Steady‐state solution of incompressible Navier–Stokes equations using discrete least‐squares meshless method

A fractional step method for the solution of the steady state incompressible Navier–Stokes equations is proposed in this paper in conjunction with a meshless method, named discrete least‐squares meshless (DLSM). The proposed fractional step method is a first‐order accurate scheme, named semi‐incremental fractional step method, which is a general form of the previous first‐order fractional step methods, i.e. non‐incremental and incremental schemes. One of the most important advantages of the proposed scheme is its capability to use large time step sizes for the solution of incompressible Navier–Stokes equations. DLSM method uses moving least‐squares shape functions for function approximation and discrete least‐squares technique for discretization of the governing differential equations and their boundary conditions. As there is no need for a background mesh, the DLSM method can be called a truly meshless method and enjoys symmetric and positive‐definite properties. Several numerical examples are used to demonstrate the ability and the efficiency of the proposed scheme and the discrete least‐squares meshless method. The results are shown to compare favorably with those of the previously published works. Copyright © 2010 John Wiley & Sons, Ltd.     

A Classical Cosmological Model for Triviality

The aim of this paper is to study the triviality of λ ϕ⁴ theory in a classical gravitational model. Starting from a conformal invariant scalar tensor theory with a self-interaction term λ ϕ⁴, we investigate the effect of a conformal symmetry breaking emerging from the gravitational coupling of the large-scale distribution of matter in the universe. Taking in this cosmological symmetry breaking phase the infinite limit of the maximal length (the size of the universe) and the zero limit of the minimal length (the Planck length) implies triviality, i.e. a vanishing coupling constant λ. It suggests that the activity of the self-interaction term λ ϕ⁴ in the cosmological context implies that the universe is finite and a minimal fundamental length exists.     

Rapid and Efficient Synthesis of Imidazolines and Bisimidazolines Under Microwave and Ultrasonic Irradiation

Summary. Small assemblies of 2-imidazolines and bisimidazolines from appropriate nitriles and ethylenediamine with catalytic amounts of P₂S₅ employing a microwave assisted protocol were prepared. Sonication of this system also led to successful synthesis of 2-imidazolines and bisimidazolines. Another advantage of these systems is the ability to carry out large scale reactions.     

Design of the novel calix[n]BODIPY molecules (n = 4–8): TDDFT and AIM study

Journal of Inclusion Phenomena and Macrocyclic Chemistry - In this study, based on BODIPY molecule, new calix-like structures with significant electrical and optical properties were designed. These...     

Distinguishing between evidence and its explanations in the steering of atomic clocks

Quantum theory reflects within itself a separation of evidence from explanations. This separation leads to a known proof that: (1) no wave function can be determined uniquely by evidence, and (2) any chosen wave function requires a guess reaching beyond logic to things unforeseeable. Chosen wave functions are encoded into computer-mediated feedback essential to atomic clocks, including clocks that step computers through their phases of computation and clocks in space vehicles that supply evidence of signal propagation explained by hypotheses of spacetimes with metric tensor fields.     

An Adaptive Hydrogen-Bonded Organic Framework for the Exclusive Recognition of p-Xylene

Separation of xylene isomers is one of the most important but most challenging and energy-intensive separation processes in the petrochemical industry. Here, we report an adaptive hydrogen-bonded organic framework (HOF-29) constructed from a porphyrin based organic building block 4,4′,4′′,4′′′-(porphyrin-5,10,15,20-tetrayl) tetrabenzonitrile (PTTBN), exhibiting the exclusive molecular recognition of p-xylene (pX) over its isomers of o-xylene (oX) and m-xylene (mX), as clearly demonstrated in the single crystal structure transformation and ¹H NMR studies. Single crystal structure studies show that single-crystal-to-single-crystal transformation from the as-synthesized HOF-29 to the pX exclusively included HOF-29⊃pX is triggered by the encapsulation of pX molecules, accompanied by sliding of the 2D layers and local distortion of the ligand, which provides multiple C−H⋅⋅⋅π interactions.     

Physical properties of suspension ZnO nanoparticles prepared by wet chemical method: Comparison study

In this work a suspension of Nano-crystalline of ZnO particle is prepared by wet chemical at different temperature and concentration. From FTIR spectral exhibit present of Zn–O bond which indicate to formation ZnO particles. While all suspension and nano films exhibit a high transmittance in visible region about 90% which falls sharply in the UV region. The particle size is measured by using effective mass approximation (EMA), which was approximation (1.7–1.96 nm), and the band gap changes from 3.95 to 4.52eV for nanoparticles in suspension, and change from 3.76 to 3.94 eV for nanoparticles in ZnO film, which is change as function of concentration, temperature and aging time. Hall Effect measurements for ZnO films exhibit n-type conductivity for films deposited with activation energy 0.742eV at high temperature and 0.178eV at low temperature which is different as prepared sample conditions. Also the nanoparticle suspension and nanoparticle film could be implemented as a filter with variable cut off (8.9 × 10¹⁴–1.28 × 10¹⁵) H_Z.     

Nitrite and Nitrate Production by NO and NO2 Dissolution in Water Utilizing Plasma Jet Resembling Gas Flow Pattern

This study investigated the reactive dissolution of nitric oxide (NO) and nitrogen dioxide (NO₂) mixtures in deionized water. The dissolution study was carried out in a flat surface type gas–liquid reaction chamber utilizing a gas flow-pattern resembling plasma jets which are often used in biomedical applications. The concentration of NO and NO₂ in the gas mixtures was varied in a broad range by oxidizing up to 800 ppm of nitric oxide in Ar carrier gas with variable amount of ozone. The production of nitrite (NO₂^?) and nitrate (NO₃^?) in the water was proportional to treatment time up to 50 min. The concentration of NO₃^? was a power function of gas phase NO₂ while the concentration of NO₂^? increased approximately linearly with gas phase NO₂. The formation of NO₂^? and NO₃^? could be described by reactions between dissolved NO₂ and NO in the water while the production rate was determined by diffusion-limited mass transport of nitrogen oxides to the bulk of the liquid. At higher NO₂ concentrations, the formation of dinitrogen tetraoxide (N₂O₄) increased the formation rate of NO₂^? and NO₃^?. The identified mass transport limitation by diffusion suggests that convection of water created by the gas jet is insufficient and dissolution of nitrogen oxides can be increased by additional mixing. In respect of practical applications, the ratio of NO₂^? /NO₃^? in water could be varied from 0.8 to 5.3 with treatment time and gas phase NO₂ and NO concentrations.