The transverse field Richtmyer-Meshkov instability in magnetohydrodynamics

The magnetohydrodynamic Richtmyer-Meshkov instability is investigated for the case where the initial magnetic field is unperturbed and aligned with the mean interface location. For this initial condition, the magnetic field lines penetrate the perturbed density interface, forbidding a tangential velocity jump and therefore the presence of a vortex sheet. Through simulation, we find that the vorticity distribution present on the interface immediately after the shock acceleration breaks up into waves traveling parallel and anti-parallel to the magnetic field, which transport the vorticity. The interference of these waves as they propagate causes the perturbation amplitude of the interface to oscillate in time. This interface behavior is accurately predicted over a broad range of parameters by an incompressible linearized model derived presently by solving the corresponding impulse driven, linearized initial value problem. Our use of an equilibrium initial condition results in interface motion produced solely by the impulsive acceleration. Nonlinear compressible simulations are used to investigate the behavior of the transverse field magnetohydrodynamic Richtmyer-Meshkov instability, and the performance of the incompressible model, over a range of shock strengths, magnetic field strengths, perturbation amplitudes and Atwood numbers

Lignin dynamics in two13C-labelled arable soils during 18 years

Lignin has long been considered a relatively stable component of soil organic matter. However, recent studies suggest that lignin may turn over within years to decades in arable soil. Here we analyzed lignin concentrations in an 18 year field experiment under continuous silage maize where two soils were sampled at six points in time. Our objectives were to examine the long-term dynamics of (i) lignin derived from a previous C3-vegetation and (ii) lignin derived from maize, as influenced by two levels of maize biomass input. Total lignin concentrations in soil were quantified by gas chromatography of lignin cupric oxide oxidation products. Compound-specific 13C isotope analysis allowed discrimination between C3-derived lignin and maize-derived lignin. Degradation dynamics of C3-derived lignin were independent of biomass input level, suggesting that priming did not affect soil lignin concentrations over almost two decades. After 18 years approximately two thirds of the initial C3-derived lignin remained in the soils, whereas, on average, 10 % of the recent maize-derived lignin input was retained. We suggest that lignin is effectively stabilized in these arable soils, although the mechanisms involved remain unclear

Gradient-based estimation of Manning's friction coefficient from noisy data

We study the numerical recovery of Manning's roughness coefficient for the diffusive wave approximation of the shallow water equation. We describe a conjugate gradient method for the numerical inversion. Numerical results for one-dimensional model are presented to illustrate the feasibility of the approach. Also we provide a proof of the differentiability of the weak form with respect to the coefficient as well as the continuity and boundedness of the linearized operator under reasonable assumptions using the maximal parabolic regularity theory.Comment: 19 pages, 3 figure

Sparse 3D reconstructions in electrical Impedance Tomography using real data

We present a 3D reconstruction algorithm with sparsity constraints for Electrical Impedance Tomography (EIT). EIT is the inverse problem of determining the distribution of conductivity in the interior of an object from simultaneous measurements of currents and voltages on its boundary. The feasibility of the sparsity reconstruction approach is tested with real data obtained from a new planar EIT device developed at the Institut für Physik, Johannes Gutenberg Universität, Mainz, Germany. The complete electrode model is adapted for the given device to handle incomplete measurements and the inhomogeneities of the conductivity are a priori assumed to be sparse with respect to a certain basis. This prior information is incorporated into a Tikhonov-type functional by including a sparsity-promoting l1-regularization term. The functional is minimized with an iterative soft shrinkage-type algorithm