A kinetic formulation for a model coupling free surface and pressurised flows in closed pipes

The aim of this paper is to present a kinetic formulation of a model for the coupling of transient free surface and pressurised flows. Firstly, we revisit the system of Saint-Venant equations for free surface flow: we state some properties of Saint-Venant equations, we propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises (in some general case) an energy and preserves the still water steady state. Secondly, we propose a model for pressurised flows in a Saint-Venant-like conservative formulation. We then propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises in any case an energy and preserves the still water steady state. Finally, we propose a dual model that couples these two types of flow.     

Binuclear Uranium(VI) Complexes with a “Pacman” Expanded Porphyrin: Computational Evidence for Highly Unusual Bis‐Actinyl Structures

On the basis of uranyl complexes reacting with a polypyrrolic ligand (H₄L), we explored structures and reaction energies of a series of new binuclear uranium(VI) complexes using relativistic density functional theory. Full geometry optimizations on [(UO₂)₂(L)], in which two uranyl groups were initially placed into the pacman ligand cavity, led to two minimum‐energy structures. These complexes with cation–cation interactions (CCI) exhibit unusual coordination modes of uranyls: one is a T‐shaped ( T ) skeleton formed by two linear uranyls {O_exo?U₂?O_endo→U₁(?O_exo)₂}, and another is a butterfly‐like ( B ) unit with one linear uranyl coordinating side‐by‐side to a second cis‐uranyl. The CCI in T was confirmed by the calculated longest distance and lowest stretching vibrational frequency of U₂?O_endo among the four U?O bonds. Isomer B is more stable than T , for which experimental tetrameric analogues are known. The formation of B and T complexes from the mononuclear [(UO₂)(H₂L)(thf)] ( M ) was found to be endothermic. The further protonation and dehydration of B and T are thermodynamically favorable. As a possible product, we have found a trianglelike binuclear uranium(VI) complex having a O?U?O?U?O unit.     

Computation of mixed mode stress intensity factors in a four-point bend specimen

Four-point bend specimen is one of the most important specimens of the fracture mechanics because it can produce mixed modes I and II. Therefore, computation of stress intensity factors in this specimen is of practical interest. Several relations have been suggested that no one of them has completely considered the effects of the loading point and crack geometry. In this paper, mixed mode stress intensity factors of the bend specimen are computed by finite element method (FEM) and after validating by comparing with the available results in the literature, the results will be assessed to determine the effects of different crack location and loading distances from the middle of the specimen. Finally, two new coefficients comprising these effects are introduced.     

On the physical interpretation of asymptotically flat gravitational fields

A problem in general relativity is how to extract physical information from solutions to the Einstein equations. Most often information is found from special conditions, e.g., special vector fields, symmetries or approximate symmetries. Our concern is with asymptotically flat space–times with approximate symmetry: the BMS group. For these spaces the Bondi four-momentum vector and its evolution, found at infinity, describes the total energy–momentum and the energy–momentum radiated. By generalizing the simple idea of the transformation of (electromagnetic) dipoles under a translation, we define (analogous to center of charge) the center of mass for asymptotically flat Einstein–Maxwell fields. This gives kinematical meaning to the Bondi four-momentum, i.e., the four-momentum and its evolution which is described in terms of a center of mass position vector, its velocity and spin-vector. From dynamical arguments, a unique (for our approximation) total angular momentum and evolution equation in the form of a conservation law is found. Third Award in the 2008 Essay Competition of the Gravity Research Foundation.     

An optimal rigidity theorem for complete submanifolds in a sphere

It is proved that if M^n is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in S^n＋p（1）, and if supM S 〈 α（n, H）, where α（n,H）=n＋n^3/2（n-1）H^2-n（n-2）/n（n-1）√n^2H^4＋4（n-1）H^2,then M^n must be the totally urnbilical sphere S^n（1/√1＋H^2）.An example to show that the pinching constant α（n, H） appears optimal is given.     

Formation mechanism of ethanol-water excimer

The fluorescent spectrum and the excitation spectrum were used to present the cluster molecular structure feature in ethanol-water solutions.Through analyzing the fluorescent characteristics of an excimer,it is proposed that the excimers are formed between the ethanol-water cluster molecules in the excited state and in the ground state.The fluorescent lifetime and the fluorescent intensity decay process give information about the photo-physical and photo-chemical processes of the formation and the dissociation of an excimer.The theoretical calculation and physical analysis coincide with the experimental results.The preliminary conclusion about the structure feature of ethanol-water cluster molecule is that it has a planar one like a sandwich.     

Aluminum/Nitrogen Cycles and an Open Cage with Al–H and N–H Functions

The cyclic tert‐butyl‐amino alane dimer [tBu–N(H)AlH₂]₂ ( 1 ) was obtained from reaction between alane with tert‐butylamine and its boranate derivative [tBu–N(H)–Al(BH₄)₂)]₂ ( 2 ) subsequently from 1 by hydride/chloride exchange using PbCl₂ followed by reaction with LiBH₄. Both compounds form four‐membered Al₂N₂ cycles with typical Al–N bond lengths of 1.940(5) Å ( 1 ) and 1.945(5) Å ( 2 ) as found from X‐ray diffraction analysis. The tert‐butyl substituents at the nitrogen atoms may be situated at the same side of the ring (cis) or at opposite sides (trans). For compound 1 both isomers are present in solution, showing particular temperature dependent NMR shifts. In the solid both compounds 1 and 2 adopt the trans arrangement. When 1 is reacted with PbCl₂ in half of the molarity ratio used for 2 , surprisingly the novel compound 3 , a zwitterion, can be obtained: [(tBu–N)(Al–H)₃(tBu–N(H))₃Cl((H)N–tBu)₃(Al–H)₂(Al–Cl)(N–tBu)]⁺[(tBu–N)(tBu–N(H))(AlCl₂)₂]^–. X‐ray structure analysis reveals that the anion is made of a tert‐butyl amino aluminum dichloride dimer (central Al₂N₂ ring) with one of the two nitrogen atoms being deprotonated. The cationic counterpart consists of three entities: (i) There is a first seco‐norcubane like Al₃N₄ basket with tert‐butyl groups at the nitrogen atoms, two hydride and one chloride ligand at the aluminum atoms and three hydrogen atoms on the open side of the basket, all pointing in the same direction; (ii) There is a second similar Al₃N₄ basket with the same substituent pattern except that all aluminum atoms have exclusively hydrogen ligands; (iii) Both baskets coordinate a central chloride through the six protons at the open nitrogen face of the baskets in such a way that the chloride lies in the center of a H₆ trigonal anti‐prism [mean H–Cl–H = 56.1(9)°]. As each of the open cages has a positive charge the overall charge by combination with the chloride adds to +1. The structure of the cationic part of 3 is unprecedented in AlN polycycles.     

β‐AgVO3 Nanorods as Peroxidase Mimetic for Colorimetric Determination of Glucose

β‐AgVO₃ nanorods have been demonstrated to exhibit intrinsic peroxidase‐like activity. The oxidation of glucose can be catalyzed by glucose oxidase (GOx ) to generate H₂O₂ in the presence of O₂ . The β‐AgVO₃ nanorods can catalytically oxidize peroxidase substrates including o‐phenylenediamine (OPD ), 3,3′,5,5′‐tetramethylbenzidine (TMB ), and diammonium 2,2′‐azino‐bis(3‐ethylbenzothiazoline‐6‐sulfonate) (ABTS ) by H₂O₂ to produce typical color reactions: OPD from colorless to orange, TMB from colorless to blue, and ABTS from colorless to green. The catalyzed reaction by the β‐AgVO₃ nanorods was found to follow the characteristic Michaelis–Menten kinetics. Compared with horseradish peroxidase and AgVO₃ nanobelts, β‐AgVO₃ nanorods showed a higher affinity for TMB with a lower Michaelis–Menten constant (K _m) value (0.04118 mM ) at the optimal condition. Taking advantage of their high catalytic activity, the as‐synthesized β‐AgVO₃ nanorods were utilized to develop a colorimetric sensor for the determination of glucose. The linear range for glucose was 1.25–60 μM with the lower detection limit of 0.5 μM . The simple and sensitive GOx ‐β–AgVO₃ nanorods–TMB sensing system shows great promise for applications in the pharmaceutical, clinical, and biosensor detection of glucose.     

Size effect in the titanium/diamond‐like carbon bilayer films: effect of relative thickness on their structure and mechanical properties

Titanium/diamond‐like carbon (Ti/DLC) bilayer films with different relative thickness were fabricated by direct‐current and pulsed cathode arc plasma method. Microstructure, morphological characteristics, and mechanical properties of the films were investigated in dependence of the thickness of Ti and DLC layers by Raman spectroscopy, atomic force microscopy, Knoop sclerometer, and surface profilometer. Raman spectra of Ti/DLC bilayers show the microstructure evolution (the size and ordering degree of sp²‐hybridized carbon clusters) with varying the thicknesses of Ti interlayer and DLC layer. Nano‐scaled Ti interlayer of 12–20 nm thickness presents the largest size effect. The catalytic effect of the sublayer is most pronounced in the carbon layer of less than 106 nm. In these thickness ranges, the bilayer films possessed the highest micro‐hardness and reactivity between atoms at interface. Internal stress in the bilayer monotonically decreases, with the thickness of Ti interlayer increasing to 30 nm and then becomes stable with the thickness. These results are associated with the occurrence of atomic diffusion process at Ti/C interface, and they are of cardinal significance to optimize the structure and mechanical properties of carbon‐based multilayer films. Copyright © 2016 John Wiley & Sons, Ltd.     

Fabrication of urchin‐like Ag/ZnO hierarchical nano/microstructures based on galvanic replacement mechanism and their enhanced photocatalytic properties

Urchin‐like Ag/ZnO hierarchical nano/microstructures have been synthesized through a facile low‐temperature hydrothermal growth method based on galvanic replacement mechanism. The experimental results show that the urchin‐like Ag/ZnO heterostructures are formed through the epitaxial growth of ZnO nanorods on the {111} facets of Ag nanoparticles along their own c‐axis. The photocatalytic properties of the products were evaluated by the degradation of RhB dye solution under ultraviolet irradiation, and the results show that the products exhibit significantly enhanced photocatalytic properties comparing with pure ZnO nanorods. The products with a Ag content of 35.64 atom % prepared with a Ag⁺ concentration in solution of 5 mM exhibit surprisingly high degradation rate (99.5%) for RhB dye solution (4 mg/L) after photocatalytic reaction for only 14 min under ultraviolet irradiation. The Schottky barrier formed at the metal‐semiconductor interfaces improves the segregation of charges and prevents the charge recombination, and thus significantly enhances the photocatalytic activities of the products. On the other hand, the high stability of the urchin‐like Ag/ZnO hierarchical nano/microstructures can effectively prevent the aggregation of nanostructures with simultaneously preserving high photocatalytic properties due to the existence of nanosized unites. Copyright © 2016 John Wiley & Sons, Ltd.