A convergent and precise finite element scheme for Landau–Lifschitz–Gilbert equation

In this paper, we propose a new scheme for the numerical integration of the Landau–Lifschitz–Gilbert (LLG) equations in their full complexity, in particular including stray-field interactions. The scheme is consistent up to order 2 (in time), and unconditionally stable. It combines a linear inner iteration with a non-linear renormalization stage for which a rigorous proof of convergence of the numerical solution toward a weak solution is given, when both space and time stepsizes tend to \(0\) . A numerical implementation of the scheme shows its performance on physically relevant test cases. We point out that to the knowledge of the authors this is the first finite element scheme for the LLG equations which enjoys such theoretical and practical properties.     

Synthesis of transparent silica aerogels using tetraalkylammonium fluoride catalysts

Tetraalkylammonium fluoride salts have been employed as catalysts for the synthesis of silica aerogels by a two-step, sol–gel method. Aerogel materials were characterized by N₂ physisorption and SEM. The effect of the type of catalyst on the optical transparency of obtained aerogels has been examined. It has been found that such compounds allow the synthesis of silica aerogels with the highest optical transmittance ever reported for such materials. The optimal catalysts are tetrabutyl and tetraoctyl ammonium fluoride, with which aerogels with transparency as high as 96% and extinction coefficient as low as 3.5 m⁻¹ can be prepared.     

Release studies of corrosion inhibitors from cerium titanium oxide nanocontainers

Cerium titanium oxide nanocontainers were synthesized through a two-step process and then loaded with corrosion inhibitors 2-mercaptobenzothiazole (2-MB) and 8-hydroxyquinoline (8-HQ). First, polystyrene nanospheres (PS) were produced using polymerization in suspension. Second, the PS spheres were coated via the sol–gel method to form a cerium titanium oxide layer. Finally, the nanocontainers were made by calcination of the coated PS nanospheres. The size of the containers was 180 ± 10 nm as determined by Scanning Electron Microscopy (SEM). X-Ray Diffraction Analysis (XRD) showed that the nanocontainers consist of anatase and cerianite crystalline phases. The presence and loading of the inhibitors in the nanocontainers was confirmed with Fourier Transform Infrared Spectroscopy (FT–IR) and Thermo Gravimetric Analysis (TGA), respectively. TGA revealed the amount of 10.43 and 4.61% w/w for 2-MB and 8-HQ in the nanocontainers, respectively. Furthermore, the release kinetics of the inhibitors from the nanocontainers was studied in corrosive environment using electrochemical impedance spectroscopy (EIS) in the presence of aluminum alloys 2024-T3 (AA2024-T3).     

Probing the Mechanism of Allylic Substitution of Morita–Baylis–Hillman Acetates (MBHAs) by using the Silyl Phosphonite Paradigm: Scope and Applications of a Versatile Transformation

A P?C bond‐forming reaction between silyl phosphonites and Morita–Baylis–Hillman acetates (MBHAs) is explored as a general alternative towards medicinally relevant β‐carboxyphosphinic structural motifs. Conversion rates of diversely substituted MBHAs to phosphinic acids 9 or 14 that were recorded by using ³¹P NMR spectroscopy revealed unexpected reactivity differences between ester and nitrile derivatives. These kinetic profiles and DFT calculations support a mechanistic scenario in which observed differences can be explained from the “lateness” of transition states. In addition, we provide experimental evidence suggesting that enolates due to initial P‐Michael addition are not formed. Based on the proposed mechanistic scenario in conjunction with DFT calculations, an interpretation of the E/Z stereoselectivity differences between ester and nitriles is proposed. Synthetic opportunities stemming from this transformation are presented, which deal with the preparation of several synthetically capricious phosphinic building blocks, whose access through the classical P‐Michael synthetic route is not straightforward.     

The thermo-mechanical behavior of thin metal films under nanosecond laser pulse excitation above the thermoelastic regime

This article presents experimental results supported by advanced three-dimensional modeling for the dynamics emerging from the interaction of nanosecond laser pulses with thin metal films on dielectric substrates, especially at the melting and ablation regimes. Matter dynamics, such as the generation and propagation of surface acoustic waves and permanent deformations, are imaged with the use of a very high spatial and temporal resolution interferometric method accompanied by white-light interferometry. A three-dimensional finite element model is developed aiming to fully describe the spatiotemporal dynamics and predict with high accuracy the thermo-mechanical phenomena around melting and ablation regimes where phase changes take place. The ability of very high spatial and temporal resolution, the whole-field three-dimensional imaging as well as the simultaneous study of the laser pulse–thin film interaction regimes, makes this study valuable for applications where detailed knowledge of the thermo-mechanical behavior of matter under pulsed laser excitation is critical.     

A convergent finite element approximation for Landau–Lifschitz–Gilbert equation

This paper describes a finite element formulation for Landau–Lifschitz–Gilbert equation (LLGE) that is proved to converge as the time and space steps tend to 0 toward a weak solution of LLGE. An order two (in time) scheme is also given and numerical results are presented showing the applicability of the method.     

On the distribution of integer points of rational curves

Let F(X,Y) be an absolutely irreducible polynomial in such that the algebraic curve C: F(X,Y) = 0 has infinitely many integer points. In this paper we obtain an explicit estimate on the distribution of integer points of C.