Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic structure. The domain occupied by the fluid depends on time. It is taken into account in the Navier-Stokes equations rewritten with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The resulting coupled system is discretized by the STDGM using piecewise polynomial approximations of the sought solution both in space and time. The developed method can be applied to the solution of the compressible flow for a wide range of Mach numbers and Reynolds numbers. For the simulation of elastic deformations two models are used: the linear elasticity model and the nonlinear neo-Hookean model. The main goal is to show the robustness and applicability of the method to the simulation of the air flow in a simplified model of human vocal tract and the flow induced vocal folds vibrations. It will also be shown that in this case the linear elasticity model is not adequate and it is necessary to apply the nonlinear model.     

Cortical disinhibition occurs in chronic neuropathic,but not in chronic nociceptive pain

Background  

The aim of this study was to examine the relationship between chronic neuropathic pain after incomplete peripheral nerve lesion, chronic nociceptive pain due to osteoarthritis, and the excitability of the motor cortex assessed by transcranial magnetic stimulation (TMS). Hence in 26 patients with neuropathic pain resulting from an isolated incomplete lesion of the median or ulnar nerve (neuralgia), 20 patients with painful osteoarthritis of the hand, and 14 healthy control subjects, the excitability of the motor cortex was tested using paired-pulse TMS to assess intracortical inhibition and facilitation. These excitability parameters were compared between groups, and the relationship between excitability parameters and clinical parameters was examined.     

Noisy scale-free networks

The impact of observational noise on the analysis of scale-free networks is studied. Various noise sources are modeled as random link removal, random link exchange and random link addition. Emphasis is on the resulting modifications for the node-degree distribution and for a functional ranking based on betweenness centrality. The implications for estimated gene-expressed networks for childhood acute lymphoblastic leukemia are discussed.     

Global Geometric Deformations of Current Algebras as Krichever-Novikov Type Algebras

We construct algebraic-geometric families of genus one (i.e. elliptic) current and affine Lie algebras of Krichever-Novikov type. These families deform the classical current, respectively affine Kac-Moody Lie algebras. The construction is induced by the geometric process of degenerating the elliptic curve to singular cubics. If the finite-dimensional Lie algebra defining the infinite dimensional current algebra is simple then, even if restricted to local families, the constructed families are non-equivalent to the trivial family. In particular, we show that the current algebra is geometrically not rigid, despite its formal rigidity. This shows that in the infinite dimensional Lie algebra case the relations between geometric deformations, formal deformations and Lie algebra two-cohomology are not that close as in the finite-dimensional case. The constructed families are e.g. of relevance in the global operator approach to the Wess-Zumino-Witten-Novikov models appearing in the quantization of Conformal Field Theory. The algebras are explicitly given by generators and structure equations and yield new examples of infinite dimensional algebras of current and affine Lie algebra type.     

Quantitative pharmacokinetic analysis of DCE-MRI data without an arterial input function: a reference region model

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can assess tumor perfusion, microvascular vessel wall permeability and extravascular-extracellular volume fraction. Analysis of DCE-MRI data is usually based on indicator dilution theory that requires knowledge of the concentration of the contrast agent in the blood plasma, the arterial input function (AIF). A method is presented that compares the tissues of interest (TOI) curve shape to that of a reference region (RR), thereby eliminating the need for direct AIF measurement. By assigning literature values for Ktrans (the blood perfusion-vessel permeability product) and v(e) (extravascular-extracellular volume fraction) in a reference tissue, it is possible to extract the Ktrans and v(e) values for a TOI without knowledge of the AIF. The operational RR equation for DCE-MRI analysis is derived, and its sensitivity to noise and incorrect assignment of the RR parameters is tested via simulations. The method is robust at noise levels of 10%, returning accurate (+/-20% in the worst case) and precise (+/-15% in the worst case) values. Errors in the TOI Ktrans and v(e) values scale approximately linearly with the errors in the assigned RR Ktrans and v(e) values. The methodology is then applied to a Lewis Lung Carcinoma mouse tumor model. A slowly enhancing TOI yielded Ktrans=0.039+/-0.002 min-1 and v(e)=0.46+/-0.01, while a rapidly enhancing region yielded Ktrans=0.35+/-0.05 min-1 and v(e)=0.31+/-0.01. Parametric Ktrans and v(e) mappings manifested a tumor periphery with elevated Ktrans (>0.30 min-1) and v(e) (>0.30) values. The main advantage of the RR approach is that it allows for quantitative assessment of tissue properties without having to obtain high temporal resolution images to characterize an AIF. This allows for acquiring images with higher spatial resolution and/or SNR, and therefore, increased ability to probe tissue heterogeneity.     

Observations of cavitation erosion pit formation

Previous investigations showed that a single cavitation bubble collapse can cause more than one erosion pit (Philipp & Lauterborn [1]). But our preliminary study showed just the opposite – that in some cases a single cavitation pit can result from more than one cavitation event. The present study shows deeper investigation of this phenomenon. An investigation of the erosion effects of ultrasonic cavitation on a thin aluminum foil was made. In the study we observed the formation of individual pits by means of high speed cameras (>1000 fps) and quantitatively evaluated the series of images by stereoscopy and the shape from shading method. This enabled the reconstruction of the time evolution of the pit shape. Results show how the foil is deformed several times before a hole is finally punctured. It was determined that larger single pits result from several impacts of shock waves on the same area, which means that they are merely special cases of pit clusters (pit clusters where pits overlap perfectly). Finally it was shown that a thin foil, which is subjected to cavitation, behaves as a membrane. It was concluded that the physics behind erosion depends significantly on the means of generating cavitation (acoustic, hydrodynamic, laser light) and the specimen characteristics (thin foil, massive specimen), which makes comparison of results of materials resistance to cavitation from different experimental set-ups questionable.Further development of the shape from shading method in the scope of cavitation erosion testing will enable better evaluation of cavitation erosion models.     

Full C1,α-regularity for free and constrained local minimizers of elliptic variational integrals¶with nearly linear growth

We consider local minimizers of elliptic variational integrals with integrand f of nearly linear growth. In the scalar case N= 1 a side condition of the type u≥Φ may be incorporated, for N > 1 u is an unconstrained minimizer and f is required just to depend on the modulus of Du. We show in both cases that u has H?lder continuous first derivatives in the interior of the domain Ω.     

Chemistry of the phenoxathiins. III. Synthesis of benzo[1″,2″:5,6:5″,4″:5′,6′]bis[1,4]oxathiino[3,2-b:3′,2′-b']dipyridine

As a result of studies dealing with the synthesis of 1-azaphenoxathiins, the synthesis of benzo[1″,2″:5,6:5″,4″:5′,6′]bis[1,4]oxathiino[3,2-b:3′,2′-b']dipyridine was examined. Unique evidence of solvent participation in the synthesis of these compounds by the structure elucidation of a novel minor by-product formed during the synthesis of the title compound is also reported.