An unexpected property of quadrilaterals*

These notes discuss several related propositions in geometry that can be explored in a dynamic geometry environment. The propositions involve an unexpected property of quadrilaterals.     

Looking for Pythagoras between the folds

The purpose of this short paper is to describe a new proof of the Pythagorean Theorem that involves paper folding.     

First principles study and comparison of vibrational and thermodynamic properties of XBi(X= In,Ga, B,Al)

In the present work, vibrational and thermodynamic properties of XBi(X = B, Al, Ga, In) compounds are compared and investigated. The calculation is carried out using density functional theory(DFT) within the generalized gradient approximation(GGA) in a plane wave basis, with ultrasoft pseudopotentials. The lattice dynamical properties are calculated using density functional perturbation theory(DFPT) as implemented in Quantum ESPRESSO(QE) code. Thermodynamic properties involving phonon density of states(DOS) and specific heat at constant volume are investigated using quasiharmonic approximation(QHA) package within QE. The phonon dispersion diagrams for InBi, GaBi, BBi, and AlBi indicate that there is no imaginary phonon frequency in the entire Brillouin zone, which proves the dynamical stability of these materials. BBi has the highest thermal conductivity and InBi has the lowest thermal conductivity. AlBi has the largest and GaBi has the smallest reststrahlen band which somehow suggests the polar property of XBi materials. The phonon gaps for InBi, GaBi, BBi and AlBi are about 160 cm~(-1), 150 cm~(-1), 300 cm~(-1), and 150 cm~(-1), respectively. For all compounds,the three acoustic modes near the gamma point have a linear behavior. C_V is a function of T~3 at low temperatures while for higher temperatures it asymptotically tends to a constant as expected.     

Pore-Scale Network Modeling of Three-Phase Flow Based on Thermodynamically Consistent Threshold Capillary Pressures. I. Cusp Formation and Collapse

We present a pore-scale network model of two- and three-phase flow in disordered porous media. The model reads three-dimensional pore networks representing the pore space in different porous materials. It simulates wide range of two- and three-phase pore-scale displacements in porous media with mixed-wet wettability. The networks are composed of pores and throats with circular and angular cross sections. The model allows the presence of multiple phases in each angular pore. It uses Helmholtz free energy balance and Mayer–Stowe–Princen (MSP) method to compute threshold capillary pressures for two- and three-phase displacements (fluid configuration changes) based on pore wettability, pore geometry, interfacial tension, and initial pore fluid occupancy. In particular, it generates thermodynamically consistent threshold capillary pressures for wetting and spreading fluid layers resulting from different displacement events. Threshold capillary pressure equations are presented for various possible fluid configuration changes. By solving the equations for the most favorable displacements, we show how threshold capillary pressures and final fluid configurations may vary with wettability, shape factor, and the maximum capillary pressure reached during preceding displacement processes. A new cusp pore fluid configuration is introduced to handle the connectivity of the intermediate wetting phase at low saturations and to improve model’s predictive capabilities. Based on energy balance and geometric equations, we show that, for instance, a gas-to-oil piston-like displacement in an angular pore can result in a pore fluid configuration with no oil, with oil layers, or with oil cusps. Oil layers can then collapse to form cusps. Cusps can shrink and disappear leaving no oil behind. Different displacement mechanisms for layer and cusp formation and collapse based on the MSP analysis are implemented in the model. We introduce four different layer collapse rules. A selected collapse rule may generate different corner configuration depending on fluid occupancies of the neighboring elements and capillary pressures. A new methodology based on the MSP method is introduced to handle newly created gas/water interfaces that eliminates inconsistencies in relation between capillary pressures and pore fluid occupancies. Minimization of Helmholtz free energy for each relevant displacement enables the model to accurately determine the most favorable displacement, and hence, improve its predictive capabilities for relative permeabilities, capillary pressures, and residual saturations. The results indicate that absence of oil cusps and the previously used geometric criterion for the collapse of oil layers could yield lower residual oil saturations than the experimentally measured values in two- and three-phase systems.     

An optimal analysis for Darcy–Forchheimer 3D flow of nanofluid with convective condition and homogeneous–heterogeneous reactions

Here Darcy–Forchheimer 3D stretching flow of nanoliquid in the presence of convective condition and homogeneous–heterogeneous reactions is analyzed. Impacts of thermophoresis, Brownian diffusion and zero nanoparticles mass flux condition are considered. Adequate transformation procedure give rise to system in terms of ordinary differential equations. The governing mathematical system has been tackled by optimal homotopic technique. Graphical results have been presented for temperature and concentration dsitributions. Numerical benchmark is provided to study the values of skin friction coefficients and local Nusselt number. Skin friction coefficients are declared increasing functions of porosity and Forchheimer parameters. Furthermore the local Nusselt number is reduced for larger values of porosity and Forchheimer parameters.     

One‐pot synthesis of 2,3‐disubstituted‐2,3‐dihydroquinazolin‐4(1H)‐ones using [Hmim][NO3]: An eco‐friendly protocol

An efficient method for the synthesis of a series of 2,3‐disubstituted‐2,3‐dihydroquinazolin‐4(1H)‐ones is described via one‐pot condensation reaction of isatoic anhydride, aryl aldehydes, and primary amines using a Brønsted acidic ionic liquid, [Hmim][NO₃], as a catalyst and medium. The present protocol enjoys convenient reaction and simple work‐up, greenness, short reaction times, and reusable catalyst as well as mild reaction conditions. J. Heterocyclic Chem., (2011).     

A new building block for electroactive organic materials? Synthesis, cyclic voltammetry, single crystal X-ray structure, and DFT treatment of a unique boron-based viologen

A boronium-based paraquat analog undergoes reductions at more negative potentials than paraquat itself, making it a promising building block for electroactive materials.     

Determination of nickel using cold-induced aggregation microextraction based on ionic liquid followed by flame atomic absorption spectrometry

Cold-induced aggregation microextraction (CIAME) combined with flame atomic absorption spectrometry (FAAS) was applied to preconcentration and determination of nickel(II) ions in natural water samples. The proposed method used 1-hexyl-3-methylimidazolium hexafluorophosphate ([Hmim][PF ₆ ]) as the extraction solvent and 1-(2-thiazolylazo)-2-naphthol (TAN) as the complexing agent. The extraction solvent was dissolved in the sample solution at 45°C. After dissolving, the solution was cooled in the ice bath and a cloudy solution of IL fine droplets was formed due to the decrease of IL solubility. After centrifugation, the fine droplets of extractant phase were settled at the bottom of the conical-bottom centrifuge tube. Analysis was carried out by a FAAS. Several important parameters influencing the CIAME extraction efficiency such as pH, complexing agent concentration, extraction solvent volume, salt effect, solution temperature, extraction time, centrifugation time and heating time were investigated and optimized. Under the optimum conditions, the limit of detection (LOD) was 0.8 ng/mL, and the relative standard deviation (RSD) was 3.4% for 50 ng/mL of nickel. The performance of the method was evaluated for extraction and determination of nickel in tap, mineral and seawater samples, and satisfactory results were obtained.     

A novel method of flat YBCO rings development for shield-type superconducting fault current limiters fabrication

The application of flat superconductor rings has been investigated in the structure of inductive shield-type high temperature superconducting fault current limiters, HT_c-SFCL. A laboratory scale inductive shield-type HT_c-SFCL has been designed and fabricated using flat superconductor rings. The fabrication process has been fully presented. YBCO powder has been used for the fabrication of superconductor rings. This fabrication process, being quite innovative, is introduced completely. The method of the trapped field measurement has been used for the critical current density measurement of the fabricated superconductor rings. The device with nominal current of 2 A was tested in a 30 V circuit. The SFCL successfully limited the fault currents of up to 10 times the nominal current to an approximately fixed value of 3 A. The voltage-current characteristic of the fabricated prototype has also been obtained and has shown compatibility with the fault current limitation results.