Semi-empirical Formulation Research Articles

Heavy-ion energy loss

Abstract Recent data on the stopping of heavy ions in matter are compared to Ziegler, Biersack and Littmark's semi-empirical stopping power calculations, which are frequently used for the simulation of ion beam analysis spectra. Data giving new insights into the physical basis of the semi-empirical stopping power formulation are discussed.

Application of a General Technique for Prediction of Riser Vortex-Induced Response in Waves and Current

Abstract This paper describes applications of an extension to a recently developed calculation method for vortex-induced response of risers and tethers. The vortex-induced vibration response for the excited modes is generated using a semi-empirical formulation which is applied within a time domain calculation. This makes it possible to take account of the variation of flow properties along the riser length, as well as in time. The calculation method has been verified by comparison with model test data for vortex-induced response to surface vessel motions in still water. This paper presents applications of the technique for vortex shedding due to the combined action of current, surface vessel motions and waves. The mathematics of the extended prediction technique is described and results are illustrated by presenting typical vortex-induced responses for single-tube risers. The results of the prediction method are used to highlight the relative magnitudes and nature of vortex-induced response excited by currents, surface vessel motions and waves.

Radar cross section of complex targets

A summary of the development and verifications of a computer code, RECOTA (return from complex target), developed at Boeing Aerospace for calculating the radar cross section of complex targets is presented. The code utilizes a computer-aided design package for modeling target geometry in terms of facets and wedges. It is based on physical optics, physical theory of diffraction, ray tracing, and semiempirical formulations, and it accounts for shadowing, multiple scattering and discontinuities for monostatic calculations. >

A comparison of empirical and semiempirical efficiency calculations for Ge detectors

Empirical and semiempirical formulations for calculating the full energy peak efficiency (FEPE) of Ge detectors are reviewed. By comparing the predictions of these formulae with experimental data obtained from an 86 cm 3 Ge(HP) crystal, it is found that the most precise predictions, over the largest possible energy range, are obtained using the semiempirical formula of Hajnal and Klusek [Nucl. Instr. and Meth. 122 (1974) 559]. Mean deviations of 1.8% were recorded over the energy range 59.6–3253.6 keV. The calculated efficiency curve was found to be in good agreement with Monte Carlo calculations.

A prediction technique for vortex induced transverse response of marine risers and tethers

A theoretical time domain analysis is presented for simulating the vortex shedding induced transverse response of long tensioned submerged flexible members which are subjected to oscillatory displacements at their upper end. Such flexible tubular members are used for tensioned buoyant platform tethers as well as drilling and production marine risers in offshore service. The member vortex induced vibration response for the excited modes is generated by using a semi-empirical formulation. The method takes account of variations of relative flow properties in space and time as well as the influence of different modes on one another. Although it is applied here to investigate riser or tether response to surface vessel motion, the technique is more general in character and may also be adapted to calculate the response due to current and wave action. The predicted vortex induced response time histories and spectra from the theoretical model are compared with experimental data from a specially developed still water test tank. These comparisons demonstrate that theory predicts the measured vortex shedding induced transverse dynamic response with reasonable accuracy for both frequencies and amplitudes of response.

A modified turbulent energy model for diffusion from elevated and ground point sources in neutral boundary layers

A simple model for turbulent diffusion is proposed based on a turbulent energy model modified by Galperin and Hassid (1986) wherein local equilibrium in the concentration flux equation is assumed resulting in a turbulent diffusivity tensor. The early stage of plume development is simulated through adjustment of the integral length scale of diffusion. A simple semi-empirical formulation is also proposed for the dissipation length scale of concentration variance. Although it is substantially simpler than that of Sykes et al. (1984), the model is shown to compare well with the measurements of Fackrell and Robins (1982a, b).

Mechanisms and kinetic modeling of calcium oxalate crystal aggregation in a urinelike liquor. Part II: Kinetic modeling

AbstractA general form of the population balance equation, including aggregation and rupture terms, was solved numerically to model the experimental calcium oxalate distributions generated in Part I of this series. Semiempirical formulations for the aggregation and disruption functions were found that resulted in excellent matches between experimental and predicted distributions. Both the aggregation and the disruption rates were found to vary with oxalate concentration and inner cylinder rpm of the aggregator.

The importance of multicenter integrals in semiempirical calculations of nuclear spin-spin coupling constants. 2. Anisotropic coupling

A molecular orbital (MO) study of anisotropic nuclear spin-spin coupling is presented in terms of a semiempirical formulation with inclusion of all multicenter integrals in the Fermi contact, orbital, and spin-dipolar contributions. This formulation extends existing semiempirical MO theories to include the large class of coupling constant anisotropies involving protons. Calculations for representative molecules are based on the first-order polarization propagator approach, which is equivalent to coupled Hartree-Fock theory, and the semiempirical INDO MO level of approximation for the wave-functions. The calculated results agree with ab initio MO results, but the very large errors in most of the experimental data make detailed comparisons difficult. The asymmetry features of the anisotropic coupling tensors are also discussed.

Experimental Study of Drilled Cuttings Transport Using Common Drilling Muds

Abstract Experiments are conducted with actual drilling muds to study the behavior of drilled cuttings in a vertical annulus. The effect of parameters such as particle size, flow rate, apparent viscosity, and yield point to plastic viscosity ratio on mud-carrying capacity are studied. The applicability of a semiempirical transport model developed by Zeidler also is investigated. It has been shown that in vertical annuluses, the fluid annular velocity has a major effect on the carrying capacity of muds, while the other parameters have an effect only at low to medium fluid annular velocities. We also conclude that Zeidler's semiempirical formulations for the prediction of drilled cuttings behavior are valid with certain limitations.

Rossby similarity and turbulent formulations

The structure of the Planetary Boundary Layer in the stationary case is investigated. The dynamic equations are written in an universal form deduced from Rossby Similarity. Then the system is closed using two semi-empirical formulations for the turbulent fluxes (Prandtl's formulation and the turbulent energy scheme) with a mixing-length chosen to be compatible with Rossby Similarity. For each formulation the system is solved using a new numerical procedure to compute universal profiles of wind and also the Similarity functions A and B in terms of stability. These profiles and functions are then compared to experimental data and good agreement is obtained. Investigating simpler formulations, it appears that good results are obtained with a simple two-layer model, patching a diabatic Ekman spiral with surface-layer profiles. Its formulation is analytical and it can incorporate constant baroclinicity.

Experimental observations on the relationship between diffusion characteristics and spectral coherence

The direct relationship of spectral coherence to space-time correlation is used to infer various characteristics of diffusion processes. Data gathered at three levels and at various downwind instrumental separations, along the mean wind direction are analyzed in terms of horizontal coherence of the longitudinal and lateral components of the wind. The analysis is within the framework of Davenport's ( Q. Jl R. met. Soc. 87, 194–211. 1961) empirical representation of coherence and a semi-empirical formulation of the decay parameter. The characteristics of the decay parameter are found to be consistent with its latest formulation which incorporates the relative importance of turbulent intensity and lateral diffusion. Atmospheric stability is seen to be the controlling factor in the results. The noted characteristics of the decay parameter are used to confirm its inverse relationship to Pasquill's β. This, in turn, confirms the usefulness of the determination of the latter from single point observations. Furthermore, Pasquill's nondimensional lateral dispersion function is shown to be stability dependent which must be borne in mind when calculating the lateral dispersion parameter of Gaussian models.

Effect of radial electric field on heat and momentum transfers in dielectric organic liquid for laminar flow through concentric annuli

Experiments were conducted to investigate changes in convective heat transfer in flows of dielectric organic liquids in annuli between copper tube and concentric wires. Also investigated was longitudinal pressure drop in the flow which could be induced by applying electric fields of direct current between the wall of the tube and the central wire electrode. In the laminar range of Reynolds number, heat transfer rates at the outer wall increased in the thermally well-developed region, and the thermal development was advanced. On the other hand, pressure drops were also increased in liquids of small Prandtl number. In the transitional and turbulent range, however, neither changes of heat nor momentum transfer were noticeable. To express these results in the low Reynolds number range a semi-empirical formulation in non-dimensional terms was derived from the similarity principle.

E′center in glassy SiO2: Microwave saturation properties and confirmation of the primarySi29hyperfine structure

Electron-spin-resonance studies of a series of air-annealed samples of glassy Si${\mathrm{O}}_{2}$ having various degrees of enrichment (or depletion) in the $^{29}\mathrm{Si}$ isotope have confirmed that a $\ensuremath{\gamma}$-ray-induced doublet of 420-G splitting is the $^{29}\mathrm{Si}$ hyperfine structure of the well-known ${E}^{\ensuremath{'}}$ center. This finding validates the widely accepted model of the ${E}^{\ensuremath{'}}$ center as an unpaired electron spin in a dangling $s{p}^{3}$ hybrid orbital of a silicon bonded to three oxygens in the glass structure and eliminates a recently proposed alternative model. Continuous-wave microwave saturation measurements at \ensuremath{\sim}9.2 GHz were carried out in order to establish spin-lattice relaxation behavior and to determine absolute line intensities in the low-power limit. The spin-lattice relaxation process for the $^{29}\mathrm{Si}$ ${E}^{\ensuremath{'}}$ center is shown to be dominated by a hyperfine mechanism. Spin-lattice relaxation times ${T}_{1}$ could be extracted from the cw saturation data only by means of a semiempirical formulation differing from the usual approaches found in the literature.

Mean charged hadron multiplicities in high energy collisions — a new approach

A semi-empirical formulation for the energy dependence of multiplicity in p–p collision has been proposed. It has been found that experimental data for the multiplicity show a remarkable agreement with this formulation in the entire energy region 10 GeV to 106 GeV.

Heisenberg's model revisited to study the angular distribution in inelastic hadron hadron collision at high energy

A semi empirical formulation for the angular distribution of the secondaries in inelastic hadronic collision has been proposed. It has been found that the experimental data show remarkable agreement with this formulation in the entire energy region (1 to 104 GeV).

Modified Heisenberg's Approach for the Mean Charged Hadron Multiplicity in High Energy Collisions

The semiempirical formulation of Ghosh et al. for the energy dependence of multiplicity in hadronic collisions has been applied to account for the experimental multiplicity data of π±p and K±p collisions. A remarkable agreement has been found over the entire energy range.

Energy spikes in Si and Ge due to heavy ion bombardment

Abstract The number of displaced atoms/ion, N∗D , produced by heavy ion bombardment (10-250 keV) of Si and Ge at 35 K is reported. A semi-empirical formulation is given, based upon the separation of the damage into a “spike” component and a “collisional” component, which adequately predicts N∗D , for all ions and energies investigated. The “spike” concept is also tested by investigation of damage enhancement effects occuring for diatomic bombardment with equal atom dose and equal energy/atom corresponding to the monatomic bombardments. The semiempirical model is found to adequately predict the diatomic damage enhancement for heavy ions, e.g. Te+2, but shows discrepancies for lower mass ions. The reasons for such discrepancies are discussed. For Si targets, the “spike” component appears to fit a thermal-spike model, whereas for Ge it is suggested that a damage-spike (localized lattice collapse within the individual cascade) better interprets the experimental results. Spike diameters, DS, for various ions a...

A Different Approach to the Multiplicity Problem in Hadron Collisions

AbstractThe models frequently applied to estimate the target mass in high energy interactions are used in conjunction with the HEISENBERG formula to obtain a semi empirical formulation for multiplicity.It is seen that the experimental data obtained by us and other authors on multiplicity fit into that formulation when considering the initial colliding systems to be either π ‐ p or π ‐ π. Also the values of Cos θ (θ being the emission angle of the secondaries in lab system) averaged over all emitted particles estimated from the above formulation are in good agreement with our experimental data.

A Numerical Model of the Sea-Breeze Phenomenon over a Lake or Gulf

A two-dimensional primitive equation model is constructed and used to investigate the circulations induced by differential heating in the vicinity of a land-locked semi-infinite body of water. The semi-empirical boundary-layer formulation of Clarke is used with an expanding σ grid of 15 vertical levels. Surface temperature is computed by means of a heat-flux balance equation and a radiation condition is used at the lateral boundaries. For purposes of comparison, one run was also made with reflective boundary conditions and it was found that the two solutions differ significantly only when the sea-breeze front is in the vicinity of a lateral boundary. The model reproduces the vast sea breezes of Australia, some of which have been observed to penetrate distances of 200–300 km inland. This feature of the model is attributed to the detailed boundary-layer formulation, in which the momentum and heat exchange coefficients are expressed as functions of stability and wind shear at all levels, and also to the determination of surface temperature through a balance of heat fluxes. The latter aspect of the model allows horizontal gradients of surface temperature to exist ahead of and behind the front and thus to produce a greater discrepancy between the sensible heat fluxes on either side of the front, which in turn produces a stranger thermal gradient across the front. A secondary “cutoff” circulation is seen to develop in the late afternoon when the sea-breeze front is well inland. This low-level phenomenon lasts only a couple of hours and is basically due to the modification of air of marine origin as it flows inland. A land breeze develops gradually from the ground surface upward under an opposing overriding flow in much the same manner as has been described in observations studies. However, the model land breeze begins at the center of the body of water and an explanation is given in terms of the limited size of the water area. A run is made in which the water width is slightly more than doubled and it is found that a stronger breeze results. This lake breeze also moves inland at a faster rate. Stronger vertical velocities are obtained, but downward motion over the water is found to be more intense for the smaller lake. All these effects can he traced to the fact that heat produced over the water by advection in the return flow and by subsidence in the very stable lower layers has a lesser area in which to distribute itself in the cast of the smaller lake. The model is integrated for gradient winds of 5 m s−1 front the east, northeast and north. Comparison with limited observations reveals good agreement. It is also seen that the interaction of circulations from opposite shorelines produces effects which could not be predicted by modeling the lake or gulf breeze at one shoreline alone.

Effect of electrically induced convection on heat transfer of air flow in an annulus.

This paper presents the results of an investigation of heat transfer to a flow of air in an annulus under an electric field applied between the wall of a tube and a concentric wire electrode. By electrically induced disturbance, the heat transfer rate in the low Reynolds number region is increased, being accompanied by the augmentation of axial pressure drop. At high Reynolds number, however, this augmentation is not noticiable. Augmented heat transfer and pressure drop coefficients were correlated in non-dimensional terms derived from the similarity principle and analytical cinsideration of the predominant electric effect. Moreover, semiempirical formulations of these augmenting mechanisms were attempted by analyzing the measured temperature profiles and flow behaviour.