Quasi-minimality and tightness by range in spaces with unconditional basis

We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e., of type (4) in the Ferenczi-Rosendal list within the framework of Gowers’ classification program of Banach spaces. The space is an unconditional variant of the Gowers Hereditarily Indecomposable space with an asymptotically unconditional basis.     

VOF simulations of the contact angle dynamics during the drop spreading: Standard models and a new wetting force model

Introduction

In this study,a novel numerical implementation for the adhesion of liquid droplets impacting normally on solid dry surfaces is presented. The advantage of this new approach, compared to the majority of existing models, is that the dynamic contact angle forming during the surface wetting process is not inserted as a boundary condition, but is derived implicitly by the induced fluid flow characteristics (interface shape) and the adhesion physics of the gas–liquid-surface interface (triple line), starting only from the advancing and receding equilibrium contact angles. These angles are required in order to define the wetting properties of liquid phases when interacting with a solid surface.

Methodology

The physical model is implemented as a source term in the momentum equation of a Navier-Stokes CFD flow solver as an “adhesion-like” force which acts at the triple-phase contact line as a result of capillary interactions between the liquid drop and the solid substrate. The numerical simulations capture the liquid–air interface movement by considering the volume of fluid (VOF) method and utilizing an automatic local grid refinement technique in order to increase the accuracy of the predictions at the area of interest, and simultaneously minimize numerical diffusion of the interface.

Results

The proposed model is validated against previously reported experimental data of normal impingement of water droplets on dry surfaces at room temperature. A wide range of impact velocities, i.e. Weber numbers from as low as 0.2 up to 117, both for hydrophilic (θ_adv = 10° – 70°) and hydrophobic (θ_adv = 105° – 120°) surfaces, has been examined. Predictions include in addition to droplet spreading dynamics, the estimation of the dynamic contact angle; the latter is found in reasonable agreement against available experimental measurements.

Conclusion

It is thus concluded that theimplementation of this model is an effective approach for overcoming the need of a pre-defined dynamic contact angle law, frequently adopted as an approximate boundary condition for such simulations. Clearly, this model is mostly influential during the spreading phase for the cases of low We number impacts (We < ˜80) since for high impact velocities, inertia dominates significantly over capillary forces in the initial phase of spreading.     

Oxidative cycloaddition of 1,1,3,3-tetramethyldisiloxane to alkynes catalyzed by supported gold nanoparticles

Gold nanoparticles supported on TiO(2) (0.1-1% mol) catalyze at room temperature and at extremely mild conditions the unprecedented oxidative cycloaddition of 1,1,3,3-tetramethyldisiloxane to alkynes, forming substituted 2,5-dihydro-1,2,5-oxadisiloles, with concomitant evolution of hydrogen gas. For the majority of the substrates, the yields are exceptional (up to 99%). The reaction proceeds at room temperature, tolerates a variety of functional groups, and can be performed in several solvents.     

Mineralised organic remains from cesspits at the Roman town of Silchester: processes and preservation

Mineralised organic remains (including apple pips and cereal grains) collected during the ongoing excavations of Insula IX at the Roman town of Silchester, Hampshire have been analysed by a combination of SEM-EDX, powder XRD and IR spectroscopy. The experiments included mapping experiments using spatially resolved versions of each technique. IR and powder XRD mapping have been carried out utilising the synchrotron source at The Daresbury Laboratory on stations 11.1 and 9.6. It is concluded that these samples are preserved by rapid mineralisation in the carbonate-substituted calcium phosphate mineral, dahllite. The rapid mineralisation leads to excellent preservation of the samples and a small crystal size. The value of IR spectroscopy in studying materials like this where the crystal size is small is demonstrated. A comparison is made between the excellent preservation seen in this context and the much poorer preservation of mineralised remains seen in Context 5276 or Cesspit 5251. Comments on the possible mechanism of mineralisation of these samples are made.     

A highly porous interpenetrated metal-organic framework from the use of a novel nanosized organic linker

The initial use of a novel elongated tricarboxylic acid H(3)hmpib in metal-organic framework (MOF) chemistry resulted in a [Zn(4)O(hmpib)(2)] MOF (UCY-1) with pyrite topology. The compound displays a remarkably high internal surface area despite its double-interpenetrated structure as well as high CO(2) uptake and selective adsorption for it over CH(4).     

Heptanuclear heterometallic [Cu6Ln] clusters: trapping lanthanides into copper cages with artificial amino acids

Employment of the artificial amino acid 2-amino-isobutyric acid, aibH, in Cu(II) and Cu(II)/Ln(III) chemistry led to the isolation and characterization of 12 new heterometallic heptanuclear [Cu(6)Ln(aib)(6)(OH)(3)(OAc)(3)(NO(3))(3)] complexes consisting of trivalent lanthanide centers within a hexanuclear copper trigonal prism (aibH = 2-amino-butyric acid; Ln = Ce (1), Pr (2), Nd (3), Sm (4), Eu (5), Gd (6), Tb (7), Dy (8), Ho (9), Er (10), Tm (11), and Yb (12)). Direct curent magnetic susceptibility studies have been carried out in the 5-300 K range for all complexes, revealing the different nature of the magnetic interactions between the 3d-4f metallic pairs: dominant antiferromagnetic interactions for the majority of the pairs and dominant ferromagnetic interactions for when the lanthanide center is Gd(III) and Dy(III). Furthermore, alternating current magnetic susceptibility studies reveal the possibility of single-molecule magnetism behavior for complexes 7 and 8. Finally, complexes 2, 5-8, 10, and 12 were analyzed using positive ion electrospray mass spectrometry (ES-MS), establishing the structural integrity of the heterometallic heptanuclear cage structure in acetonitrile.     

Velocity-based reciprocal theorems in elastodynamics and BIEM implementation issues

Reciprocal theorems in elastodynamics are introduced as extensions of respective theorems from elastostatics. Inasmuch as the latter is a subset of the former, the aim here is to present an elastodynamic reciprocal theorem that also includes elastostatics as a special case when the time variable becomes irrelevant. This is accomplished by introducing a velocity-based reciprocal theorem, whose basic properties are subsequently explored. The next step is to use this theorem and formulate a numerical approach based on boundary integral equation statements and compare them with existing formulations based on conventional reciprocity relations. The applications presented here involve the standard mechanical oscillator and the unidimensional axial element as two simple, yet important problems of structural dynamics. Along with the numerical results, a thorough stability analysis of the corresponding time-stepping algorithms is formulated. In both cases, the superior performance of the methodologies built on velocity-based reciprocal theorems is clearly demonstrated.     

Exploring the Strength of the H‐Bond in Synthetic Models for Heme Proteins: The Importance of the N−H Acidity of the Distal Base

The distal hydrogen bond (H‐bond) in dioxygen‐binding proteins is crucial for the discrimination of O₂ with respect to CO or NO. We report the preparation and characterization of a series of Zn^II porphyrins, with one of three meso‐phenyl rings bearing both an alkyl‐tethered proximal imidazole ligand and a heterocyclic distal H‐bond donor connected by a rigid acetylene spacer. Previously, we had validated the corresponding Co^II complexes as synthetic model systems for dioxygen‐binding heme proteins and demonstrated the structural requirements for proper distal H‐bonding to Co^II‐bound dioxygen. Here, we systematically vary the H‐bond donor ability of the distal heterocycles, as predicted based on pK_a values. The H‐bond in the dioxygen adducts of the Co^II porphyrins was directly measured by Q‐band Davies‐ENDOR spectroscopy. It was shown that the strength of the hyperfine coupling between the dioxygen radical and the distal H‐atom increases with enhanced acidity of the H‐bond donor.