Graphical Interpolation Research Articles

Four-bar synthesis for the coordination of coupler point displacement with the rotations of both cranks

The correlation of the motion of the coupler point of a four-bar linkage with that of both cranks (partially or fully) is of some practical importance as shown by Hain[1] who gave solutions based either on point position reduction or graphical interpolation. Point position reduction, which loses the infinity of possible designs, and graphical interpolation are replaced in the present paper by improved procedures.

Systematics of reaction cross sections and interaction barriers for charged particles

Experimentally determined total reactin cross sections ${\ensuremath{\sigma}}_{R}$ have been used to obtain the systematics of interaction barriers in reactions between charged nuclei. The real potential was assumed to be parabolic at its maximum and hence the characteristic parameters are barrier height, radius, and curvature, ${E}_{0}$, ${R}_{0}$, and $\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$, respectively. Barrier heights and radii follow clear systematic trends and therefore these systematics can be used to predict total reaction cross sections for energies close to and greater than the barrier. Experimental data for incident energies below the barrier are sparse and therefore they cannot be well systematized at this time. The cross section patterns for low incident energies seem to reflect individuality of the collision partners.NUCLEAR REACTIONS Total cross sections ${\ensuremath{\sigma}}_{R}$ for charged particle reactions are systematized in terms of a real inverted parabolic barrier. Graphical interpolation and extrapolation of the interaction barrier ${E}_{0}$ permit prediction of ${\ensuremath{\sigma}}_{R}$.

Mixed convection above a heated horizontal surface

Buoyancy effects are determined analytically for the laminar boundary-layer region above an isothermally heated, semi-infinite horizontal surface located in a horizontal uniform stream. The flow conditions are determined under which the boundary layer consists of a forced-flow-dominated near region and a buoyancy-dominated far region connected by an intermediate region in which forced and natural convection are of comparable magnitude. Perturbation expansions are obtained for the near and far regions with results for the intermediate region being obtained by graphical interpolation. Although it is well-known that, at fixed Reynolds and Grashof number, the effect of buoyancy decreases monotonically as the Prandtl number increases, it is found for the present problem that, for fixed U ∞ and ΔT, the effect of natural convection in gases is not only more important than in large-σ oils but also than in small-σ liquid metals; this is attributable to the relatively small kinematic viscosity and coefficient of thermal expansion of liquid metals. In any case, if ΔT ≲ 20° C then U ∞ must be quite small (≲ 20 cm/s) if buoyancy effects are to become significant before turbulent transition occurs. Presentation of the theoretical results in terms of G/R 5 2 versus σ leads to a clear demarcation of the forced-convection, mixed-convection and natural-convection heat-transfer regimes.

A practical application of Buekner's formulation for determining stress intensity factors for cracked bodies

Making use of Buckner's [1] formulation in conjunction with a standard finite element program an efficient and accurate method of determining stress intensity factors for cracked arbitrary bodies is developed. The method avoids the need for graphical interpolation of data, the introduction of special tip elements or the need for minute elements in the near tip region. Stress intensity factors for test specimens or permissible defect size in load carrying components may be determined with equal facility.

Raman spectra of Ba2NaNb5O15

The Raman spectra of Ba2NaNb5O15 single crystals were recorded for various scattering configurations from 77°K to 843°K. Splittings of the vibrational modes due to electrostatic and anisotropic forces were found to be small. The line-widths of the 650 cm-1 and the 280 cm-1 modes were found to increase with increasing temperature. The 'soft' A1(z) mode at 723°K was fitted by means of a graphical interpolation to an overdamped lineshape with an undamped mode frequency of 40 cm-1 and a damping constant of 2.

Mass transfer across a nonequilibrium interface

AbstractThe problem of mass transfer with nonequilibrium at, and significant convection across, the interface has been studied by the method of matched asymptotic expansions. The inner solution for small values of t or z/Um was found in terms of fk functions which were obtained in closed analytical form. The outer solution for large values of t or z/Um was found in terms of gk functions which had to be determined numerically. With these solutions, calculation of concentratration distributions or instantaneous rates of mass transfer is straightforward, but determination of the total amount of mass transfer as a function of time is complicated by the lack of an intersection wherein the inner and outer solutions overlap and converge. To avoid the need for graphical interpolation and integration of the interfacial concentration as a function of time to obtain the total mass transferred, the constant of integration M1 is found to be (−kγ\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt \pi $\end{document}/2h) by assuming that the ratio of mass transferred with an equilibrium interface to that with a nonequilibrium interface is independent of whether or not Vy convection is negligible in the system as t → ∞.The effect of a nonequilibrium interface is greatest for small t in unsteady systems and z/Um in steady state systems. This occurs because the departure from their equilibrium values of the interfacial concentrations of the phases in contact is greatest when they are first brought into contact. The larger the interfacial mass transfer coefficient α, the smaller is the time required for the interfacial concentrations to achieve their equilibrium values.Other things being equal, the rate of mass transfer is greatest when the driving force xA*‐x is greatest. Since the departure from equilibrium at the interface is greatest for small values of time, it follows that nonequilibrium interfacial phenomena can be observed most easily in systems where the rate of mass transfer is high. This is also the case when one cannot neglect the effect of finite velocity at the interface which is shown in the present work to be a significant effect.The method of analysis can be used to study a variety of problems in addition to the specific system considered here. In particular, both batch and flow reverse osmosis problems can be attacked by the present approach.

Rapid calculation of radioimmunoassay results.

Abstract Most methods available for expressing radioimmunoassay (RIA) results yield nonlinear dose-response curves, making graphical or numerical dose interpolation difficult. Several methods have been proposed for the linearization of dose-response curves in order to facilitate the rapid and accurate calculation of results with desktop electronic calculators. ∗ ∗Detailed procedures for computation with the use of an electronic desk-top calculator will be sent on request. The relationships between these methods, their limitations, advantages, and ranges of applicability are reviewed in this report.

Low Temperature Growth of Type E Clostridium botulinum Spores. 2. Effects of Solutes and Incubation Temperature

SUMMARY— The inhibition of outgrowth of spores of Clostridium botulinum Type E by the addition of different concentrations of various solutes to a trypticase‐peptone‐sucrose‐yeast extract medium (TPSY) was studied at different incubation temperatures. Solutes added to TPSY medium were sodium chloride (NaCl), sodium formate (NaCOOH), potassium chloride (KCI), sucrose and glucose. Incubation was at 30, 21.1, 15.6, 10 and 7.2°C, and growth was confirmed by mouse toxin assay. The effect of the solutes on the equilibrium relative humidities (ERHI of the various media was measured using the graphical interpolation method and expressed as water activity (aw). The possibility of an osmotic effect was also investigated. The molar (M) concentrations and osmotic pressures of the different solutes were calculated and related to the approximate inhibitory concentrations of 5.0% NaCl (aw 0.975), 6.0% KCI (aw 0.974), 5.5% NeCOOH (aw 0.9711, 38.5% sucrose (aw 0.976) and 22.5%. glucose (aw 0.970).The inhibitory salt concentrations were approximately 0.80 M and produced osmotic pressures of about 36.0 atmospheres. The approximate osmotic pressure of the inhibitory 1.12 and 1.24 M sucrose and glucose solutions were 25.08 and 27.97 atmospheres respectively.Growth response decreased as the incubation temperature decreased as measured by delayed outgrowth times and in decreased amount of cellular material produced by the Type E strains tested.

Tabulated correction factors for the drop-weight-volume determination of surface and interfacial tensions

The determination of boundary tensions by the drop-weight or drop-volume method entails using correction factors derived by Harkins and Brown from their data relating the volume of a drop falling from a capillary tip and the radius of the capillary to the volume of a hypothetical ideal drop. In practice it is often necessary to interpolate between tabulated values of the correction factors. To eliminate the errors associated with either linear or graphic interpolation, the original data were subjected to regression analysis and a “best-fit” equation was obtained. This equation was used to generate a table of correction factors at 0.001 unit intervals of r/V13, where r is capillary radius and V is drop volume. Statistical analyses of the data and the regression are also reported.

The flexural stress-strain relationship of concrete confined by rectangular transverse reinforcement

Summary To understand the plastic deformation capacity of critical regions reinforced with longitudinal and transverse reinforcement, it was felt that the stress-strain relationship of bound concrete in flexure must first be established. Sixteen specimens were tested in a specially constructed testing frame under the action of a major and a minor load. The stress-strain relationship for the concrete was obtained by an approach similar to that used by Hognestad, Hanson and McHenry in conjunction with a special graphical interpolation technique. A generalized relationship was finally developed expressed as a function of: the spacing of binders; the ratio of the bound area to the total area under compression; the size of the binders; and the shape of the concrete cross-section.

Application of dn/dc Data for Determination of Partial Specific Volumes of Dissolved Macromolecules

Abstract The principles of a method are outlined whereby one can determine the partia specific volume of a solute, V, by means of measurements of dn/dc using a suitable pair of equations and a simple graphical interpolation procedure. The method yields V data which compare well with densitometrically obtained V data if the polarizability of both solvent and solute molecules is unaffected by the solution process. It is tested successfully on solutions of polystyrene in various solvents. The method appears to be particularly attractive for measurements of the change of V with temperature and also for conveniently following the time rate of changes in V such as during the coil → helix transition.

Application of dn/dc data for the determination of partial specific volumes of dissolved macromolecules

AbstractThe principles of a method are outlined whereby one can determine the partial specific volume of a solute, V̄, by means of measurements of dn/dc using a suitable pair of equations and a simple graphical interpolation procedure. The method yields V̄ data which compare well with densitometrically obtained V̄ data if the polarizability of both solvent and solute molecules is unaffected by the solution process. It is tested successfully on solutions of polystyrene in various solvents. The method appears to be particularly attractive for measurements of the change of V̄ with temperature and also for conveniently following the time rate of changes in ‐ such as during the coil → helix transition.

Optics of the total reflection of nuclear resonant radiation by Fe 57

In an earlier publication (1) we described our measurements of the intensity of a single line Fe 57 λ-ray source totally reflected from an Fe 57 metal mirror as a function of angle of incidence and frequency of the source and compared the measurements with values calculated from theory. In this report several theoretical and computational aspects of the total reflection of Mossbauer radiation are discussed which were not emphasized in the previous work. Curves of reflectivity vs. glancing angle for a set of frequencies are given, showing how the curve shapes vary as the frequency of the λ-rays passes through the resonance frequency. Complete diagrams of the variation of coherent scattering amplitude with frequency for Fe 57 are given, from which the reflectivity as a function of frequency in the resonance region may be obtained by graphical interpolation. The polarization and changes in phase produced on reflection as a function of frequency are discussed, and calculated curves are shown. Because of the importance of the nuclear scattering in the resonance region the polarization and changes of phase produced on reflection are appreciable.

918. Some progress with the chick embryo technique: McLaughlin, J., Jr., Marliac, J.-P., Verrett, M. Jacqueline & Fitzhugh, O. G. (1965). Toxicity of some food additive chemicals as measured by the chick embryo technique. Toxic appl. Pharmac.7, 491. Abaza, R., Denney, A., Millar, H. C. & Greenwood, D. A. (1965). Toxicity and biological effects of 1,2-benzpyrene, 1,2,5,6-dibenzanthracene and 3-methylcholanthrene in

Bioassay tests were conducted with twenty three pesticides taking a fresh water teleost, Saccobranchus fossilis as test animal. Acute toxic ranges and LC50 values for 7 organochlorine, (thiotox, endosulfan, heptachlor, chlordane, aldrin, lindane and BHC), 14 organophosphorus (zolone, ekalux, diazinon, rogor, DDVP, malatox, sumithion, ekatin, metasystox, malathion, phosvel, dipterex, formothion and abate) and 2 carbamate pesticides (carbofuran and sevin) were determined using static testing procedures for a period of 24, 48, 72 and 96 h both by graphical interpolation and probit analysis. 95% fiducial limits and heterogeneity factors X2) only for 96 h LC50 values were calculated. The relative potency of all the 23 pesticides have been calculated with respect to abate. It was in the decreasing order from organochlorines (1–7), to organophosphorus (8–21) and carbamate pesticides (22, 23), respectively. The presumable safe concentrations were computed, using 0.021, 0.024 and 0.026 as arbitrary application factors based on other species for organochlorines, organophosphorus and carbamate pesticides, respectively.

A Space-Limited Construction for the Smith Chart

Smith chart conversion of complex numbers from rectangular form to polar form, and vice versa, often involves the construction of one or more constant magnitude circular arcs. If the magnitude is being sought, it is frequently necessary to resort to graphical interpolation between the arcs. In any event, should the magnitude, given or desired, be between approximately one-fourth and four, the centers of the constant magnitude arcs inconveniently lie off the conventional Smith chart. This paper presents geometric methods with brief proofs for keeping all magnitude constructions on the commercial chart and for increasing the accuracy of results by referring interpolations to the accurately printed scalings on the horizontal axis.

A generalized graphical interpolation method for evaluating experimental dependences of two independent variables

A generalized graphical interpolation method for evaluating experimental dependences of two independent variables

Békésy Audiometry at 20 Frequencies from 0.2 to 6 kc/sec

Absolute intensive thresholds are presented from 26 men yielding Békésy audiograms at 20 frequencies. Results validate the practice of graphic interpolation between thresholds in octave steps to predict mean thresholds at half octave points. Thresholds are almost indistinguishable from those by conventional audiometry in a very similar population. Data are interpreted to confirm in general the practicability of using the proposed 1964 ISO reference threshold level as the norm for young otoscopically negative adults.

Experimental data on dilute polymer solutions. Hydrodynamic properties and statistical coil dimensions of poly(n‐butyl methacrylate). Part II

AbstractViscometric measurements were carried out on poly(n‐butyl methacrylate) fractions in chloroform, benzene, toluene, and dioxane. Light‐scattering and viscometric measurements on these fractions were carried out in isopropanol over a narrow range of temperatures. The Flory‐Fox Θ‐temperature was obtained by graphical interpolation on a plot of the second virial coefficient versus the reciprocal of the absolute temperature. Values of Φ, calculated according to the Flory‐Fox equation were found to be abnormally low, notwithstanding the application of heterodispersity corrections, a mean value of 1.62 × 1023 being found in isopropanol in the temperature range investigated. The dependence of [η] on the mean radii of gyration is found to be less than that predicted by the Flory‐Fox theory. The light‐scattering dimensions systematically appear to be too large in the ideal solvent, a discrepancy that cannot be explained by accumulated experimental factors.

Plane strain extrusion through partially rough curved dies

Some classes of slip line fields are proposed for extrusion through curved dies of arbitrary contour on the surface of which the shear stress is arbitrarily prescribed. A method of graphical interpolation is used for the construction of the field pattern which allows the boundary conditions for stress and velocity on the die surface to be satisfied simultaneously.

The asymptotic form of the laminar boundary-layer mass-transfer rate for large interfacial velocities

The convective diffusion of matter from a stationary object to a moving fluid stream is distinct from pure heat transfer because of the appearance of a finite interfacial velocity at the solid surface. This velocity is related to the rate of mass transfer by a dimensionless groupBin such a way that for −1 <B< 0 the transfer is from the bulk to the surface while for 0 <B< ∞ the transfer is from the surface to the main stream. In this paper, asymptotic solutions to the two-dimensional laminar boundary-layer equations are developed for the caseB[Gt ] 1, and for rather general systems. It is shown that in most instances the asymptotic expressions for the rate of mass transfer become accurate whenB> 3 and that the transition region between the pure heat-transfer analogy (B∼ 0) and theB[Gt ] 1 asymptote may be described by a simple graphical interpolation. These results may easily be extended to three-dimensional surfaces of revolution by the usual co-ordinate transformations of boundary-layer theory.