Momentum transfer in an agitated vessel with off-centred impellers

Momentum transfer was investigated in an unbaffled agitated vessel of inner diameter 0.3 m equipped with different off-centred impellers. The distribution of the shear rate on the tank wall as a function of the impeller type and Reynolds number was studied in the turbulent regime of the Newtonian liquid flow. The dependences of the averaged dimensionless shear rate, friction coefficient, and dissipated energy on the Reynolds number and eccentricity ratio were approximated using four-parameter equations. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Lithium insertion into In2S3 studied by perturbed γ-γ angular correlation

Li_xIn₂S₃ was electrochemically prepared with different small amounts x of lithium (0?x?0.13) in order to maintain the initial crystallographic structure of the thiospinel In₂S₃. About 10¹² radioactive ¹¹¹In ions have been implanted into these samples at 400 keV to perform PAC experiments in the temperature range from 10 to 773 K. The results are compared to previous experiments with undoped In₂S₃ samples. According to the structure of In₂S₃ in the β-phase, which belongs to the I4₁/amd space group having a unit cell with 32 In and 48 S atoms and the cell parameters α=7.61 Å and c=32.28 Å, three different electric field gradients were observed. Within two different temperature ranges dynamical EFGs occur, which are clearly influenced by the insertion of Lithium. The strong dependence of one EFG on the Li concentration x can be correlated to the effective charge of the In ions. This correlation is discussed with respect to XRD analyses of the Li_xIn₂S₃ samples and to XANES measurements on a similar sample.     

Spectrochemical Properties of Noncubical Transition Metal Complexes in Solution. XII. Angular Overlap Studies of Salicylideneethylenediamine Cu(II) Complex in Various Solvents

As a part of our general interest in the UV-Vis spectroscopy of multidentate mixed-donor ligands, the (salicylideneethylenediamine)Cu(II) complex has been prepared and characterized by elemental analyses, solubility in common solvents, molar conductivities, and ultraviolet (UV), and visible (Vis) spectroscopy. The combined results of spectrophotometric measurements and EPR spectra, as well as known the X-ray structure for solids, were used to determine the structure of the investigated complex in solutions. The spectra of [Cu(salen)] (H₂salen = salicylideneethylenediamine), were measured in various solvents at room temperature, resolved by Gaussian analysis, and angular overlap model (AOM) treated in C _2v symmetry. Because of overparametrization problems, the bis(salicylaldehyde)Cu(II) complex has been characterized and AOM treated. The results of this have been used for AOM studies of [Cu(salen)]. The effect of the solvents upon the - and -bonding ligand abilities is discussed.     

A new method for the derivation of exact vibration-rotational kinetic energy operator in internal coordinates

An efficient angular momentum method is presented and used to derive analytic expressions for the vibration-rotational kinetic energy operator of polyatomic molecules.The vibration-rotational kinetic energy operator is expressed in terms of the total angular momentum operator J,the angular momentum operator J and the momentum operator p conjugate to Z in the molecule-fixed frame Not only the method of derivation is simpler than that in the previous work,but also the expressions ot the kinetic energy operators arc more compact.Particularly,the operator is easily applied to different vibrational or rovibrational problems of the polyatomic molecules by variations of matrix elements Gn of a mass-dependent constant symmetric matrix     

Lattice dynamical study of body-centred tetragonal indium

The phonon dispersion curves, phonon frequency distribution function as well as the lattice specific heat of body-centred tetragonal indium have been deduced using a lattice dynamical model which includes central, angular and volume forces. Six elastic constants, four zone boundary frequencies and an equilibrium condition were used in the evaluation of the force constants. It is shown that this model is elastically consistent and satisfies the symmetry requirements of the lattice, the phonon frequencies of indium deduced from it are in very good agreement with the experimental values of Reichardt and Smith and the theoretical values of Garrett and Swihart, and theθ _D values compare well with the experimental values over a wide temperature range. The apparent discrepancies in the phonon dispersion curves and theθ _D-T curves obtained from deficient models, importance of umklapp processes and the significance of angular forces in the lattice dynamical models are discussed.     

Degradation in gain for a free electron laser amplifier due to electron momentum spread

A finite spread in axial momentum for the electron beam in a free electron laser amplifier is shown to decrease the small-signal gain. For millimeter and sub-millimeter wave amplifiers, where exponential growth dominates the gain, it is shown that the gain is approximately 3 db below that for a cold beam if the relative momentum spread (u/u)_1/2 = (G_o/248)^1/2 (_o/L), where G_o1 is the gain in db for the cold-beam case, _o is the magnetic wiggler period, and L is the amplifier length. Exact numerical examples are given for representative FEL amplifiers at 35 and 550 GHz.This research was sponsored by the U.S. Office of Naval Research, and by the U.S.-Israel Binational Science Foundation.     

The nonsymmetric pressure tensor in polyatomic fluids

Nonequilibrium molecular dynamics calculations are used to show that polyatomic fluids can support antisymmetric stress. In a homogeneous system where the time dependence of vorticity is a step function, it is shown that the rate at which intrinsic angular velocity approaches its steady-state value ( = 1/2 × u) is determined by the magnitude of the antisymmetric part of the pressure tensor.     

Statistical inference and modelling of momentum in stock prices

The following results are obtained, (i) It is possible to obtain a time series of market data {y(t)} in which the fluctuations in fundamental value have been compensated for. An objective test of the efficient market hypothesis (EMH), which would predict random correlations about a constant value, is thereby possible, (ii) A time series procedure can be used to determine the extent to which the differences in the data and the moving averages are significant. This provides a model of the form y(t)-y(t-l)=0.5{y(t- l)-y(t-2)}+ε(t)+0.8ε(r-1) where ε(t) is the error at time t, and the coefficients 0.5 and 0.8 are determined from the data. One concludes that today's price is not a random perturbation from yesterday's; rather, yesterday's rate of change is a significant predictor of today's rate of change. This confirms the concept of momentum that is crucial to market participants. (iii) The model provides out-of-sample predictions that can be tested statistically. (iv) The model and coefficients obtained in this way can be used to make predictions on laboratory experiments to establish an objective and quantitative link between the experiments and the market data. These methods circumvent the central difficulty in testing market data, namely, that changes in fundamentals obscure intrinsic trends and autocorrelations. This procedure is implemented by considering the ratio of two similar funds (Germany and Future Germany) with the same manager and performing a set of statistical tests that have excluded fluctuations in fundamental factors. For the entire data of the first 1149 days beginning with the introduction of the latter fund, a standard runs test indicates that the data is 29 standard deviations away from that which would be expected under a hypothesis of random fluctuations about the fundamental value. This and other tests provide strong evidence against the efficient market hypothesis and in favour of autocorrelations in the data. An ARIMA time series finds strong evidence (9.6 and 21.6 standard deviations in the two coefficients) that the data is described by a model that involves the first difference, indicating that momentum is the significant factor. The first quarter's data is used to make out-of-sample predictions for the second quarter with results that are significant to 3 standard deviations. Finally, the ARIMA model and coefficients are used to make predictions on laboratory experiments of Porter and Smith in which the intrinsic value is clear. The model's forecasts are decidedly more accurate than that of the null hypothesis of random fluctuations about the fundamental value.     

Accuracy of high‐order density‐based compressible methods in low Mach vortical flows

At low Mach numbers, Godunov‐type approaches, based on the method of lines, suffer from an accuracy problem. This paper shows the importance of using the low Mach number correction in Godunov‐type methods for simulations involving low Mach numbers by utilising a new, well‐posed, two‐dimensional, two‐mode Kelvin–Helmholtz test case. Four independent codes have been used, enabling the examination of several numerical schemes. The second‐order and fifth‐order accurate Godunov‐type methods show that the vortex‐pairing process can be captured on a low resolution with the low Mach number correction applied down to 0.002. The results are compared without the low Mach number correction and also three other methods, a Lagrange‐remap method, a fifth‐order accurate in space and time finite difference type method based on the wave propagation algorithm, and fifth‐order spatial and third‐order temporal accurate finite volume Monotone Upwind Scheme for Conservation Laws (MUSCL) approach based on the Godunov method and Simple Low Dissipation Advection Upstream Splitting Method (SLAU) numerical flux with low Mach capture property. The ability of the compressible flow solver of the commercial software, ANSYS FLUENT , in solving low Mach flows is also demonstrated for the two time‐stepping methods provided in the compressible flow solver, implicit and explicit. Results demonstrate clearly that a low Mach correction is required for all algorithms except the Lagrange‐remap approach, where dissipation is independent of Mach number. © 2013 Crown copyright. International Journal for Numerical Methods in Fluids. © 2013 John Wiley & Sons, Ltd.     

Effects of multi-Schell beams on orbital angular momentum of entangled signal photons in low-order turbulence aberration channels

We model the detection and crosstalk probability of orbital angular momentum (OAM) states of the entangled signal photon in the Kolmogorov channels of the low-order turbulence aberrations and by the Rytov approximation. The results show that lower OAM mode number of signal photons and larger sub-beam number of multi-Gaussian Schell-model pump beam, the less susceptible of the detection probability of the signal photon to spatial coherence of source and turbulence aberrations is achieved. The maximum crosstalk probability is decrease as the decreasing of the sub-beam number of multi-Gaussian Schell-model. Enlarging OAM difference value or decreasing sub-beam number of multi-Gaussian Schell-model pump beam results in a lower crosstalk probability of the OAM of entangled signal photons.