Determination Of Velocity Distribution Research Articles

Laser ablated Ti velocity distribution dynamics

Emissive plumes resulting from pulsed ablation of titanium (Ti) targets have been observed using a gated intensified charged coupled device (ICCD) camera to characterize the evolution of velocity distributions as the plume expands into vacuum, Ar, and He backgrounds. The gated imagery allows for the collection of time-of-flight spectra with highly sampled spatial resolution and the characterization of the velocity changing collisional dynamics. Multimodal, shifted Maxwell–Boltzmann distributions with flow speeds of u>0.1 cm/μs are adequate only for expansion into vacuum. Neutral Ti time-of-flight data clearly indicate three distinct distributions, with the fastest component consistent with the ionized Ti velocity distribution and maximum kinetic energies exceeding 20 eV. Expansion into He and Ar are clearly non-Maxwellian, with the highest velocity groups suffering collisions in the shock front. Leading-edge velocities of ∼1.6 cm/μs decrease more rapidly for Ar at rates of ∼30% per cm, consistent with momentum conservation. Expansion into He maintains the appearance of the vacuum distribution at low velocities but shows a decrease in the leading-edge velocity and an enhancement of the intensity of the highest-velocity groups at farther target distances. Determination of velocity distributions from time-of-flight data is complicated by translation-to-electronic excitation rates, intraplume collisional dynamics, and nonhydrodynamic conditions.

A guided-ion beam study of the collisions and reactions of I(+) and I2 (+) with I2.

Growing interest in developing and testing iodine Hall effect thrusters requires measurements of the cross sections of reactions that generate low energy plasma following discharge. Limited experimental and theoretical work necessitates a decisive experiment to elucidate the charge exchange and collision-induced dissociation channels. To this end, we have used guided-ion beam techniques to measure cross sections for both I(+) + I2 and I2 (+)+I2 collisions. We present total collision cross sections as well as collision-induced dissociation cross sections for center-of-mass collision energies ranging from 0.5 to 200 eV for molecular iodine cations. Similarly, we present total collision cross section and charge-exchange cross sections for atomic iodine cations for center-of-mass collision energies ranging from 0.67 to 167 eV. Time-of-flight measurements of the collision products allow determination of velocity distributions, which show evidence of complex formation of I3 (+) from the I(+) + I2 reaction at collision energies below 6 eV.

Correlation and distribution of shear stress for turbulent flow in a smooth rectangular open channel

Calculation of shear stresses in open channel flow is very important in civil engineering applications such as structural design, determination of velocity distribution and sediment transport. It is argued in literature that the velocity distribution equations for pipe flow may be used in open-channel flow analysis. However, due to irregular boundary sheer stress, this claim seems to be unreasonable and the irregularities should be taken into consideration. In this study, wall shear stresses for turbulent flow in rectangular open channel are investigated. Using mean velocity measurements and assuming validity of the logarithmic velocity distribution perpendicular to wetted perimeter, dimensionless shear stresses in the unified velocity distribution are determined.A semi-theoretical method is applied for the solutions of non-linear equations.A shear stress distribution equation is proposed to calculate irregular boundary shear stresses on the wall and bed in smooth rectangular channels.

Determination of velocity distribution, angular distribution, and vector correlation of photofragments using sub-Doppler fluorescence-imaging method

With sub-Doppler resolution, the fluorescence-imaging techniques can be modified to determine velocity distribution, angular distribution, and vector correlation of state-selected photofragments, even in an uncollimated molecular beam. This new method is proposed as “sub-Doppler fluorescence-imaging” in which two experimental schemes are developed. The dependence of fluorescence intensities, at any selected velocity and recoil angle in the scattering plane, with respect to the variation of polarization vectors of the probe laser and emitted fluorescence is derived using density matrix formalism. The intensity patterns of photofragments with v–J and μ–v–J correlations are simulated. The laser ablation of B atoms at 248 nm demonstrates the feasibility of this method. Two-dimensional velocity distribution of the laser-ablated B(2P1/2,3/20) atoms is measured and the ablation mechanism is discussed.

Ground-probing radar as a tool for heterogeneity estimation in gravel deposits: advances in data-processing and facies analysis

Pleistocene gravely braided-river deposits in river valleys constitute a large fraction of the natural ground-water reservoirs in Switzerland. The knowledge of the distribution and variability of hydraulic conductivity within these deposits are key factors for the estimation of water residence times and of description of large-scale mixing procesess in aquifers such as macrodispersion. It has been shown elsewhere that the spatial variability of hydraulic conductivity is related to the composition and the characteristic dimensions of sedimentary structures, which are themselves related to the dynamics of ancient braided-river systems. In many contamination problems, sedimentological information is sparse and drill-core descriptions and pumping-tests only give a limited picture of the geometry of inhomogeneities. The ground-probing radar (GPR) method is a promising tool for resolving changes of physical properties in gravel deposits at the scale of natural inhomogeneities arising from changing sedimentary composition. However, the main limitation of GPR is the rapid attenuation of electromagnetic waves in subsurface sediments such as gravels, which leads to a limited penetration of the order of 10 to 15 m for a 250 MHz antenna. The objectives of our present work are: 1. (1) To show how digital processing methods similar to reflection seismics may be applied for velocity and profile processing. These methods can improve both the resolution of radar profiles, in particular at greater depths, and the determination of velocity distributions from CDP experiments. 2. (2) To examine whether and to what extent the characteristic lithofacies of Pleistocene gravel deposits can be recognized as mappable reflection patterns on ground-probing radar (GPR) reflection profiles in order to gain information about the geometry of inhomogeneities. Using modern digital data processing methods, such as band pass, high- or low-cut filtering, deconvolution and velocity analysis, much more significant information can be obtained from the recorded GRP field data-sets. Our results demonstrate that on GPR reflection images the basic fluvial forms such as (1) pool deposits generated at the junction of two channels, and (2) channel deposits may be distiguished. Their shape and characteristic spatial dimensions may be recognized from a series of profiles in different directions. Because the method can detect changes in the water content, the reflection image may be related even to small changes in the degree of saturation of the sediments. Thus reflectors can indicate the changing composition of sediments.

Non-Linear Reflection Tomography

Reflection tomography, the determination of velocity distribution and reflector position from reflection travel-time data, is a very non-linear inverse problem. Unlike in transmission tomography, ray paths have to be iteratively updated, because travel-time variations cannot be computed by integration of slowness along the original unperturbed ray paths. From a study of parameter sensitivity we conclude that in seismic reflection experiments the vertical variation of slowness inside layers is poorly resolved from travel-time data. For this reason, in each layer the slowness was modelled with functions varying only in the horizontal direction. A B-spline representation is adopted for lateral velocity heterogeneity and interfaces. These splines are local and well adapted for tomography because the spline parameters have a geometrical interpretation and they may be explicitly used as unknowns in the inverse problem. For each iteration, and for every source-receiver pair, two-point ray tracing was performed by paraxial ray tracing, and the inverse problem was solved by iterative least-squares. A priori data, necessary to stabilize the inverse problem, were introduced by a penalty function approach. This method is equivalent to using a priori convariance matrices, but it has a simpler physical interpretation and is faster to use. Damping was used to improve the convergence. The method was first tested in the inversion of synthetic data. These synthetic examples illustrate the limitations of reflection tomography: non-linearity effects, poor vertical resolution of the velocity, and decrease of the resolution with the ratio of maximum offset to interface depth. Finally, we inverted a data set from the Paris Basin. The inversion method reduces the residual norm to 6 ms, which is less than the expected error on the data.

Determination of velocity distribution of metallic atoms in plasma devices with a rapid-frequency-scan dye laser

A rapid-frequency-scan dye laser was developed for the measurement of the velocity-distribution functions of impurity atoms sputtered due to the high-temperature plasma-surface interaction. In order to confirm the effectiveness of this rapid-scan technique, measurements of the Doppler profiles of Fe atoms sputtered by Ar ion-beam bombardment with energy 3 keV were performed. A scanning range of more than 40 pm at λ ≈300 nm was obtained with a spectral bandwidth of 1.5 ∼2 pm and good linearity. Doppler profiles were determined in various scattering conditions, and excellent performance of this technique was demonstrated. The distortion error caused by line saturation was analytically discussed, and it is shown that the effect of this error is not so serious (less than 10%) even for highly saturated excitation.

Determination of Velocity Distributions in Molecular Beam Frequency Standards from Measured Resonance Curves

It is shown that the Ramsey resonance curves for most atomic beam machines can be conceived as depending on two distributions of velocity, ρ(V) and ξ(V), the second being a correction for beam width.An analysis and computer program are described which permit one to obtain ρ, ξ and the nominal microwave power parameter from three or more measured Ramsey resonance curves at properly spaced power levels whose ratios are known. The determination from the functions (ρ, ξ) of bias errors due to second order Doppler shift, cavity phase difference, and cavity pulling is described.The method may also be used to improve an experimentally obtained velocity distribution (i.e., one obtained through the pulse technique); to provide the proper function ξ; and to provide diagnostic checks of the measurement technique and the validity of the model chosen for the transition probability.The method is applied to the NBS frequency standard. Error estimates indicate that it is feasible by microwave power shift measurements to evaluate the total bias error due to the above sources to within one part in 1013.

Experimental investigation of velocity distribution and flow resistance in a triangular array of parallel rods

The experimental study described deals with the determination of velocity distribution and flow resistance for fully developed turbulent flow parallel to a triangular array of rods. The effects of Reynolds number and rod spacing were investigated. The results obtained appear to agree satisfactorily with theoretical predictions given in a previous paper.

On the Numerical Evaluation of Singular Integrals of Cauchy Type

Previous article Next article On the Numerical Evaluation of Singular Integrals of Cauchy TypeCharles E. StewartCharles E. Stewarthttps://doi.org/10.1137/0108021PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] H. Lomax and , P. F. Byrd, Theoretical aerodynamic characteristics of a family of slender wing-tail-body combinations, National Advisory Committee for Aeronautics, TN 2554 (1951), Google Scholar[2] H. Lomax and , M. A. Heaslet, Damping-in-roll calculations for slender swept-back wings and slender wing-body combinations, National Advisory Committee for Aeronautics, TN 1950 (1949), Google Scholar[3] H. Multhopp, Methods for calculating the lift distribution of wings (subsonic lifting-surface theory), Aero. Res. Council, Rep. and Memo., 1950 (1950), 96 pp. (1955), British Royal Aircraft Establishment, January MR0072628 Google Scholar[4] T. Theodorsen and , I. E. Garrick, General potential theory of arbitrary wing sections, National Advisory Committee for Aeronautics, Report 452, (1932), Google Scholar[5] Eric Reissner and , John E. Stevens, Effect of finite span on the airload distributions for oscillating wings. II. Methods of calculation and examples of application, Tech. Notes Nat. Adv. Comm. Aeronaut., 1947 (1947), 97 pp. (34 plates) MR0021804 Google Scholar[6] S. G. Mikhlin, Integral equations and their applications to certain problems in mechanics, mathematical physics and technology, Pergamon Press, New York, 1957xii+338, (Translation from the Russian edition by A. H. Armstrong) MR0087877 0077.09903 Google Scholar[7] N. I. Muskhelishvili, Singular Integral Equations, Moscow, 1946, (Translation from the Russian edited by J. R. M. Radok, P. Noordhoff, N. V., Holland, 1953.) Google Scholar[8] F. G. Tricomi, Integral equations, Pure and Applied Mathematics. Vol. V, Interscience Publishers, Inc., New York, 1957viii+238 MR0094665 0078.09404 Google Scholar[9] R. C. MacCamy, The numerical solution of singular integral equations, Air Force Office of Scientific Research, TN 57-515, 1957 Google Scholar[10] I. Flügge-Lotz, Mathematical improvement of method for computing Poisson integrals involved in determination of velocity distribution on airfoils, Tech. Notes Nat. Adv. Comm. Aeronaut., 1951 (1951), 84– MR0046750 Google Scholar[11] M. D. Van Dyke, Second order subsonic airfoil theory including edge effects, National Advisory Committee for Aeronautics, Report 1274, (1956), Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Piecewise-Polynomial Quadratures for Cauchy Singular Integrals14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 23, No. 4AbstractPDF (1201 KB)The Numerical Evaluation of the Cauchy Transform on Simple Closed Curves3 August 2006 | SIAM Journal on Numerical Analysis, Vol. 9, No. 2AbstractPDF (1057 KB)Differentiation of Singular Integrals of Cauchy TypeRaimond A. Struble10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 8, No. 2AbstractPDF (321 KB) Volume 8, Issue 2| 1960Journal of the Society for Industrial and Applied Mathematics History Submitted:20 April 1959Published online:10 July 2006 InformationCopyright © 1960 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0108021Article page range:pp. 342-353ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics