For the vorticity–velocity–pressure form of the Navier–Stokes equations on a bounded plane domain with corners

We show existence and regularity for the boundary value problems of the Navier–Stokes equations with non-standard BCs on a bounded plane domain with non-convex corners. We assign the vorticity value $\omega ={\omega }_0$ and the velocity normal component $u?n=u_0?n$ over the non-convex corner, the dynamic pressure value $p+{\left|u\right|}^2/2=p_0$ over inflow and outflow boundaries, and so on. We construct the corner singularity functions for the Stokes operator with zero vorticity and velocity normal component BCs, subtract its leading singularity from the solution by defining the coefficient of the singularity and show increased regularity for the remainder. The solution is determined by the smoother part and the coefficients of the singularities. It is seen from the singularity that the dynamic pressure has a transition layer that changes the sign (at $\theta =\pi /2$ in the domain). The obtained results can be applied to general polygonal domains and the cavity flows.     

Uniform distribution of TiO2 nanocrystals on reduced graphene oxide sheets by the chelating ligands

Reduced graphene oxide-TiO(2) hybrids were successfully prepared by the hydrothermal approach using triethanolamine and acetylacetone as the chelating agents. Without any additive, large aggregated TiO(2) clusters were randomly distributed dominantly at the edge and less on the basil plane of coagulated reduced graphene oxide (RGO) layers. The presence of chelating ligands remarkably facilitated the selective growth and regular spread of TiO(2) nanocrystals onto individually exfoliated RGO sheet. Such sandwich-like structure with stronger coupling and chemical interaction resulted in the surface area increase, the rearrangement of energy level, the enhanced concentration of oxygen vacancies, leading to much higher adsorbability and photocatalytic degradation of Rhodamine B under both UV and visible irradiations. These RGO-TiO(2) hybrid systems are potentially beneficial for widely practical applications in air/water purification, electronic devices, batteries, solar cells or supercapacitors.     

Blue upconversion luminescence of CaMoO4:Li+/Yb3+/Tm3+ phosphors prepared by complex citrate method

Li⁺/Tm³⁺/Yb³⁺ co-doped CaMoO₄ upconversion (UC) phosphor was prepared by complex citrate-gel method and UC luminescence properties were investigated. Li⁺/Tm³⁺/Yb³⁺ co-doped CaMoO₄ has intense blue emission induced by ¹G₄??³H₆ transition at 476?nm that is improved 10 times more than that of Li⁺ undoped sample and weak red emission at 647 nm generated by ³F₂??³H₆ transition under excitation at 980?nm. The optimum doping concentration of Li⁺ ions was investigated and UC mechanism of Li⁺/Tm³⁺/Yb³⁺ co-doped CaMoO₄ was discussed in detail.     

SPH simulation of fuel drop impact on heated surfaces

The interaction of liquid drops and heated surfaces is of great importance in many applications. This paper describes a numerical method, based on smoothed particle hydrodynamics (SPH), for simulating n-heptane drop impact on a heated surface. The SPH method uses numerical Lagrangian particles, which obey the laws of fluid dynamics, to describe the fluid flows. By incorporating the Peng–Robinson equation of state, the present SPH method can directly simulate both the liquid and vapor phases and the phase change process between them. The numerical method was validated by two experiments on drop impact on heated surfaces at low impact velocities. The numerical method was then used to predict drop-wall interactions at various temperatures and velocities. The model was able to predict the different outcomes, such as rebound, spread, splash, breakup, and the Leidenfrost phenomenon, consistent with the physical understanding.     

The Pressure Singularity for Compressible Stokes Flows in a Concave Polygon

A compressible Stokes system is studied in a polygon with one concave vertex. A corner singularity expansion is obtained up to second order. The expansion contains the usual corner singularity functions for the velocity plus an “associated” velocity singular function, and a pressure singular function. In particular the singularity of pressure is not local but occurs along the streamline emanating from the incoming concave vertex. It is observed that certain first derivatives of the pressure become infinite along the streamline of the ambient flow emanating from the concave vertex. Higher order regularity is shown for the remainder. This work was supported by the Com2MaC-SRC/ERC program of MOST/KOSEF (grant R11-1999-054), and by the U.S. National Science Foundation.     

Site-specific amide hydrogen exchange in melittin probed by electron capture dissociation Fourier transform ion cyclotron resonance mass spectrometry

Electron capture dissociation (ECD) has been proposed to be a non-ergodic process, i.e. to provide backbone dissociation of gas-phase peptides faster than randomization of the imparted energy. One potential consequence could be that ECD can fragment deuterated peptides without causing hydrogen scrambling and thereby provide amino acid residue-specific amide hydrogen exchange rates. Such a feature would improve the resolution of approaches involving solution-phase amide hydrogen exchange combined with mass spectrometry for protein structural characterization. Here, we explore this hypothesis using melittin, a haemolytic polypeptide from bee venom, as our model system. Exchange rates in methanol calculated from consecutive c-type ion pairs show some correlation with previous NMR data: the amide hydrogens of leucine 13 and alanine 15, located at the unstructured kink surrounding proline 14 in the melittin structure adopted in methanol, appear as fast exchangers and the amide hydrogens of leucine 16 and lysine 23, buried within the helical regions of melittin, appear as slow exchangers. However, calculations based on c-type ions for other amide hydrogens do not correlate well with NMR data, and evidence for deuterium scrambling in ECD was obtained from z*-type ions.     

Defect‐Assisted Covalent Binding of Graphene to an Amorphous Silica Surface: A Theoretical Prediction

We propose a mechanism for defect‐assisted covalent binding of graphene to the surface of amorphous silica (a‐SiO₂) based on first‐principles density functional calculations. Our calculations show that a dioxasilirane group (DOSG) on a‐SiO₂ may react with graphene to form two Si? O? C linkages with a moderate activation barrier (≈0.3 eV) and considerable exothermicity (≈1.0 eV). We also examine DOSG formation via the adduction of molecular O₂ to a silylene center, which is an important surface defect in a‐SiO₂, and briefly discuss modifications in the electronic structure of graphene upon the DOSG‐assisted chemical binding onto the a‐SiO₂ surface.