Fractional Supersymmetry and Fth-Roots of Representations

A generalization of super-Lie algebras is presented. It is then shown that all known examples of fractional supersymmetry can be understood in this formulation. However, the incorporation of three dimensional fractional supersymmetry in this framework needs some care. The proposed solutions lead naturally to a formulation of a fractional supersymmetry starting from any representation D of any Lie algebra g. This involves taking the Fth-roots of D in an appropriate sense. A fractional supersymmetry in any space-time dimension is then possible. This formalism finally leads to an infinite dimensional extension of g, reducing to the centerless Virasoro algebra when g=sl(2,R).Comment: 23 pages, 1 figure, LaTex file with epsf.st

Extended Complex Trigonometry in Relation to Integrable 2D-Quantum Field Theories and Duality

Multicomplex numbers of order n have an associated trigonometry (multisine functions with (n-1) parameters) leading to a natural extension of the sine-Gordon model. The parameters are constrained from the requirement of local current conservation. In two dimensions for n < 6 known integrable models (deformed Toda and non-linear sigma, pure affine Toda...) with dual counterparts are obtained in this way from the multicomplex space MC itself and from the natural embedding \MC_n \subset \MMC_m, n < m. For $n \ge 6$ a generic constraint on the space of parametersis obtained from current conservation at first order in the interaction Lagragien.Comment: 11 pages, no figure, LaTex with amsmath accepted by Phys. Lett.

Unexpected Features of Supersymmetry with Central Charges

It is shown that N=2 supersymmetric theories with central charges present some hidden quartic symmetry. This enables us to construct representations of the quartic structure induced by superalgebra representations.Comment: 14 pages, more details have been given, to appear in J. Phys.

Calculation of AGARD Wing 445.6 Flutter Using Navier-Stokes Aerodynamics

An unsteady, 3D, implicit upwind Euler/Navier-Stokes algorithm is here used to compute the flutter characteristics of Wing 445.6, the AGARD standard aeroelastic configuration for dynamic response, with a view to the discrepancy between Euler characteristics and experimental data. Attention is given to effects of fluid viscosity, structural damping, and number of structural model nodes. The flutter characteristics of the wing are determined using these unsteady generalized aerodynamic forces in a traditional V-g analysis. The V-g analysis indicates that fluid viscosity has a significant effect on the supersonic flutter boundary for this wing

Proliferation of anomalous symmetries in colloidal monolayers subjected to quasiperiodic light fields

Quasicrystals provide a fascinating class of materials with intriguing properties. Despite a strong potential for numerous technical applications, the conditions under which quasicrystals form are still poorly understood. Currently, it is not clear why most quasicrystals hold 5- or 10-fold symmetry but no single example with 7 or 9-fold symmetry has ever been observed. Here we report on geometrical constraints which impede the formation of quasicrystals with certain symmetries in a colloidal model system. Experimentally, colloidal quasicrystals are created by subjecting micron-sized particles to two-dimensional quasiperiodic potential landscapes created by n=5 or seven laser beams. Our results clearly demonstrate that quasicrystalline order is much easier established for n = 5 compared to n = 7. With increasing laser intensity we observe that the colloids first adopt quasiperiodic order at local areas which then laterally grow until an extended quasicrystalline layer forms. As nucleation sites where quasiperiodicity originates, we identify highly symmetric motifs in the laser pattern. We find that their density strongly varies with n and surprisingly is smallest exactly for those quasicrystalline symmetries which have never been observed in atomic systems. Since such high symmetry motifs also exist in atomic quasicrystals where they act as preferential adsorption sites, this suggests that it is indeed the deficiency of such motifs which accounts for the absence of materials with e.g. 7-fold symmetry

Local strain distribution in real three-dimensional alveolar geometries

Mechanical ventilation is not only a life saving treatment but can also cause negative side effects. One of the main complications is inflammation caused by overstretching of the alveolar tissue. Previously, studies investigated either global strains or looked into which states lead to inflammatory reactions in cell cultures. However, the connection between the global deformation, of a tissue strip or the whole organ, and the strains reaching the single cells lining the alveolar walls is unknown and respective studies are still missing. The main reason for this is most likely the complex, sponge-like alveolar geometry, whose three-dimensional details have been unknown until recently. Utilizing synchrotron-based X-ray tomographic microscopy, we were able to generate real and detailed three-dimensional alveolar geometries on which we have performed finite-element simulations. This allowed us to determine, for the first time, a three-dimensional strain state within the alveolar wall. Briefly, precision-cut lung slices, prepared from isolated rat lungs, were scanned and segmented to provide a three-dimensional geometry. This was then discretized using newly developed tetrahedral elements. The main conclusions of this study are that the local strain in the alveolar wall can reach a multiple of the value of the global strain, for our simulations up to four times as high and that thin structures obviously cause hotspots that are especially at risk of overstretching

Comparison of [18F]-Tracers in Various Experimental Tumor Models by PET Imaging and Identification of an Early Response Biomarker for the Novel Microtubule Stabilizer Patupilone

Purpose: The suitability of [18F]FDG, [18F]FLT, [18F]FET, and [18F]FCH as non-invasive positron emission tomography (PET) biomarkers for monitoring response to chemotherapy was analyzed in various experimental tumor models. Procedures: Tracer uptake into three syngeneic rodent tumor models and ten human xenograft models was evaluated using semiquantitative analysis of small-animal PET data. Murine RIF-1 fibrosarcomas and [18F]FLT were selected to monitor the effects of the novel cytotoxic patupilone. Results: Except [18F]FCH, all tracers provided good tumor visualization. Highest [18F]FDG uptake was identified in syngeneic tumors. Xenograft models, however, showed low [18F]FDG SUVs and were better visualized by [18F]FLT. Monitoring the effects of patupilone on [18F]FLT uptake in RIF-1 tumors revealed a significant decrease of tracer uptake after 24h, which strongly negatively correlated with apoptosis. Conclusion: [18F]FLT PET of experimental tumors is a viable complement to [18F]FDG for preclinical drug development. [18F]FLT may be an excellent biomarker for patupilone-induced apoptosi

Recent Enhancements to the Development of CFD-Based Aeroelastic Reduced-Order Models

Recent enhancements to the development of CFD-based unsteady aerodynamic and aeroelastic reduced-order models (ROMs) are presented. These enhancements include the simultaneous application of structural modes as CFD input, static aeroelastic analysis using a ROM, and matched-point solutions using a ROM. The simultaneous application of structural modes as CFD input enables the computation of the unsteady aerodynamic state-space matrices with a single CFD execution, independent of the number of structural modes. The responses obtained from a simultaneous excitation of the CFD-based unsteady aerodynamic system are processed using system identification techniques in order to generate an unsteady aerodynamic state-space ROM. Once the unsteady aerodynamic state-space ROM is generated, a method for computing the static aeroelastic response using this unsteady aerodynamic ROM and a state-space model of the structure, is presented. Finally, a method is presented that enables the computation of matchedpoint solutions using a single ROM that is applicable over a range of dynamic pressures and velocities for a given Mach number. These enhancements represent a significant advancement of unsteady aerodynamic and aeroelastic ROM technology

Tangential View and Intraoperative Three-Dimensional Fluoroscopy for the Detection of Screw-Misplacements in Volar Plating of Distal Radius Fractures

Background: Volar locking plate fixation has become the gold standard in the treatment of unstable distal radius fractures. Juxta-articular screws should be placed as close as possible to the subchondral zone, in an optimized length to buttress the articular surface and address the contralateral cortical bone. On the other hand, intra-articular screw misplacements will promote osteoarthritis, while the penetration of the contralateral bone surface may result in tendon irritations and ruptures. The intraoperative control of fracture reduction and implant positioning is limited in the common postero-anterior and true lateral two-dimensional (2D)-fluoroscopic views. Therefore, additional 2D-fluoroscopic views in different projections and intraoperative three-dimensional (3D) fluoroscopy were recently reported. Nevertheless, their utility has issued controversies. Objectives: The following questions should be answered in this study; 1) Are the additional tangential view and the intraoperative 3D fluoroscopy useful in the clinical routine to detect persistent fracture dislocations and screw misplacements, to prevent revision surgery? 2) Which is the most dangerous plate hole for screw misplacement? Patients and Methods: A total of 48 patients (36 females and 13 males) with 49 unstable distal radius fractures (22 x 23 A; 2 x 23 B, and 25 x 23 C) were treated with a 2.4 mm variable angle LCP Two-Column volar distal radius plate (Synthes GmbH, Oberdorf, Switzerland) during a 10-month period. After final fixation, according to the manufactures' technique guide and control of implant placement in the two common perpendicular 2D-fluoroscopic images (postero-anterior and true lateral), an additional tangential view and intraoperative 3D fluoroscopic scan were performed to control the anatomic fracture reduction and screw placements. Intraoperative revision rates due to screw misplacements (intra-articular or overlength) were evaluated. Additionally, the number of surgeons, time and radiation-exposure, for each step of the operating procedure, were recorded. Results: In the standard 2D-fluoroscopic views (postero-anterior and true lateral projection), 22 screw misplacements of 232 inserted screws were not detected. Based on the additional tangential view, 12 screws were exchanged, followed by further 10 screws after performing the 3D fluoroscopic scan. The most lateral screw position had the highest risk for screw misplacement (accounting for 45.5% of all exchanged screws). The mean number of images for the tangential view was 3 ± 2.5 images. The mean surgical time was extended by 10.02 ± 3.82 minutes for the 3D fluoroscopic scan. An additional radiation exposure of 4.4 ± 4.5seconds, with a dose area product of 39.2 ± 14.5 cGy/cm2 were necessary for the tangential view and 54.4 ± 20.9 seconds with a dose area product of 2.1 ± 2.2 cGy/cm2, for the 3D fluoroscopic scan. Conclusions: We recommend the additional 2D-fluoroscopic tangential view for detection of screw misplacements caused by overlength, with penetration on the dorsal cortical surface of the distal radius, predominantly observed for the most lateral screw position. The use of intraoperative 3D fluoroscopy did not become accepted in our clinical routine, due to the technical demanding and time consuming procedure, with a limited image quality so far

Application of the FUN3D Unstructured-Grid Navier-Stokes Solver to the 4th AIAA Drag Prediction Workshop Cases

FUN3D Navier-Stokes solutions were computed for the 4th AIAA Drag Prediction Workshop grid convergence study, downwash study, and Reynolds number study on a set of node-based mixed-element grids. All of the baseline tetrahedral grids were generated with the VGRID (developmental) advancing-layer and advancing-front grid generation software package following the gridding guidelines developed for the workshop. With maximum grid sizes exceeding 100 million nodes, the grid convergence study was particularly challenging for the node-based unstructured grid generators and flow solvers. At the time of the workshop, the super-fine grid with 105 million nodes and 600 million elements was the largest grid known to have been generated using VGRID. FUN3D Version 11.0 has a completely new pre- and post-processing paradigm that has been incorporated directly into the solver and functions entirely in a parallel, distributed memory environment. This feature allowed for practical pre-processing and solution times on the largest unstructured-grid size requested for the workshop. For the constant-lift grid convergence case, the convergence of total drag is approximately second-order on the finest three grids. The variation in total drag between the finest two grids is only 2 counts. At the finest grid levels, only small variations in wing and tail pressure distributions are seen with grid refinement. Similarly, a small wing side-of-body separation also shows little variation at the finest grid levels. Overall, the FUN3D results compare well with the structured-grid code CFL3D. The FUN3D downwash study and Reynolds number study results compare well with the range of results shown in the workshop presentations