Unfolding of Surfaces

This paper deals with the approximation of the unfolding of a smooth globally developable surface (i.e. "isometric" to a domain of ) with a triangulation. We prove the following result: let T_n be a sequence of globally developable triangulations which tends to a globally developable smooth surface S in the Hausdorff sense. If the normals of T_n tend to the normals of S, then the shape of the unfolding of T_n tends to the shape of the unfolding of S. We also provide several examples: first, we show globally developable triangulations whose vertices are close to globally developable smooth surfaces; we also build sequences of globally developable triangulations inscribed on a sphere, with a number of vertices and edges tending to infinity. Finally, we also give an example of a triangulation with strictly negative Gauss curvature at any interior point, inscribed in a smooth surface with a strictly positive Gauss curvature. The Gauss curvature of these triangulations becomes positive (at each interior vertex) only by switching some of their edges.     

Height Preserving Minimal Interval Extensions

We consider minimal interval extensions of a partial order which preserve the height of each vertex. We show that minimal interval extensions having this property bijectively correspond to the maximal chains of a sublattice of the lattice of maximal antichains of the given order. We show that they also correspond to the set of minimal interval extensions of a certain extension of this order.     

A comprehensive study of the spontaneous formation of nanoassemblies in water by a "lock-and-key" interaction between two associative polymers

Nanoassemblies (NAs) with sizes ranging from 60 to 160nm were spontaneously formed in water after mixing a host polymer (polymerized cyclodextrin (pβ-CD)) and a guest polymer (dextran grafted with lauroyl side chains (MD)). The combination of microscopy, dynamic light scattering (DLS), nuclear magnetic resonance ((1)H NMR), isothermal titration calorimetry (ITC) and molecular modelling was used to investigate the parameters which govern the association between MD and pβ-CD. Remarkably, when pβ-CD was progressively added to a solution of MD, NAs with a well-defined diameter were spontaneously formed and their diameter was constant whatever the composition of the system. According to NMR data, almost all the alkyl chains of MD were included into CDs' cavities of the polymer when the molar ratio lauroyl chain (C(12))/CD was ?1. The hydrophobic interaction between C(12) and the hydrophobic cavities of CDs appears as the main driving force for NAs' formation, with a minor contribution arising from van der Waals' interactions. The inclusion of C(12) into β-CD cavities is almost a completely enthalpy-driven process, whereas the MD-C(12)/pβ-CD interaction was found to be an entropy-driven process. Major conclusions which can be drawn from these studies are that the interactions between the two polymers are restricted neither by the MD substitution yield, nor by the micellization of MD. The simultaneous effects of several CD linked together in pβ-CD and of many alkyl chains grafted on dextran were necessary to generate these stable NAs.     

An SPH multi‐fluid model based on quasi buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios

We introduce a smoothed particle hydrodynamics (SPH) concept for the stabilization of the interface between 2 fluids. It is demonstrated that the change in the pressure gradient across the interface leads to a force imbalance. This force imbalance is attributed to the particle approximation implicit to SPH. To stabilize the interface, a pressure gradient correction is proposed. In this approach, the multi‐fluid pressure gradients are related to the (gravitational and fluid) accelerations. This leads to a quasi‐buoyancy correction for hydrostatic (stratified) flows, which is extended to nonhydrostatic flows. The result is a simple density correction that involves no parameters or coefficients. This correction is included as an extra term in the SPH momentum equation. The new concept for the stabilization of the interface is explored in 5 case studies and compared with other multi‐fluid models. The first case is the stagnant flow in a tank: The interface remains stable up to density ratios of 1:1000 (typical for water and air), in combination with artificial wave speed ratios up to 1:4. The second and third cases are the Rayleigh‐Taylor instability and the rising bubble, where a reasonable agreement between SPH and level‐set models is achieved. The fourth case is an air flow across a water surface up to density ratios of 1:100, artificial wave speed ratios of 1:4, and high air velocities. The fifth case is about the propagation of internal gravity waves up to density ratios of 1:100 and artificial wave speed ratios of 1:4. It is demonstrated that the quasi‐buoyancy model may be used to stabilize the interface between 2 fluids up to high density ratios, with real (low) viscosities and more realistic wave speed ratios than achieved by other weakly compressible SPH multi‐fluid models. Real wave speed ratios can be achieved as long as the fluid velocities are not very high. Although the wave speeds may be artificial in many cases, correct and realistic wave speed ratios are essential in the modelling of heat transfer between 2 fluids (eg, in engineering applications such as gas turbines).     

Modeling Phononic Crystals via the Weighted Relaxed Micromorphic Model with Free and Gradient Micro-Inertia

In this paper the relaxed micromorphic continuum model with weighted free and gradient micro-inertia is used to describe the dynamical behavior of a real two-dimensional phononic crystal for a wide range of wavelengths. In particular, a periodic structure with specific micro-structural topology and mechanical properties, capable of opening a phononic band-gap, is chosen with the criterion of showing a low degree of anisotropy (the band-gap is almost independent of the direction of propagation of the traveling wave). A Bloch wave analysis is performed to obtain the dispersion curves and the corresponding vibrational modes of the periodic structure. A linear-elastic, isotropic, relaxed micromorphic model including both a free micro-inertia (related to free vibrations of the microstructures) and a gradient micro-inertia (related to the motions of the microstructure which are coupled to the macro-deformation of the unit cell) is introduced and particularized to the case of plane wave propagation. The parameters of the relaxed model, which are independent of frequency, are then calibrated on the dispersion curves of the phononic crystal showing an excellent agreement in terms of both dispersion curves and vibrational modes. Almost all the homogenized elastic parameters of the relaxed micromorphic model result to be determined. This opens the way to the design of morphologically complex meta-structures which make use of the chosen phononic material as the basic building block and which preserve its ability of “stopping” elastic wave propagation at the scale of the structure.     

Plasma for special applications

Summary The large development of industrial plasma techniques is due to new understanding of chemical concepts of reactive gases excited by electron impact. In this way, it is possible to obtain larger operational facilities of the processes, i.e.: the elimination of wet treatment and flexibility of tools. Therefore, many engineers agree on the widespread application of these technologies.The numerous advantages of plasma techniques are realized by two different concepts according to the equilibrium of the reactive systems (atmospheric system with gas temperature = electronic temperature) or non-equilibrium systems (rotational temperature = translational temperature = 500° K — vibrational temperature = 500° K — vibrational temperature >3,100° K — electronic temperature > 1 to 2 eV).For the high pressure torch, both the thermal and chemical properties of the plasma mixture are employed at the same moment which lead to high temperature reactions, high kinetic rates, and short residence times. These tools are used today for extractive metallurgy, oil treatment, plasma spray, optical fibers, and production of high purity materials. We have chosen to present them through the example of silicon refining by a RF plasma torch. The multiphase extractive process controls the efficiency of the treatment. At the liquid-plasma interface the evaporation of the impurities is measured by emission spectroscopy with an optical fiber (K, Na, Mg). The working parameters of the system [plasma gas composition (O₂, H₂, Ar), Rf-power source, speed of the treatment] can be adjusted by such measures. The photovoltaic efficiency of the materials has been determined in correlation with the spectroscopic measurements.For the low pressure plasma reactor, the chemical properties are studied by measuring the vibrational level of the excited molecular species. For instance, reactive levels of vibrational states increase the kinetic rate by a factor of 10⁴ to 10⁶ with a gas temperature approaching room temperature. In this way, a large number of industrial applications has been developed with a glow discharge reactor and a corona discharge reactor essentially for surface treatment such as etching, grafting, polymerization, nitriding, deposition etc. We have chosen to explain the nitriding process of metals and silicon in order to point out the role of vibrational species and particularly, those of the NH molecules. These results are correlated with the evolution of the hardness of the material and the conversion rate of the reactive molecule.

---

Plasma für spezielle Anwendungen

Zusammenfassung Die starke Entwicklung industrieller Plasmaverfahren ist auf neue chemische Konzepte der Anregung von reaktiven Gasen durch Elektronenstöße zurückzuführen. So wird es möglich, die Durchführung des Prozesses besser zu steuern, d. h. eine nasse Behandlung zu vermeiden und flexibler zu sein. Entsprechend bevorzugen viele Ingenieure diese Verfahren.Die Vorteile der Plasmaverfahren kann man in verschiedenen Systemen realisieren, nämlich in reaktiven Systemen im thermischen Gleichgewicht (atmosphärischer Druck, wobei Gastemperatur und Elektronentemperatur gleich sind) oder in Systemen, die nicht im thermischen Gleichgewicht sind (Rotationstemperatur Elektronentemperatur oder Rotationstemperatur = Translationstemperatur = 500 K, Vibrationstemperatur >3100 K, Elektronentemperatur >1–2 eV).Im Falle eines bei hohem Druck betriebenen Plasmabrenners bewerkstelligen die thermischen und die chemischen Eigenschaften des Plasmas eine Reaktion bei hoher Temperatur, hohe Reaktionskonstanten und kurze Aufenthaltszeiten. Diese Verfahren werden heute eingesetzt in der extraktiven Metallurgie, in der Behandlung von Ölen, in der Plasmaspritztechnik und für die Herstellung von optischen Fasern und Reinststoffen. Sie werden in diesem Beitrag anhand der Darstellung von hochreinem Silicium in einem Hochfrequenzplasmareaktor besprochen. Die Ausbeute der Behandlung wird über einen vielphasigen Extraktionsprozeß gesteuert. Die Verflüchtigung von Verunreinigungen (K, Mg, Na) im Grenzbereich zwischen Flüssigphase und Plasma wird mit Hilfe von optischen Fasern emissionsspektrometrisch gemessen. Die Betriebsparameter des Systems und Zusammensetzung des Plasmagases (O₂, H₂, Ar), Hochfrequenzleistung, Reaktionsgeschwindigkeit werden hierüber gesteuert. Die photovoltaischen Eigenschaften des hergestellten Siliciums wurden untersucht und ihre Korrelation mit den spektroskopisch gemessenen Größen überprüft.Im Fall von Plasmareaktoren bei niedrigem Druck sind die chemischen Eigenschaften von den Vibrationsniveaus der angeregten Moleküle abhängig. Zum Beispiel nimmt die Reaktionsgeschwindigkeit bei einer Gastemperatur, die in der Nähe der Umgebungstemperatur liegt, infolge reaktiver Vibrationsniveaus um einen Faktor 10⁴ bis 10⁶ zu. Zahlreiche industrielle Anwendungen von Glimmentladungen oder Coronarentladungen wurden dementsprechend entwickelt, hauptsächlich für Oberflächenbehandlungen wie Ätzen, Implantieren, Polymerisieren, Nitrieren oder Beschichten. Anhand der Nitrierung von Metallen und von Silicium wird der Einfluß des Vibrationsniveaus, insbesondere von NH-Molekülen besprochen. Die Ergebnisse stehen in Zusammenhang mit der Härte des Materials sowie der Reaktionsrate des reaktiven Moleküls.

     

Lamb wave reflection at the free edge of a plate

This study concentrates on the reflection of Lamb waves at the free end of a plate. The conversion phenomena are examined in detail over a large frequency range and the energy conversion coefficients are obtained by three different ways: theoretically, numerically (finite element method) and experimentally. The experimental energy determination is obtained from the measurement of the plate normal displacements, by mean of a laser interferometer. All results are in relatively good agreement and the energy balance between incident and reflected waves is discussed in each case.     

Isotopic study of post-anthesis foliar incorporation of sulphur and nitrogen in wheat

Nitrogen (N) and sulphur (S) supplies have a strong influence on the quality and quantity of wheat storage proteins, which play an important role in the bread-making process. In order to relate the incorporation and distribution of foliar N and S fertilisers at the post-anthesis stage to the quality of wheat, 15N and 34S isotopes were used as tracers. The incorporation of these tracers in different plant parts (leaves, stems, ears) and in each storage protein fraction (gliadins, HMW and LMW glutenin subunits) was determined by isotopic ratio mass spectrometry coupled with an elemental analyser (EA-IRMS). By this means, the true recovery coefficient of N and S (TRCNfertiliser and TRCSfertiliser) and the N and S derived from fertilisers (Ndff and Sdff) could be determined. The TRCNfertiliser and TRCSfertiliser values of the different plant parts provide evidence of the applied N and S assimilation and translocation from wheat leaves to the seeds. The determination of Ndff and Sdff incorporated into storage proteins shows the efficiency and the influence of N and S incorporation into each storage protein fraction. Moreover, a favourable stage for fertiliser application can be determined by the TRCNfertiliser values in the grain and in the whole plant. The fertilisers enriched in stable isotope used in the culture techniques can be a means of understanding the effectiveness of fertilisers in the expression of wheat quality.     

Three-and two-dimensional calculations for the interface anisotropy dependence of magnetic properties of exchange-spring Nd2Fe(14)B/α-Fe multilayers with out-of-plane easy axes

Hysteresis loops,energy products and magnetic moment distributions of perpendicularly oriented Nd2Fe(14)B/α-Fe exchange-spring multilayers are studied systematically based on both three-dimensional(3D)and one-dimensional(1D)micromagnetic methods,focused on the influence of the interface anisotropy.The calculated results are carefully compared with each other.The interface anisotropy effect is very palpable on the nucleation,pinning and coercive fields when the soft layer is very thin.However,as the soft layer thickness increases,the pinning and coercive fields are almost unchanged with the increment of interface anisotropy though the nucleation field still monotonically rises.Negative interface anisotropy decreases the maximum energy products and increases slightly the angles between the magnetization and applied field.The magnetic moment distributions in the thickness direction at various applied fields demonstrate a progress of three-step magnetic reversal,i.e.,nucleation,evolution and irreversible motion of the domain wall.The above results calculated by two models are in good agreement with each other.Moreover,the in-plane magnetic moment orientations based on two models are different.The 3D calculation shows a progress of generation and disappearance of vortex state,however,the magnetization orientations within the film plane calculated by the 1D model are coherent.Simulation results suggest that negative interface anisotropy is necessarily avoided experimentally.