The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow

We propose a mathematical derivation of Brinkman’s force for a cloud of particles immersed in an incompressible viscous fluid. Specifically, we consider the Stokes or steady Navier-Stokes equations in a bounded domain Ω⊂ℝ³ for the velocity field u of an incompressible fluid with kinematic viscosity ν and density 1. Brinkman’s force consists of a source term 6π ν j where j is the current density of the particles, and of a friction term 6π ν ρ u where ρ is the number density of particles. These additional terms in the motion equation for the fluid are obtained from the Stokes or steady Navier-Stokes equations set in Ω minus the disjoint union of N balls of radius ε=1/N in the large N limit with no-slip boundary condition. The number density ρ and current density j are obtained from the limiting phase space empirical measure , where x _k is the center of the k-th ball and v _k its instantaneous velocity. This can be seen as a generalization of Allaire’s result in [Arch. Ration. Mech. Anal. 113:209–259, [1991]] who considered the case of periodically distributed x _k s with v _k =0, and our proof is based on slightly simpler though similar homogenization arguments. Similar equations are used for describing the fluid phase in various models for sprays.     

Phase transitions and magnetoelectric coupling in BiFe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Zn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>3</Subscript> multiferroics

Multiferroic BiFe_1?xZn _x O₃ ceramics were prepared by solution combustion method. Their structure, magnetoelectric, dielectric, magnetic, thermal characteristics were studied. The magnetic M(T) and heat capacity C _p (T) measurements demonstrate an antiferromagnetic to paramagnetic phase transition (T _N ) around 635 K. The anomaly on the temperature dependence of the dielectric constant near T _N was observed, which could be induced by the magnetoelectric coupling between electric and magnetic ordering. The magnetoelectric behavior was also confirmed by the linear relation between Δε and M², which is in the agreement of the Ginzburg-Landau theory for the second-order phase transition.     

Engineered Ferritin with Eu3+ as a Bright Nanovector: A Photoluminescence Study

Ferritin nanoparticles play many important roles in theranostic and bioengineering applications and have been successfully used as nanovectors for the targeted delivery of drugs due to their ability to specifically bind the transferrin receptor (TfR1, or CD71). They can be either genetically or chemically modified for encapsulating therapeutics or probes in their inner cavity. Here, we analyzed a new engineered ferritin nanoparticle, made of the H chain mouse ferritin (HFt) fused with a specific lanthanide binding tag (LBT). The HFt-LBT has one high affinity lanthanide binding site per each of the 24 subunits and a tryptophane residue within the tag that acts as an antenna able to transfer the energy to the lanthanide ions via a LRET process. In this study, among lanthanides, we selected europium for its red emission that allows to reduce overlap with tissue auto-fluorescence. Steady state emission measurements and time-resolved emission spectroscopy have been employed to investigate the interaction between the HFt-LBT and the Eu³⁺ ions. This allowed us to identify the Eu³⁺ energy states involved in the process and to pave the way for the future use of HFt-LBT Eu³⁺ complex in theranostics.     

Electron-Poor Acridones and Acridiniums as Super Photooxidants in Molecular Photoelectrochemistry by Unusual Mechanisms

Electron-deficient acridones and in situ generated acridinium salts are reported as potent, closed-shell photooxidants that undergo surprising mechanisms. When bridging acyclic triarylamine catalysts with a carbonyl group (acridones), this completely diverts their behavior away from open-shell, radical cationic, ‘beyond diffusion’ photocatalysis to closed-shell, neutral, diffusion-controlled photocatalysis. Brønsted acid activation of acridones dramatically increases excited state oxidation power (by +0.8 V). Upon reduction of protonated acridones, they transform to electron-deficient acridinium salts as even more potent photooxidants (*E_1/2=+2.56–3.05 V vs SCE). These oxidize even electron-deficient arenes where conventional acridinium salt photooxidants have thusfar been limited to electron-rich arenes. Surprisingly, upon photoexcitation these electron-deficient acridinium salts appear to undergo two electron reductive quenching to form acridinide anions, spectroscopically-detected as their protonated forms. This new behaviour is partly enabled by a catalyst preassembly with the arene, and contrasts to conventional SET reductive quenching of acridinium salts. Critically, this study illustrates how redox active chromophoric molecules initially considered photocatalysts can transform during the reaction to catalytically active species with completely different redox and spectroscopic properties.     

NMR Self-Diffusion and Transverse Relaxation Time in Bitumen: The Effect of Aging

In this investigation the dynamics of two types of bitumens with different penetration grade were tested by using dynamic shear rheometry (DSR) and Nuclear Magnetic Resonance (NMR) at unaged conditions, and upon both short- and long-term artificial aging. The gel-sol transition temperature was found to increase with increasing the time of aging treatment. Arrhenius parameters of the viscosity were found, unexpectedly, to be correlated with those of simple liquids, suggesting that the two kinds of systems, although chemically and physically quite different, share the same basic process at the molecular level. The molecular dynamics has been then investigated by NMR Pulsed Field Gradient Stimulated-Echo (PFGSE) and relaxometry (Carr-Purcell-Meiboom-Gill, CPMG, spin-echo pulse sequence) to capture the effect of aging upon dynamics variables such as self-diffusion coefficients D and transverse relaxation times T₂. The translational diffusion at T> of the light molecular components of both types of bitumens was characterized by broad distributions of D which were found independent of the experimental time scale up to 0.2 s. Similarly, T₂ data could be described as a continuous unimodal distributions of relaxation times determined both at T< and T> .     

Vine copula modeling dependence among cyber risks: A dangerous regulatory paradox

Dependence among different cyber risk classes is a fundamentally underexplored topic in the literature. However, disregarding the dependence structure in cyber risk management leads to inconsistent estimates of potential unintended losses. To bridge this gap, this article adopts a regulatory perspective to develop vine copulas to capture dependence. In quantifying the solvency capital requirement gradient for cyber risk measurement according to Solvency II, a dangerous paradox emerges: an insurance company does not tend to provide cyber risk hedging products as they are excessively expensive and would require huge premiums that it would not be possible to find policyholders.     

Structural effects in poly(3-alkylthiophene)s on the exposition to poor solvent

The exposure to pentane vapour of poly(3-alkylthiophene)s with different alkyl chains produces a modification in the optical properties of the thin films. The treatment induces a red-shift of the electronic absorption maximum and the appearance of vibronic structure in the UV spectra. We have followed these changes with IR and Raman spectroscopies to monitor the modification of the backbone conjugation, and with X-ray diffraction to evidence the structural order of the chains.     

Tailor-made polymers and copolymers from aziridines and 1,3-oxacyclanes

Telechelic poly(tert-butylaziridine)s (polyTBA) and poly(1,3,6-trioxocane)s (polyTOC) and macromonomers were synthesized mainly by living cationic polymerization. Both, molecular weight and end-functionality distributions of polyTOC oligomers and polymers were studied using a combination of HPLC under “critical conditions”, gradient HPLC and SEC with double detection following a preparative HPLC fractionation. Monofunctional and bifunctional polyTBA with various end-groups were synthesized by the end-capping method. Several modification reactions were examined for terminal transformation of polyTBA and polyTOC hydroxy-telechelics into mono- and bifunctional vinyl ether macromonomers. Various tailor-made polymers based on uniform size telechelics and macromonomers were prepared using: 1. polymer-polymer coupling to produce block copolymers; 2. polyaddition of amino-functionalized telechelics to bisacrylamides; 3. addition of amino-polyTBA to polydienes; 4. synthesis of graft copolymers with well-defined graft component and networks.     

Influence of “controlled processing conditions” on the solidification of iPP,PET and PA6

In this work reliable experimental data for three semicrystalline polymers (iPP, PA6, PET) crystallised under pressure and high cooling rates are supplied. These results were achieved on the basis of a model experiment where drastic “controlled” solidification conditions are applied. The final objective was to quantify the effect of two typical operating conditions (pressure and cooling rate) on the final properties and morphology of the obtained product. The influence of processing conditions on some macroscopically relevant properties, such as density and micro hardness is stressed, together with the influence of processing conditions on the product morphology, investigated by means of Wide Angle X-Ray Scattering (WAXS). Results on the iPP samples display a decrease of density and micro hardness, due to the pressure increase, in a wide range of cooling rates (from 0.01 to 20°C/s). PET samples exhibit an opposite behaviour with density and micro hardness increasing at higher pressures in the whole range of cooling rates investigated. PA6 samples behave similarly to PET displaying a less significant increase of density and micro hardness with pressure than PET samples.