On the geometry of Siegel-Jacobi domains

We study the holomorphic unitary representations of the Jacobi group based on Siegel-Jacobi domains. Explicit polynomial orthonormal bases of the Fock spaces based on the Siegel-Jacobi disk are obtained. The scalar holomorphic discrete series of the Jacobi group for the Siegel-Jacobi disk is constructed and polynomial orthonormal bases of the representation spaces are given.Comment: 15 pages, Latex, AMS fonts, paper presented at the the International Conference "Differential Geometry and Dynamical Systems", August 25-28, 2010, University Politehnica of Bucharest, Romani

Thermal conductivity of the thermoelectric layered cobalt oxides measured by the Harman method

In-plane thermal conductivity of the thermoelectric layered cobalt oxides has been measured using the Harman method, in which thermal conductivity is obtained from temperature gradient induced by applied current. We have found that the charge reservoir block (the block other than the CoO$_2$ block) dominates the thermal conduction, where a nano-block integration concept is effective for material design. We have further found that the thermal conductivity shows a small but finite in-plane anisotropy between $a$ and $b$ axes, which can be ascribed to the misfit structure.Comment: 4 pages, 4 figures, J. Appl. Phys. (scheduled on July 1, 2004

Spectrophotometric Determination of Iron (III) after Separation by Adsorption of its N-Benzoyl-N-Phenyl Hydroxylamine Complex on Naphthalene

The novel method for the spectrophotometric determination of trace amount of iron (III) after separation of its BPA complex by adsorption on microcrystalline naphthalene is described. The epsilon/ sub max/ of the DMF solution of the adsorbate containing iron (III)- BPA complex at lambda/sub max/ 437 nm has been found to be 4.47 X 10/sup 3/. The effect of variables and interfering ions on the efficacy method has been studied. Sensitivity (in Sandell's notation) is 1.25 X 10/sup -2/ micro g of iron (III)/cm/sup 2/ and at a mean absorbance of 0.40000 is 1.25%. The method is useful for the analysis of standard reference materials and environmental samples. The results are comparable with those obtained using ortho phenanthroline

Spectrophotometric Determination of Iron(III) after Separation by Adsorption of its Pyrrolidinedithiocarbamate on Nephthalene

A method for the spectrophotometric determination of trace amounts of iron(III) after adsorption of its pyrrolidindeithiocarbamate on naphthalene is presented. Iron(III) forms a water-insoluble chelate with ammonium pyrrolidinedithiocarbamate in the pH range 2.9-6.6. This chelate is quantitatively adsorbed onto mycrocrystalline naphthalene at room temperature. The effects of variablesm, such as pH, amount of reagent and napthalene, digestion and shaking time, and diverse ions, have been examined. The method has been applied to the determination of iron(III) in standard reference and environmental samples and the results compared with 1,10-phenanthroline method

Benchmark Test of Drift-kinetic and Gyrokinetic Codes through Neoclassical Transport Simulations

Two simulation codes that solve the drift-kinetic or gyrokinetic equation in toroidal plasmas are benchmarked by comparing the simulation results of neoclassical transport. The two codes are the drift-kinetic delta f Monte Carlo code (FORTEC-3D) and the gyrokinetic full- f Vlasov code (GT5D), both of which solve radially-global, five-dimensional kinetic equation with including the linear Fokker-Planck collision operator. In a tokamak configuration, neoclassical radial heat flux and the force balance relation, which relates the parallel mean flow with radial electric field and temperature gradient, are compared between these two codes, and their results are also compared with the local neoclassical transport theory. It is found that the simulation results of the two codes coincide very well in a wide rage of plasma collisionality parameter nu = 0.01 ~ 10 and also agree with the theoretical estimations. The time evolution of radial electric field and particle flux, and the radial profile of the geodesic acoustic mode frequency also coincide very well. These facts guarantee the capability of GT5D to simulate plasma turbulence transport with including proper neoclassical effects of collisional diffusion and equilibrium radial electric field

Eulerian variational formulations and momentum conservation laws for kinetic plasma systems

The Eulerian variational principle for the Vlasov-Poisson-Amp\`{e}re system of equations in a general coordinate system is presented. The invariance of the action integral under an arbitrary spatial coordinate transformation is used to obtain the momentum conservation law and the symmetric pressure in a more direct way than using the translational and rotational symmetries of the system. Next, the Eulerian variational principle is given for the collisionless drift kinetic equation, where particles' phase-space trajectories in given electromagnetic fields are described by Littlejohn's guiding center equations~[R. G. Littlejohn, J. Plasma Phys.\ {\bf 29}, 111 (1983)]. Then, it is shown that, in comparison with the conventional moment method, the invariance under a general spatial coordinate transformation yields a more convenient way to obtain the momentum balance as a three-dimensional vector equation in which the symmetric pressure tensor, the Lorentz force, and the magnetization current are properly expressed. Furthermore, the Eulerian formulation is presented for the extended drift kinetic system, for which, in addition to the drift kinetic equations for the distribution functions of all particle species, the quasineutrality condition and Amp\`{e}re's law to determine the self-consistent electromagnetic fields are given. Again, the momentum conservation law for the extended system is derived from the invariance under the general spatial coordinate transformation. Besides, the momentum balances are investigated for the cases where the collision and/or external source terms are added into the Vlasov and drift kinetic equations