Newton methods for nonlinear inverse problems with random noise

We study the convergence of regularized Newton methods applied to nonlinear operator equations in Hilbert spaces if the data are perturbed by random noise. We show that under certain conditions it is possible to achieve the minimax rates of the corresponding linearized problem if the smoothness of the solution is known. If the smoothness is unknown and the stopping index is determined by Lepskij's balancing principle, we show that the rates remain the same up to a logarithmic factor due to adaptation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling aspects of flow and solute transport simulations in water disinfection tanks

Water disinfection tanks such as chlorine and ozone contactors typically consist of multiple compartments featuring a serpentine flow pattern. Due to the complex hydrodynamics, the design and optimization of these tanks are often carried out by employing computational fluid dynamics (CFD) simulations. The present study demonstrates the influence of certain modeling aspects when the widely used Reynolds-Averaged Navier Stokes (RANS) based CFD approach to predict hydrodynamics and disinfection performance is employed. Three different contact tank geometries are examined numerically using RANS. The time-averaged velocity predictions are reasonably accurate when compared to validation data. However, in baffled contact tanks, the time-averaged flow differs quite significantly from the instantaneous flow, with the consequence that RANS-based models require careful calibration of the turbulent mixing parameter, i.e., the turbulent Schmidt number, when computing transport of solutes.     

Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog

We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green-Kubo relation and the Chapman-Enskog approach. The dissipative particle collisions are described by the coefficient of restitution epsilon which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, epsilon=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of epsilon on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for epsilon=const both methods lead to the same result for the self-diffusion coefficient. For the case of impact-velocity dependent coefficients of restitution, the Green-Kubo method is, however, either restrictive or too complicated for practical application, therefore we compute the diffusion coefficient using the Chapman-Enskog method. We conclude that in application to granular gases, the Chapman-Enskog approach is preferable for deriving kinetic coefficients.     

How 5 f Electron Polarisability Drives Covalency and Selectivity in Actinide N-Donor Complexes

We report a series of isostructural tetravalent actinide (Th, U−Pu) complexes with the N-donor ligand N,N’-ethylene-bis((pyrrole-2-yl)methanimine) (H₂ L , H₂pyren). Structural data from SC-XRD analysis reveal [An(pyren)₂] complexes with different An−N_imine versus An−N_pyrrolide bond lengths. Quantum chemical calculations elucidated the bonding situation, including differences in the covalent character of the coordinative bonds. A comparison to the intensely studied analogous N,N′-ethylene-bis(salicylideneimine) (H₂salen)-based complexes [An(salen)₂] displays, on average, almost equal electron sharing of pyren or salen with the An^IV, pointing to a potential ligand-cage-driven complex stabilisation. This is shown in the fixed ligand arrangement of pyren and salen in the respective An^IV complexes. The overall bond strength of the pure N-donor ligand pyren to An^IV (An=Th, U, Np, Pu) is slightly weaker than to salen, with the exception of the Pa^IV complex, which exhibits extraordinarily high electron sharing of pyren with Pa^IV. Such an altered ligand preference within the early An^IV series points to a specificity of the 5f¹ configuration, which can be explained by polarisation effects of the 5 f electrons, allowing the strongest f electron backbonding from Pa^IV (5f¹) to the N donors of pyren.     

Insights into the Electronic Structure of a U(IV) Amido and U(V) Imido Complex

Reaction of the N-heterocylic carbene ligand ⁱPrIm (L¹) and lithium bis(trimethylsilyl)amide (TMSA) as a base with UCl₄ resulted in U(IV) and U(V) complexes. Uranium's +V oxidation state in (HL¹)₂[U(V)(TMSI)Cl₅] (TMSI=trimethylsilylimido) ( 2 ) was confirmed by HERFD-XANES measurements. Solid state characterization by SC-XRD and geometry optimisation of [U(IV)(L¹)₂(TMSA)Cl₃] ( 1 ) indicated a silylamido ligand mediated inverse trans influence (ITI). The ITI was examined regarding different metal oxidation states and was compared to transition metal analogues by theoretical calculations.     

Evolutionary history and diversity of arthropod hemocyanins

Hemocyanins are copper-containing, multi-subunit proteins that transport oxygen in the hemolymph of many molluscs and arthropods [Markl and Decher, Adv. Comp. Environ. Physiol. 13 (1992) 325; 15563]. Arthropod hemocyanins originated more than 550 million years ago from oxygen-consuming phenoloxidases. Hemocyanins are present in various Onychophora, Chelicerata, Myriapoda, Crustacea, and Hexapoda, but subunit evolution differs striking in these arthropod subphyla. Hemocyanins also gave rise to non-respiratory proteins (crustacean pseudo-hemocyanins, insect hexamerins, and hexamerin receptors), which most likely have storage functions.     

The final NETLIB-LP results

With standard linear programming solvers there is always some uncertainty about the precise values of the optimal solutions. We implemented a program using exact rational arithmetic to compute proofs for the feasibility and optimality of an LP solution. This paper reports the exact optimal objective values for all NETLIB problems.     

On radiation conditions for rough surface scattering problems

^** Email: arens{at}numathics.com^*** Email: hohage{at}math.uni-goettingen.de It is well known that Sommerfeld's radiation condition is nota valid characterization of outgoing waves for scattering problemsat rough surfaces. Instead, a radiation condition called upwardpropagating radiation condition (UPRC) is commonly used. Recently,a different radiation condition called the pole condition hasbeen investigated for scattering problems at bounded obstacles.In this paper we show the equivalence between the UPRC and thepole condition. In doing so, we give a rigorous interpretationof a formula called the angular spectrum representation forDirichlet data in the space of bounded continuous functions.     

String picture for a model of frustrated quantum magnets and dimers

We study the effect of quantum dynamics on geometrically frustrated magnets for a transverse field Ising model at finite temperatures. We develop a microscopic derivation of the Landau-Ginzburg-Wilson action for this model and show that it can be interpreted as the free energy of a 3D elastic lattice of noncrossing strings. As a first application, we quantitatively predict the phase diagram and correlations, confirming excellently a key prediction of recent simulations about the existence of unusual phase transitions and an ordered phase. We discuss the implications of our string picture for the understanding of the effect of quenched disorder in such quantum frustrated systems.