On the boundary limits of monotone Sobolev functions in variable exponent Orlicz spaces

Our aim in this note is to deal with boundary limits of monotone Sobolev functions with ▽u∈ Lp(·)logLq(·)(B) for the unit ball BRn. Here p(·) and q(·) are variable exponents satisfyingthe log-Hlder and the log log-Hlder conditions, respectively.     

Analysing the sintering of heterogeneous powder structures by in situ microtomography

This work analyses the microstructure changes of various copper-based powder systems during sintering from 3D images provided by in situ synchrotron microtomography. The investigated systems include a copper powder with a wide particle size distribution of 0–63 µm poured into a quartz capillary, a pre-sintered copper compact with artificially created large pores and a mixture of copper and alumina particles. The experiments were carried out at the European Synchrotron in Grenoble, France. Powders were sintered up to 1060°C under reducing atmosphere in a furnace located between the X-ray source and the detector. During each experiment, 3D images were taken at various times of the thermal cycle. We have obtained images with a resolution of 1.5 µm and the time of acquisition of every image was ～1 min. Quantitative analysis of these images allowed the changes of various important parameters to be followed. Such parameters characterise the sintering process at the particle length scale: interparticle coordination, pore size distribution and particle centre-to-centre distance. Moreover, by tracking the displacement of each particle centre and comparing it to the displacement predicted by classical mean field assumption, we have been able to assess the magnitude of particle rearrangement occurring during sintering. From these data, the sintering behaviour of heterogeneous powder systems is discussed with particular emphasis of collective particle phenomena.     

Development of high resolution resonance ionization mass spectrometry for trace analysis of 93mNb

⁹³Nb(n, n′)^93mNb reaction allows retrospective estimation of integrated fast neutron dose in nuclear reactor. We proposed isomer-selective trace analysis of ^93mNb by Resonance Ionization Mass Spectrometry (RIMS) combined with a gas-jet atomic source and an injection locked Ti:Sapphire laser system operated at several kHz. Resonant ionization spectroscopy of Nb in gas-jet using Ti:Sapphire laser was demonstrated.     

Basic [Au25(SCH2CH2Py)18]−⋅Na+ Clusters: Synthesis,Layered Crystallographic Arrangement,and Unique Surface Protonation

The synthesis of high‐purity and high‐yield Au₂₅ clusters protected by the basic pyridyl ethanethiol (HSCH₂CH₂Py, 4‐PyET and 2‐PyET) is presented. Single‐crystal X‐ray diffraction of the [Au₂₅(4‐PyET)₁₈]^??Na⁺ clusters has revealed a structure similar to that known for the phenyl ethanethiolate analogue, but with pyridyl‐N coordination to Na⁺, a more relaxed ligand shell, and a profoundly layered arrangement in the solid state. Because of the pendant Py moiety, the [Au₂₅(PyET)₁₈]^? clusters are endowed with unique (de)protonation equilibria, which has been characterized in detail by UV/Vis absorption and ¹H NMR spectroscopy. [Au₂₅(PyET)₁₈]^? clusters showed an unexpectedly H⁺‐dependent solubility that is tunable in aqueous and organic solvents. The successful synthesis of the basic Py‐terminated thiolate‐protected Au₂₅ clusters paves the way to realize a new family of metalloid clusters possessing basic properties.     

Coexistence of Spin–Lattice Relaxation and Phonon-Bottleneck Processes in GdIII–Phthlocyaninato Triple-Decker Complexes under Highly Diluted Conditions

Gd³⁺ complexes have been shown to undergo unusual slow magnetic relaxation processes similar to those of single-molecule magnets (SMMs), even though Gd³⁺ does not exhibit strong magnetic anisotropy. To reveal the origin of the slow magnetic relaxation of Gd³⁺ complexes, we have investigated the magnetic properties and heat capacities of two Gd³⁺-phthalocyaninato triple-decker complexes, one of which has intramolecular Gd³⁺–Gd³⁺ interactions and the other does not. It was found that the Gd³⁺–Gd³⁺ interactions accelerate the magnetic relaxation processes. In addition, magnetically diluted samples, prepared by doping a small amount of the Gd³⁺ complexes into a large amount of diamagnetic Y³⁺ complexes, underwent dual magnetic relaxation processes. A detailed dynamic magnetic analysis revealed that the coexistence of spin–lattice relaxation and phonon-bottleneck processes is the origin of the dual magnetic relaxation processes.     

Trudinger's inequality for Riesz potentials of functions in Musielak–Orlicz spaces

In this paper we are concerned with Trudinger's inequality for Riesz potentials of functions in Musielak–Orlicz spaces.     

Simulation of semidilute suspensions of non-Brownian fibers in shear flow

Particle-level simulations are performed to study semidilute suspensions of monodispersed non-Brownian fibers in shear flow, with a Newtonian fluid medium. The incompressible three-dimensional Navier-Stokes equations are used to describe the motion of the medium, while fibers are modeled as chains of fiber segments, interacting with the fluid through viscous drag forces. The two-way coupling between the solids and the fluid phase is taken into account by enforcing momentum conservation. The model includes long-range and short-range hydrodynamic fiber-fiber interactions, as well as mechanical interactions. The simulations rendered the time-dependent fiber orientation distribution, whose time average was found to agree with experimental data in the literature. The viscosity and first normal stress difference was calculated from the orientation distribution using the slender body theory of Batchelor [J. Fluid Mech. 46, 813 (1971)], with corrections for the finite fiber aspect ratios. The viscosity was also obtained from direct computation of the shear stresses of the suspension for comparison. These two types of predictions compared well in the semidilute regime. At higher concentrations, however, a discrepancy was seen, most likely due to mechanical interactions, which are only accounted for in the direct computation method. The simulated viscosity determined directly from shear stresses was in fair agreement with experimental data found in the literature. The first normal stress difference was found to be proportional to the square of the volume concentration of fibers in the semidilute regime. As concentrations approached the concentrated regime, the first normal stress difference became proportional to volume concentration. It was also found that the coefficient of friction has a strong influence on the tendency for flocculation as well as the apparent viscosity of the suspension in the semidilute regime.     

Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces

We define and study Musielak-Orlicz-Sobolev spaces with zero boundary values on any metric space endowed with a Borel regular measure. We extend many classical results, including completeness, lattice properties and removable sets, to Musielak-Orlicz-Sobolev spaces on metric measure spaces. We give sufficient conditions which guarantee that a Sobolev function can be approximated by Lipschitz continuous functions vanishing outside an open set. These conditions are based on Hardy type inequalities.