Equivalence Groups for First-Order Balance Equations and Applications to Electromagnetism

We investigate the groups of equivalence transformations for first-order balance equations involving an arbitrary number of dependent and independent variables. We obtain the determining equations and find their explicit solutions. The approach to this problem is based on a geometric method that depends on Cartan's exterior differential forms. The general solutions of the determining equations for equivalence transformations for first-order systems are applied to a class of the Maxwell equations of electrodynamics.     

On input/output stabilization of singular integrodifferential systems

In this paper we consider a class of systems described by singular integrodifferential equations. This type of systems appear, for example, in the modeling of certain aeroelastic control problems. We study these systems in frequency domain framework and show the existence of finite-dimensional stabilizing controllers. An algorithmic procedure is outlined for the construction of such controllers. In order to illustrate the numerical aspects of this algorithm, we present an example involving the classical Theodorsen model of an airfoil, which fits in the class of systems considered here.This work was supported in part by the National Science Foundation under Grants DMS-8907019 and MSS-9203418.     

Exact traveling wave solutions of perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law nonlinearity

By using new solutions of nonlinear partial differential equation, a direct algebraic method is described to construct the exact traveling wave solutions for perturbed nonlinear Schrödinger's equation (NLSE). Exact traveling wave solutions are explicitly obtained by this method.     

Study of phase transition in a [CdHgI4 : 0.2AgI] mixed conducting composite system doped with KI and K2SO4

New composite superionic systems, [CdHgI₄?:?0.2AgI]?:?0.xKI and [CdHgI₄?:?0.2AgI]?:?0.xK₂SO₄ (x?=?0.2, 0.4, 0.6?mol. wt%), were prepared, using [CdHgI₄?:?0.2AgI] mixed composite system as the host. Electrical conductivity was measured to study the transition behavior at frequencies of 100?Hz, 120?Hz, 1?kHz, and 10?kHz in the temperature range from 150°C to 250°C using a GENRAD 1659 RLC Digibridge. A sharp increase in conductivity was observed during β?→?α phase transition. Upon increasing the dopant-to-host ratio, the conductivity of the superionic systems exhibited Arrhenius (thermally activated)-type behavior. Differential thermal analysis, differential scanning calorimetry, thermogravimetric analysis, and X-ray powder diffraction were performed to confirm the doping effect and transition in the host. The phase transition temperature increased with an increase in the dopant concentration. Activation energies in eV for pre- and post-transition phase behavior are reported.     

Effects of inclined magnetic field on mixed convection in a nanofluid filled double lid-driven cavity with volumetric heat generation or absorption using finite element method

A computational analysis has been performed on mixed convection in a double sided lid-driven cavity in the presence of volumetric heat generation or absorption. Effects of inclined magnetic field are also studied. The governing parameters are solved via Galerkin weighted residual finite element method in space and the Crank–Nicolson in time. Governing parameters are nanoparticle volume fraction (0.0?≤???≤?0.04), Richardson number (0.01?≤?Ri?≤?10), internal heat generation or absorption parameter $(?10\le q\le 10),$ inclination angle of magnetic field (0°?≤?γ?≤?90°) and Hartmann number (0?≤?Ha?≤?100). It is observed that the highest heat transfer is obtained in case of the maximum value of heat absorption. As a further finding, heat transfer decreases with increasing of Hartmann number and increases with increasing of nanoparticle volume fraction.     

On geometric interpretations of split quaternions

Quaternions are an important tool that provides a convenient and effective mathematical method for representing reflections and rotations in three-dimensional space. A unit timelike split quaternion represents a rotation in the Lorentzian space. In this paper, we give some geometric interpretations of split quaternions for lines and planes in the Minkowski 3-space with the help of mutual pseudo orthogonal planes. We classified mutual planes with respect to the casual character of the normals of the plane as follows; if the normal is timelike, then the mutual plane is isomorphic to the complex plane; if the normal is spacelike, then the plane is isomorphic to the hyperbolic number plane (Lorentzian plane); if the normal is lightlike, then the plane is isomorphic to the dual number plane (Galilean plane).     

Improvement in magnetic properties of La substituted BaFe12O19 particles prepared with an unusually low Fe/Ba molar ratio

In this study, effect of lanthanum substitution on the phase composition, lattice parameters and magnetic properties of barium hexaferrite has been studied in samples synthesized in ammonium nitrate melt. Samples, prepared with different lanthanum amount and having various initial Fe/(Ba+La) ratios in between 12 and 2 {(Ba_1−xLa_x)·n Fe₂O₃, where 0≤x≤1 and 1≤n≤6)}, are sintered at temperatures from 800 to 1200 °C. The lattice parameters, both a and c, decreases with increasing La amount which results in a decrease of the unit cell volume. The scanning electron microscope micrographs show that the pure and La-substituted sample with x=0.3, both calcinated at 1000 °C, have grain sizes smaller than 1 μm. The coercivities of the La-substituted samples increase with increasing La amount and reaches to a maximum value of 5.73 kOe, when x=0.3. Sintering at higher temperatures (above 1000 °C) decreases the coercivity, resembling a transition from single to multi-domain behavior of the particles, while saturation magnetization of the samples continues to increase due to the increasing grain size. Magnetization measurements of the samples prepared with different Fe/(Ba+La) molar ratios, n's, revealed that the specific saturation magnetization slightly increases with decreasing n, while coercivities fluctuates around 5.5 kOe. However, a sharp increase in the saturation magnetization has been observed in the sample having n=1 and washed in HCl. It was measured as 59.2 emu/g at 15 kOe, which is higher than that of the pure sample (57.5 emu/g). Thus, the magnetic parameters are optimized in the sample Ba_0.7La_0.3Fe₁₂O₁₉ so as to maximize both coercivity and specific saturation magnetization in the HCl-washed sample synthesized by starting with an unusually low Fe/(Ba+La) molar ratio of 2 (or n=1).     

Temperature derivatives of the bulk modulus of ZrB2 calculated by using the pressure derivative of the bulk modulus

The temperature dependence of the bulk modulus of ZrB₂ above room temperature was calculated by using the equations by Garai and Laugier (J. Appl. Phys. 101 (2007) p.023514) and Lawson and Ledbetter (Philos Mag. 91 (2011) p.1425). The present calculations involve the accurate data for pressure derivative of the bulk modulus for the Anderson–Grüneisen parameter in addition to the other experimental parameters involved. It is interesting to note that the cited equations derived by different thermodynamic approaches give almost equivalent values for the temperature dependencies of the bulk modulus of ZrB₂. The present results for the temperature derivatives of the bulk modulus of ZrB₂ vary from ?0.016?GPa/K at 300–400?K to ?0.022?GPa/K at 1500–1600?K, being in good agreements with the corresponding experimental values.     

Cross section measurements of the Pd(p, γ)Ag, Sn(p, γ)Sb, and Sn(α, γ)Te reactions relevant to the astrophysical rp- and γ-processes

Total cross section measurements for the ¹⁰²Pd(p, γ)¹⁰³Ag and ¹¹⁶Sn(p, γ)¹¹⁷Sb reactions have been performed in the proton energy range 2.6 to 4.25 MeV, and for the ¹¹²Sn(α, γ)¹¹⁶Te reaction over the alpha beam energy range 7.0 to 10.5 MeV. An activation technique was used in which gamma rays from decays of the reaction products were detected off-line by two hyper-pure germanium detectors in a low background environment. Where possible, reaction rates are derived and the results compared to those of calculations generated by the NON-SMOKER and the MOST statistical model codes so as to judge their applicability for describing the cross sections needed for network calculations of nucleosynthesis in explosive astrophysical environments via the γ- and rp-processes.