurcation occurs through a pitchfork bifurcation, which is true under zero-flux boundary conditions. However, under fixed boundary conditions, the Turing bifurcation becomes generically transcritical. We derive these algebraic results through weakly nonlinear analysis and apply them to the Schnakenberg kinetics. We observe that the combination of kinetics and boundary conditions produce their own uncommon boundary complexities that we explore numerically. Overall, this work demonstrates that it is not enough to only consider parameter perturbations in a sensitivity analysis of a specific application. Variations in boundary conditions should also be considered

Random blebbing motion: a simple model linking cell structural properties to migration characteristics

If the plasma membrane of a cell is able to delaminate locally from its actin cortex a cellular bleb can be produced. Blebs are pressure driven protrusions, which are noteworthy for their ability to produce cellular motion. Starting from a general continuum mechanics description we restrict ourselves to considering cell and bleb shapes that maintain approximately spherical forms. From this assumption we obtain a tractable algebraic system for bleb formation. By including cell-substrate adhesions we can model blebbing cell motility. Further, by considering mechanically isolated blebbing events, which are randomly distributed over the cell we can derive equations linking the macroscopic migration characteristics to the microscopic structural parameters of the cell. This multiscale modelling framework is then used to provide parameter estimates, which are in agreement with current experimental data. In summary the construction of the mathematical model provides testable relationships between the bleb size and cell motility

2006 Housing in the Nation's Capital

Explores the interdependent relationship between public school systems and housing markets, and examines the ability of coordinated investment in affordable housing and quality education to revitalize Washington, D.C., metropolitan area neighborhoods