hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

Anatomic foveal reconstruction of the triangular fibrocartilage complex with a tendon graft

An acute injury to the triangular fibrocartilage complex (TFCC) with avulsion of the foveal attachment can produce distal radioulnar joint (DRUJ) instability. The avulsed TFCC is translated distally so the footprint will be bathed in synovial fluid from the DRUJ and will become covered in synovitis. If the TFCC fails to heal to the footprint, then persistent instability can occur. The authors describe a surgical technique indicated for the treatment of persistent instability of the DRUJ due to foveal detachment of the TFCC. The procedure utilizes a loop of palmaris longus tendon graft passed through the ulnar aspect of the TFCC and into an osseous tunnel in the distal ulna to reconstruct the foveal attachment. This technique provides stability of the distal ulna to the radius and carpus. We recommend this procedure for chronic instability of the DRUJ due to TFCC avulsion, but recommend that suture repair remain the treatment of choice for acute instability. An arthroscopic assessment includes the trampoline test, hook test, and reverse hook test. DRUJ ballottement under arthroscopic vision details the direction of instability, the functional tear pattern, and unmasks concealed tears. If the reverse hook test demonstrates a functional instability between the TFCC and the radius, then a foveal reconstruction is contraindicated, and a reconstruction that stabilizes the radial and ulnar aspects of the TFCC is required. The foveal reconstruction technique has the advantage of providing a robust anatomically based reconstruction of the TFCC to the fovea, which stabilizes the DRUJ and the ulnocarpal sag.

Interaction of the Trinuclear Triangular Secondary Building Unit [Cu 3 (μ 3 -OH)(μ-pz) 3 ] 2+ with 4,4′-Bipyridine. Structural Characterizations of New Coordination Polymers and Hexanuclear Cu II Clusters. 2°

By reacting 4,4′-bipyridine (bpy) with selected trinuclear triangular CuII complexes, [Cu3(μ3-OH)(μ-pz)3(RCOO)2(LL′)] [pz = pyrazolate anion; R = CH3, CH3CH2, CH2═CH, CH2═C(CH3); L, L′ = Hpz, H2O, MeOH] in MeOH, the substitution of monotopic ligands by ditopic bpy was observed. Depending on the stoichiometric reaction ratios, different compounds were isolated and structurally characterized. One- and two-dimensional coordination polymers (CPs), as well as two hexanuclear CuII clusters were identified. One of the hexanuclear clusters self-assembles into a supramolecular three-dimensional structure, and its crystal packing shows the presence of two intersecting channels, one of which is almost completely occupied by guest bpy, while in the second one guest water molecules are present. This compound also shows a reversible, thermally induced, single-crystal-to-single-crystal transition.

Synthesis and Structural Characterizations of New Coordination Polymers Generated by the Interaction Between the Trinuclear Triangular SBU [Cu 3 (μ 3 -OH)(μ-pz) 3 ] 2+ and 4,4′-Bipyridine. 3°

The reactions of 4,4′-bipyridine with selected trinuclear triangular copper(II) complexes, [Cu3(μ3-OH)(μ-pz)3(RCOO)2Lx], [pz = pyrazolate anion, R = CH3(CH2)n (2 ≤ n ≤ 5); L = H2O, MeOH, EtOH] yielded a series of 1D coordination polymers (CPs) based on the repetition of [Cu3(μ3-OH)(μ-pz)3] secondary building units joined by bipyridine. The CPs were characterized by conventional analytical methods (elemental analyses, ESI-MS, IR spectra) and single crystal XRD determinations. An unprecedented 1D CP, generated through the bipyridine bridging hexanuclear copper clusters moieties, two 1D CPs presenting structural analogies, and two monodimensional tapes having almost exactly superimposable structures, were obtained. In one case, the crystal packing makes evident the presence of small, not-connected pores, accounting for ca. 6% of free cell volume.

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.

Multibeam Network Design and Measurement for Triangular Array of Three Radiating Elements

Nowadays, more a more base stations are equipped with active conformal antennas. These antenna designs combine phase shift systems with multibeam networks providing multi-beam ability and interference rejection, which optimize multiple channel systems. GEODA is a conformal adaptive antenna system designed for satellite communications. Operating at 1.7 GHz with circular polarization, it is possible to track and communicate with several satellites at once thanks to its adaptive beam. The antenna is based on a set of similar triangular arrays that are divided in subarrays of three elements called `cells'. Transmission/Receiver (T/R) modules manage beam steering by shifting the phases. A more accurate steering of the antenna GEODA could be achieved by using a multibeam network. Several multibeam network designs based on Butler network will be presented

3x3 Multibeam Network for a Triangular Array of Three Radiating Elements

A multibeam antenna study based on Butler network will be undertaken in this document. These antenna designs combines phase shift systems with multibeam networks to optimize multiple channel systems. The system will work at 1.7 GHz with circular polarization. Specifically, result simulations and measurements of 3 element triangular subarray will be shown. A 45 element triangular array will be formed by the subarrays. Using triangular subarrays, side lobes and crossing points are reduced.

6x3 Microstrip Beam Forming Network for Multibeam Triangular Array

A six inputs and three outputs structure which can be used to obtain six simultaneous beams with a triangular array of 3 elements is presented. The beam forming network is obtained combining balanced and unbalanced hybrid couplers and allows to obtain six main beams with sixty degrees of separation in azimuth direction. Simulations and measurements showing the performance of the array and other detailed results are presented

ITEM: Inter-Texture Error Measurement for 3D Meshes

We introduce a simple and innovative method to compare any two texture maps, regardless of their sizes, aspect ratios, or even masks, as long as they are both meant to be mapped onto the same 3D mesh. Our system is based on a zero-distortion 3D mesh unwrapping technique which compares two new adapted texture atlases with the same mask but different texel colors, and whose every texel covers the same area in 3D. Once these adapted atlases are created, we measure their difference with ITEM-RMSE, a slightly modified version of the standard RMSE defined for images. ITEM-RMSE is more meaningful and reliable than RMSE because it only takes into account the texels inside the mask, since they are the only ones that will actually be used during rendering. Our method is not only very useful to compare the space efficiency of different texture atlas generation algorithms, but also to quantify texture loss in compression schemes for multi-resolution textured 3D meshes.

Multi-Resolution Texture Coding for Multi-Resolution 3D Meshes

We present an innovative system to encode and transmit textured multi-resolution 3D meshes in a progressive way, with no need to send several texture images, one for each mesh LOD (Level Of Detail). All texture LODs are created from the finest one (associated to the finest mesh), but can be re- constructed progressively from the coarsest thanks to refinement images calculated in the encoding process, and transmitted only if needed. This allows us to adjust the LOD/quality of both 3D mesh and texture according to the rendering power of the device that will display them, and to the network capacity. Additionally, we achieve big savings in data transmission by avoiding altogether texture coordinates, which are generated automatically thanks to an unwrapping system agreed upon by both encoder and decoder.

Non-degenerate developable triangular Bézier patches

In this talk we show a construction for characterising developable surfaces in the form of Bézier triangular patches. It is shown that constructions used for rectangular patches are not useful, since they provide degenerate triangular patches. Explicit constructions of non-degenerate developable triangular patches are provided.