Constrained Hyperbolic Divergence Cleaning for Smoothed Particle Magnetohydrodynamics

We present a constrained formulation of Dedner et al's hyperbolic/parabolic divergence cleaning scheme for enforcing the \nabla\dot B = 0 constraint in Smoothed Particle Magnetohydrodynamics (SPMHD) simulations. The constraint we impose is that energy removed must either be conserved or dissipated, such that the scheme is guaranteed to decrease the overall magnetic energy. This is shown to require use of conjugate numerical operators for evaluating \nabla\dot B and \nabla{\psi} in the SPMHD cleaning equations. The resulting scheme is shown to be stable at density jumps and free boundaries, in contrast to an earlier implementation by Price & Monaghan (2005). Optimal values of the damping parameter are found to be {\sigma} = 0.2-0.3 in 2D and {\sigma} = 0.8-1.2 in 3D. With these parameters, our constrained Hamiltonian formulation is found to provide an effective means of enforcing the divergence constraint in SPMHD, typically maintaining average values of h |\nabla\dot B| / |B| to 0.1-1%, up to an order of magnitude better than artificial resistivity without the associated dissipation in the physical field. Furthermore, when applied to realistic, 3D simulations we find an improvement of up to two orders of magnitude in momentum conservation with a corresponding improvement in numerical stability at essentially zero additional computational expense.Comment: 28 pages, 25 figures, accepted to J. Comput. Phys. Movies at http://www.youtube.com/playlist?list=PL215D649FD0BDA466 v2: fixed inverted figs 1,4,6, and several color bar

Does Time-Symmetry Imply Retrocausality? How the Quantum World Says "Maybe"

It has often been suggested that retrocausality offers a solution to some of the puzzles of quantum mechanics: e.g., that it allows a Lorentz-invariant explanation of Bell correlations, and other manifestations of quantum nonlocality, without action-at-a-distance. Some writers have argued that time-symmetry counts in favour of such a view, in the sense that retrocausality would be a natural consequence of a truly time-symmetric theory of the quantum world. Critics object that there is complete time-symmetry in classical physics, and yet no apparent retrocausality. Why should the quantum world be any different? This note throws some new light on these matters. I call attention to a respect in which quantum mechanics is different, under some assumptions about quantum ontology. Under these assumptions, the combination of time-symmetry without retrocausality is unavailable in quantum mechanics, for reasons intimately connected with the differences between classical and quantum physics (especially the role of discreteness in the latter). Not all interpretations of quantum mechanics share these assumptions, however, and in those that do not, time-symmetry does not entail retrocausality.Comment: 22 pages, 6 figures; significant revision

A Neglected Route to Realism About Quantum Mechanics

Bell's Theorem assumes that hidden variables are not influenced by future measurement settings. The assumption has sometimes been questioned, but the suggestion has been thought outlandish, even by the taxed standards of the discipline. (Bell thought that it led to fatalism.) The case for this reaction turns out to be surprisingly weak, however. We show that QM easily evades the standard objections to advanced action. And the approach has striking advantages, especially in avoiding the apparent conflict between Bell's Theorem and special relativity. The second part of the paper considers the broader question as to why advanced action seems so counterintuitive. We investigate the origins of our ordinary intuitions about causal asymmetry. It is argued that the view that the past does not depend on the future is largely anthropocentric, a kind of projection of our own temporal asymmetry. Many physicists have also reached this conclusion, but have thought that if causation has no objective direction, there is no objective content to an advanced action interpretation of QM. This turns out to be a mistake. From the ordinary subjective perspective, we can distinguish two sorts of objective world: one "looks as if" it contains only forward causation, the other ``looks as if'' it involves a mix of backward and forward causation. This clarifies the objective core of an advanced action interpretation of QM, and shows that there is an independent symmetry argument in favour of the approach.Comment: 35 pages, LaTex (forthcoming in MIND, July 1994; written for a philosophical audience, but perhaps of some interest here

Organisational Memetics?: Organisational Learning as a Selection Process

Companies are not only systems created and controlled by those who manage them but also self-organising entities that evolve through learning. Whereas an organism is a creation of natural replicators, genes, an organisation can be seen as a product of an alternative replicator, the meme or mental model, acting, like a gene, to preserve itself in an Evolutionary Stable System. The result is an organisation which self organises around a set of unspoken and unwritten rules and assumptions. Biological evolution is stimulated by environmental change and reproductive isolation; the process of punctuated equilibrium. Corporate innovation shows the same pattern. Innovations in products and processes occur in groups isolated from prevailing mental norms. Successful organic strains possess a genetic capability for adaptation. Organisations which wish to foster learning can develop an equivalent, mental capability. Unlike their biological counterparts they can exert conscious choice and puncture the memetic codes that seek to keep them stable; the mental models of individuals, and the strategies, paradigms and unwritten rules at the company level

The Effects of Higher Admission Standards on NCAA Student-Athletes: An Analysis of Proposition 16

This study examines the effect of an increase in minimum admissions standards on college enrollment and graduation rates of student-athletes. In 1996, the NCAA enacted Proposition 16, which increased the admission standards for freshmen student-athletes at Division I schools in an effort to improve graduation rates. Results indicate that Proposition 16 increased graduation rates significantly for black student-athletes, and had no significant impact on graduation rates for white student-athletes. Results also indicate that graduation rates declined for black student-athletes at Division II schools, which may be driven by students transferring to Division I. As a result of the higher admission standard Division I schools changed recruiting patterns and relied less on freshmen student-athletes, particularly black student-athletes, to fill scholarships. Even though fewer black freshmen student-athletes enrolled in Division I schools, the overall number of black student-athletes did not change, suggesting that greater proportion of transfer students into Division I schools were black