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.

To cite this version:Stéphane Balac, Fabrice Mahé. Embedded Runge-Kutta scheme for step-size control in the interaction picture method. Computer Physics Communications, Elsevier, 2013, 184 (4) AbstractWhen solving certain evolution type PDE such as the Schrödinger 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 4with 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 provide a local error estimate at no significant extra cost.

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.