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).     

Sol‐to‐Gel Transition in Fast Evaporating Systems Observed by in Situ Time‐Resolved Infrared Spectroscopy

The in situ observation of a sol‐to‐gel transition in fast evaporating systems is a challenging task and the lack of a suitable experimental design, which includes the chemistry and the analytical method, has limited the observations. We synthesise an acidic sol, employing only tetraethylorthosilicate, SiCl₄ as catalyst and deuterated water; the absence of water added to the sol allows us to follow the absorption from the external environment and the evaporation of deuterated water. The time‐resolved data, obtained by attenuated total reflection infrared spectroscopy on an evaporating droplet, enables us to identify four different stages during evaporation. They are linked to specific hydrolysis and condensation rates that affect the uptake of water from external environment. The second stage is characterized by a decrease in hydroxyl content, a fast rise of condensation rate and an almost stationary absorption of water. This stage has been associated with the sol‐to‐gel transition.     

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.     

Interaction between inner and outer layer in drag-reduced turbulent flows

Effects of wall-based skin-friction drag reduction strategies on the statistical properties of large-scale motions in moderate Reynolds number turbulent flows have been investigated by exploiting Direct Numerical Simulation of turbulent channels. To educe large scales, a new efficient parallel distributed memory algorithm has been implemented which delivers data-driven modes of increasing characteristic lengthscales: the Fast and Adaptive Bidimensional Empirical Mode Decomposition (FABEMD). The influence of wall-based skin friction reduction on large scales is studied by comparing single point statistics, such as r.m.s. fluctuations, and two-point statistics, as cross-correlation functions in controlled and uncontrolled channel flow fields at constant friction Reynolds number. The traditional way of observing large-scale footprinting at the wall, as cross-correlation of the streamwise velocity components at different wall distances, has been found to be unreliable when comparing drag-reduced flows, due to the arbitrary choice of a reference plane in the logarithmic layer. A more sound way of observing the footprinting via the correlation of the streamwise velocity with the friction velocity is addressed and shows an increase of the footprinting in drag-reduced flows. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)