Fermions in odd space-time dimensions: back to basics

It is a well known feature of odd space-time dimensions $d$ that there exist two inequivalent fundamental representations $A$ and $B$ of the Dirac gamma matrices. Moreover, the parity transformation swaps the fermion fields living in $A$ and $B$. As a consequence, a parity invariant Lagrangian can only be constructed by incorporating both the representations. Based upon these ideas and contrary to long held belief, we show that in addition to a discrete exchange symmetry for the massless case, we can also define chiral symmetry provided the Lagrangian contains fields corresponding to both the inequivalent representations. We also study the transformation properties of the corresponding chiral currents under parity and charge conjugation operations. We work explicitly in 2+1 dimensions and later show how some of these ideas generalize to an arbitrary number of odd dimensions.Comment: 8 pages, no figure

Maximum power, ecological function and efficiency of an irreversible Carnot cycle. A cost and effectiveness optimization

In this work we include, for the Carnot cycle, irreversibilities of linear finite rate of heat transferences between the heat engine and its reservoirs, heat leak between the reservoirs and internal dissipations of the working fluid. A first optimization of the power output, the efficiency and ecological function of an irreversible Carnot cycle, with respect to: internal temperature ratio, time ratio for the heat exchange and the allocation ratio of the heat exchangers; is performed. For the second and third optimizations, the optimum values for the time ratio and internal temperature ratio are substituted into the equation of power and, then, the optimizations with respect to the cost and effectiveness ratio of the heat exchangers are performed. Finally, a criterion of partial optimization for the class of irreversible Carnot engines is herein presented.Comment: 17 pages, 4 figures. Submitted to Energy Convers. Manag

Magnetism and Magnetic Isomers in Free Chromium Clusters

We have used the Stern-Gerlach deflection technique to study magnetism in chromium clusters of 20-133 atoms. Between 60 K and 100 K, we observe that these clusters have large magnetic moments and respond superparamagnetically to applied magnetic fields. Using superparamagnetic theory, we have determined the moment per atom for each cluster size and find that it often far exceeds the moment per atom present anywhere in the bulk antiferromagnetic lattice. Remarkably, our cluster beam contains two magnetically distinguishable forms of each cluster size with >= 34 atoms. We attribute this observation to structural isomers

Study of the magnetic turbulence in a corotating interaction region in the interplanetary medium

International audienceWe study the geometry of magnetic fluctuations in a CIR observed by Pioneer 10 at 5 AU between days 292 and 295 in 1973. We apply the methodology proposed by Bieber et al. to make a comparison of the relative importance of two geometric arrays of vector propagation of the magnetic field fluctuations: slab and two-dimensional (2D). We found that inside the studied CIR this model is not applicable due to the restrictions imposed on it. Our results are consistent with Alfvenic fluctuations propagating close to the radial direction, confirming Mavromichalaki et al.'s findings. A mixture of isotropic and magnetoacoustic waves in the region before the front shock would be consistent with our results, and a mixture of slab/2D and magnetoacoustic waves in a region after the reverse shock. We base the latter conclusions on the theoretical analysis made by Kunstmann. We discuss the reasons why the composite model can not be applied in the CIR studied although the fluctuations inside it are two dimensional

4-Holes in point sets

We consider a variant of a question of Erdos on the number of empty k-gons (k-holes) in a set of n points in the plane, where we allow the k-gons to be non-convex. We show bounds and structural results on maximizing and minimizing the number of general 4-holes, and maximizing the number of non-convex 4-holes. In particular, we show that for n >= 9, the maximum number of general 4-holes is ((pi)(4)); the minimum number of general 4-holes is at least 5/2 n(2) - circle minus(n); and the maximum number of non-convex 4-holes is at least 1/2 n(3) - circle minus(n(2) logn) and at most 1/2 n(3) - circle minus(n(2)). 2014 (c) Elsevier B.V. All rights reserved.Postprint (author’s final draft

Recombinants between Deformed wing virus and Varroa destructor virus-1 may prevail in Varroa destructor-infested honeybee colonies

We have used high-throughput Illumina sequencing to identify novel recombinants between deformed wing virus (DWV) and Varroa destructor virus-1 (VDV-1), which accumulate to higher levels than DWV in both honeybees and Varroa destructor mites. The recombinants, VDV-1VVD and VDV-1DVD, exhibit crossovers between the 5’-untranslated region (5’-UTR), and/or the regions encoding the structural (capsid) and non-structural viral proteins. This implies the genomes are modular and that each region may evolve independently, as demonstrated in human enteroviruses. Individual honeybee pupae were infected with a mixture of observed recombinants and DWV. The strong correlation between VDV-1DVD levels in honeybee pupae and the associated mites was observed, suggesting that this recombinant, with a DWV-derived 5’-UTR and non-structural protein region flanking VDV- 1-derived capsid encoding region, is better adapted to transmission between V. destructor and honeybees than the parental DWV or a recombinant bearing the VDV-1-derived 5’-UTR (VDV-1VVD)