Penetration and blown air effect in granular media

Sand is known to oppose an increasing resistance to penetration with depth. This is different from what happens in liquids since granular media, usually nonthermal systems, oppose solid friction to the motion. We report another striking and "counterintuitive" difference between the penetration dynamics observed in sand and in liquids. When pushing a top-closed shell (e.g., an upside down glass) into a liquid, the trapped air increases the buoyancy and opposes the penetration. It is more difficult to push a top capped cylinder than an opened one vertically into liquids. In contrast, the penetration is considerably easier in dense sand when cylinders are top capped. In this discrete and biphasic medium, the trapped air escapes from the shell, fluidizes the sand, and eases the motion.     

Allylsilanes in "tin-free" oximation, alkenylation, and allylation of alkyl halides

Tin-free oximation, vinylation, and allylation of alkyl halides have been developed by using allylsilanes as di-tin surrogates. Initiation of the radical process with a peroxide provides the silyl radical, which can abstract a halogen from the corresponding alkyl halide. The resulting carbon-centered radical then adds to various acceptors, including a sulfonyloxime, a vinylsulfone, and an allylsulfone, leading to formation of the desired products along with the corresponding allylsulfone resulting from the reaction of the PhSO(2) radical with the allylsilane precursor. Better results were generally obtained with methallylsilane 1b than with 1a. This observation was rationalized by invoking the higher nucleophilicity of 1b and the faster β-fragmentation of the corresponding β-silyl radical intermediate. Calculation of the energy barrier for the β-fragmentation of a series of β-silyl radicals at the DFT level supported this hypothesis. Finally, a second version of these oximation and vinylation reactions, based on the utilization of 3-tris(trimethylsilyl)silylthiopropene, was devised, affording the desired oximes and olefins in reasonable yields. This strategy allowed the title reaction to be performed under milder conditions (AIBN, benzene, 80 °C), as a result of the easier β-fragmentation of the C-S bond as compared with the C-Si bond.     

Macroscopic Diffusion from a Hamilton-like Dynamics

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of Hamiltonian dynamics in a confined phase space: it is deterministic, periodic, reversible and conservative. Randomness enters the model as a way to model ignorance about initial conditions and interactions between the components of the system. The orbits of the particles are non-intersecting random loops. We prove, by a weak law of large number, the validity of a diffusion equation for the macroscopic observables of interest for times that are arbitrary large, but small compared to the minimal recurrence time of the dynamics.     

Evolution temporelle d'une poche de tourbillon singuliere

We study here regularity of solutions of the two dirnensional incompressible Euler system whose initial data are vortez patches with singular boundary. We show the persislance of conormal regularity apart from a closed subset. As a consequence, we obtain the following result for vories patches : if the initial boundary is regular apart from a closed subset, it remairw regular for all time apart from the closed subset transported by the pow.     

Nonstationary Positive Definite Tapering On The Plane

A common problem in spatial statistics is to predict a random field f at some spatial location t ₀ using observations f(t ₁), …, f(t_n ) at . Recent work by Kaufman et al. and Furrer et al. studies the use of tapering for reducing the computational burden associated with likelihood-based estimation and prediction in large spatial datasets. Unfortunately, highly irregular observation locations can present problems for stationary tapers. In particular, there can exist local neighborhoods with too few observations for sufficient accuracy, while others have too many for computational tractability. In this article, we show how to generate nonstationary covariance tapers T(s, t) such that the number of observations in {t: T(s, t) > 0} is approximately a constant function of s. This ensures that tapering neighborhoods do not have too many points to cause computational problems but simultaneously have enough local points for accurate prediction. We focus specifically on tapering in two dimensions where quasi-conformal theory can be used. Supplementary materials for the article are available online.     

How to obtain accurate results with molecular iodine and density functional theory?

Molecular iodine is found in many organic synthetic methodologies, both as reagent and as catalyst. Naturally, many groups have carried out computational studies involving this element. However, the choice of computational method proves to be more challenging than for other non-metals. We quantify herein the errors that some common theory levels can introduce in terms of both structural and energetic deviations. We also evaluate multiple post hoc corrections, namely, vibrational entropy, dispersion, and counter-poise corrections. Our results indicate the triple- $$ basis sets are essential to obtain quality results and that post hoc corrections are overall detrimental.     

Spectral Projections of the Complex Cubic Oscillator

We prove the spectral instability of the complex cubic oscillator \({-\frac{{\rm d}^{2}}{{\rm d}x^{2}} + ix^{3} + i \alpha x}\) for non-negative values of the parameter α, by getting the exponential growth rate of \({\|\Pi_{n}(\alpha)\|}\) , where \({\Pi_{n}(\alpha)}\) is the spectral projection associated with the nth eigenvalue of the operator. More precisely, we show that for all non-negative α $$\lim\limits_{n \to + \infty} \frac{1}{n} {\rm log}\|\Pi_{n}(\alpha)\| = \frac{\pi}{\sqrt{3}}$$ .     

Fractal Pattern for Multiscale Digital Image Correlation

Background:

Digital Image Correlation (DIC) is based on the matching, between reference and deformed state images, of features contained in patterns that are deposited on test sample surfaces. These features are often suitable for a single scale, and there is a current lack of multiscale patterns capable of providing reliable displacement measurements over a wide range of scales.

Objective:

Here, we aim to demonstrate that a pattern based on a fractal (self-affine) surface would make a suitable pattern for multiscale DIC.

Methods:

A method to numerically generate patterns directly from a desired auto-correlation function is introduced. It is then enhanced by a Mean Intensity Gradient (MIG) improvement process based on grey level redistribution. Numerical experiments at multiple scales are performed for two different imposed displacement fields and results for one of the patterns generated are compared with those obtained for a random pattern and a Perlin noise one.

Results:

The proposed pattern is shown to lead to DIC errors comparable to those found with the two others for the first scales, but has much greater robustness. More importantly, the pattern generated here exhibits stable errors and robustness with respect to the scale whereas these two outputs become significantly degraded for the other two patterns as the scale increases.

Conclusions:

As a result, scale invariance properties of the pattern based on fractal surfaces correspond to scale invariance in DIC errors as well. This is of great interest regarding the use of such patterns in multiscale DIC.

     

A “Multi-Heavy-Atom” Approach toward Biphotonic Photosensitizers with Improved Singlet-Oxygen Generation Properties

Two trispicolinate 1,4,7-triazacyclonane (TACN)-based ligands bearing three picolinate biphotonic antennae were synthetized and their Yb³⁺ and Gd³⁺ complexes isolated. One series differs from the other by the absence ( L¹ )/presence ( L² ) of bromine atoms on the antenna backbone, offering respectively improved optical and singlet-oxygen generation properties. Photophysical properties of the ligands, complexes and micellar Pluronic suspensions were investigated. Complexes exhibit high two-photon absorption cross-section combined either with NIR emission (Yb) or excellent ¹O₂ generation (Gd). The very large intersystem crossing efficiency induced by the combination of bromine atom and heavy rare-earth element was corroborated with theoretical calculations. The ¹O₂ generation properties of L² Gd micellar suspension under two-photon activation leads to tumour cell death, suggesting the potential of such structures for theranostic applications.