Navier-Stokes equations as a differential-algebraic system

Nonsteady Navier-Stokes equations represent a differential-algebraic system of strangeness index one after any spatial discretization. Since such systems are hard to treat in their original form, most approaches use some kind of index reduction. Processing this index reduction it is important to take care of the manifolds contained in the differential-algebraic equation (DAE). We investigate for several discretization schemes for the Navier-Stokes equations how the consideration of the manifolds is taken into account and propose a variant of solving these equations along the lines of the theoretically best index reduction. Applying this technique, the error of the time discretisation depends only on the method applied for solving the DAE

Efficient time step parallelization of full multigrid techniques

This paper deals with parallelization methods for time-dependent problems where the time steps are shared out among the processors. A Full Multigrid technique serves as solution algorithm, hence information of the preceding time step and of the coarser grid is necessary to compute the solution at each new grid level. Applying the usual extrapolation formula to process this information, the parallelization will not be very efficient. We developed another extrapolation technique which causes a much higher parallelization effect. Test examples show that no essential loss of exactness appears, such that the method presented here shall be well-applicable

Enhancement of the upper critical field in codoped iron-arsenic high-temperature superconductors

We present the first study of codoped iron-arsenide superconductors of the 122 family (Sr/Ba)_(1-x)K_xFe_(2-y)Co_yAs_2 with the purpose to increase the upper critical field H_c2 compared to single doped (Sr/Ba)Fe_2As_2 materials. H_c2 was investigated by measuring the magnetoresistance in high pulsed magnetic fields up to 64 T. We find, that H_c2 extrapolated to T = 0 is indeed enhanced significantly to ~ 90 T for polycrystalline samples of Ba_0.55K_0.45Fe_1.95Co_0.05As_2 compared to ~75 T for Ba_0.55K_0.45Fe_2As_2 and BaFe_1.8Co_0.2As_2 single crystals. Codoping thus is a promising way for the systematic optimization of iron-arsenic based superconductors for magnetic-field and high-current applications.Comment: 7 pages, 5 figures, submitted to Journal of Applied Physic

Quantifying the improvement of surrogate indices of hepatic insulin resistance using complex measurement techniques

We evaluated the ability of simple and complex surrogate-indices to identify individuals from an overweight/obese cohort with hepatic insulin-resistance (HEP-IR). Five indices, one previously defined and four newly generated through step-wise linear regression, were created against a single-cohort sample of 77 extensively characterised participants with the metabolic syndrome (age 55.6±1.0 years, BMI 31.5±0.4 kg/m2; 30 males). HEP-IR was defined by measuring endogenous-glucose-production (EGP) with [6–62H2] glucose during fasting and euglycemic-hyperinsulinemic clamps and expressed as EGP*fasting plasma insulin. Complex measures were incorporated into the model, including various non-standard biomarkers and the measurement of body-fat distribution and liver-fat, to further improve the predictive capability of the index. Validation was performed against a data set of the same subjects after an isoenergetic dietary intervention (4 arms, diets varying in protein and fiber content versus control). All five indices produced comparable prediction of HEP-IR, explaining 39–56% of the variance, depending on regression variable combination. The validation of the regression equations showed little variation between the different proposed indices (r2 = 27–32%) on a matched dataset. New complex indices encompassing advanced measurement techniques offered an improved correlation (r = 0.75, P<0.001). However, when validated against the alternative dataset all indices performed comparably with the standard homeostasis model assessment for insulin resistance (HOMA-IR) (r = 0.54, P<0.001). Thus, simple estimates of HEP-IR performed comparable to more complex indices and could be an efficient and cost effective approach in large epidemiological investigations

Nonlinear Diffusion on the 2D Euclidean Motion Group

Linear and nonlinear diffusion equations are usually considered on an image, which is in fact a function on the translation group. In this paper we study diffusion on orientation scores, i.e. on functions on the Euclidean motion group SE(2). An orientation score is obtained from an image by a linear invertible transformation. The goal is to enhance elongated structures by applying nonlinear left-invariant diffusion on the orientation score of the image. For this purpose we describe how we can use Gaussian derivatives to obtain regularized left-invariant derivatives that obey the non-commutative structure of the Lie algebra of SE(2). The Hessian constructed with these derivatives is used to estimate local curvature and orientation strength and the diffusion is made nonlinearly dependent on these measures. We propose an explicit finite difference scheme to apply the nonlinear diffusion on orientation scores. The experiments show that preservation of crossing structures is the main advantage compared to approaches such as coherence enhancing diffusion

Peculiar long-range superexchange in Cu2A2O7 (A = P, As, V) as a key element of the microscopic magnetic model

A microscopic magnetic model for alpha-Cu2P2O7 is evaluated in a combined theoretical and experimental study. Despite a dominant intradimer coupling J1, sizable interdimer couplings enforce long-range magnetic ordering at T_N=27 K. The spin model for alpha-Cu2P2O7 is compared to the models of the isostructural beta-Cu2V2O7 and alpha-Cu2As2O7 systems. As a surprise, coupled dimers in alpha-Cu2P2O7 and alternating chains in alpha-Cu2As2O7 contrast with a honeycomb lattice in beta-Cu2V2O7. We find that the qualitative difference in the coupling regime of these isostructural compounds is governed by the nature of AO4 side groups: d-elements (A = V) hybridize with nearby O atoms forming a Cu-O-A-O-Cu superexchange path, while for p-elements (A = P, As) the superexchange is realized via O-O edges of the tetrahedron. Implications for a broad range of systems are discussed.Comment: 8 pages, 5 figures, 1 table; discussion extende

Fast parallel algorithms for a broad class of nonlinear variational diffusion approaches

Variational segmentation and nonlinear diffusion approaches have been very active research areas in the fields of image processing and computer vision during the last years. In the present paper, we review recent advances in the development of efficient numerical algorithms for these approaches. The performance of parallel implement at ions of these algorithms on general-purpose hardware is assessed. A mathematically clear connection between variational models and nonlinear diffusion filters is presented that allows to interpret one approach as an approximation of the other, and vice versa. Numerical results confirm that, depending on the parametrization, this approximation can be made quite accurate. Our results provide a perspective for uniform implement at ions of both nonlinear variational models and diffusion filters on parallel architectures

Digital cultural heritage imaging via osmosis filtering

In Cultural Heritage (CH) imaging, data acquired within different spectral regions are often used to inspect surface and sub-surface features. Due to the experimental setup, these images may suffer from intensity inhomogeneities, which may prevent conservators from distinguishing the physical properties of the object under restoration. Furthermore, in multi-modal imaging, the transfer of information between one modality to another is often used to integrate image contents. In this paper, we apply the image osmosis model proposed in [4, 10, 12] to solve correct these problems arising when diagnostic CH imaging techniques based on reflectance, emission and fluorescence mode in the optical and thermal range are used. For an efficient computation, we use stable operator splitting techniques to solve the discretised model. We test our methods on real artwork datasets: the thermal measurements of the mural painting “Monocromo” by Leonardo Da Vinci, the UV-VIS-IR imaging of an ancient Russian icon and the Archimedes Palimpsest dataset

Universal signatures of the metamagnetic quantum critical endpoint: Application to CeRu2Si2

A quantum critical endpoint related to a metamagnetic transition causes distinct signatures in the thermodynamic quantities of a compound. We argue that, irrespective of the microscopic details of the considered material, the diverging differential susceptibility combined with the Ising symmetry of the endpoint give rise to a number of characteristic metamagnetic phenomena. In the presence of a magnetoelastic coupling, one finds a correspondence of susceptibility, magnetostriction and compressibility and, as a result, a pronounced crystal softening, a diverging Grueneisen parameter, a sign change of thermal expansion alpha(H), and a minimum in the specific heat coefficient gamma(H). We illustrate these signatures and their relation on the metamagnetic crossover at 8 T in the prototypical heavy-fermion system CeRu2Si2.Comment: 8 pages, 6 figures, v2: changed title, minor modification

Huge First-Order Metamagnetic Transition in the Paramagnetic Heavy-Fermion System CeTiGe

We report on the observation of large, step-like anomalies in the magnetization ($\Delta M = 0.74$\,$\mu_{\rm B}$/Ce), in the magnetostriction ($\Delta l/l_{0} = 2.0 \cdot 10^{-3}$), and in the magnetoresistance in polycrystals of the paramagnetic heavy-fermion system CeTiGe at a critical magnetic field $\mu_0 H_c \approx$ 12.5\,T at low temperatures. The size of these anomalies is much larger than those reported for the prototypical heavy-fermion metamagnet CeRu$_2$Si$_2$. Furthermore, hysteresis between increasing and decreasing field data indicate a real thermodynamic, first-order type of phase transition, in contrast to the crossover reported for CeRu$_2$Si$_2$. Analysis of the resistivity data shows a pronounced decrease of the electronic quasiparticle mass across $H_c$. These results establish CeTiGe as a new metamagnetic Kondo-lattice system, with an exceptionally large, metamagnetic transition of first-order type at a moderate field.Comment: 5 pages, 4 figure