A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.     

Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network

In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy’s law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D–1D coupled model.     

X-ray diffraction study of mesogenic 4-methoxyphenyl-4′-n-nonyloxybenzoate

4-methoxyphenyl-4′-n-nonyloxybenzoate have been investigated by single crystal X-ray structural analysis. Crystal packing of the compounds does not represent a precursor of the mesophse although the typical for liquid crystal compounds separation of crystal packing on aromatic and aliphatic areas is observed here. Possible reason for monotropic properties are discussed.     

含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性

本文研究了一类含分布时滞的时滞微分系统的多步龙格-库塔方法的稳定性.基于辐角原理，本文给出了多步龙格-库塔方法弱时滞相关稳定性的充分条件，并通过数值算例验证了理论结果的有效性.     

On weak–strong uniqueness for the compressible Navier–Stokes system with non-monotone pressure law

We show the weak–strong uniqueness property for the compressible Navier–Stokes system with general non-monotone pressure law. A weak solution coincides with the strong solution emanating from the same initial data as long as the latter solution exists.     

Finely dispersed palladium on silk‐fibroin as an efficient and ligand‐free catalyst for Heck cross‐coupling reaction

A palladium–fibroin complex (Pd/Fib.) was prepared by the addition of sonicated fibroin fiber in water to palladium acetate solution. Pd (OAc)₂ was absorbed by fibroin and reduced with NaBH₄ at room temperature to the Pd(0) nanoparticles. Powder‐X‐ray diffraction, scanning electron microscopy–energy‐dispersive X‐ray spectroscopy, Fourier transform‐infrared, CHN elemental analysis and inductively coupled plasma‐atomic emission spectroscopy were carried out to characterize the Pd/Fib. catalyst. Catalytic activity of this finely dispersed palladium was examined in the Heck coupling reaction. The catalytic coupling of aryl halides (‐Cl, ‐Br, ‐I) and olefins led to the formation of the corresponding coupled products in moderate to high yields under air atmosphere. A variety of substrates, including electron‐rich and electron‐poor aryl halides, were converted smoothly to the targeted products in simple procedure. Heterogeneous supported Pd catalyst can be recycled and reused several times.     

Reducing the computational cost of NMR crystallography of organic powders at natural isotopic abundance with the help of 13C-13C dipolar couplings

Structure determination of functional organic compounds remains a formidable challenge when the sample exists as a powder. Nuclear magnetic resonance crystallography approaches based on the comparison of experimental and Density Functional Theory (DFT)-computed ¹H chemical shifts have already demonstrated great potential for structure determination of organic powders, but limitations still persist. In this study, we discuss the possibility of using ¹³C-¹³C dipolar couplings quantified on powdered theophylline at natural isotopic abundance with the help of dynamic nuclear polarization, to realize a DFT-free, rapid screening of a pool of structures predicted by ab initio random structure search. We show that although ¹³C-¹³C dipolar couplings can identify structures possessing long range structural motifs and unit cell parameters close to those of the true structure, it must be complemented with other data to recover information about the presence and the chemical nature of the supramolecular interactions.     

Screening of Three Transition Metal‐Mediated Reactions Compatible with DNA‐Encoded Chemical Libraries

The construction of DNA‐encoded chemical libraries (DECLs) crucially relies on the availability of chemical reactions, which are DNA‐compatible and which exhibit high conversion rates for a large number of diverse substrates. In this work, we present our optimization and validation procedures for three copper and palladium‐catalyzed reactions (Suzuki cross‐coupling, Sonogashira cross‐coupling, and copper(I)‐catalyzed alkyne‐azide cycloaddition (CuAAC)), which have been successfully used by our group for the construction of large encoded libraries.     

Covalent Grafting of BPin functions on Carbon Nanotubes and Chan–Lam–Evans Post-Functionalization

The chemical functionalization of carbon nanotubes is often a prerequisite prior to their use in various applications. The covalent grafting of 4,4,5,5-tetramethyl-1,3,2-dioxaborolane (BPin) functional groups directly on the surface of multi- and single-walled carbon nanotubes, activated by nucleophilic addition of nBuLi, was carried out. Thermogravimetric analysis (TGA) coupled with mass spectrometry, Raman spectroscopy, X-ray photoelectron spectroscopy (XPS) and time-of-flight secondary ions mass spectrometry (ToF-SIMS) confirmed the efficiency of this methodology and proved the integrity and covalent grafting of the BPin functional groups. These groups were further reacted with various nucleophiles in the presence of a copper(II) source in the conditions of the aerobic Chan–Lam–Evans coupling. The resulting materials were characterized by TGA, XPS and ToF-SIMS. This route is efficient, reliable and among the scarce reactions that enable the direct grafting of heteroatoms at carbonaceous material surfaces.