A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements,Spectral Elements,and Discontinuous Galerkin

Numerical weather prediction (NWP) is in a period of transition. As resolutions increase, global models are moving towards fully nonhydrostatic dynamical cores, with the local and global models using the same governing equations; therefore we have reached a point where it will be necessary to use a single model for both applications. The new dynamical cores at the heart of these unified models are designed to scale efficiently on clusters with hundreds of thousands or even millions of CPU cores and GPUs. Operational and research NWP codes currently use a wide range of numerical methods: finite differences, spectral transform, finite volumes and, increasingly, finite/spectral elements and discontinuous Galerkin, which constitute element-based Galerkin (EBG) methods. Due to their important role in this transition, will EBGs be the dominant power behind NWP in the next 10 years, or will they just be one of many methods to choose from? One decade after the review of numerical methods for atmospheric modeling by Steppeler et al. (Meteorol Atmos Phys 82:287–301, 2003), this review discusses EBG methods as a viable numerical approach for the next-generation NWP models. One well-known weakness of EBG methods is the generation of unphysical oscillations in advection-dominated flows; special attention is hence devoted to dissipation-based stabilization methods. Since EBGs are geometrically flexible and allow both conforming and non-conforming meshes, as well as grid adaptivity, this review is concluded with a short overview of how mesh generation and dynamic mesh refinement are becoming as important for atmospheric modeling as they have been for engineering applications for many years.     

Fast template tracking in video sequences

Tracking of poorly defined, rotating and/or distorted objects in a video sequence poses significant problems especially in medical diagnostics including ultrasound (sonographic) video used for examination and diagnosis of internal movement of tissue or muscle and nerve action. Cross-correlation techniques have been successful in retrieving dynamic information directly from ultrasound video data. We outline a fast implementation of tracking based on normalized cross-correlation using an adaptive template and present results from our application, developed in MATLAB?, which successfully tracks arbitrarily selected objects in deformed or severely compromised images. Common ultrasound image evaluation is qualitative but there is need to retrieve quantitative dynamic information such as the trajectory or velocity of selected areas. Our approach uses normalized two-dimensional cross-correlation to find the position of an initially selected template enclosing the feature of interest and map its trajectory frame-by-frame to produce displacement and velocity plots. We illustrate operation of the application using routine ultrasound data and demonstrate its performance using test video of objects rotating full circle and rolling down a ramp. We analyse errors associated with sampling to compare performance of our implementation with a more rigorous but tedious and computationally expensive correlation of a resampled, rotated, and shifted template.     

Multimodal focus attention and stress detection and feedback in an augmented driver simulator

This paper presents a driver simulator, which takes into account the information about the user’s state of mind (level of attention, fatigue state, stress state). The user’s state of mind analysis is based on video data and biological signals. Facial movements such as eyes blinking, yawning, head rotations, etc., are detected on video data: they are used in order to evaluate the fatigue and the attention level of the driver. The user’s electrocardiogram and galvanic skin response are recorded and analyzed in order to evaluate the stress level of the driver. A driver simulator software is modified so that the system is able to appropriately react to these critical situations of fatigue and stress: some audio and visual messages are sent to the driver, wheel vibrations are generated and the driver is supposed to react to the alert messages. A multi-threaded system is proposed to support multi-messages sent by the different modalities. Strategies for data fusion and fission are also provided. Some of these components are integrated within the first prototype of OpenInterface: the multimodal similar platform.     

Compensation for gaze perturbation during inactivation of the caudal fastigial nucleus in the head-unrestrained cat

Muscimol injection in the caudal part of the fastigial nucleus (cFN) leads, in the head-unrestrained cat, to a characteristic dysmetria of saccadic gaze shifts toward visual targets. The goal of the current study was to test whether this pharmacological cFN inactivation impaired the ability to compensate for unexpected perturbations in gaze position during the latency period of the saccadic response. Such perturbations consisted of moving gaze away from the target by a transient electrical microstimulation in the deep layers of the superior colliculus simultaneously with extinction of the visual target. After injection of muscimol in the cFN, targets located in the contralesional hemifield elicited gaze shifts that fell short of the target in both "perturbed" and "unperturbed" trials. The amplitude of the compensatory contraversive gaze shifts in perturbed trials coincided with the predicted amplitude of unperturbed responses starting from the same position. Targets located in the opposite hemifield elicited hypermetric gaze shifts in both trial types, and the error of compensatory responses was not statistically different from that of unperturbed gaze shifts. These results indicate that inactivation of the cFN does not interfere with the ability of the head-unrestrained cat to compensate for ipsiversive or contraversive perturbations in gaze position. Thus the gaze-related feedback signals that are used to compute a reference signal of desired gaze displacement are not impaired by cFN inactivation.     

Retention mechanism of weak polar solutes in reversed phase liquid chromatography

The retention mechanism of a weak polar solute, a series of 10 benzodiazepines in reversed phase liquid chromatography, was investigated over a wide range of mobile phase compositions. The values of enthalpy (ΔH°) and entropy (ΔS°) of transfer from the mobile to the stationary phases were determined. The method studied each factor (water fraction Φ in the acetonitrile (ACN)/water mixture and column temperature) controlling the retention mechanism. The changes in ΔH° and ΔS° as a function of the water fraction Φ in the ACN/water mixture were examined. These variations are explained using the organization of organic modifier (ACN) in clusters in the ACN/water mixture. A change in the retention mechanism thus indicated when the ACN/water mixture was used instead of the hydrogen-bonded mobile phase such as CH(3)OH/water. Enthalpy-entropy compensation revealed that the retention mechanism was independent of the water fraction Φ but showed that differences between the molecular structures of the benzodiazepines contributed more significantly to changes in the retention process in the CH(3)OH/water mixture than in the ACN/water mixture.