Thermal expansion and heat capacity measurements on Ba10?xCsx(PO4)6Cl2?δ, (x?=?0, 0.5) chloroapatites synthesized by sonochemical process

Ba_10−x Cs _x (PO₄)₆Cl₂, (x = 0, 0.5) chloroapatite ceramics were prepared by sonochemical method of synthesis. The measured room temperature lattice parameters of Ba₁₀ (PO₄)₆Cl₂ and Ba_9.5Cs_0.5 (PO₄)₆Cl_2−δ are practically the same; that is, a = 10.26 (8), c = 7.65 (7) and a = 10.27 (7), c = 7.65 (5), respectively. Heat capacity measurements were carried out on these materials by differential scanning calorimetry (DSC) in the temperature range 298–800 K. The heat capacity values of Ba_9.5Cs_0.5(PO₄)₆Cl_2−δ are found to be slightly higher at all temperatures than those of Ba₁₀(PO₄)₆Cl₂. From the heat capacity data, other thermodynamic functions such as enthalpy and entropy increments were computed. The heat capacity values of Ba₁₀(PO₄)₆Cl₂ and Ba_9.5Cs_0.5(PO₄)₆Cl_2−δ at 298 K are 0.3912 and 0.4310 J K⁻¹ g⁻¹, respectively. Thermal expansion property of the doped and undoped barium chloroapatites was measured by using a home built dilatometer which uses LVDT as displacement sensor. The bulk thermal expansion of Ba₁₀(PO₄)Cl₂ and Ba_9.5Cs_0.5(PO₄)Cl_2−δ is observed to be about 0.9% in the temperature range of 298–973 K.     

Character tables of n-dimensional hyperoctahedral groups and their applications*

We have shown that powerful matrix-type-based multinomial generators together with combinatorial techniques can be applied to derive the conjugacy classes, irreducible representations and the character tables of n-dimensional hyperoctahedral or hypercube groups of order n! × 2ⁿ, which are generalisations of non-rigid molecular theory formulated by Longuet-Higgins. The hyperoctahedral groups appear in the symmetry groups of non-rigid molecules, non-rigid water clusters, and other weakly bound van der Waals complexes that exhibit rapid tunnelling motion among various low-lying surmountable potential energy minima. These groups also have applications in quantum chromodynamics in the classification of states of quarks. The associated combinatorics has applications in enumerations, nuclear spin statistics and NMR spectroscopy. Finally, the groups enhance understanding of chirality in biosystems, that is, the functionality of intrinsically disordered proteins. We have derived the character tables of hyperoctahedral groups of sixth dimension, and techniques have been outlined to generalise for higher dimensions in the form of matrix generators.     

Synthesis of silver nanoparticles and antimony oxide nanocrystals by pulsed laser ablation in liquid media

Pulsed laser ablation in liquid media (PLALM) is a prominent technique for the controlled fabrication of nanomaterials via rapid reactive quenching of ablated species at the interface between the plasma and liquid. Results on nanoparticles and nanocrystals formed by PLALM of silver (Ag) and antimony (Sb) solid targets in different liquid environments (Sodium Dodecyl Sulfate, distilled water) are presented. These experiments were done by irradiating solid targets of Ag and Sb with a nanosecond pulsed Nd:YAG laser output of wavelength 532 nm. Nanoparticles of silver and nanocrystals of antimony oxide (Sb₂O₃) obtained were characterized using UV-Vis spectrometry, Scanning Electron Microscopy (SEM), transmission electron microscopy (TEM), X-ray Energy Dispersion Analysis (EDAX) and X-ray diffractometry (XRD). The morphology of nanomaterials formed is studied as a function of surfactant environment. The silver nanoparticles obtained were spherical of size in the order of 10–35 nm in solution of SDS having different concentrations. In case of the Sb target, ablation was performed in two different molarities of SDS solution and distilled water. Nanocrystals of Sb₂O₃ in powder form having cubic and orthorhombic phases were formed in SDS solution and as fibers of nanocrystals of cubic Sb₂O₃ in distilled water.     

Finite element study of free surface turbulent flow in rotating channels

Under certain conditions of liquid flow through rotating channels, the Coriolis force can induce a free surface to be formed. This problem is of practical importance in a Coriolis wear tester, which is used for determining the sliding wear coefficient of wear materials in slurry handling equipment. A deforming Galerkin finite element method is presented for predicting two‐dimensional turbulent free surface mean flow in rotating channels. Reynolds‐averaged Navier–Stokes (RANS) equations are cast into weak(algebraic) form using primitive variables (velocity and pressure). Eddy viscosity is determined via a mixing length model. Velocity is interpolated biquadratically, while pressure is interpolated bilinearly. The kinematic condition is used to form the Galerkin residual for the free surface. The free surface is represented by Hermite polynomials of zeroeth order for continuity of position and slope. Combined Newton's iteration is used to simultaneously solve for the free surface and the field variables. Results of velocity and pressure fields, as well as the free surface are shown to converge with mesh‐size refinement. There is excellent respect for mass conservation. Results are presented for various values of Rossby number (Ro) and height‐based Reynolds number (Re_H). Parameter continuation in Ro and Re_H space is used to compute solutions at higher values of flow rate and angular velocity. Copyright © 2002 John Wiley & Sons, Ltd.     

An Epidemic Model with a Time Delay in Transmission

We study a mathematical model which was originally suggested by Greenhalgh and Das and takes into account the delay in the recruitment of infected persons. The stability of the equilibria are also discussed. In addition, we show that the introduction of a time delay in the transmission term can destabilize the system and periodic solutions can arise by Hopf bifurcation.     

On the integration of data and mathematical modeling languages

This paper examines ways in which the addition of data modeling features can enhance the capabilities of mathematical modeling languages. It demonstrates how such integration is achieved as an application of the embedded languages technique proposed by Bhargava and Kimbrough [4]. Decision-making, and decision support systems, require the representation and manipulation of both data and mathematical models. Several data modeling languages as well as several mathematical modeling languages exist, but they have different sets of these capabilities. We motivate with a detailed example the need for the integration of these capabilities. We describe the benefits that might result, and claim that this could lead to a significant improvement in the functionality of model management systems. Then we present our approach for the integration of these languages, and specify how the claimed benefits can be realized.The author's work on this paper was performed in conjunction with research funded by the Naval Postgraduate School.     

Theoretical study of possible products of the combination of H2O and HCN

Twenty-two structures with the empirical formula H₃CNO are presented. These structures are examined since they have the same formula as the H₂O…HCN complex. The H₂O…HCN potential energy surface is of interest to chemists studying the water catalyzed polymerization of HCN. Structures, thermodynamics, and vibrational spectra are examined.     

Multi-channel gain and noise figure evaluation of Raman/EDFA hybrid amplifiers

We present detailed multi-channel experimental characterization of different configurations of single pump hybrid Raman-erbium doped fiber (EDF) amplifiers. The incorporation of an EDF section in a dispersion compensating Raman amplifier is demonstrated to provide superior performance than Raman only system. It is shown that the multi-channel gain spectrum is quite different form the single-channel case. We have also measured the polarization dependent gain (PDG) of the hybrid amplifier configurations and results show that different configurations of hybrid amplifiers have different PDG effects on long-haul optically amplified link.     

Elastic constants of sodium chlorate from 77 K to 350 K

The elastic constantsC ₁₁,C ₁₂ andC ₄₄ of sodium chlorate single crystal have been evaluated using 10 MHz ultrasonic pulse echo superposition technique. The values areC ₁₁=4.90,C ₁₂=1.39,C ₄₄=1.17 (× 10¹⁰ N/m ²) at 298 K and 6.15, 2.16, 1.32 (×10¹⁰ N/m ²) at 77 K. The data agree well with the values measured earlier up to 223 K. Brief mention is also made of the low temperature bonding problems in these soft crystals.