We describe measurements of the decay of pure superfluid turbulence in superfluid 3 He-B, in the low temperature regime where the normal fluid density is negligible. We follow the decay of the turbulence generated by a vibrating grid as detected by vibrating wire resonators. Despite the absence of any classical normal fluid dissipation processes, the decay is consistent with turbulence having the classical Kolmogorov energy spectrum and is remarkably similar to that measured in superfluid 4 He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by the superfluid circulation quantum rather than kinematic viscosity.PACS numbers: 67.57. Fg, 67.57.De, 67.57.Hi In this paper we present the first quantitative measurements of the decay of turbulence in a pure superfluid system. This is a subject of considerable interest since no conventional dissipation mechanisms are available.In a classical fluid, turbulence at high Reynolds numbers is characterized by a range of eddy sizes obeying the well-known Kolmogorov spectrum. On large length scales the motion is dissipationless, whereas on small scales viscosity comes into play. Decay of the turbulence proceeds as energy is transferred by non-linear interactions from the largest non-dissipative length scales d (typically the size of the turbulent region) to smaller length scales where the motion is dissipated by viscous forces. The dissipation per unit volume is given by ρνω 2 where ρ is the fluid density, ν the kinematic viscosity and ω 2 the mean square vorticity [1]. An interesting question, which has received much theoretical speculation [1], is what happens in a pure superfluid with no viscous interactions?Conceptually, turbulence in a superfluid is greatly simplified. Superfluids such as He-II and 3 He-B are described by macroscopic wavefunctions with a well defined phase φ. The superfluid velocity is determined by gradients of the phase, v S = ( /m)∇φ where m is the mass of the entities constituting the superfluid (the mass of a 4 He atom for He-II or twice the mass of a 3 He atom, 2m 3 , for the Cooper pairs in 3 He-B). Consequently, in contrast to classical fluids, superfluid motion is inherently irrotational and vorticity may only be created in the superfluid by the injection of vortex lines. A superfluid vortex is a line defect around which the phase changes by 2π (ignoring here more complex structures such as in 3 He-A). The superfluid order parameter is distorted within the relatively narrow core of the vortex where all the circulation is concentrated. The superfluid flows around the core with a velocity, at distance r, given by v S = /mr corresponding to a quantized circulation κ = h/m. Vortex lines are topological defects. They cannot terminate in free space, and therefore must either form loops or * Electronic Address: s.fisher@lancaster.ac.uk terminate on container walls. Turbulence in a superfluid takes the form of a tangle of vortex lines.Superfluid hydrodynamics is further simplified by the superfluid compon...

A series of tetranuclear copper(II) and nickel(II) complexes is described, all of which form by a strict self-assembly process involving just a single ligand and the metal salt. The ligands POAP, POAPZ, PZOAP, and 6POAP contain terminal pyridine and pyrazine residues bound to a central flexible diazine subunit (N−N) and contain two potentially bridging groups (alkoxo and diazine). In all cases but one the metals are linked by alkoxo oxygens alone, forming essentially square [M4(μ2-O)4] clusters. A rectangular copper(II) complex [Cu4(μ2-N2)2(μ2-O)2] involves a mixture of two alkoxo and two diazine bridges. The square Cu4O4 clusters exhibit ferromagnetic coupling between the metal centers, associated with the orthogonal arrangement of magnetic orbitals, while for the Ni4O4 clusters the nickel(II) centers are coupled antiferromagnetically. The [Cu4(μ2-N2)2(μ2-O)2] cluster exhibits strong antiferromagnetic coupling through a trans Cu(N-N)Cu bridging arrangement, typical for systems of this sort. X-ray structures are reported for [Cu4 (POAP-H)4(H2O)2](NO3)4·4H2O (2), [Cu4(POAPZ-H)4(H2O)](NO3)4·3H2O (3), [Cu4(6POAP-H)4](ClO4)4 (4), [Cu4(PZOAP-H)4](NO3)4·3H2O (5), [Ni4(POAP-H)4 (H2O)4](NO3)4·8H2O (6), and [Ni4(PZOAP-H)4(H2O)4](ClO4)4·5H2O (9). 2 crystallized in the monoclinic system, space group C2/c, with a = 20.479(3) Å, b = 14.920(2) Å, c = 19.671(3) Å, β = 90.591(4)°, and Z = 8. 3 crystallized in the monoclinic system, space group P21/c, with a = 14.12(1) Å, b = 14.116(3) Å, c = 29.043(4) Å, β = 94.50(3)°, and Z = 4. 4 crystallized in the monoclinic system, space group C2/c, with a = 22.646(4) Å, b = 25.842(5) Å, c = 12.349(5) Å, β = 110.34(2)°, and Z = 4. 5 crystallized in the monoclinic system, space group P2/n, with a = 14.3573(4) Å, b = 10.8910(6) Å, c = 20.5360(10) Å, β = 96.975(4)°, and Z = 4. 6 crystallized in the triclinic system, space group P1̄, with a = 12.0509(6) Å, b = 12.7498(6) Å, c = 23.1208 Å, α = 93.1050(10)°, β = 100.1500(10)°, γ = 108.5050(11)°, and Z = 2. 9 crystallized in the orthorhombic system, space group Pbcn, with a = 14.368(4) Å, b = 25.469(7) Å, c = 18.479(5) Å, and Z = 4.

Heat stress and extreme temperatures negatively affect plant development by disrupting regular cellular and biochemical functions, ultimately leading to reduced crop production. Alfalfa (Medicago sativa) is an important forage crop grown worldwide as forage for livestock feed. Limiting the effects of abiotic stress by developing alfalfa cultivars that are stress tolerant would help mitigate losses to crop production. Members of the microRNA156 (miR156) family regulate the Squamosa Promoter-Binding Protein-Like (SPL) genes that in turn impact plant growth and development by regulating downstream genes in response to various abiotic stresses. In this study, alfalfa with miR156 overexpression and SPL13 RNAi knockdown show increased tolerance to heat stress (40°C). Transgenic plants show high water potential and increased non-enzymatic antioxidant content under heat stress. Moreover, anthocyanin content and chlorophyll abundance were increased under stress. Expression of some important transcription factors and downstream genes involved in abiotic stress response were altered in miR156-overexpressing genotypes under heat. Taken together, our results demonstrate that the miR156/SPL13 network contributes to improving heat stress tolerance in alfalfa.