Numerical methods for all-speed flows for the Euler equations including well-balancing of source terms

This thesis regards the numerical simulation of inviscid compressible ideal gases which are described by the Euler equations. We propose a novel implicit explicit (IMEX) relaxation scheme to simulate flows from compressible as well as near incompressible regimes based on a Suliciu-type relaxation model. The Mach number plays an important role in the design of the scheme, as it has great influence on the flow behaviour and physical properties of solutions of the Euler equations. Our focus is on an accurate resolution of the Mach number independent material wave. A special feature of our scheme is that it can account for the influence of a gravitational field on the fluid flow and is applicable also in small Froude number regimes. The time step of the IMEX scheme is constrained only by the eigenvalues of the explicitly treated part and is independent of the Mach number allowing for large time steps independent of the flow regime. In addition, the scheme is provably asymptotic preserving and well-balanced for arbitrary a priori known hydrostatic equilibria independently of the considered Mach and Froude regime. Also, the scheme preserves the positivity of density and internal energy throughout the simulation, it is well suited for physical applications. To increase the accuracy, a natural extension to second order is provided. The theoretical properties of the given schemes are numerically validated by various test cases performed on Cartesian grids in multiple space dimensions

On high-accuracy L∞-stable IMEX schemes for scalar hyperbolic multi-scale equations

We present a framework to build high-accuracy IMEX schemes that fulfill the maximum principle, applied to a scalar hyperbolic multi-scale equation. Motivated by the findings in [Gottlieb, Shu, Tadmor, 2001] that implicit R-K schemes are not L∞-stable, our scheme, for which we can prove the L ∞ stability, is based on a convex combination between a first-order and a class of second-order IMEX schemes. We numerically demonstrate the advantages of our scheme, especially for discontinuous problems, and give a MOOD procedure to increase the accuracy

An implicit-explicit solver for a two-fluid single-temperature model

We present an implicit-explicit finite volume scheme for two-fluid single-temperature flow in all Mach number regimes which is based on a symmetric hyperbolic thermodynamically compatible description of the fluid flow. The scheme is stable for large time steps controlled by the interface transport and is computational efficient due to a linear implicit character. The latter is achieved by linearizing along constant reference states given by the asymptotic analysis of the single-temperature model. Thus, the use of a stiffly accurate IMEX Runge Kutta time integration and the centered treatment of pressure based quantities provably guarantee the asymptotic preserving property of the scheme for weakly compressible Euler equations with variable volume fraction. The properties of the first and second order scheme are validated by several numerical test cases

Cortico-cerebellar functional connectivity and sequencing of movements in schizophrenia

<p>Abstract</p> <p>Background</p> <p>Abnormal execution of several movements in a sequence is a frequent finding in schizophrenia. Successful performance of such motor acts requires correct integration of cortico-subcortical processes, particularly those related to cerebellar functions. Abnormal connectivity between cortical and cerebellar regions with resulting cognitive dysmetria has been proposed as the core dysfunction behind many signs and symptoms of schizophrenia. The aim of the present study was to assess if these proposed abnormalities in connectivity are a unifying feature of schizophrenia, or, rather, reflect a specific symptom domain of a heterogeneous disease. We predicted that abnormal functional connectivity between the motor cortex and cerebellum would be linked with abnormal performance of movement sequencing.</p> <p>Methods</p> <p>We examined 24 schizophrenia patients (SCH) and 24 age-, sex-, and handedness-matched healthy controls (HC) using fMRI during a modified finger-tapping task. The ability to perform movement sequencing was tested using the Neurological Evaluation Scale (NES). The subjects were categorized into two groups, with (SQ+) and without (SQ-) movement sequencing abnormalities, according to the NES-SQ score. The effects of diagnosis and movement sequencing abnormalities on the functional connectivity parameters between the motor cortex and cerebellum (MC-CRBL) and the supplementary motor cortex and cerebellum (SMA-CRBL) activated during the motor task were analyzed.</p> <p>Results</p> <p>We found no effect of diagnosis on the functional connectivity measures. There was, however, a significant effect on the SQ group: SQ + patients showed a lower level of MC-CRBL connectivity than SQ- patients and healthy controls. Moreover, the level of MC-CRBL and SMA-CRBL negatively correlated with the magnitude of NES-SQ abnormalities, but with no other NES domain.</p> <p>Conclusions</p> <p>Abnormal cortico-cerebellar functional connectivity during the execution of a motor task is linked with movement sequencing abnormalities in schizophrenia, but not with the diagnosis of schizophrenia per se. It seems that specific patterns of inter-regional connectivity are linked with corresponding signs and symptoms of clinically heterogeneous conditions such as schizophrenia.</p

Widespread occurrence of non-canonical transcription termination by human RNA polymerase III

Human RNA polymerase (Pol) III-transcribed genes are thought to share a simple termination signal constituted by four or more consecutive thymidine residues in the coding DNA strand, just downstream of the RNA 3′-end sequence. We found that a large set of human tRNA genes (tDNAs) do not display any T≥4 stretch within 50 bp of 3′-flanking region. In vitro analysis of tDNAs with a distanced T≥4 revealed the existence of non-canonical terminators resembling degenerate T≥5 elements, which ensure significant termination but at the same time allow for the production of Pol III read-through pre-tRNAs with unusually long 3′ trailers. A panel of such non-canonical signals was found to direct transcription termination of unusual Pol III-synthesized viral pre-miRNA transcripts in gammaherpesvirus 68-infected cells. Genome-wide location analysis revealed that human Pol III tends to trespass into the 3′-flanking regions of tDNAs, as expected from extensive terminator read-through. The widespread occurrence of partial termination suggests that the Pol III primary transcriptome in mammals is unexpectedly enriched in 3′-trailer sequences with the potential to contribute novel functional ncRNAs

Consensus Paper: Radiological Biomarkers of Cerebellar Diseases

Hereditary and sporadic cerebellar ataxias represent a vast and still growing group of diseases whose diagnosis and differentiation cannot only rely on clinical evaluation. Brain imaging including magnetic resonance (MR) and nuclear medicine techniques allows for characterization of structural and functional abnormalities underlying symptomatic ataxias. These methods thus constitute a potential source of radiological biomarkers, which could be used to identify these diseases and differentiate subgroups of them, and to assess their severity and their evolution. Such biomarkers mainly comprise qualitative and quantitative data obtained from MR including proton spectroscopy, diffusion imaging, tractography, voxel-based morphometry, functional imaging during task execution or in a resting state, and from SPETC and PET with several radiotracers. In the current article, we aim to illustrate briefly some applications of these neuroimaging tools to evaluation of cerebellar disorders such as inherited cerebellar ataxia, fetal developmental malformations, and immune-mediated cerebellar diseases and of neurodegenerative or early-developing diseases, such as dementia and autism in which cerebellar involvement is an emerging feature. Although these radiological biomarkers appear promising and helpful to better understand ataxia-related anatomical and physiological impairments, to date, very few of them have turned out to be specific for a given ataxia with atrophy of the cerebellar system being the main and the most usual alteration being observed. Consequently, much remains to be done to establish sensitivity, specificity, and reproducibility of available MR and nuclear medicine features as diagnostic, progression and surrogate biomarkers in clinical routine