Geometry of intensive scalar dissipation events in turbulence

Maxima of the scalar dissipation rate in turbulence appear in form of sheets and correspond to the potentially most intensive scalar mixing events. Their cross-section extension determines a locally varying diffusion scale of the mixing process and extends the classical Batchelor picture of one mean diffusion scale. The distribution of the local diffusion scales is analysed for different Reynolds and Schmidt numbers with a fast multiscale technique applied to very high-resolution simulation data. The scales take always values across the whole Batchelor range and beyond. Furthermore, their distribution is traced back to the distribution of the contractive short-time Lyapunov exponent of the flow.Comment: 4 pages, 5 Postscript figures (2 with reduced quality

Finding Efficient Collective Variables: The Case of Crystallization

Several enhanced sampling methods such as umbrella sampling or metadynamics rely on the identification of an appropriate set of collective variables. Recently two methods have been proposed to alleviate the task of determining efficient collective variables. One is based on linear discriminant analysis, the other on a variational approach to conformational dynamics, and uses time-lagged independent component analysis. In this paper, we compare the performance of these two approaches in the study of the homogeneous crystallization of two simple metals. We focus on Na and Al and search for the most efficient collective variables that can be expressed as a linear combination of X-ray diffraction peak intensities. We find that the performances of the two methods are very similar. However, the method based on linear discriminant analysis, in its harmonic version, is to be preferred because it is simpler and much less computationally demanding

Communion and the Trinity: distinct relations with Father, Son and Spirit

Communion with the triune God is necessarily Trinitarian. But does that simply mean that all three divine persons are involved, or is there a case for the Christian communing distinctly with each person? This thesis argues for the latter. Distinct communion has not flourished within western Christianity, although the Puritan, John Owen, breaks the mould. In order to arrive at the concept, two preliminary steps must be taken. First, the range of New Testament terminology for communion with God must be appreciated; only then will the authors’ devotional Trinitarianism become properly visible. Secondly, the triune God must be viewed through the lenses of the redemptive storyline; only then will the Three be recognised in their full distinctness, and a theological framework established within which tri-personal communion makes sense. In this thesis these two areas are foregrounded, but other, related matters are also addressed. Not all biblical communion distinguishes between the three persons. Then there is the person of the Spirit, the direct worship of whom may appear problematic. There are also more ‘practical’ issues associated with (especially public, liturgical) distinct communion: for instance, the advisability of shifting focus within a single prayer from one divine person to another. John Owen rightly recognised the importance of distinct communion. The doctrine of the Trinity is not dry and irrelevant, a theme only fit for academic speculation. It is the central truth of biblical religion, and must, therefore, be appropriated at the level of ordinary Christian piety

Harper operators, Fermi curves, and Picard-Fuchs equations

This paper is a continuation of the work on the spectral problem of Harper operator using algebraic geometry. We continue to discuss the local monodromy of algebraic Fermi curves based on Picard-Lefschetz formula. The density of states over approximating components of Fermi curves satisfies a Picard-Fuchs equation. By the property of Landen transformation, the density of states has a Lambert series as the quarter period. A $q$-expansion of the energy level can be derived from a mirror map as in the B-model.Comment: v2, 13 pages, minor changes have been mad

Protective Measures, Personal Experience, and the Affective Psychology of Time

We examined the role of time and affect in intentions to purchase a risk-protective measure (Studies 1 and 2) and explored participant abilities to factor time into the likelihood judgments that presumably underlie such intentions (Study 3). Participants worried more about losing their possessions and were more likely to purchase a protective measure given a longer term lease than a short-term lease, but only if their belongings were described in affect-poor terms. If described instead as being particularly special and affect-rich, participants neglected time and were about equally likely to purchase a risk-protective measure for shorter and longer term leases. However, and consistent with prior literature, the cognitive mechanism underlying this time-neglect-with-affect-richness effect seemed to be the greater use of the affect heuristic in the shorter term than the longer term. Study 2 results demonstrated that prior experience with having been burglarized amplified the interactive effect of time and affect. Greater deliberation did not attenuate this effect as hypothesized whether deliberation was measured through numeracy or manipulated through instructions. The results of Study 3 indicated that few participants are able to calculate correctly the risk numbers necessary to take time into account. Two possible solutions to encourage more purchases of protective measures in the long term are discussed