Semiclassical degeneracies and ordering for highly frustrated magnets in a field

We discuss ground state selection by quantum fluctuations in frustrated magnets in a strong magnetic field. We show that there exist dynamical symmetries -- one a generalisation of Henley's gauge-like symmetry for collinear spins, the other the quantum relict of non-collinear weathervane modes -- which ensure a partial survival of the classical degeneracies. We illustrate these for the case of the kagome magnet, where we find zero-point energy differences to be rather small everywhere except near the collinear `up-up-down` configurations, where there is rotational but not translational symmetry breaking. In the effective Hamiltonian, we demonstrate the presence of a term sensitive to a topological `flux'. We discuss the connection of such problems to gauge theories by casting the frustrated lattices as medial lattices of appropriately chosen simplex lattices, and in particular we show how the magnetic field can be used to tune the physical sector of the resulting gauge theories.Comment: 10 pages, 8 figure

Missing energies at pair creation

Wilson cloud chamber measurements of the separated spectra of positrons and electrons produced by gamma quanta of 6.14 MeV differ considerably from the theoretically predicted spectra by BETHE and HEITLER, but are in good agreement with those of a modified theory of pair creation

Non-Linear Massive Gravity with Additional Primary Constraint and Absence of Ghosts

We complete the Hamiltonian analysis of specific model of non-linear massive gravity that was started in arXiv:1112.5267. We identify the primary constraint and corresponding secondary constraint. We show that they are the second class constraints and hence they lead to the elimination of the additional scalar mode. We also find that the remaining constraints are the first class constraints with the structure that corresponds to the manifestly diffeomorphism invariant theory. Finally we determine the number of physical degrees of freedom and we show that it corresponds to the number of physical modes of massive gravity.Comment: 13 page

The Effect of a Uniform Cross-flow on the Circulation of Vortex Rings

This paper describes observations and measurements of the effects of a uniform cross flow on the vorticity field and circulation of a laminar vortex ring ejected from an elevated pipe. From particle-image velocimetry (PIV) in the plane defined by the axis of the vortex ring and the direction of the cross flow, we observe the growth and decay of the vortex-ring and its interaction with the shear layer which is produced by the cross flow over the surface of the elevated pipe. As the vortex ring is generated it passes through and disrupts this shear layer. Some rotational fluid from the shear layer is carried with the vortex ring as it moves away from the elevated pipe. From the PIV data, we calculate a positive-core circulation on the upstream side of the vortex ring and a negative circulation on the other side. The growth rate of positive-core circulation is reduced by cancellation with the cross-flow shear-layer vorticity which is of opposite sign. The initial negative circulation is equal to the circulation of the cross-flow shear layer, but the cross flow and the cross-flow shear layer have no effect of the growth rate of the negative circulation

P–C and C–H Bond Cleavages of dppm in the Thermal Reaction of [Ru\u3csub\u3e3\u3c/sub\u3e(CO)\u3csub\u3e10\u3c/sub\u3e(μ-dppm)] with Benzothiophene: X-ray structures of [Ru\u3csub\u3e6\u3c/sub\u3e(μ-CO)(CO)\u3csub\u3e13\u3c/sub\u3e{μ\u3csub\u3e4\u3c/sub\u3e-PhP(C\u3csub\u3e6\u3c/sub\u3eH\u3csub\u3e4\u3c/sub\u3e)PPh}(μ\u3csub\u3e6\u3c/sub\u3e-C)] and [Ru\u3csub\u3e4\u3c/sub\u3e(CO)\u3csub\u3e9\u3c/sub\u3e(μ\u3csub\u3e3\u3c/sub\u3e-η\u3csup\u3e2\u3c/sup\u3e-PhPCH\u3csub\u3e2\u3c/sub\u3ePPh\u3csub\u3e2\u3c/sub\u3e)(μ\u3csub\u3e4\u3c/sub\u3e-η\u3csup\u3e6\u3c/sup\u3e:η\u3csup\u3e1\u3c/sup\u3e:η\u3csup\u3e1\u3c/sup\u3e-C\u3csub\u3e6\u3c/sub\u3eH\u3csub\u3e4\u3c/sub\u3e)(μ-H)]

The thermal reaction of [Ru3(CO)10(μ-dppm)] (1) with benzothiophene in refluxing toluene gives a complex mixture of products. These include the known compounds [Ru2(CO)6{μ-CH2PPh(C6H4)PPh}] (2), [Ru2(CO)6{μ-C6H4PPh(CH2)PPh}] (3), [Ru3(CO)9{μ3-η3-(Ph)PCH2P(Ph)C6H4}] (4) and [Ru3(CO)10{μ-η2-PPh(CH2)(C6H4)PPh}] (6), as well as the new clusters [Ru6(μ-CO)(CO)13{μ3-η2-PhP(C6H4)PPh}(μ6-C)] (5) and [Ru4(CO)9(μ3-η2-PhPCH2PPh2)(μ4-η6:η1:η1-C6H4)(μ-H)] (7). The solid-state molecular structures of 5 and 7 were confirmed by single crystal X-ray analyses. Compound 5 consists of interesting example of a hexaruthenium interstitial carbido cluster having a tetradentate diphosphine ligand derived from the activation of P–C and C–H bonds of the dppm ligand in 1. The tetranuclear compound 7 consists of a unique example of a non-planar spiked triangular metal fragment of ruthenium [Ru(1), Ru(2) and Ru(3)] unit with Ru(4) being bonded to Ru(1). The μ4-η1:η6:η1-benzyne ligand in this compound represents a previously uncharacterized bonding mode for benzyne. Compounds 5 and 7 do not contain any benzothiophene-derived ligand. The reaction of 4 with benzothiophene gives 2, 3, 5 and 6. Thermolysis of 1 in refluxing toluene gives 2, 3 and 4; none of 5 and 7 is detected in reaction mixture

Ruthenium and osmium carbonyl clusters incorporating stannylene and stannyl ligands

The reaction of [Ru₃ (CO)₁₂] with Ph₃SnSPh in refluxing benzene furnished the bimetallic Ru-Sn compound [Ru₃(CO)₈(μ-SPh)₂(μ3-SnPh₂)(SnPh₃)₂] 1 which consists of a SnPh₂ stannylene bonded to three Ru atoms to give a planar tetra-metal core, with two peripheral SnPh₃ ligands. The stannylene ligand forms a very short bond to one Ru atom [Sn-Ru 2.538(1) Å] and very long bonds to the other two [Sn-Ru 3.074(1) Å]. The germanium compound [Ru₃(CO)₈(μ-SPh)₂(μ₃-GePh₂)(GePh₃)₂] 2 was obtained from the reaction of [Ru₃ (CO)₁₂] with Ph₃GeSPh and has a similar structure to that of 1 as evidenced by spectroscopic data. Treatment of [Os₃(CO)₁₀(MeCN)₂] with Ph₃SnSPh in refluxing benzene yielded the bimetallic Os-Sn compound [Os₃(CO)₉(μ-SPh)(μ₃-SnPh₂)(MeCN)(ƞ¹-C₆H₅)] 3. Cluster 3 has a superficially similar planar metal core, but with a different bonding mode with respect to that of 1. The Ph₂Sn group is bonded most closely to Os(2) and Os(3) [2.7862(3) and 2.7476(3) Å respectively] with a significantly longer bond to Os(1), 2.9981(3) Å indicating a weak back-donation to the Sn. The reaction of the bridging dppm compound [Ru₃(CO)₁₀(μ-dppm)] with Ph₃SnSPh afforded [Ru₃(CO)₆(μ-dppm)(μ₃-S)(μ₃-SPh)(SnPh₃)] 5. Compound 5 contains an open triangle of Ru atoms simultaneously capped by a sulfido and a PhS ligand on opposite sides of the cluster with a dppm ligand bridging one of the Ru-Ru edges and a Ph₃Sn group occupying an axial position on the Ru atom not bridged by the dppm ligand

Accuracy of Circulation Estimation Schemes Applied to Discretised Velocity Field Data

Numerical experiments are conducted on the velocity field of the Oseen vortex to determine the effect of random errors in the velocity field on the circulation estimate. The circulation is estimated by either a velocity integral or a vorticity integral over a particular region of integration. A novel method for the determination of this region is used. The accuracy of circulation estimation schemes is characterised in terms of the velocity sample spacing, the amount of random noise in the velocity field and the vorticity estimation scheme used. It is found that, in general, the velocity integral outperforms the vorticity integral in terms of reducing total error

Mitochondrial DNA depletion syndrome presenting with ataxia and external ophthalmoplegia: Case report

The mitochondrial DNA depletion syndromes are autosomal recessive disorders characterized by decreased mitochondrial DNA copy number in affected tissues.Mutations in 2 genes involved in deoxyribonucleotide metabolism, the deoxyguanosine kinase gene and the thymidine kinase 2 gene, had been related to this syndrome. This study aims to describe the clinical, histochemical, biochemical and molecular diagnosis of one Egyptian pediatric patient with the myopathic form of mitochondrial depletion syndrome. The patient presented to Cairo University Pediatric Hospital with the clinical suspicion of mitochondrial encephalomyopathy. Histochemical and biochemical studies of the respiratory chain complexes were performed on the muscle biopsy specimen from the patient. Molecular diagnosis was done by quantitative radioactive Southern blot and sequencing analysis of the whole coding regions of the TK2 gene. Histochemical staining revealed cytochrome oxidase negative fibers and increased staining for succinate dehydrogenase. The activity of complex I was not detected and complex IV activity was about 46%of age matched controls. Southern blot analysis showed reduction of the mitochondrial/nuclear DNA ratio, the degree of depletion was around 30% of aged-matched controls. Sequencing analysis of the TK2 gene revealed no sequence variation. Targeted molecular diagnosis based on the biochemical analysis of the respiratory chain enzymes makes the molecular evaluation of mitochondrial disorders much easier. Involvement of other nuclear genes rather than TK2 gene in the pathogenesis of the myopathic form of mitochondrial depletion syndrome should be considered.Keywords: Mitochondrial; Nuclear; Sequencing; Depletion; Mutation