On the Chemical Mixing Induced by Internal Gravity Waves

Detailed modeling of stellar evolution requires a better understanding of the (magneto)hydrodynamic processes that mix chemical elements and transport angular momentum. Understanding these processes is crucial if we are to accurately interpret observations of chemical abundance anomalies, surface rotation measurements, and asteroseismic data. Here, we use two-dimensional hydrodynamic simulations of the generation and propagation of internal gravity waves in an intermediate-mass star to measure the chemical mixing induced by these waves. We show that such mixing can generally be treated as a diffusive process. We then show that the local diffusion coefficient does not depend on the local fluid velocity, but rather on the wave amplitude. We then use these findings to provide a simple parameterization for this diffusion, which can be incorporated into stellar evolution codes and tested against observations

Comment on “What Determines the Static Force Chains in Stressed Granular Media?”

Comment on O. Gendelman, Y. G. Pollack, I. Procaccia, S. Sengupta, and J. Zylberg, Physical Review Letters 116, 078001 (2016).Comment: 1 pag

Bulldozing of granular material

We investigate the bulldozing motion of a granular sandpile driven forwards by a vertical plate. The problem is set up in the laboratory by emplacing the pile on a table rotating underneath a stationary plate; the continual circulation of the bulldozed material allows the dynamics to be explored over relatively long times, and the variation of the velocity with radius permits one to explore the dependence on bulldozing speed within a single experiment. We measure the time-dependent surface shape of the dune for a range of rotation rates, initial volumes and radial positions, for four granular materials, ranging from glass spheres to irregularly shaped sand. The evolution of the dune can be separated into two phases: a rapid initial adjustment to a state of quasi-steady avalanching perpendicular to the blade, followed by a much slower phase of lateral spreading and radial migration. The quasi-steady avalanching sets up a well-defined perpendicular profile with a nearly constant slope. This profile can be scaled by the depth against the bulldozer to collapse data from different times, radial positions and experiments onto common ‘master curves' that are characteristic of the granular material and depend on the local Froude number. The lateral profile of the dune along the face of the bulldozer varies more gradually with radial position, and evolves by slow lateral spreading. The spreading is asymmetrical, with the inward progress of the dune eventually arrested and its bulk migrating to larger radii. A one-dimensional depth-averaged model recovers the nearly linear perpendicular profile of the dune, but does not capture the finer nonlinear details of the master curves. A two-dimensional version of the model leads to an advection-diffusion equation that reproduces the lateral spreading and radial migration. Simulations using the discrete element method reproduce in more quantitative detail many of the experimental findings and furnish further insight into the flow dynamic

Evidence for explosive silicic volcanism on the Moon from the extended distribution of thorium near the Compton-Belkovich Volcanic Complex

We reconstruct the abundance of thorium near the Compton-Belkovich Volcanic Complex on the Moon, using data from the Lunar Prospector Gamma Ray Spectrometer. We enhance the resolution via a pixon image reconstruction technique and find that the thorium is distributed over a larger (40km × 75 km) area than the (25km × 35 km) high-albedo region normally associated with Compton-Belkovich. Our reconstructions show that inside this region, the thorium concentration is 14–26ppm. We also find additional thorium, spread up to 300km eastward of the complex at ∼2 ppm. The thorium must have been deposited during the formation of the volcanic complex, because subsequent lateral transport mechanisms, such as small impacts, are unable to move sufficient material. The morphology of the feature is consistent with pyroclastic dispersal, and we conclude that the present distribution of thorium was likely created by the explosive eruption of silicic magma

Fluid effects in model granular flows

Pore fluid plays a crucial role in many granular flows, especially those in geophysical settings. However, the transition in behaviour between dry flows and fully saturated flows and the underlying physics that relate to this are poorly understood. In this paper, we report the results of small-scale flume experiments using monodisperse granular particles with varying water content and volume in which the basal pore pressure, total pressure, flow height and velocity profile were measured at a section. We compare the results with theoretical profiles for granular flow and with flow regimes based on dimensional analysis. The runout and the centre of mass were also calculated from the deposit surface profiles. As the initial water content by mass was increased from zero to around 10%, we first observed a drop in mobility by approximately 50%, as surface tension caused cohesive behaviour due to matric suction. As the water content was further increased up to 45%, the mobility also increased dramatically, with increased flow velocity up to 50%, increased runout distance up to 240% and reduced travel angle by up to 10° compared to the dry case. These effects can be directly related to the basal pore pressure, with both negative pressures and positive pore pressures being measured relative to atmospheric during the unsteady flow. We find that the initial flow volume plays a role in the development of relative pore pressure, such that, at a fixed relative water content, larger flows exhibit greater positive pore pressures, greater velocities and greater relative runout distances. This aligns with many other granular experiments and field observations. Our findings suggest that the fundamental role of the pore fluid is to reduce frictional contact forces between grains thus increasing flow velocity and bulk mobility. While this can occur by the development of excess pore pressure, it can also occur where the positive pore pressure is not in excess of hydrostatic, as shown here, since buoyancy and lubrication alone will reduce frictional forces

Approximate Consistency and Prediction Algorithms in Quantum Mechanics

This dissertation investigates questions arising in the consistent histories formulation of the quantum mechanics of closed systems. Various criteria for approximate consistency are analysed. The connection between the Dowker-Halliwell criterion and sphere packing problems is shown and used to prove several new bounds on the violation of probability sum rules. The quantum Zeno effect is also analysed within the consistent histories formalism and used to demonstrate some of the difficulties involved in discussing approximate consistency. The complications associated with null histories and infinite sets are briefly discussed. The possibility of using the properties of the Schmidt decomposition to define an algorithm which selects a single, physically natural, consistent set for pure initial density matrices is investigated. The problems that arise are explained, and different possible algorithms discussed. Their properties are analysed with the aid of simple models. A set of computer programs is described which apply the algorithms to more complicated examples. Another algorithm is proposed that selects the consistent set (formed using Schmidt projections) with the highest Shannon information. This is applied to a simple model and shown to produce physically sensible histories. The theory is capable of unconditional probabilistic prediction for closed quantum systems, and is strong enough to be falsifiable. Ideas on applying the theory to more complicated examples are discussed.Comment: 176 pages, 11 figures, 19 program

Maximum information and quantum prediction algorithms.

This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm uses a maximum information principle to select from among the consistent sets formed by projections defined by the Schmidt decomposition. The algorithm unconditionally predicts the possible events in closed quantum systems and ascribes probabilities to these events. A simple spin model is described and a complete classification of all exactly consistent sets of histories formed from Schmidt projections in the model is proved. This result is used to show that for this example the algorithm selects a physically realistic set. Other tentative suggestions in the literature for set selection algorithms using ideas from information theory are discussed

Random Hamiltonian Models and Quantum Prediction Algorithms

This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm select from among the consistent sets formed by projections defined by the Schmidt decomposition by making projections at the earliest possible time. The algorithm unconditionally predicts the possible events in closed quantum systems and ascribes probabilities to these events. A simple random Hamiltonian model is described and the results of applying the algorithm to this model using computer programs are discussed and compared with approximate analytic calculations.Comment: 25 pages, 11 figures, LaTeX2