Comparison of stochastic and interval methods for uncertainty quantification of metal forming processes

Various sources of uncertainty can arise in metal forming processes, or their numerical simulation, or both, such as uncertainty in material behavior, process conditions, and geometry. Methods from the domain of uncertainty quantification can help assess the impact of such uncertainty on metal forming processes and their numerical simulation, and they can thus help improve robustness and predictive accuracy. In this paper, we compare stochastic methods and interval methods, two classes of methods receiving broad attention in the domain of uncertainty quantification, through their application to a numerical simulation of a sheet metal forming process.     

Alternative strategies for the stereoselective synthesis of enantioenriched 6-arylated piperidin-2-ones

Two alternative synthetic approaches to a variety of enantioenriched 6-arylated piperidin-2-ones have been developed. The first one is based on the hydrogenation of suitably arylated chiral cyclic enehydrazides. The second approach relies on the asymmetric catalytic hydrogenation of the corresponding N-alkylated precursors.     

Adaptation of the Generic PDE’s Results to the Notion of Prevalence

Many generic results have been proved, especially concerning the qualitative behaviour of solutions of partial differential equations. Recently, a new notion of “almost always”, the prevalence, has been developed for vectorial spaces. This notion is interesting since, for example, prevalence sets are equivalent to the full Lebesgue measure sets in finite dimensional spaces. The purpose of this article is to adapt the generic PDE’s results to the notion of prevalence. In particular, we consider the cases where Sard–Smale theorems or arguments of analytic perturbations of the parameters are used. Dedicated to Professor Pavol Brunovsky in honor of his 70th birthday.     

Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint

We report the results of a study on the spectral properties of Laplace and Stokes operators modified with a volume penalization term designed to approximate Dirichlet conditions in the limit when a penalization parameter, \(\eta \) , tends to zero. The eigenvalues and eigenfunctions are determined either analytically or numerically as functions of \(\eta \) , both in the continuous case and after applying Fourier or finite difference discretization schemes. For fixed \(\eta \) , we find that only the part of the spectrum corresponding to eigenvalues \(\lambda \lesssim \eta ^{-1}\) approaches Dirichlet boundary conditions, while the remainder of the spectrum is made of uncontrolled, spurious wall modes. The penalization error for the controlled eigenfunctions is estimated as a function of \(\eta \) and \(\lambda \) . Surprisingly, in the Stokes case, we show that the eigenfunctions approximately satisfy, with a precision \(O(\eta )\) , Navier slip boundary conditions with slip length equal to \(\sqrt{\eta }\) . Moreover, for a given discretization, we show that there exists a value of \(\eta \) , corresponding to a balance between penalization and discretization errors, below which no further gain in precision is achieved. These results shed light on the behavior of volume penalization schemes when solving the Navier–Stokes equations, outline the limitations of the method, and give indications on how to choose the penalization parameter in practical cases.     

Exponentiality of First Passage Times of Continuous Time Markov Chains

Let \((X,\mathbb{P}_{x})\) be a continuous time Markov chain with finite or countable state space S and let T be its first passage time in a subset D of S. It is well known that if μ is a quasi-stationary distribution relative to T, then this time is exponentially distributed under  \(\mathbb {P}_{\mu}\) . However, quasi-stationarity is not a necessary condition. In this paper, we determine more general conditions on an initial distribution μ for T to be exponentially distributed under  \(\mathbb{P}_{\mu}\) . We show in addition how quasi-stationary distributions can be expressed in terms of any initial law which makes the distribution of T exponential. We also study two examples in branching processes where exponentiality does imply quasi-stationarity.     

Nucleation and Growth of Chrysotile Nanotubes in H2SiO3/MgCl2/NaOH Medium at 90 to 300 °C

Herein, we report new insights into the nucleation and growth processes of chrysotile nanotubes by using batch and semi‐continuous experiments. For the synthesis of this highly carcinogenic material, the influences of temperature (90, 200, and 300 °C), Si/Mg molar ratio, and reaction time were investigated. From the semi‐continuous experiments (i.e., sampling of the reacting suspension over time) and solid‐state characterization of the collected samples by XRPD, TGA, FTIR spectroscopy, and FESEM, three main reaction steps were identified for chrysotile nucleation and growth at 300 °C: 1) formation of the proto‐serpentine precursor within the first 2 h of the reaction, accompanied by the formation of brucite and residual silica gel; 2) spontaneous nucleation and growth of chrysotile between about 3 and 8 h reaction time, through a progressive dissolution of the proto‐serpentine, brucite, and residual silica gel; and 3) Ostwald ripening growth of chrysotile from 8 to 30 h reaction time, as attested to by BET and FESEM measurements. Complementary results from batch experiments confirmed a significant influence of the reaction temperature on the kinetics of chrysotile formation. However, FESEM observations revealed some formation of chrysotile nanotubes at low temperatures (90 °C) after 14 days of reaction. Finally, doubling the Si/Mg molar ratio promoted the precipitation of pure smectite (stevensite‐type) under the same P (8.2 MPa)/T (300 °C)/pH (13.5) conditions.     

Multitasking Water‐Soluble Synthetic G‐Quartets: From Preferential RNA–Quadruplex Interaction to Biocatalytic Activity

Natural G‐quartets, a cyclic and coplanar array of four guanine residues held together through a Watson–Crick/Hoogsteen hydrogen‐bond network, have received recently much attention due to their involvement in G‐quadruplex DNA, an alternative higher‐order DNA structure strongly suspected to play important roles in key cellular events. Besides this, synthetic G‐quartets (SQ), which artificially mimic native G‐quartets, have also been widely studied for their involvement in nanotechnological applications (i.e., nanowires, artificial ion channels, etc.). In contrast, intramolecular synthetic G‐quartets (iSQ), also named template‐assembled synthetic G‐quartets (TASQ), have been more sparingly investigated, despite a technological potential just as interesting. Herein, we report on a particular iSQ named ^PNADOTASQ, which demonstrates very interesting properties in terms of DNA and RNA interaction (notably its selective recognition of quadruplexes according to a bioinspired process) and catalytic activities, through its ability to perform peroxidase‐like hemin‐mediated oxidations either in an autonomous fashion (i.e., as pre‐catalyst for TASQzyme reactions) or in conjunction with quadruplex DNA (i.e., as enhancing agents for DNAzyme processes). These results provide a solid scientific basis for TASQ to be used as multitasking tools for bionanotechnological applications.