Fabrice Mahé

Embedded Runge–Kutta scheme for step-size control in the interaction picture method

Abstract When solving certain evolution type PDEs such as the Schrodinger equation, the Interaction Picture method is a valuable alternative to Split-Step methods. The Interaction Picture method has good computational features when used together with the standard 4th order Runge–Kutta scheme (giving rise to the RK4-IP method). In this paper we present an embedded Runge–Kutta scheme with orders 3 and 4 with the aim to deliver an estimation of the local error for adaptive step-size control purposes in the Interaction Picture method. The corresponding ERK4(3)-IP method preserves the features of the RK4-IP method and provides a local error estimate at no significant extra cost.

Kinetic behaviour investigations and crystal structure of nitric acid dihydrate

X-ray powder diffraction experiments are performed to prove the possible crystallization of nitric acid dihydrate (HNO(3).2H(2)O, further denoted NAD) and to determine the best thermal conditions for growing a single crystal. It is shown that the kinetic behaviour of NAD strongly depends on the preliminary thermal treatment. One good single crystal obtained by an in situ adapted Bridgman method procedure enabled determination of the crystal structure. The intensities of diffracted lines with h odd are all very weak. The H atom of nitric acid is delocalized to one water molecule leading to an association of equimolar nitrate (NO(3)(-)) and an H(5)O(2)(+) ionic group. The asymmetric unit contains two such molecules. These two molecules are related by a pseudo a/2 translation (with a 0.3 A mean atomic distance difference), except for one H atom of the water molecules (0.86 A) because of their different orientations in the two molecules. The two molecules, linked by very strong hydrogen bonds, are arranged in layers. Two layers which are linked by weaker hydrogen bonds are approximately oriented along the c axis. The structure may be described by translations of this set of two layers along the c axis without hydrogen bonds leading to a two-dimensional hydrogen-bond network. The structures of the monohydrate (NAM) and trihydrate (NAT) are re-determined for comparisons. These structures may be described by one- and three-dimensional hydrogen-bond networks, respectively.

A new crystalline phase of nitric acid dihydrate.

The crystal structure of a new high-temperature phase of nitric acid dihydrate, HNO(3).2H(2)O, has been determined at 225 K by single-crystal X-ray diffraction. The H atom of the nitric acid is delocalized to one water molecule, leading to an association of equimolar NO(3)(-) and H(5)O(2)(+) ionic groups. The asymmetric unit contains two molecules of HNO(3).2H(2)O. The two independent molecules are related by a pseudo-twofold c axis, by a translation of 0.54 (approximately (1/2)) along b, with a mean atomic distance difference of 0.3 A, except for one H atom of the water molecules (1.5 A), because of their different orientations in the two molecules. The two independent molecules, linked by strong hydrogen bonds, are arranged in layers. These layers are linked by weaker hydrogen bonds oriented approximately along the c axis. A three-dimensional hydrogen-bond network is observed.

A guided mode in the range of the radiation modes for a rib waveguide

The stratified cladding of integrated optical waveguides is dispersive, which induces quite original phenomena. We present an example of a dielectric waveguide for which there exists a guided mode which propagates faster than some waves in the stratified cladding. Such a guide presents a specific symmetry and the key point is a separate study of the symmetrical and antisymmetrical modes.

A new mathematical model of bacterial interactions in two-species oral biofilms

Periodontitis are bacterial inflammatory diseases, where the bacterial biofilms present on the tooth-supporting tissues switch from a healthy state towards a pathogenic state. Among bacterial species involved in the disease, Porphyromonas gingivalis has been shown to induce dysbiosis, and to induce virulence of otherwise healthy bacteria like Streptococcus gordonii. During biofilm development, primary colonizers such as S. gordonii first attach to the surface and allow the subsequent adhesion of periodontal pathogens such as P. gingivalis. Interactions between those two bacteria have been extensively studied during the adhesion step of the biofilm. The aim of the study was to understand interactions of both species during the growing phase of the biofilm, for which little knowledge is available, using a mathematical model. This two-species biofilm model was based on a substrate-dependent growth, implemented with damage parameters, and validated thanks to data obtained on experimental biofilms. Three different hypothesis of interactions were proposed and assayed using this model: independence, competition between both bacteria species, or induction of toxicity by one species for the other species. Adequacy between experimental and simulated biofilms were found with the last hypothetic mathematical model. This new mathematical model of two species bacteria biofilms, dependent on different substrates for growing, can be applied to any bacteria species, environmental conditions, or steps of biofilm development. It will be of great interest for exploring bacterial interactions in biofilm conditions.

Improved integrated resonators in polymer technology for tunable filter

In order to create thermally tunable filter, we fabricate integrated micro-ring resonators with specific polymers. Their high index contrast (Δn ~ 0.15 at the wavelength of 1550 nm) allows to make small size waveguides (typically with cross sections of 1.2 × 1.5 μm2). We study the impact of different ring radii and gaps on the response of filters. Compared to the state of the art with polymers, we have obtained ring resonators with good characteristics. These results and the high thermo-optic coefficient of polymers enable us to plan the creation of thermally tunable resonators. For that purpose, we develop a thermal model of the polymer waveguide behaviour in order to minimize the electrical consumption of a tunable filter. First experiments of thermal tunability of the micro-ring filter are also reported to work on a range of 40 °C giving a 5 nm shift of the dropped wavelength.

On Nonlinear Inverse Problems of Heat Transfer with Radiation Boundary Conditions: Application to Dehydration of Gypsum Plasterboards Exposed to Fire

The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions . Numerical simulations illustrate several numerical optimization methods, examples, and realistic cases, in which several interesting phenomena are observed. A large amount of computational effort is required to solve the coupled state equation and the adjoint equation (which is backwards in time), and the algebraic gradient equation (which implements the coupling between the adjoint and control variables). The state and adjoint equations are solved using the finite element method.

The pVHL 172 isoform is not a tumor suppressor and up-regulates a subset of pro-tumorigenic genes including TGFB1 and MMP13

The von Hippel-Lindau (VHL) tumor suppressor gene is often deleted or mutated in ccRCC (clear cell renal cell carcinoma) producing a non-functional protein. The gene encodes two mRNA, and three protein isoforms (pVHL213, pVHL160 and pVHL172). The pVHL protein is part of an E3 ligase complex involved in the ubiquitination and proteasomal degradation of different proteins, particularly hypoxia inducible factors (HIF) that drive the transcription of genes involved in the regulation of cell proliferation, angiogenesis or extracellular matrix remodelling. Other non-canonical (HIF-independent) pVHL functions have been described. A recent work reported the expression of the uncharacterized protein isoform pVHL172 which is translated from the variant 2 by alternative splicing of the exon 2. This splice variant is sometimes enriched in the ccRCCs and the protein has been identified in the respective samples of ccRCCs and different renal cell lines. Functional studies on pVHL have only concerned the pVHL213 and pVHL160 isoforms, but no function was assigned to pVHL172. Here we show that pVHL172 stable expression in renal cancer cells does not regulate the level of HIF, exacerbates tumorigenicity when 786-O-pVHL172 cells were xenografted in mice. The pVHL172-induced tumors developed a sarcomatoid phenotype. Moreover, pVHL172 expression was shown to up regulate a subset of pro-tumorigenic genes including TGFB1, MMP1 and MMP13. In summary we identified that pVHL172 is not a tumor suppressor. Furthermore our findings suggest an antagonistic function of this pVHL isoform in the HIF-independent aggressiveness of renal tumors compared to pVHL213.The von Hippel-Lindau (VHL) tumor suppressor gene is often deleted or mutated in ccRCC (clear cell renal cell carcinoma) producing a non-functional protein. The gene encodes two mRNA, and three protein isoforms (pVHL213, pVHL160 and pVHL172). The pVHL protein is part of an E3 ligase complex involved in the ubiquitination and proteasomal degradation of different proteins, particularly hypoxia inducible factors (HIF) that drive the transcription of genes involved in the regulation of cell proliferation, angiogenesis or extracellular matrix remodelling. Other non-canonical (HIF-independent) pVHL functions have been described. A recent work reported the expression of the uncharacterized protein isoform pVHL172 which is translated from the variant 2 by alternative splicing of the exon 2. This splice variant is sometimes enriched in the ccRCCs and the protein has been identified in the respective samples of ccRCCs and different renal cell lines. Functional studies on pVHL have only concerned the pVHL213 and pVHL160 isoforms, but no function was assigned to pVHL172. Here we show that pVHL172 stable expression in renal cancer cells does not regulate the level of HIF, exacerbates tumorigenicity when 786-O-pVHL172 cells were xenografted in mice. The pVHL172-induced tumors developed a sarcomatoid phenotype. Moreover, pVHL172 expression was shown to up regulate a subset of pro-tumorigenic genes including TGFB1, MMP1 and MMP13. In summary we identified that pVHL172 is not a tumor suppressor. Furthermore our findings suggest an antagonistic function of this pVHL isoform in the HIF-independent aggressiveness of renal tumors compared to pVHL213.

Cathodoluminescence hyperspectral analysis of whispering gallery modes in active semiconductor wedge resonators

Whispering gallery mode resonators are key devices for integrated photonics. Despite their generalization in fundamental and applied science, information on spatial confinement of light in these structures is mostly retrieved from purely spectral analysis. In this work, we present a detailed spectral and spatial characterization of whispering gallery modes in active semiconductor microdisk resonators by use of hyperspectral cathodoluminescence. By comparing our experimental findings to finite element simulations, we demonstrate that the combination of spectral and spatial measurements enables unique identification of the modes and even reveals specific features of the microresonator geometry, such as a wedge profile.

Exemple d'un mode guidé plongé parmi les modes de radiation pour un guide ruban

The stratified cladding of integrated optical waveguides is dispersive, which induces quite original phenomena. We present an example of a dielectric waveguide for which there exists a guided mode which propagates faster than some waves in the stratified cladding. Such a guide presents a specific symmetry and the key point is a separate study of the symmetrical and antisymmetrical modes.