3-D kinematical conservation laws (KCL): Evolution of a surface in R-3 - in particular propagation of a nonlinear wavefront

3-D KCL are equations of evolution of a propagating surface (or a wavefront) Omega(t), in 3-space dimensions and were first derived by Giles, Prasad and Ravindran in 1995 assuming the motion of the surface to be isotropic. Here we discuss various properties of these 3-D KCL.These are the most general equations in conservation form, governing the evolution of Omega(t) with singularities which we call kinks and which are curves across which the normal n to Omega(t) and amplitude won Omega(t) are discontinuous. From KCL we derive a system of six differential equations and show that the KCL system is equivalent to the ray equations of 2, The six independent equations and an energy transport equation (for small amplitude waves in a polytropic gas) involving an amplitude w (which is related to the normal velocity m of Omega(t)) form a completely determined system of seven equations. We have determined eigenvalues of the system by a very novel method and find that the system has two distinct nonzero eigenvalues and five zero eigenvalues and the dimension of the eigenspace associated with the multiple eigenvalue 0 is only 4. For an appropriately defined m, the two nonzero eigenvalues are real when m > 1 and pure imaginary when m < 1. Finally we give some examples of evolution of weakly nonlinear wavefronts.

Size effect on the lattice parameter of KCl during mechanical milling

The size effect on the lattice parameter of ionic KCl nanocrystals was studied systematically during mechanical milling of Pure KCl powder under vacuum. The results suggest anomalous lattice expansion, with the lattice parameter increasing from 6.278 angstrom at d = 6 mu m to 6.30307 angstrom at d = 85 mn. The defects generated during ball milling of KCl and surface stress are deemed to be responsible for this lattice parameter expansion. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Eigenvalues of kinematical conservation laws (KCL) based 3-D weakly nonlinear ray theory (WNLRT)

System of kinematical conservation laws (KCL) govern evolution of a curve in a plane or a surface in space, even if the curve or the surface has singularities on it. In our recent publication K. R. Arun, P. Prasad, 3-D kinematical conservation laws (KCL): evolution of a surface in R-3-in particular propagation of a nonlinear wavefront, Wave Motion 46 (2009) 293-311] we have developed a mathematical theory to study the successive positions and geometry of a 3-D weakly nonlinear wavefront by adding an energy transport equation to KCL. The 7 x 7 system of equations of this KCL based 3-D weakly nonlinear ray theory (WNLRT) is quite complex and explicit expressions for its two nonzero eigenvalues could not be obtained before. In this short note, we use two different methods: (i) the equivalence of KCL and ray equations and (ii) the transformation of surface coordinates, to derive the same exact expressions for these eigenvalues. The explicit expressions for nonzero eigenvalues are important also for checking stability of any numerical scheme to solve 3-D WNLRT. (C) 2010 Elsevier Inc. All rights reserved.

Microstructural and dielectric properties of KCl-added bismuth vanadate ceramics

The effect of KCI addition on the microstructural, structural and dielectric properties of bismuth vanadate, Bi2VO5.5 (BiV) has been examined. The average grain size of BN ceramics increases with increase in KCl content (from an average grain size of TO to 80 mu m) as a result of the increased liquid-phase formation of KCI, at the grain boundaries. Differential scanning calorimetry (DSC) carried out on the KCl-added samples indicates an upward shift in the transition temperature (T-c), from 723 K (for BN) to 734 K (for 5 mol% KCl-added BiV). On further increase in the KCI content, T-c shifts down to about 722 K for 10 mol%. This trend is consistent with that of the lattice strain data. The relative permittivity as well as the dielectric loss decrease by more than half of the original values upon the addition of KCI. The relative permittivities of the KCl-added ceramics are comparable with the values predicted by the logarithmic mixture rule. Impedance analyses suggest that the grain boundary resistance of the KCl-added BiV ceramics is higher by two orders of magnitude than that of BN ceramics. The KCl-added BN ceramics exhibit ferroelectric domains and the domain density decreases as the grain boundary region is approached.

Low temperature synthesis of ferromagnetic (LaK)MnO3 from KCl, KBr and KI fluxes

Potassium doped lanthanum manganites have been synthesized from KCl, KBr and KI fluxes at 900, 850 and 750 °C respectively. While all the flux-grown oxides are ferromagnetic metals (Tc=290–330 K), the oxides grown from KCl and KBr fluxes crystallize in the rhombohedral structure and that synthesized from KI flux adopts the cubic structure. The enhancement in Tc correlates with the increasing tendency of the flux to get oxidized and decreasing melting points of the flux. Nearly stoichiometric (LaK)MnO3 with 33 % of Mn4+ concentration could be prepared at temperature as low as 750 °C. Composition of all the phases have been obtained from the chemical analysis of the elements present.

KCL, Ray Theories and Application to Sonic Boom

We first review a general formulation of ray theory and write down the conservation forms of the equations of a weakly nonlinear ray theory (WNLRT) and a shock ray theory (SRT) for a weak shock in a polytropic gas. Then we present a formulation of the problem of sonic boom by a maneuvering aerofoil as a one parameter family of Cauchy problems. The system of equations in conservation form is hyperbolic for a range of values of the parameter and has elliptic nature else where, showing that unlike the leading shock, the trailing shock is always smooth.

Solubilities of Pb+2, Bi+3, Sb+3 and Cu+1 sulphides in (NaCl KCl Na2S) melts

Solubilities of common metal sulfides have been determined in the (NaCl+KCl) eutectic melt with and without Na2S. A novel gas-phase equilibrium technique has been used for PbS, Bi2S3, and So2S3, and an improved liquid phase equilibrium technique for Cu2S, which eliminates the errors due to physical entrapment of the sulfide phase and segregation on quenching, enabling precise measurements to be made. Solubilities in the (NaCl+KCl) eutectic melt were determined as a function of temperature in the rante 700° to 950°C, and were found to be small. The partial molar heats of mixing of the sulfides in the eutectic melt have been calculated from the solubility measurements, to be 13.3, 31.4, 37.1, and 49.0 kcal for PbSs), Sb2S2(l), and Cu2S(s), respectively. Sodium sulfide addition was observed to enhance these solubilities, the effect being largest for Cu2S followed by Sb2S3, Bi2S3, and PbS. This effect is explained qualitatively. It was observed that PbS and Sb2S3 obey Henry's law up to saturation in (NaCl+KCl+Na2S) melts.

Control for oriented growth of large size KCl crystals by the competition between spontaneous and induced nucleation/growth on a Langmuir-Blodgett film

Langmuir-Blodgett (LB) film of stearic acid was used as template to induce the nucleation and growth of KCl crystals when the KCl solution was cooled from 50 to 25 degrees C. When the LB film template was vertically dipped into the solution, only induced crystals with (1 1 0) orientation were formed. However, if the template was horizontally placed into solutions, both the induced nuclei at the solution/film interface and spontaneous nuclei formed in solution were simultaneously absorbed onto the LB film, and then grew further to form crystals. X-ray diffraction (XRD) patterns and optical microscopy images showed that the orientation and morphology of the crystals were controlled properly by changing the orientation and position of the LB films in the solutions.

Electrochemical behavior of Nd3+ and Ho3+ in LiCl-KCl eutectic melt

The electrochemical behavior of Nd3+ and Ho3+ ions on molybdenum electrode in the LiCl-KCl eutectic melts has been studied by cyclic voltammetry and open-circuit potentiometry. The results show that the reduction process of Nd3+ and Ho3+ ions on molybdenum electrode is one-step three electron reversible reaction. The diffusion coefficients of Nd3+ and Ho3+ ions are 1.13 x 10(-6) cm(2).s(-1)(450 degrees C) and 2.142 x 10(-5) cm(2).s(-1)(450 degrees C), respectively. The measured standard electrode potential of Ho3+/Ho is 2.987 V(vs. Cl/Cl-), being more negative than the theoretical one, the reason of which is also discussed.

KCl-LiCl共晶熔体中Nd~(3+)和Ho~(3+)的电化学行为

用循环伏安法和恒电流电解后的电位时间曲线法，研究了ＬｉＣｌＫＣｌ熔体中Ｎｄ３＋和Ｈｏ３＋在Ｍｏ电极上的电化学行为。结果表明，Ｎｄ３＋和Ｈｏ３＋在Ｍｏ电极上的还原都为一步３电子可逆过程。其扩散系数分别为：１１３×１０－６和２１４２×１０－５ｃｍ２·ｓ－１（４５０℃），４５０℃下Ｈｏ３＋／Ｈｏ电极对的标准氧化还原电位为２９８７Ｖ（ｖｓ·Ｃｌ／Ｃｌ－１），并讨论了实验值较理论值偏负的原因。

ELECTROCHEMICAL-BEHAVIOR OF YTTRIUM ION IN LICL-KCL-NACL EUTECTIC MELT

The electrochemical reduction of yttrium ion on a molybdenum electrode in a LiCl-KCl-NaCl eutectic melt at 723 K was found to be almost reversible and to proceed by a one-step three electron reaction. The diffusion coefficient D of the Y(III) ion was measured to be (3.3 +/- 0.4) x 10(-6) cm2 s-1 by cyclic voltammetry, (5.0 +/- 0.9) x 10(-6) cm2 s-1 by the rotating disk electrode method, and (7.1 +/- 0.7) x 10(-6) cm2 s-1 by chronopotentiometry. The D values obtained by the latter two methods are in fairly good agreement with each other. The rather low D value obtained by cyclic voltammetry might be attributed to the fact that yttrium metal can dissolve slightly in the chloride melt. The standard potential of Y(III)/Y(0) couple was determined to be (-3.174 +/- 0.006) V (vs. Cl2/Cl-) by open-circuit potentiometry, (-3.15 +/- 0.02) V (vs. Cl2/Cl-) by the rotating disk electrode method and (-3.16 +/- 0.02) V (vs. Cl2/Cl) by chronopotentiometry. These three values are in good agreement with each other. Several types of Ni-Y intermetallic compounds were found to be formed on a nickel electrode.

STRUCTURE-ANALYSIS OF MOLTEN CACL2-KCL SYSTEM BY X-RAY-DIFFRACTION

Radial distribution function of CaCl2-KCl (1:2 mol) melt was measured by X-ray scattering of high temperature liquid. The nearest neighbour distances of Ca2+-Cl-, K+-Cl- and Cl--Cl- ionic pairs are 0.278, 0.306 and 0.380 nm, respectively, Discussion on the relation between structure and physicochemical properties in the melt was simply done in this paper.