Global wellposedness for quasi-linear symmetric hyperbolic systems with regularized coefficients

Following the abstract setting of [8] and using the global results of [2], global wellposedness and regularity results are proved for the solutions of quasi-linear symmetric hyperbolic systems with bounded coefficients which are regularized by a convolution in the space variables with a regularizing function. In the case of unbounded regularized coefficients, local existence of classical solutions is proved, as well as uniqueness and regularity of (not necessarily existing) global weak solutions with initial value in a Sobolev space. As the regularizing function tends to Dirac's δ, local-in-time convergence to the classical solution of the non-regularized problem is proved.     

Symmetry Groups and Non-Planar Collisionless Action-Minimizing Solutions of the Three-Body Problem in Three-Dimensional Space

Periodic and quasi-periodic solutions of the n-body problem can be found as minimizers of the Lagrangian action functional restricted to suitable spaces of symmetric paths. The main purpose of this paper is to develop a systematic approach to the equivariant minimization for the three-body problem in three-dimensional space. First we give a finite complete list of symmetry groups fitting to the minimization of the action, with the property that any other symmetry group can be reduced to be isomorphic to one of these representatives. A second step is to prove that the resulting (local and global) symmetric action-minimizers are always collisionless (when they are not already bound to collisions). Furthermore, we prove some results which address the question of whether minimizers are planar or non-planar; as a consequence of our theory we will give general criteria for a symmetry group to yield planar or homographic minimizers (either homographic or not, as in the Chenciner-Montgomery eight solution). On the other hand we will provide a rigorous proof of the existence of some interesting one-parameter families of periodic and quasi-periodic non-planar orbits. These include the choreographic Marchal's P₁₂ family with equal masses – together with a less-symmetric choreographic family (which anyway probably coincides with the P₁₂ family).     

Sub-Riemannian Curvature in Contact Geometry

We compare different notions of curvature on contact sub-Riemannian manifolds. In particular, we introduce canonical curvatures as the coefficients of the sub-Riemannian Jacobi equation. The main result is that all these coefficients are encoded in the asymptotic expansion of the horizontal derivatives of the sub-Riemannian distance. We explicitly compute their expressions in terms of the standard tensors of contact geometry. As an application of these results, we obtain a sub-Riemannian version of the Bonnet–Myers theorem that applies to any contact manifold.     

Holderian Weak Invariance Principle for Stationary Mixing Sequences

We provide some sufficient mixing conditions on a strictly stationary sequence in order to guarantee the weak invariance principle in Hölder spaces. Strong mixing and \(\rho \)-mixing conditions are investigated as well as \(\tau \)-dependent sequences. The main tools are deviation inequalities for mixing sequences.     

Uniaxial Modeling of Multivariant Shape-Memory Materials with Internal Sublooping using Dissipation Functions

Models for the macroscopic behavior of Shape Memory Materials can be conveniently constructed within the Ziegler–Green–Naghdi framework where all the constitutive information is encoded in two ingredients: the free energy and the dissipation function. In a previous work, we have proposed various expressions for the basic functions suitable to model pseudoelasticity with complete transformations cycles. In this work we consider additional effects due to Martensite reorientation and to transformation reversal prior to transformation completion. The new constitutive model allows for the modeling of a variety of effects including: shape memory associated with thermally induced transformation, internal pseudoelastic subloops and the determination of limit cycles associated with repetitive stress cycling.     

Models for one-variant shape memory materials based on dissipation functions

Some simple models for the macroscopic behavior of shape memory materials whose microstructure can be described as a mixture of two phases are derived on the basis of a free energy and a dissipation function. Keeping a common expression for the free energy, each model is based on a different expression for the dissipation function. Temperature-induced as well as isothermal, adiabatic and convective stress-induced transformations are studied. Attention is paid to closed form solutions, comparison among the models and parameter identification.     

Opening the Pandora's jar of molecule‐to‐material conversion in chemical vapor deposition: Insights from theory

First‐principles modeling can be a powerful tool for the understanding and optimization of bottom‐up processes for nanomaterials fabrication, such as chemical vapor deposition (CVD), a key technology for the development of advanced systems and devices. Molecule‐to‐material conversion by CVD involves complex chemical phenomena, which are often obscure and still largely unexplored. A proper modeling would require high level of accuracy, large sized models and should include both temperature effects and statistical sampling of reactive events. By presenting a few selected examples, this perspective surveys such problems and discusses currently available approaches for their solution. Possible strategies for future advances in the field are also highlighted. © 2013 Wiley Periodicals, Inc.     

Coke formation during the methanol-to-olefin conversion: in situ microspectroscopy on individual H-ZSM-5 crystals with different Brønsted acidity

Coke formation during the methanol‐to‐olefin (MTO) conversion has been studied at the single‐particle level with in situ UV/Vis and confocal fluorescence microscopy. For this purpose, large H‐ZSM‐5 crystals differing in their Si/Al molar ratio have been investigated. During MTO, performed at 623 and 773 K, three major UV/Vis bands assigned to different carbonaceous deposits and their precursors are observed. The absorption at 420 nm, assigned to methyl‐substituted aromatic compounds, initiates the buildup of the optically active coke species. With time‐on‐stream, these carbonaceous compounds expand in size, resulting in the gradual development of a second absorption band at around 500 nm. An additional broad absorption band in the 600 nm region indicates the enhanced formation of extended carbonaceous compounds that form as the reaction temperature is raised. Overall, the rate of coke formation decreases with decreasing aluminum content. Analysis of the reaction kinetics indicates that an increased Brønsted acid site density facilitates the formation of larger coke species and enhances their formation rate. The use of multiple excitation wavelengths in confocal fluorescence microscopy enables the localization of coke compounds with different molecular dimensions in an individual H‐ZSM‐5 crystal. It demonstrates that small coke species evenly spread throughout the entire H‐ZSM‐5 crystal, whereas extended coke deposits primarily form near the crystal edges and surfaces. Polarization‐dependent UV/Vis spectroscopy measurements illustrate that extended coke species are predominantly formed in the straight channels of H‐ZSM‐5. In addition, at higher temperatures, fast deactivation leads to the formation of large aromatic compounds within channel intersections and at the external zeolite surface, where the lack of spatial restrictions allows the formation of graphite‐like coke.     

The porosity, acidity, and reactivity of dealuminated zeolite ZSM-5 at the single particle level: the influence of the zeolite architecture

A combination of atomic force microscopy (AFM), high‐resolution scanning electron microscopy (HR‐SEM), focused‐ion‐beam scanning electron microscopy (FIB‐SEM), X‐ray photoelectron spectroscopy (XPS), confocal fluorescence microscopy (CFM), and UV/Vis and synchrotron‐based IR microspectroscopy was used to investigate the dealumination processes of zeolite ZSM‐5 at the individual crystal level. It was shown that steaming has a significant impact on the porosity, acidity, and reactivity of the zeolite materials. The catalytic performance, tested by the styrene oligomerization and methanol‐to‐olefin reactions, led to the conclusion that mild steaming conditions resulted in greatly enhanced acidity and reactivity of dealuminated zeolite ZSM‐5. Interestingly, only residual surface mesoporosity was generated in the mildly steamed ZSM‐5 zeolite, leading to rapid crystal coloration and coking upon catalytic testing and indicating an enhanced deactivation of the zeolites. In contrast, harsh steaming conditions generated 5–50 nm mesopores, extensively improving the accessibility of the zeolites. However, severe dealumination decreased the strength of the Brønsted acid sites, causing a depletion of the overall acidity, which resulted in a major drop in catalytic activity.