The meccano method for simultaneous volume parametrization and mesh generation of complex solids

[EN]The meccano method is a novel and promising mesh generation method for simultaneously creating adaptive tetrahedral meshes and volume parametrizations of a complex solid. We highlight the fact that the method requires minimum user intervention and has a low computational cost. The method builds a 3-D triangulation of the solid as a deformation of an appropriate tetrahedral mesh of the meccano. The new mesh generator combines an automatic parametrization of surface triangulations, a local refinement algorithm for 3-D nested triangulations and a simultaneous untangling and smoothing procedure. At present, the procedure is fully automatic for a genus-zero solid. In this case, the meccano can be a single cube. The efficiency of the proposed technique is shown with several applications...

The meccano method for automatic 3-d triangulation and volume parametrization of complex solids

[EN]In this paper we review the novel meccano method. We summarize the main stages (subdivision, mapping, optimization) of this automatic tetrahedral mesh generation technique and we concentrate the study to complex genus-zero solids. In this case, our procedure only requires a surface triangulation of the solid. A crucial consequence of our method is the volume parametrization of the solid to a cube. We construct volume T-meshes for isogeometric analysis by using this result. The efficiency of the proposed technique is shown with several examples. A comparison between the meccano method and standard mesh generation techniques is introduced.-1…

Adaptive Finite Element Method with a local element parametrization nested meses

[EN]This work presents a novel approach to solve a two dimensional problem by using an adaptive finite element approach. The most common strategy to deal with nested adaptivity is to generate a mesh that represents the geometry and the input parameters correctly, and to refine this mesh locally to obtain the most accurate solution. As opposed to this approach, the authors propose a technique using independent meshes : geometry, input data and the unknowns. Each particular mesh is obtained by a local nested refinement of the same coarse mesh at the parametric space…

A dictionary of modular threefolds

The thesis deals with the modularity conjecture for three-dimensional Calabi-Yau varieties. This is a generalization of the work of A. Wiles and others on modularity of elliptic curves. Modularity connects the number of points on varieties with coefficients of certain modular forms. In chapter 1 we collect the basics on arithmetic on Calabi-Yau manifolds, including general modularity results and strategies for modularity proofs. In chapters 2, 3, 4 and 5 we investigate examples of modular Calabi-Yau threefolds, including all examples occurring in the literature and many new ones. Double octics, i.e. Double coverings of projective 3-space branched along an octic surface, are studied in detail. In chapter 6 we deal with examples connected with the same modular forms. According to the Tate conjecture there should be correspondences between them. Many correspondences are constructed explicitly. We finish by formulating conjectures on the occurring newforms, especially their levels. In the appendices we compile tables of coefficients of weight 2 and weight 4 newforms and many examples of double octics.

Structural design, manufacturing and testing of the new wing for the CSIR's Modular UAS in composite materials

In the framework of an international collaboration with South Africa CSIR, the structural design, manufacturing and testing of the new wing for the Modular UAS in composite materials has been performed.

Severe Accident Simulation of Small Modular Reactors

Since the Three Mile Island Unit 2 (TMI-2), accident in 1979 which led to the meltdown of about one half of the reactor core and to limited releases of radioactive materials to the environment, an important international effort has been made on severe accident research. The present work aims to investigate the behaviour of a Small Modular Reactor during severe accident conditions. In order to perform these analyses, a SMR has been studied for the European reference severe accident analysis code ASTEC, developed by IRSN and GRS. In the thesis will be described in detail the IRIS Small Modular Reactor; the reference reactor chosen to develop the ASTEC input deck. The IRIS model was developed in the framework of a research collaboration with the IRSN development team. In the thesis will be described systematically the creation of the ASTEC IRIS input deck: the nodalization scheme adopted, the solution used to simulate the passive safety systems and the strong interaction between the reactor vessel and the containment. The ASTEC SMR model will be tested against the RELAP-GOTHIC coupled code model, with respect to a Design Basis Accident, to evaluate the capability of the ASTEC code on reproducing correctly the behaviour of the nuclear system. Once the model has been validated, a severe accident scenario will be simulated and the obtained results along with the nuclear system response will be analysed.

Crystallization of Escherichia coli Catabolite Gene Activator Protein with its DNA Binding Site: The use of Modular DNA

To obtain crystals of the Escherichia coli catabolite gene activator protein (CAP) complexed with its DNA-binding site, we have searched for crystallization conditions with 26 different DNA segments ≥28 base-pairs in length that explore a variety of nucleotide sequences, lengths, and extended 5′ or 3′ termini. In addition to utilizing uninterrupted asymmetric lac site sequences, we devised a novel approach of synthesizing half-sites that allowed us to efficiently generate symmetric DNA segments with a wide variety of extended termini and lengths in the large size range (≥28 bp) required by this protein. We report three crystal forms that are suitable for X-ray analysis, one of which (crystal form III) gives measurable diffraction amplitudes to 3 Å resolution. Additives such as calcium, n-octyl-β-d-glucopyranoside and spermine produce modest improvements in the quality of diffraction from crystal form III. Adequate stabilization of crystal form III is unexpectedly complex, requiring a greater than tenfold reduction in the salt concentration followed by addition of 2-methyl-2,4-pentanediol and then an increase in the concentration of polyethylene glycol.

Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.

Computations of Vector-Valued Siegel Modular Forms

We carry out some computations of vector-valued Siegel modular forms of degree two, weight (k, 2) and level one, and highlight three experimental results: (1) we identify a rational eigenform in a three-dimensional space of cusp forms; (2) we observe that non-cuspidal eigenforms of level one are not always rational; (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. (C) 2013 Elsevier Inc. All rights reserved.

Verifying Harder's Conjecture for Classical and Siegel Modular Forms

A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form. Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.

Zeros of Weakly Holomorphic Modular Forms of Levels 2 and 3

Let M-k(#)(N) be the space of weakly holomorphic modular forms for Gamma(0)(N) that are holomorphic at all cusps except possibly at infinity. We study a canonical basis for M-k(#)(2) and M-k(#)(3) and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a lower boundary arc of the fundamental domain.

Enzymatic formation of modular cell-instructive fibrin analogs for tissue engineering

The molecular engineering of cell-instructive artificial extracellular matrices is a powerful means to control cell behavior and enable complex processes of tissue formation and regeneration. This work reports on a novel method to produce such smart biomaterials by recapitulating the crosslinking chemistry and the biomolecular characteristics of the biopolymer fibrin in a synthetic analog. We use activated coagulation transglutaminase factor XIIIa for site-specific coupling of cell adhesion ligands and engineered growth factor proteins to multiarm poly(ethylene glycol) macromers that simultaneously form proteolytically sensitive hydrogel networks in the same enzyme-catalyzed reaction. Growth factor proteins are quantitatively incorporated and released upon cell-derived proteolytic degradation of the gels. Primary stromal cells can invade and proteolytically remodel these networks both in an in vitro and in vivo setting. The synthetic ease and potential to engineer their physicochemical and bioactive characteristics makes these hybrid networks true alternatives for fibrin as provisional drug delivery platforms in tissue engineering.