A new Australian species of Luffa (Cucurbitaceae) and typification of two Australian Cucumis names, all based on specimens collected by Ferdinand Mueller in 1856

As a result of his botanical explorations in northern Australia, Ferdinand von Mueller named several Cucurbitaceae that molecular data now show to be distinct, requiring their resurrection from unjustified synonymy. We here describe and illustrate Luffa saccata F. Muell. ex I.Telford, validating a manuscript name listed under L. graveolens Roxb. since 1859, and we lectotypify Cucumis picrocarpus F. Muell. and C. jucundus F. Muell. The lectotype of the name C. jucundus, a synonym of C. melo, is mounted on the same sheet as the lectotype of C. picrocarpus, which is the sister species of the cultivated C. melo as shown in a recent publication

Orthogonality relations for triple modes at dielectric boundary surfaces

We work out the orthogonality relations for the set of Carniglia-Mandel triple modes which provide a set of normal modes for the source-free electromagnetic field in a background consisting of a passive dielectric half-space and the vacuum, respectively. Due to the inherent computational complexity of the problem, an efficient strategy to accomplish this task is desirable, which is presented in the paper. Furthermore, we provide all main steps for the various proofs pertaining to different combinations of triple modes in the orthogonality integral.Comment: 15 page

When Do Measures on the Space of Connections Support the Triad Operators of Loop Quantum Gravity?

In this work we investigate the question, under what conditions Hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain non-Abelian analogues of the electric flux. We give the problem a precise mathematical formulation and start its investigation. For the technically simple case of U(1) as gauge group, we establish a number of "no-go theorems" asserting that for certain classes of measures, the flux operators can not be represented on the corresponding Hilbert spaces. The flux-observables we consider play an important role in loop quantum gravity since they can be defined without recourse to a background geometry, and they might also be of interest in the general context of quantization of non-Abelian gauge theories.Comment: LaTeX, 21 pages, 5 figures; v3: some typos and formulations corrected, some clarifications added, bibliography updated; article is now identical to published versio

Dynamical Backreaction in Robertson-Walker Spacetime

The treatment of a quantized field in a curved spacetime requires the study of backreaction of the field on the spacetime via the semiclassical Einstein equation. We consider a free scalar field in spatially flat Robertson-Walker space time. We require the state of the field to allow for a renormalized semiclassical stress tensor. We calculate the sigularities of the stress tensor restricted to equal times in agreement with the usual renormalization prescription for Hadamard states to perform an explicit renormalization. The dynamical system for the Robertson Walker scale parameter $a(t)$ coupled to the scalar field is finally derived for the case of conformal and also general coupling.Comment: Obtained equation of motion for non-conformal coupling, not just counter terms as in previous version. Typos fixed, renormalization term proportional to R adde

Stress-energy tensor correlators from the world-sheet

The large $N$ limit of symmetric orbifold theories was recently argued to have an AdS/CFT dual world-sheet description in terms of an $\mathfrak{sl}(2,\mathbb{R})$ WZW model. In previous work the world-sheet state corresponding to the symmetric orbifold stress-energy tensor was identified. We calculate certain 2- and 3-point functions of the corresponding vertex operator on the world-sheet, and demonstrate that these amplitudes reproduce exactly what one expects from the dual symmetric orbifold perspective.Comment: 16+9 page

Clebsch Representation in the Theory of Minimum Energy Equilibrium Solutions in Magnetohydrodynamics

The introduction of Clebsch representations allows one to formulate the problem of finding minimum energy solutions for a magneto-fluid as a well-posed problem in the calculus of variations of multiple integrals. When the latter is subjected to integral constraints, the Euler–Lagrange equations of the resulting isoperimetric problem imply that the fluid velocities are collinear with the magnetic field. If, in particular, one constraint is abolished, Alfvén velocities are obtained. In view of the idealized nature of the model treated here, further investigations of more sophisticated structures by means of Clebsch representations are anticipated. Preliminary results of a similar calculation utilizing a modified two fluid model are discusse

The comfortable roller coaster -- on the shape of tracks with constant normal force

A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is: what shape of the track gives a normal force of constant magnitude? Here we solve this problem. It turns out that the solution is related to the Kepler problem; the trajectories in velocity space are conic sections.Comment: 10 pages, 4 figure

Deep Genetic Divergence between Disjunct Refugia in the Arctic-Alpine King’s Crown, Rhodiola integrifolia (Crassulaceae)

Despite the strength of climatic variability at high latitudes and upper elevations, we still do not fully understand how plants in North America that are distributed between Arctic and alpine areas responded to the environmental changes of the Quaternary. To address this question, we set out to resolve the evolutionary history of the King’s Crown, Rhodiola integrifolia using multi-locus population genetic and phylogenetic analyses in combination with ecological niche modeling. Our population genetic analyses of multiple anonymous nuclear loci revealed two major clades within R. integrifolia that diverged from each other ~ 700 kya: one occurring in Beringia to the north (including members of subspecies leedyi and part of subspecies integrifolia), and the other restricted to the Southern Rocky Mountain refugium in the south (including individuals of subspecies neomexicana and part of subspecies integrifolia). Ecological niche models corroborate our hypothesized locations of refugial areas inferred from our phylogeographic analyses and revealed some environmental differences between the regions inhabited by its two subclades. Our study underscores the role of geographic isolation in promoting genetic divergence and the evolution of endemic subspecies in R. integrifolia. Furthermore, our phylogenetic analyses of the plastid spacer region trnL-F demonstrate that among the native North American species, R. integrifolia and R. rhodantha are more closely related to one another than either is to R. rosea. An understanding of these historic processes lies at the heart of making informed management decisions regarding this and other Arctic-alpine species of concern in this increasingly threatened biome

Deep Genetic Divergence Between Disjunct Refugia in the Arctic-Alpine King\u27s Crown, Rhodiola integrifolia (Crassulaceae)

Despite the strength of climatic variability at high latitudes and upper elevations, we still do not fully understand how plants in North America that are distributed between Arctic and alpine areas responded to the environmental changes of the Quaternary. To address this question, we set out to resolve the evolutionary history of the King’s Crown, Rhodiola integrifolia using multi-locus population genetic and phylogenetic analyses in combination with ecological niche modeling. Our population genetic analyses of multiple anonymous nuclear loci revealed two major clades within R. integrifolia that diverged from each other ~ 700 kya: one occurring in Beringia to the north (including members of subspecies leedyi and part of subspecies integrifolia), and the other restricted to the Southern Rocky Mountain refugium in the south (including individuals of subspecies neomexicana and part of subspecies integrifolia). Ecological niche models corroborate our hypothesized locations of refugial areas inferred from our phylogeographic analyses and revealed some environmental differences between the regions inhabited by its two subclades. Our study underscores the role of geographic isolation in promoting genetic divergence and the evolution of endemic subspecies in R. integrifolia. Furthermore, our phylogenetic analyses of the plastid spacer region trnL-F demonstrate that among the native North American species, R. integrifolia and R. rhodantha are more closely related to one another than either is to R. rosea. An understanding of these historic processes lies at the heart of making informed management decisions regarding this and other Arctic-alpine species of concern in this increasingly threatened biome