Scrambled and Unscrambled Turbulence

The linked fluid dynamics videos depict Rayleigh-Taylor turbulence when driven by a complex acceleration profile involving two stages of acceleration interspersed with a stage of stabilizing deceleration. Rayleigh-Taylor (RT) instability occurs at the interface separating two fluids of different densities, when the lighter fluid is accelerated in to the heavier fluid. The turbulent mixing arising from the development of the miscible RT instability is of key importance in the design of Inertial Confinement Fusion capsules, and to the understanding of astrophysical events, such as Type Ia supernovae. By driving this flow with an accel-decel-accel profile, we have investigated how structures in RT turbulence are affected by a sudden change in the direction of the acceleration first from destabilizing acceleration to deceleration, and followed by a restoration of the unstable acceleration. By studying turbulence under such highly non-equilibrium conditions, we hope to develop an understanding of the response and recovery of self-similar turbulence to sudden changes in the driving acceleration.Comment: 3 pages article, Two videos are include

Where is wisdom to be found – now that we have stopped looking for it?

Ancient scribal culture had two faces. After arduous and largely impractical training, scribes were admitted to an elite circle and became custodians of a cultural tradition. But scribal teachers were also credited with opening the eyes of their students and ‘forming humanity’ in them. Scribal writers created and challenged tradition. Both faces are still evident in modern ‘scribal culture’. Nietzsche, who occupies an ambiguous position in this regard, is used to illuminate aspects of tension between the two ‘faces’, which, given the world situation, seems relevant to the future of the academic enterprise. Finally, it is suggested that ancient wisdom still has something to tell us about these matters. The article is dedicated to Hendrik Bosman in view of his abiding interest in scribal culture, wisdom literature and הוהי תא

Old ideas: wisdom, virtue and moral formation

The wisdom writings of the Old Testament may be regarded as largely a repository of ‘old ideas’ that were preserved across cultures and ages because they generally served human life. To study the material from this angle, focusing less on reconstructing the past and more on serving the present, will require several adjustments to usual scholarly approaches. Comparisons going beyond Israel’s Umwelt will also be fruitful. Comparisons with the teachings of Confucius and Aristotle may be particularly helpful. Such studies have to be respectfully critical, taking the sages of the past seriously as interlocutors while recognizing the limits of their vision.Department of HE and Training approved lis

Rhetorical appeal and the uncertainty of hope

The article examines an article that Dirk Smit wrote about rhetoric and theology against the background of other of his articles, particularly about the Confession of Belhar. It argues that Smit’s article is “judiciously sceptical” about rhetoric because he is committed not only to faith, but also to the uncertainty of hope. This commitment is, it is argued, compatible with rhetoric, but only with a certain type of rhetoric. Such a hopeful rhetoric, which does not accept the closure of tragedy, reaches out to others across tragic divisions as the Confession of Belhar did. The final section examines how Smit’s article is itself a rhetorical act and tries to identify the particular appeal he makes on readers.Department of HE and Training approved lis

Friction in inflaton equations of motion

The possibility of a friction term in the equation of motion for a scalar field is investigated in non-equilibrium field theory. The results obtained differ greatly from existing estimates based on linear response theory, and suggest that dissipation is not well represented by a term of the form $\eta\dot{\phi}$.Comment: 4 pages, 2 figures, RevTex4. An obscurity in the original version has been clarifie

New Curved Spacetime Dirac Equations - On the Anomalous Gyromagnetic Ratio

I propose three new curved spacetime versions of the Dirac Equation. These equations have been developed mainly to try and account in a natural way for the observed anomalous gyromagnetic ratio of Fermions. The derived equations suggest that particles including the Electron which is thought to be a point particle do have a finite spatial size which is the reason for the observed anomalous gyromagnetic ratio. A serendipitous result of the theory, is that, two of the equation exhibits an asymmetry in their positive and negative energy solutions the first suggestion of which is clear that a solution to the problem as to why the Electron and Muon - despite their acute similarities - exhibit an asymmetry in their mass is possible. The Mourn is often thought as an Electron in a higher energy state. Another of the consequences of three equations emanating from the asymmetric serendipity of the energy solutions of two of these equations, is that, an explanation as to why Leptons exhibit a three stage mass hierarchy is possible.Comment: 8 pages, errors corrected, final form of the paper and no further changes to be made. Accepted in the Foundations of Physics Journa

Nonequilibrium perturbation theory for complex scalar fields

Real-time perturbation theory is formulated for complex scalar fields away from thermal equilibrium in such a way that dissipative effects arising from the absorptive parts of loop diagrams are approximately resummed into the unperturbed propagators. Low order calculations of physical quantities then involve quasiparticle occupation numbers which evolve with the changing state of the field system, in contrast to standard perturbation theory, where these occupation numbers are frozen at their initial values. The evolution equation of the occupation numbers can be cast approximately in the form of a Boltzmann equation. Particular attention is given to the effects of a non-zero chemical potential, and it is found that the thermal masses and decay widths of quasiparticle modes are different for particles and antiparticles.Comment: 15 pages using RevTeX; 2 figures in 1 Postscript file; Submitted to Phys. Rev.

Perturbative nonequilibrium dynamics of phase transitions in an expanding universe

A complete set of Feynman rules is derived, which permits a perturbative description of the nonequilibrium dynamics of a symmetry-breaking phase transition in $\lambda\phi^4$ theory in an expanding universe. In contrast to a naive expansion in powers of the coupling constant, this approximation scheme provides for (a) a description of the nonequilibrium state in terms of its own finite-width quasiparticle excitations, thus correctly incorporating dissipative effects in low-order calculations, and (b) the emergence from a symmetric initial state of a final state exhibiting the properties of spontaneous symmetry breaking, while maintaining the constraint $\equiv 0$. Earlier work on dissipative perturbation theory and spontaneous symmetry breaking in Minkowski spacetime is reviewed. The central problem addressed is the construction of a perturbative approximation scheme which treats the initial symmetric state in terms of the field $\phi$, while the state that emerges at later times is treated in terms of a field $\zeta$, linearly related to $\phi^2$. The connection between early and late times involves an infinite sequence of composite propagators. Explicit one-loop calculations are given of the gap equations that determine quasiparticle masses and of the equation of motion for $$ and the renormalization of these equations is described. The perturbation series needed to describe the symmetric and broken-symmetry states are not equivalent, and this leads to ambiguities intrinsic to any perturbative approach. These ambiguities are discussed in detail and a systematic procedure for matching the two approximations is described.Comment: 22 pages, using RevTeX. 6 figures. Submitted to Physical Review