A rigorous formulation of the cosmological Newtonian limit without averaging

We prove the existence of a large class of one-parameter families of cosmological solutions to the Einstein-Euler equations that have a Newtonian limit. This class includes solutions that represent a finite, but otherwise arbitrary, number of compact fluid bodies. These solutions provide exact cosmological models that admit Newtonian limits but, are not, either implicitly or explicitly, averaged

Density of critical points for a Gaussian random function

Critical points of a scalar quantitiy are either extremal points or saddle points. The character of the critical points is determined by the sign distribution of the eigenvalues of the Hessian matrix. For a two-dimensional homogeneous and isotropic random function topological arguments are sufficient to show that all possible sign combinations are equidistributed or with other words, the density of the saddle points and extrema agree. This argument breaks down in three dimensions. All ratios of the densities of saddle points and extrema larger than one are possible. For a homogeneous Gaussian random field one finds no longer an equidistribution of signs, saddle points are slightly more frequent.Comment: 11 pages 1 figure, changes in list of references, corrected typo

MRI of "diffusion" in the human brain: New results using a modified CE-FAST sequence.

“Diffusion-weighted” MRI in the normal human brain and in a patient with a cerebral metastasis is demonstrated. The method employed was a modified CE-FAST sequence with imaging times of only 6-10 s using a conventional 1.5-T whole-body MRI system (Siemens Magnetom). As with previous phantom and animal studies, the use of strong gradients together with macroscopic motions in vivo causes unavoidable artifacts in diffusion-weighted images of the human brain. While these artifacts are shown to be considerably reduced by averaging of 8-16 images, the resulting diffusion contrast is compromised by unknown signal losses due to motion

Nuclear spin coherence in a quantum wire

We have observed millisecond-long coherent evolution of nuclear spins in a quantum wire at 1.2 K. Local, all-electrical manipulation of nuclear spins is achieved by dynamic nuclear polarization in the breakdown regime of the Integer Quantum Hall Effect combined with pulsed Nuclear Magnetic Resonance. The excitation thresholds for the breakdown are significantly smaller than what would be expected for our sample and the direction of the nuclear polarization can be controlled by the voltage bias. As a four-level spin system, the device is equivalent to two qubits.Comment: 5 pages, 5 figure

INI1 mutations in meningiomas at a potential hotspot in exon 9

Rhabdoid tumours have been shown to carry somatic mutations in the INI1 (SMARCB1/hSNF5) gene. A considerable fraction of these tumours exhibit allelic losses on chromosome 22. Allelic loss on 22q also is characteristic for meningiomas, however most of these alterations are considered to be associated with mutations of the NF2 gene. We examined a series of 126 meningiomas for alterations in the INI1 gene. Four identical somatic mutations in exon 9 were detected resulting in an exchange of Arg to His in position 377 of INI1. Our observations were reproduced both by using DNA from a new round of extraction and by employing overlapping primers. This mutational hotspot therefore appears to be an important target in the formation of a fraction of meningiomas. In addition, 4 novel polymorphisms of INI1 were characterized. Our data indicate that the INI1 is a second tumour suppressor gene on chromosome 22 that may be important for the genesis of meningiomas. © 2001 Cancer Research Campaign http://www.bjcancer.co

Ongoing methane discharge at well site 22/4b (North Sea)and discovery of a spiral vortex bubble plume motion

Highlights • Mega ebullition of biogenic methane from an abandoned offshore gas well, North Sea. • Evidence for midwater bubble plume intrusion, fallback, and short-circuiting of the plume. • Effective trapping of seabed released methane underneath the thermocline. • First observation of a spiral vortex methane plume and marginal turbulences. • Megaplumes appear less efficient in terms of vertical methane transport than previously thought. Abstract First direct evidence for ongoing gas seepage activity on the abandoned well site 22/4b (Northern North Sea, 57°55′ N, 01°38′ E) and discovery of neighboring seepage activity is provided from observations since 2005. A manned submersible dive in 2006 discovered several extraordinary intense seepage sites within a 60 m wide and 20 m deep crater cut into the flat 96 m deep seafloor. Capture and (isotope) chemical analyses of the gas bubbles near the seafloor revealed in situ concentrations of methane between 88 and 90%Vol. with δ13C–CH4 values around −74‰ VPDB, indicating a biogenic origin. Bulk methane concentrations throughout the water column were assessed by 120 Niskin water samples showing up to 400.000 nM CH4 in the crater at depth. In contrast, concentrations above the thermocline were orders of magnitude lower, with a median value of 20 nM. A dye tracer injection into the gas seeps revealed upwelling bubble and water motion with gas plume rise velocities up to ∼1 ms−1 (determined near the seabed). However, the dissolved dye did not pass the thermocline, but returned down to the seabed. Measurements of direct bubble-mediated atmospheric flux revealed low values of 0.7 ± 0.3 kty−1, much less than current state-of-the-art bubble dissolution models would predict for such a strong and upwelling in situ gas bubble flux at shallow water depths (i.e. ∼100 m). Acoustic multibeam water column imaging data indicate a pronounced 200 m lateral intrusion at the thermocline together with high methane concentration at this layer. A partly downward-orientated bubble plume motion is also visible in the acoustic data with potential short-circuiting in accordance to the dye experiment. This observation could partly explain the observed trapping of most of the released gas below the well-established thermocline in the North Sea. Moreover, 3D analyses of the multibeam water column data reveal that the upwelling plume transforms into a spiral expanding vortex while rising through the water column. Such a spiral vortex motion has never been reported before for marine gas seepage and might represent an important process with strong implication on plume dynamics, dissolution behavior, gas escape to the atmosphere, and is considered very important for respective modeling approaches

Finite reduction and Morse index estimates for mechanical systems

A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover, the Hessian of the reduced function preserves all the relevant information of the original one, by Schur's complement, which spontaneously appears in this context. Finally, the results are straightforwardly extended to the case of a Dirichlet problem on a bounded domain.Comment: 13 pages; v2: minor changes, to appear in Nonlinear Differential Equations and Application

On the existence of dyons and dyonic black holes in Einstein-Yang-Mills theory

We study dyonic soliton and black hole solutions of the ${\mathfrak {su}}(2)$ Einstein-Yang-Mills equations in asymptotically anti-de Sitter space. We prove the existence of non-trivial dyonic soliton and black hole solutions in a neighbourhood of the trivial solution. For these solutions the magnetic gauge field function has no zeros and we conjecture that at least some of these non-trivial solutions will be stable. The global existence proof uses local existence results and a non-linear perturbation argument based on the (Banach space) implicit function theorem.Comment: 23 pages, 2 figures. Minor revisions; references adde

Magnetic resonance lung function – a breakthrough for lung imaging and functional assessment? A phantom study and clinical trial

BACKGROUND: Chronic lung diseases are a major issue in public health. A serial pulmonary assessment using imaging techniques free of ionizing radiation and which provides early information on local function impairment would therefore be a considerably important development. Magnetic resonance imaging (MRI) is a powerful tool for the static and dynamic imaging of many organs. Its application in lung imaging however, has been limited due to the low water content of the lung and the artefacts evident at air-tissue interfaces. Many attempts have been made to visualize local ventilation using the inhalation of hyperpolarized gases or gadolinium aerosol responding to MRI. None of these methods are applicable for broad clinical use as they require specific equipment. METHODS: We have shown previously that low-field MRI can be used for static imaging of the lung. Here we show that mathematical processing of data derived from serial MRI scans during the respiratory cycle produces good quality images of local ventilation without any contrast agent. A phantom study and investigations in 85 patients were performed. RESULTS: The phantom study proved our theoretical considerations. In 99 patient investigations good correlation (r = 0.8; p ≤ 0.001) was seen for pulmonary function tests and MR ventilation measurements. Small ventilation defects were visualized. CONCLUSION: With this method, ventilation defects can be diagnosed long before any imaging or pulmonary function test will indicate disease. This surprisingly simple approach could easily be incorporated in clinical routine and may be a breakthrough for lung imaging and functional assessment