A short note on the entrainment and exit boundary conditions

An attempt is made to find out the suitable entrainment and exit boundary conditions in laminar flow situations. Streamfunction vorticity formulation of the Navier–Stokes equations are solved by ADI method. Two‐dimensional laminar plane wall jet flow is used to test different forms of the boundary conditions. Results are compared with the experimental and similarity solution and the proper boundary condition is suggested. The Kind 1 boundary condition is recommended. It consists of zero first derivative condition for velocity variable and for streamfunction equation, mixed derivative at the entrainment and exit boundaries. Copyright © 2005 John Wiley & Sons, Ltd.     

Lagrangian for the t–J Model Constructed from the Generators of the Supersymmetric Hubbard Algebra

In order to describe the dynamics of the t–J model, two different families of first-order Lagrangians in terms of the generators of the Hubbard algebra are found. Such families correspond to different dynamical second-class constrained systems. The quantization is carried out by using the path-integral formalism. In this context the introduction of proper ghost fields is needed to render the model renormalizable. In each case the standard Feynman diagrammatics is obtained and the renormalized physical quantities are computed and analyzed. In the first case a nonperturbative large-N expansion is considered with the purpose of studying the generalized Hubbard model describing N-fold-degenerate correlated bands. In this case the 1/N correction to the renormalized boson propagator is computed. In the second case the perturbative Lagrangian formalism is developed and it is shown how propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator coming from our formalism is studied in details. As an example the thermal softening of the magnon frequency is computed. The antiferromagnetic case is also analyzed, and the results are confronted with previous one obtained by means of the spin-polaron theories.     

Effect of phonon scattering from neutral and charged impurity centers on the lattice heat conductivity of PbTe:(Tl, Na)

Experimental data on the effect of thallium and sodium impurities on the lattice heat conductivity of PbTe at room temperature are reported. Because the lattice of lead chalcogenides is strongly polarized near charged impurities, the effect of impurities on the lattice heat conductivity depends substantially on their charge state. This property of the material has been used to determine the charge state of the thallium impurity in PbTe. The results obtained argue for a model of quasi-local thallium-impurity states which assumes low electron-correlation energy at an impurity center. Fiz. Tverd. Tela (St. Petersburg) 40, 1206–1208 (July 1998)     

Electron as the eigenstate of curvilinear space with torsion

Ideas previously enunciated by the author about the physical interpretation of curvilinear space with torsion are developed. With the new equations describing the eigenstates of such a space, the static centrosymmetric solution for gravitational and electric fields can be made consistent with the Newton and Coulomb laws. The asymptotic behavior of the axisymmetric solution at infinity is studied. The gyromagnetic ratio obtained is characteristic of the electron. Ural State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, p. 56–60, May, 1998.     

Orthogonal modules and nonlinear cohomologies

Ordinary cohomologies in an algebra most often exhibit themselves either as objects that describe extensions (of algebras, groups, or modules) or as subjects hindering the existence of algebraic constructions. We introduce the notion of nonlinear cohomologies at a level of cochain complexes, furnish particular examples for Lie algebras, and give an interpretation of first nonlinear cohomologies in terms of “quasiextensions” of orthogonal modules. Translated fromAlgebra i Logika, Vol. 37, No. 5, pp. 522–541, September–October, 1998.     

Thermal gradient induced sidebranching in directional solidification

The polycrystalline perovskitelike manganese oxides La_1-xA_xMnO (A = Na, and K, ) have been fabricated by sol-gel technique. For all the compositions explored in this work, the average manganese oxidation state is practically constant, at for A = Na, and for A = K, respectively. A close relationship is confirmed to hold between the Curie temperature (T_c) and the bond distance of Mn-O. Results of magnetic measurements show that these materials can be utilized as suitable candidates for magnetic refrigerants with wide applied temperature span, for their significant entropy change and the easily tuned Curie temperature. Received: 12 September 1997 / Revised: 18 December 1997 / Accepted: 21 January 1998     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

FORECASTING MINERAL SUPPLY FROM MINERAL RENT DATA

An optimal control model of exhaustible resources is used to clarify the long run relationship between mineral rent and depletion cost at the industry level. A standard first order condition of the time rate of change of rents is reformulated to reveal that rent data may be used to help forecast the rise in extraction costs resulting from resource depletion. This application of the theory of exhaustible resources is illustrated using historical mineral industry rent and extraction cost data. A forecast of U.S. coal extraction costs, following the method proposed in this paper, suggests that future rates of extraction cost increases will be similar to rates experienced in the past.     

Hydroxyl ion conduction in ytterbium-doped strontium cerate at T<580 K in H2O/air atmosphere

Open circuit voltage (OCV) measurements in H₂O/air concentration cells at T<580 K using Yb-doped SrCeO₃ electrolyte indicate that under these conditions, protons are transported through the electrolyte as -ve ions, possibly as hydroxyl (OH⁻) ions. The H⁺ ionic transport, which is generally reported, becomes the dominant mode for H₂O/air concentration cells at temperatures greater than 750 K or when H₂O/air electrodes are replaced by H₂/Ar, and the anomalous OCV sign disappears. The combination of low temperature and the presence of hydrogen and oxygen as provided by the H₂O/air system appears to be necessary for the postulated hydroxyl ion electrode reactions to take place. In addition to OCV measurements, results from impedance spectroscopy are used to provide evidence in support of the suggested hydroxyl ion mode of protonic transport under the specified conditions. These findings are directly relevant in the development of novel humidity sensors in the temperature range 450–580K and is reported in a separate paper in this conference. Paper presented at the 3rd Euroconference on Solid State Ionics, Teulada, Sardinia, Italy, Sept. 15–22, 1996