On the isoperimetric problem in the Heisenberg group \u210dn

It has been recently conjectured that, in the context of the Heisenberg groupHn endowed with its Carnot\u2013Carath\ue9odory metric and Haar measure, the isoperimetricsets (i.e., minimizers of the H-perimeter among sets of constant Haar measure) couldcoincide with the solutions to a \u201crestricted\u201d isoperimetric problem within the class ofsets having finite perimeter, smooth boundary, and cylindrical symmetry. In this paper,we derive new properties of these restricted isoperimetric sets, which we call Heisenbergbubbles. In particular, we show that their boundary has constant mean H-curvature and, quitesurprisingly, that it is foliated by the family of minimal geodesics connecting two specialpoints. In view of a possible strategy for proving that Heisenberg bubbles are actuallyisoperimetric among the whole class of measurable subsets of Hn, we turn our attentionto the relationship between volume, perimeter, and -enlargements. In particular, we provea Brunn\u2013Minkowski inequality with topological exponent as well as the fact that the Hperimeterof a bounded, open set F 82 Hn of class C2 can be computed via a generalizedMinkowski content, defined by means of any bounded set whose horizontal projection is the2n-dimensional unit disc. Some consequences of these properties are discussed

Composition of Fluids Responsible for Gold Mineralization in the Pechenga Structure-Imandra-Varzuga Greenstone Belt, Kola Peninsula, Russia.

This study presents the first fluid inclusion data from quartz of albite–carbonate–quartz altered rocks and metasomatic quartzite hosting gold mineralization in the Pechenga structure of the Pechenga– Imandra–Varzuga greenstone belt. A temperature of 275–370°C, pressure of 1.2–4.5 kbar, and the fluid composition of gold-bearing fluid are estimated by microthermometry, Raman spectroscopy, and LA-ICP-MS of individual fluid inclusions, as well as by bulk chemical analyses of fluid inclusions. In particular, the Au and Ag concentrations have been determined in fluid inclusions. It is shown that albite–carbonate–quartz altered rocks and metasomatic quartzite interacted with fluids of similar chemical composition but under different physicochemical conditions. It is concluded that the gold-bearing fluid in the Pechenga structure is similar to that of orogenic gold deposits

23rd IAEA Fusion Energy Conference: summary of sessions EX/C and ICC

An overview is given of recent experimental results in the areas of innovative confinement concepts, operational scenarios and confinement experiments as presented at the 2010 IAEA Fusion Energy Conference. Important new findings are presented from fusion devices worldwide, with a strong focus towards the scientific and technical issues associated with ITER and W7-X devices, presently under construction

Measurement of tokamak error fields using plasma response and its applicability to ITER

The nonlinear response of a low-beta tokamak plasma to non-axisymmetric fields offers an alternative to direct measurement of the non-axisymmetric part of the vacuum magnetic fields, often termed ‘error fields’. Possible approaches are discussed for determination of error fields and the required current in non-axisymmetric correction coils, with an emphasis on two relatively new methods: measurement of the torque balance on a saturated magnetic island, and measurement of the braking of plasma rotation in the absence of an island. The former is well suited to ohmically heated discharges, while the latter is more appropriate for discharges with a modest amount of neutral beam heating to drive rotation. Both can potentially provide continuous measurements during a discharge, subject to the limitation of a minimum averaging time. The applicability of these methods to ITER is discussed, and an estimate is made of their uncertainties in light of the specifications of ITER’s diagnostic systems. The use of plasma response-based techniques in normal ITER operational scenarios may allow identification of the error field contributions by individual central solenoid coils, but identification of the individual contributions by the outer poloidal field coils or other sources is less likely to be feasible

Scaling of the Plasma Rotation Needed for Stabilizing the n = 1 Resistive Wall Mode (Ideal Kink) in the DIII D Tokamak

Experiments in the DIII-D tokamak show that the n = 1 ideal kink can be stabilized by a resistive wall if the plasma is rotating fast enough. A database of the onset of the n = 1 resistive wall mode as a function of the equilibrium toroidal magnetic field, the plasma density and the toroidal rotation has been assembled for plasmas with beta between the theoretically predicted no wall and ideal wall stability limits. The critical rotation frequency is found to scale as the inverse of the Alfv\ue9n time with ? ?A 0.02 (evaluated at the q = 2 surface at ? 0.6) or ? ?S 0.7, where ?S is the sound time. The dependence of ? ? A or ? ?S on ?N/?N,no wall from 1?2 is weak and suggests the plasmas are in the \u27intermediate dissipation\u27 regime