A new method of describing bottom stress in two-dimensional hydrodynamical models of shallow homogeneous seas, estuaries, and lakes

A new expression for bottom friction is developed for use in two-dimensional hydrodynamical models of shallow homogeneous seas, estuaries, and lakes. Bottom stress is provided by a single relaxation approximation which can be used to replace the conventional parametrization in any existing explicit time-stepping model. The method produces the correct steady state flow for wind-driven circulation in shallow systems. It derives the bottom stress from the vertical eddy viscosity which can have any prescribed variation through the water column. The single relaxation approximation uses a recursive relation for bottom stress involving only values at the previous time step and a pair of precomputed coefficients at each grid point.     

Optical absorption of Co2+ doped NH4Cl: Phase transformation studies

The absorption spectrum of Co²⁺ doped NH₄Cl has been studied from the room temperature to the liquid nitrogen temperature. A sudden change in the spectrum is observed between 243° K and 233° K which is attributed to the phase transition in the crystal. From the observed spectrum it is suggested that Co²⁺ goes in interstitially as well as substitutionally. Both the types of centers exist at room temperature, but with decrease in temperature substitutional ions migrate to interstitial sites, the process being stimulated at the phase transformation point so that the 77° K spectrum seems to be mostly due to the interstitial centers. The 77° K spectrum is analyzed in the approximation of octahedral symmetry for interstitial ions and the band positions are fitted fairly well with B = 870 cm.^?1 Dq = 850 cm.^?1 and C = 4·4 B. A blue shift of about 100 cm.^?1 is observed for⁴T₁ (P) band at the phase transition which is attributed to the increase in Dq value with the anomalous lattice contraction at the phase transition. The decrease in the lattice parameter calculated from this blue shift is around 0·4% which is in good agreement with the results of X-ray measurements. Two possible models for the interstitial complex are examined and the one with fourfold chlorine coordination associated with two neutral water molecules at the first neighbour (NH₄)⁺ site lying along < 100> direction is suggested to be more probable.     

A grain boundary defect model for ZnO ceramic varistors by deep heat treatment

Studies on ZnO ceramic varistors by deep heat treatment at 650–900 C are reported. The current creep time curve exhibits a peak during the continuous action of a dc biasing voltage; the forwardV-l characteristic is improved rather than degraded after the action of the biasing voltage. We assume that the zinc interstitial cations Zn_i are out diffused rapidly and the concentration of Zn_i in the depletion layer is decreased rapidly during deep heat treatment; the oxygen anions O’_o could be accumulated at the grain interface if the out diffusion quantity of Zn_i is not enough to react with the O’_o; the current creep phenomenon above results from the migration of the interface O’_o by the biasing voltage. We suggest an improved grain boundary defect model for the ZnO varistors by deep heat treatment, and examine the model using the experimental data of lifetime positron-annihilation spectroscopy. Project supported by the National Natural Science Foundation of China.     

Full-potential LMTO study on the electronic structure of heavy-fermion compound LiV2O4

The electronic structure of heavy fermion compound LiV2O4 has been calculated using a self-consistent full-potential LMTO method. The results show that the conduction bands in this com pound are formed from V 3 d states with a bandwidth of 2.5 eV. The symmetric characteristics of con duction bands are of t2g in principle. The energy gap between conduction bands and fully occupied oxygen 2 p bands is 1.9 eV. The band dispersions near Fermi energy display complicated structures.Furthermore, the N(EF) and γcal are 11.1 (states/eV/f. u. ) and 26.7 mJ/mol@ K2 determined numer ically by LDA calculation, respectively. It is insufficient to clarify the origin of local moment in LiV2O4 from plain LDA calculations. In addition to the above LDA calculation, we also found a LSDA solution of LiV2O4 that is lower in total energy than that of LDA calculation. Similarly, LSDA + GGA calculation yields almost the identical result as that in LSDA. We conclude that the mechanism responsible for heavy fermion properties in LiV2O4 might be somewhat different from the plain Kondo mechanism in conventional 4 f and 5 f heavy fermion compounds and perhaps the quantum transition might play an adequate role in heavy-fermion behaviors in LiV2O4.     

Infrared absorption spectra of some lanthanide acetylacetonate complexes

The infrared absorption spectra of 12 lanthanide acetylacetonate complexes were measured in the region 400–2000 cm^?1 and discussed. Assignments of the bands especially those due to metal-oxygen (M—O), C=O and C=C stretching vibration is given. It is found that the band at 530 ± 5 cm^?1 is due mainly to Ln—O stretching vibration. In the carbonyl region, it is confirmed that the band at lower frequency is a C=C stretching vibration while that at higher frequency is due to C=O stretching vibration. Integral intensities for the M—O, C=O and C=C stretching vibrations were calculated in KB₁ and CHCl₃ solutions. The variation of the intensities of the M—O bands witn complexed cation were discussed in terms of crystal field stabilization energy (CFSE).     

X-Ray spectroscopic evidence for chemical bonding in manganese selenide (MnSe)

K absorption spectra of manganese and selenium have been recorded photographically in the pure metals and in the intermetallic compound manganese selenide (MnSe), employing a bent crystal X-ray spectrograph. It has been observed that the Mn K absorption discontinuity in MnSe shifts by 5·6 eV toward the high energy side with respect to the discontinuity in the pure metal. On the other hand, the Se K edge in MnSe is found to shift by 3·4 eV toward the low energy side with respect to the discontinuity in pure selenium. Also, emission work has revealed that the Mn K_β5 band in the compound shifts by about 5 eV toward the high energy side with respect to that in the pure metal. It has been shown that these results confirm the resonatingp ³ type of chemical bonding in the compound, as suggested theoretically by Pearson.     

Balance-characteristic scheme as applied to the shallow water equations over a rough bottom

The CABARET scheme is used for the numerical solution of the one-dimensional shallow water equations over a rough bottom. The scheme involves conservative and flux variables, whose values at a new time level are calculated by applying the characteristic properties of the shallow water equations. The scheme is verified using a series of test and model problems.     

Well-balanced unstaggered central schemes for one and two-dimensional shallow water equation systems

We propose a new well-balanced unstaggered central finite volume scheme for hyperbolic balance laws with geometrical source terms. In particular we construct a new one and two-dimensional finite volume method for the numerical solution of shallow water equations on flat/variable bottom topographies. The proposed scheme evolves a non-oscillatory numerical solution on a single grid, avoids the time consuming process of solving Riemann problems arising at the cell interfaces, and is second-order accurate both in space and time. Furthermore, the numerical scheme follows a well-balanced discretization that first discretizes the geometrical source term according to the discretization of the flux terms, and then mimics the surface gradient method and discretizes the water height according to the discretization of the water level. The resulting scheme exactly satisfies the C-property at the discrete level. The proposed scheme is then applied and classical one and two-dimensional shallow water equation problems with flat or variable bottom topographies are successfully solved. The obtained numerical results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential and efficiency of the proposed method.     

Full-potential LMTO study on the electronic structure of heavy-fermion compound LiV2O4

The electronic structure of heavy fermion compound LiV₂O₄ has been calculated using a self-consistent full-potential LMTO method. The results show that the conduction bands in this compound are formed from V 3 d states with a bandwidth of 2.5 eV. The symmetric characteristics of conduction bands are of t_2g in principle. The energy gap between conduction bands and fully occupied oxygen 2p bands is 1.9 eV. The band dispersions near Fermi energy display complicated structures. Furthermore, the N( E_F) and y_cal are 11.1 (states/eV/f.u.) and 26.7 mJ/mol.K₂ determined numerically by LDA calculation, respectively. It is insufficient to clarify the origin of local moment in LiV₂O₄ from plain LDA calculations. In addition to the above LDA calculation, we also found a LSDA solution of LiV₂O₄ that is lower in total energy than that of LDA calculation. Similarly, LSDA + GGA calculation yields almost the identical result as that in LSDA. We conclude that the mechanism responsible for heavy fermion properties in LiV₂O₄ might be somewhat different from the plain Kondo mechanism in conventional 4f and 5f heavy fermion compounds and perhaps the quantum transition might play an adequate role in heavy-ferrnion behaviors in LiV₂O₄.     

Interfacial long traveling waves in a two‐layer fluid with variable depth

Long wave propagation in a two‐layer fluid with variable depth is studied for specific bottom configurations, which allow waves to propagate over large distances. Such configurations are found within the linear shallow‐water theory and determined by a family of solutions of the second‐order ordinary differential equation (ODE) with three arbitrary constants. These solutions can be used to approximate the true bottom bathymetry. All such solutions represent smooth bottom profiles between two different singular points. The first singular point corresponds to the point where the two‐layer flow transforms into a uniform one. In the vicinity of this point nonlinear shallow‐water theory is used and the wave breaking criterion, which corresponds to the gradient catastrophe is found. The second bifurcation point corresponds to an infinite increase in water depth, which contradicts the shallow‐water assumption. This point is eliminated by matching the “nonreflecting” bottom profile with a flat bottom. The wave transformation at the matching point is described by the second‐order Fredholm equation and its approximated solution is then obtained. The results extend the theory of internal waves in inhomogeneous stratified fluids actively developed by Prof. Roger Grimshaw, to the new solutions types.