Existence and global bounds for a fluid model of plasma display technology

This article considers the fluid model for the discharge of plasma particle species in display technology. The fluid equations are coupled with Poisson's equation, which describes the effect of the charged particles on the electric field. The diffusion and mobility coefficients for the positive ion particles depend on the electric field, while those for the electrons depend on the electron mean energy. The reaction rates are proportional to the products of the densities of the reacting particles involved in the particular ionization, conversion or recombination reactions. Moreover, the ionization coefficients are dependent on the electric field, which varies spatially and temporally. The main ionization and discharge reactions are described by an initial-boundary value problem for a system of coupled parabolic–elliptic partial differential equations. The system is first analyzed by upper–lower solution method. By means of the a priori bounds obtained for an arbitrary time, the existence of solution for the initial-boundary value problem is proved in an appropriate Hölder space.     

Non-linear oscillations of a rotor-magnetic bearing system under superharmonic resonance conditions

The effect of non-linear magnetic forces on the non-linear response of the shaft is examined for the case of superharmonic resonance in this paper. It is shown that the steady-state superharmonic periodic solutions lose their stability by either saddle-node or Hopf bifurcations. The system exhibits many typical characteristics of the behavior of non-linear dynamical systems such as multiple coexisting solutions, jump phenomenon, and sensitive dependence on initial conditions. The effects of the feedback gains and imbalance eccentricity on the non-linear response of the system are studied. Finally, numerical simulations are performed to verify the analytical predictions.     

Fuzzy variational principle and its applications

Linear and non-linear peaky fuzzy numbers and their arithmetic operations are constructed for the analysis of engineering structures with fuzzy characteristic quantities. Fuzziness of the corresponding quantities is consistently incorporated into the functional of the total potential energy. A set of deterministic recursive equations is obtained as the alternative expressions of the fuzzy variational principle by means of the second-order perturbation technique. The fuzzy Ritz method and the fuzzy finite element method are presented as the applications of the fuzzy variational principle. Accordingly, the roundabout procedures frequently used in the formulations of the fuzzy finite element method are avoided. A benchmark problem of a bending beam with fuzzy Young's modulus under fuzzy external loading is solved by the developed fuzzy numerical methods. Numerical examples show that results determined by these two fuzzy methods are both little conservative, and are in good agreement with those obtained by the analytical method. Moreover, the fuzzy Ritz method or the fuzzy finite element method can provide more valuable information than the conventional deterministic methods.     

Luminescence switch-on detection of protein tyrosine kinase-7 using a G-quadruplex-selective probe

A series of luminescent iridium(iii) complexes were synthesised and evaluated for their ability to act as luminescent G-quadruplex-selective probes. The iridium(iii) complex 9 [Ir(pbi)₂(5,5-dmbpy)]PF₆ (where pbi = 2-phenyl-1H-benzo[d]imidazole; 5,5-dmbpy = 5,5′-dimethyl-2,2′-bipyridine) exhibited high luminescence for G-quadruplex DNA compared to dsDNA and ssDNA, and was employed to construct a G-quadruplex-based assay for protein tyrosine kinase-7 (PTK7) in aqueous solution. PTK7 is an important biomarker for a range of leukemias and solid tumors. In the presence of PTK7, the specific binding of the sgc8 aptamer sequence triggers a structural transition and releases the G-quadruplex-forming sequence. The formation of the nascent G-quadruplex structure is then detected by the G-quadruplex-selective iridium(iii) complex with an enhanced luminescent response. Moreover, the application of the assay for detecting PTK7 in cellular debris and membrane protein extract was demonstrated. To our knowledge, this is the first G-quadruplex-based assay for PTK7.     

Dual Esterase‐ and Steroid‐Responsive Energy Transfer Modulation of Ruthenium(II) and Rhenium(I) Complex Functionalized Gold Nanoparticles

A number of adamantane‐containing ruthenium(II) and rhenium(I) complexes have been synthesized, characterized, and noncovalently functionalized with β‐cyclodextrin‐capped gold nanoparticles (β‐CD–GNPs) through the host–guest interaction between cyclodextrin and adamantane. The resultant nanoconjugates have been characterized by transmission electron microscopy (TEM), energy‐dispersive X‐ray analysis (EDX), and 2D ROESY ¹H NMR experiments. The Förster resonance energy transfer (FRET) properties of the nanoconjugates can be modulated by both esterase‐accelerated hydrolysis and competitive displacement of steroid, by monitoring the emission intensity and luminescence lifetime. The FRET efficiencies are found to vary with the nature of the chromophores and the length of the spacer between the transition metal complexes and the GNPs. This work constitutes a “proof‐of‐principle” assay method for the dual‐functional detection of important classes of biomolecules, such as enzymes and steroids.     

Velocity and turbulence measurements in combustion systems

A laser-Doppler velocimeter is used in the measurement of high-temperature gas flows. A two-stage fluidization particle generator provides magnesium oxide particles to serve as optical scattering centers. The one-dimensional dual-beam system is frequency shifted to permit measurements of velocities up to 300 meters per second and turbulence intensities greater than 100 percent.Exiting flows from can-type gas turbine combustors and burners with pre-mixed oxy-acetylene flames are described in terms of the velocity, turbulence intensity, and temperature profiles.The results indicate the influence of the combustion process on turbulence.List of Symbols A exit area of combustor or burner (m²) - A/F mass air-fuel ratio - D exit diameter of combustor or burner (m) - M mass flow rate of gases (kg/s) - N _D number of Doppler bursts used in each velocity measurement - Q volumetric flow rate at T _r (m³/s) - R exit radius of combustor or burner (m) - R _1/2 distance from centerline to radius where the velocity is one-half of the local centerline velocity (m) - Re exit Reynolds number based on cold flow, QD/A - r distance from centerline of flow (m) - T temperature (°C) - T _CL centerline temperature (°C) - T _r inlet (cold) air temperature of combustor or burner (°C) - T.I. turbulence intensity, - mean velocity (m/s) - U _i instantaneous velocity individually realized by LDV (m/s) - mean velocity at centerline of flow (m/s) - mean square velocity fluctuation (m²/s² - x distance along centerline downstream of exit (m) - absolute viscosity at T _r (kg/(ms)) - density at T _r (kg/m³)     

Ruthenium carbene complexes containing bidentate and tridentate PO ligands

Treatment of [Ru(CHR)Cl₂(PCy₃)₂] (Cy = cyclohexyl) with Tl[N(Pr₂ⁱPO)₂] and AgL_OEt (L_OEt⁻ = [CpCo{P(O)(OEt)₂}₃]⁻) afforded the Ru carbene complexes [Ru(CHPh)(PCy₃)Cl{N(Pr₂ⁱPO)₂}] (1) and [L_OEtRu(CHR)(PCy₃)Cl] (2), respectively. Chloride abstraction of complex 2 with TlPF₆ in MeCN afforded [L_OEtRu(CHPh)(PCy₃)(MeCN)][PF₆] (3). Complexes 1 and 2 are capable of catalyzing ring-closing metathesis of diethyl 1,2-diallylmalonate. The crystal structure of complex 2 has been determined.