Existence of axially symmetric static solutions of the Einstein-Vlasov system

We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the implicit function theorem by perturbing off a suitable spherically symmetric steady state of the Vlasov-Poisson system.Comment: 32 page

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

A nonhomogeneous boundary value problem in mass transfer theory

We prove a uniqueness result of solutions for a system of PDEs of Monge-Kantorovich type arising in problems of mass transfer theory. The results are obtained under very mild regularity assumptions both on the reference set $\Omega\subset\mathbf{R}^n$, and on the (possibly asymmetric) norm defined in $\Omega$. In the special case when $\Omega$ is endowed with the Euclidean metric, our results provide a complete description of the stationary solutions to the tray table problem in granular matter theory.Comment: 22 pages, 2 figure

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

Dynamical elastic bodies in Newtonian gravity

Well-posedness for the initial value problem for a self-gravitating elastic body with free boundary in Newtonian gravity is proved. In the material frame, the Euler-Lagrange equation becomes, assuming suitable constitutive properties for the elastic material, a fully non-linear elliptic-hyperbolic system with boundary conditions of Neumann type. For systems of this type, the initial data must satisfy compatibility conditions in order to achieve regular solutions. Given a relaxed reference configuration and a sufficiently small Newton's constant, a neigborhood of initial data satisfying the compatibility conditions is constructed

On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27 September 201

Long-term deglacial permafrost carbon dynamics in MPI-ESM

We have developed a new module to calculate soil organic carbon (SOC) accumulation in perennially frozen ground in the land surface model JSBACH. Running this offline version of MPI-ESM we have modelled long-term permafrost carbon accumulation and release from the Last Glacial Maximum (LGM) to the pre-industrial (PI) age. Our simulated near-surface PI permafrost extent of 16.9&thinsp; × &thinsp;106&thinsp;km2 is close to observational estimates. Glacial boundary conditions, especially ice sheet coverage, result in profoundly different spatial patterns of glacial permafrost extent. Deglacial warming leads to large-scale changes in soil temperatures, manifested in permafrost disappearance in southerly regions, and permafrost aggregation in formerly glaciated grid cells. In contrast to the large spatial shift in simulated permafrost occurrence, we infer an only moderate increase in total LGM permafrost area (18.3&thinsp; × &thinsp;106&thinsp;km2) – together with pronounced changes in the depth of seasonal thaw. Earlier empirical reconstructions suggest a larger spread of permafrost towards more southerly regions under glacial conditions, but with a highly uncertain extent of non-continuous permafrost.Compared to a control simulation without describing the transport of SOC into perennially frozen ground, the implementation of our newly developed module for simulating permafrost SOC accumulation leads to a doubling of simulated LGM permafrost SOC storage (amounting to a total of  ∼ &thinsp;150&thinsp;PgC). Despite LGM temperatures favouring a larger permafrost extent, simulated cold glacial temperatures – together with low precipitation and low CO2 levels – limit vegetation productivity and therefore prevent a larger glacial SOC build-up in our model. Changes in physical and biogeochemical boundary conditions during deglacial warming lead to an increase in mineral SOC storage towards the Holocene (168&thinsp;PgC at PI), which is below observational estimates (575&thinsp;PgC in continuous and discontinuous permafrost). Additional model experiments clarified the sensitivity of simulated SOC storage to model parameters, affecting long-term soil carbon respiration rates and simulated ALDs. Rather than a steady increase in carbon release from the LGM to PI as a consequence of deglacial permafrost degradation, our results suggest alternating phases of soil carbon accumulation and loss as an effect of dynamic changes in permafrost extent, ALDs, soil litter input, and heterotrophic respiration.</p

On the structure of the set of bifurcation points of periodic solutions for multiparameter Hamiltonian systems

This paper deals with periodic solutions of the Hamilton equation with many parameters. Theorems on global bifurcation of solutions with periods $2\pi/j,$ $j\in\mathbb{N},$ from a stationary point are proved. The Hessian matrix of the Hamiltonian at the stationary point can be singular. However, it is assumed that the local topological degree of the gradient of the Hamiltonian at the stationary point is nonzero. It is shown that (global) bifurcation points of solutions with given periods can be identified with zeros of appropriate continuous functions on the space of parameters. Explicit formulae for such functions are given in the case when the Hessian matrix of the Hamiltonian at the stationary point is block-diagonal. Symmetry breaking results concerning bifurcation of solutions with different minimal periods are obtained. A geometric description of the set of bifurcation points is given. Examples of constructive application of the theorems proved to analytical and numerical investigation and visualization of the set of all bifurcation points in given domain are provided. This paper is based on a part of the author's thesis [W. Radzki, ``Branching points of periodic solutions of autonomous Hamiltonian systems'' (Polish), PhD thesis, Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, Toru\'{n}, 2005].Comment: 35 pages, 4 figures, PDFLaTe

Dynamical Systems Gradient method for solving nonlinear equations with monotone operators

A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new stopping rule. Numerical experiments show that the proposed stopping rule is efficient. Equations with monotone operators are of interest in many applications.Comment: 2 figure

Cosmological post-Newtonian expansions to arbitrary order

We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter \ep=v_T/c (0<\ep < \ep_0), where $c$ is the speed of light, and $v_T$ is a typical speed of the gravitating fluid. These solutions are shown to exist on a common spacetime slab M\cong [0,T)\times \Tbb^3, and converge as \ep \searrow 0 to a solution of the cosmological Poisson-Euler equations of Newtonian gravity. Moreover, we establish that these solutions can be expanded in the parameter \ep to any specified order with expansion coefficients that satisfy \ep-independent (nonlocal) symmetric hyperbolic equations