A Large Eddy Simulation of Turbulent Compressible Convection: Differential Rotation in the Solar Convection Zone

We present results of two simulations of the convection zone, obtained by solving the full hydrodynamic equations in a section of a spherical shell. The first simulation has cylindrical rotation contours (parallel to the rotation axis) and a strong meridional circulation, which traverses the entire depth. The second simulation has isorotation contours about mid-way between cylinders and cones, and a weak meridional circulation, concentrated in the uppermost part of the shell. We show that the solar differential rotation is directly related to a latitudinal entropy gradient, which pervades into the deep layers of the convection zone. We also offer an explanation of the angular velocity shear found at low latitudes near the top. A non-zero correlation between radial and zonal velocity fluctuations produces a significant Reynolds stress in that region. This constitutes a net transport of angular momentum inwards, which causes a slight modification of the overall structure of the differential rotation near the top. In essence, the {\it thermodynamics controls the dynamics through the Taylor-Proudman momentum balance}. The Reynolds stresses only become significant in the surface layers, where they generate a weak meridional circulation and an angular velocity `bump'.Comment: 11 pages, 14 figures, the first figure was too large and is excluded. Accepted for publication in MNRA

Getting Out of the Huddle

We got to care for the poor. We got to do something and we all go, yeah, let\u27s take a break. Go fired up. Come on. Let\u27s go back in. Let\u27s huddle again, you know, and we never actually do it. We never actually run a play. And then we wonder why the world looks at church and go, I don\u27t want to have anything to do with them

Love and the Spirit

Because the greatest command isn\u27t to go out and live my faith. That his command is to love the Lord, your God with every fiber of your being, just be passionately in love with him, with all your heart, all your soul, all your mind, all your strength. So I don\u27t I don\u27t care really how big your ministry is or how many people you\u27re impacting. My question is, is where\u27s your love

Revival Without Rebellion

Chan challenged students to talk action. Chan really pushed students to go beyond their comfort zone and go out into the world and help those in need

Financial globalization, governance, and the evolution of the home bias

Standard portfolio theories of the home bias are disconnected from corporate finance theories of insider ownership. We merge the two into what we call the optimal ownership theory of the home bias. The theory has the following components. In countries with poor governance, it is optimal for insiders to own large stakes in corporations and for large shareholders to monitor insiders. Foreign portfolio investors will exhibit a large home bias against such countries because their investment is limited by the shares held by insiders (the "direct effect" of poor governance) and domestic monitoring shareholders ("the indirect effect").> ; Foreigners can also enter as foreign direct investors; if they are from countries with good governance, they have a comparative advantage as insider monitors in countries with poor governance, so that the relative importance of foreign direct investment in total foreign equity investment is negatively related to the quality of governance. Using two datasets, we find strong evidence that the theory can help explain the evolution of the home bias. Using country-level U.S. data, we find that on average the home bias of U.S. investors towards the 46 countries with the largest equity markets did not fall over the past decade, but it decreased the most towards countries in which the ownership by corporate insiders decreased, and the importance of foreign direct investment fell in countries in which ownership by corporate insiders fell. Using firm-level data for Korea, we find evidence of the additional indirect effect of poor governance on portfolio equity investment by foreign investors.Investments, Foreign ; Globalization

Entropic Priors and Bayesian Model Selection

We demonstrate that the principle of maximum relative entropy (ME), used judiciously, can ease the specification of priors in model selection problems. The resulting effect is that models that make sharp predictions are disfavoured, weakening the usual Bayesian "Occam's Razor". This is illustrated with a simple example involving what Jaynes called a "sure thing" hypothesis. Jaynes' resolution of the situation involved introducing a large number of alternative "sure thing" hypotheses that were possible before we observed the data. However, in more complex situations, it may not be possible to explicitly enumerate large numbers of alternatives. The entropic priors formalism produces the desired result without modifying the hypothesis space or requiring explicit enumeration of alternatives; all that is required is a good model for the prior predictive distribution for the data. This idea is illustrated with a simple rigged-lottery example, and we outline how this idea may help to resolve a recent debate amongst cosmologists: is dark energy a cosmological constant, or has it evolved with time in some way? And how shall we decide, when the data are in?Comment: Presented at MaxEnt 2009, the 29th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (July 5-10, 2009, Oxford, Mississippi, USA

Efficient algorithms for finding disjoint paths in grids

The reconfiguration problem on VLSI/WSI processor arrays in the presence of faulty processors can be stated as the following integral multi-source routing problem: Given a set of N nodes (faulty processors or sources) in an m×n rectangular grid where m, n≤N, the problem to be solved is to connect the N nodes to distinct nodes at the grid boundary using a set of `disjoint' paths. This problem can be referred to as an escape problem which can be solved trivially in O(mnN) time. By exploiting all the properties of the network, planarity and regularity of a grid, integral flow, and unit capacity source/sink/flow, we can optimally compress the size of the grid from O(mn) to O(√mnN) and solve the problem in O(d√mnN), where d is the maximum number of disjoint paths found, for both the edge-disjoint and vertex-disjoint cases. In the worst case, d, m, n are O(N) and the result is O(N2.5). Note that this routing problem can also be solved with the same time complexity even if the disjoint paths have to be ended at another set of N nodes (sinks) in the grid instead of the grid boundary.published_or_final_versio