We present a series of models for the plasma properties along open magnetic flux tubes rooted in solar coronal holes, streamers, and active regions. These models represent the first self-consistent solutions that combine (1) chromospheric heating driven by an empirically guided acoustic wave spectrum; (2) coronal heating from Alfven waves that have been partially reflected, then damped by anisotropic turbulent cascade; and (3) solar wind acceleration from gradients of gas pressure, acoustic wave pressure, and Alfven wave pressure. The only input parameters are the photospheric lower boundary conditions for the waves and the radial dependence of the background magnetic field along the flux tube. We have not included multifluid or collisionless effects (e.g., preferential ion heating), which are not yet fully understood. For a single choice for the photospheric wave properties, our models produce a realistic range of slow and fast solar wind conditions by varying only the coronal magnetic field. Specifically, a two-dimensional model of coronal holes and streamers at solar minimum reproduces the latitudinal bifurcation of slow and fast streams seen by Ulysses. The radial gradient of the Alfven speed affects where the waves are reflected and damped, and thus whether energy is deposited below or above the Parker critical point. As predicted by earlier studies, a larger coronal "expansion factor" gives rise to a slower and denser wind, higher temperature at the coronal base, less intense Alfven waves at 1 AU, and correlative trends for commonly measured ratios of ion charge states and FIP-sensitive abundances that are in general agreement with observations. These models offer supporting evidence for the idea that coronal heating and solar wind acceleration (in open magnetic flux tubes) can occur as a result of wave dissipation and turbulent cascade.

http://iopscience.iop.org/article/10.1086/518001/pdf

Self-consistent Coronal Heating and Solar Wind Acceleration from Anisotropic Magnetohydrodynamic Turbulence

Solar p-mode oscillations are excited by the work of stochastic, nonadiabatic, pressure fluctuations on the compressive modes. We evaluate the expression for the radial mode excitation rate derived by Nordlund & Stein using numerical simulations of near-surface solar convection. We first apply this expression to the three radial modes of the simulation and obtain good agreement between the predicted excitation rate and the actual mode damping rates as determined from their energies and the widths of their resolved spectral profiles. These radial simulation modes are essentially the same as the solar modes at the resonant frequencies, where the solar modes have a node at the depth of the bottom of the simulation domain. We then apply this expression for the mode excitation rate to the solar modes and obtain excellent agreement with the low l damping rates determined from data obtained by the "global oscillations at low frequencies" (GOLF) instrument on SOHO. Excitation occurs close to the surface, mainly in the intergranular lanes and near the boundaries of granules (where turbulence and radiative cooling are large). The nonadiabatic pressure fluctuations near the surface are produced by small instantaneous local imbalances between the divergence of the radiative and convective fluxes near the solar surface. Below the surface, the nonadiabatic pressure fluctuations are produced primarily by turbulent-pressure fluctuations (Reynolds stresses). The frequency dependence of the mode excitation is due to effects of the mode structure and the pressure fluctuation spectrum. Excitation is small at low frequencies because of mode properties—the mode compression decreases and the mode mass increases at low frequency. Excitation is small at high frequencies because of the pressure fluctuation spectrum—pressure fluctuations become small at high frequencies because they are due to convection, which is a long-timescale phenomenon compared with the dominant p-mode periods.

https://iopscience.iop.org/article/10.1086/318218/pdf

Solar Oscillations and Convection. II. Excitation of Radial Oscillations

The seismic study of the Sun and other stars offers a unique window into the interior of these stars. Thanks to helioseismology, we know the structure of the Sun to admirable precision. In fact, our knowledge is good enough to use the Sun as a laboratory. We have also been able to study the dynamics of the Sun in great detail. Helioseismic data also allow us to probe the changes that take place in the Sun as solar activity waxes and wanes. The seismic study of stars other than the Sun is a fairly new endeavour, but we are making great strides in this field. In this review I discuss some of the techniques used in helioseismic analyses and the results obtained using those techniques. I focus on results obtained with global helioseismology, i.e., the study of the Sun using its normal modes of oscillation. I also briefly touch upon asteroseismology, the seismic study of stars other than the Sun, and discuss how seismic data of others stars are interpreted.

/pdf/global-seismology-of-the-sun-nr0kxarn4t.pdf

Global seismology of the Sun

Basketball games evolve continuously in space and time as players constantly interact with their teammates, the opposing team, and the ball. However, current analyses of basketball outcomes rely on discretized summaries of the game that reduce such interactions to tallies of points, assists, and similar events. In this article, we propose a framework for using optical player tracking data to estimate, in real time, the expected number of points obtained by the end of a possession. This quantity, called expected possession value (EPV), derives from a stochastic process model for the evolution of a basketball possession. We model this process at multiple levels of resolution, differentiating between continuous, infinitesimal movements of players, and discrete events such as shot attempts and turnovers. Transition kernels are estimated using hierarchical spatiotemporal models that share information across players while remaining computationally tractable on very large data sets. In addition to estima...

A Multiresolution Stochastic Process Model for Predicting Basketball Possession Outcomes

Solar p-mode oscillations are excited by the work of stochastic, non-adiabatic, pressure fluctuations on the compressive modes. We evaluate the expression for the radial mode excitation rate derived by Nordlund and Stein (Paper I) using numerical simulations of near surface solar convection. We first apply this expression to the three radial modes of the simulation and obtain good agreement between the predicted excitation rate and the actual mode damping rates as determined from their energies and the widths of their resolved spectral profiles. We then apply this expression for the mode excitation rate to the solar modes and obtain excellent agreement with the low l damping rates determined from GOLF data. Excitation occurs close to the surface, mainly in the intergranular lanes and near the boundaries of granules (where turbulence and radiative cooling are large). The non-adiabatic pressure fluctuations near the surface are produced by small instantaneous local imbalances between the divergence of the radiative and convective fluxes near the solar surface. Below the surface, the non-adiabatic pressure fluctuations are produced primarily by turbulent pressure fluctuations (Reynolds stresses). The frequency dependence of the mode excitation is due to effects of the mode structure and the pressure fluctuation spectrum. Excitation is small at low frequencies due to mode properties -- the mode compression decreases and the mode mass increases at low frequency. Excitation is small at high frequencies due to the pressure fluctuation spectrum -- pressure fluctuations become small at high frequencies because they are due to convection which is a long time scale phenomena compared to the dominant p-mode periods.

Solar Oscillations and Convection: II. Excitation of Radial Oscillations

Most earlier mathematical studies of baseball required particular models for advancing runners based on a small set of offensive possibilities. Other efforts considered only teams with players of identical ability. We introduce a Markov chain method that considers teams made up of players with different abilities and which is not restricted to a given model for runner advancement. Our method is limited only by the available data and can use any reasonable deterministic model for runner advancement when sufficiently detailed data are not available. Furthermore, our approach may be adapted to include the effects of pitching and defensive ability in a straightforward way. We apply our method to find optimal batting orders, run distributions per half inning and per game, and the expected number of games a team should win. We also describe the application of our method to test whether a particular trade would benefit a team.

Elliotte Rusty Harold

Papers

A Markov Chain Approach to Baseball

Dark lanes in granulation and the excitation of solar oscillations