Showing papers on "Radius published in 1974"

Hypernetted chain solutions for the classical one‐component plasma up to Γ=7000

Abstract: The hypernetted chain equation has been solved numerically for the classical one‐component plasma in a uniform background up to Γ=7000, where Γ=(Ze)2/kTa and a is the ion‐sphere radius. Numerical results are presented. The distribution functions and thermodynamical quantities obtained are in good agreement with the Monte Carlo results in the fluid region. The average potential energy Ū/NkT is in error by less than 0.8% for 20≤Γ≤160 and approaches −0.8995Γ as Γ approaches infinity. The pressure and the free energy calculated do not show any evidence of a phase transition. However, the distribution function g(r) for Γ ≳ 1500 has an unusual behavior between 2.5

Evolution of Meander Loops

Abstract: The evolution of the meanders on reaches of 10 alluvial streams in the United States is reconstructed, and a scheme for the evolution and classification of meander loops, derived from a study of the meandering pattern of 125 alluvial streams, is proposed. In the main evolutionary trend, a low symmetrical arc of approximately constant curvature tends to increase in height but decrease in radius as it grows. When its length exceeds its radius, the arc is termed a simple symmetrical meander loop. A simple loop becomes asymmetrical by the growth on its perimeter of a second arc of constant curvature, which is commonly tangent to the first and curved toward the same side of the stream. A simple loop becomes compound when a second arc on its perimeter has developed into a loop. Four main categories of loops (simple symmetrical, simple asymmetrical, compound symmetrical, and compound asymmetrical) and about 16 form types are proposed. The compound loops are regarded as aberrant forms of indefinite radius and length, but the meandering patterns can be analyzed into simple loops whose properties can be measured and treated statistically.

Surface polaritons in a circularly cylindrical interface: Surface plasmons

Abstract: A theoretical investigation of surface polaritons in the circularly cylindrical geometry is presented. The complete set of Maxwell's equations (retardation effects are not neglected) is solved with the simple dielectric function, $\ensuremath{\epsilon}(\ensuremath{\omega})=1\ensuremath{-}\frac{{\ensuremath{\omega}}_{p}^{2}}{{\ensuremath{\omega}}^{2}}$, where ${\ensuremath{\omega}}_{p}$ is the bulk plasma frequency. The resulting transcendental equation for the eigenfrequencies is solved via numerical methods for three representative values of the cylindricality constant, $\ensuremath{\alpha}=\frac{{\ensuremath{\omega}}_{p}a}{c}$, where $a$ is the cylinder radius and $c$ the velocity of light. In addition to the real nonradiative surface plasmons, various virtual radiative surface plasmons exist with properties depending rather strongly on $\ensuremath{\alpha}$. The results are compared with existing experimental data. Further experiments are proposed in order to reveal the most interesting features of the surface plasma modes.

Dynamic properties of bacterial flagellar motors

Abstract: TETHERED bacteria1 rotate at the angular velocity at which the torque generated by the flagellar motor2 is balanced by the torque due to the viscous drag In general, M = bηΩ, where M is the torque, η is the viscosity, Ω is the angular velocity, and b is a coefficient which depends on the size and the shape of the cell, the position of the axis of rotation, and the distance between the cell and the wall For a sphere of radius a (not too close to the wall) M = 8πη a3Ω (ref 3) Viscous forces are so large in comparison with inertial forces4 that Ω will change with M virtually instantaneously; any discontinuities in the one will be evident in the other Consider a cell of radius a and uniform density ρ rotating at an angular velocity Ω0; if its motor is suddenly disengaged, Ω will decay exponentially to 0 with a time constant ρ a2/15η, and the cell will stop in Ωρ a2/15η radians For Escherichia coli this is less than a millionth of a revolution The cell also is subject to rotational diffusion, but this will be evident only if the coupling between the flagellum and the body of the cell is fluid The root-mean-square deviation in the angular position is (2Dt)½, where D is the rotational diffusion constant and t is the time For a cell which can rotate freely, D = kT/bη, where k is Boltzmann's constant and T is the absolute temperature

Binary homogeneous nucleation as a mechanism for the formation of aerosols

Abstract: The rates of nucleation of liquid aerosols from the gaseous maxtures H2SO4+H2O and HNO3+H2O at 25°C for various relative humidities (10% to 100%) and various activities of acid vapor are calculated using the Flood‐Neumann‐Doring‐Reiss‐Doyle theory of binary homogeneous necleation The activities of acid vapor needed for nucleation are 25 to 300 times smaller for H2SO4+H2O than for HNO3+H2O This is due to the much larger free energy of mixing in the liquid phase for H2SO4+H2O Conversion from activities to actual pressures leads to condentrations of nitric acid which are much too high to be found under normal atmospheric conditions On the other hand, the concentrations of sulfuric acid vapor needed to nucleate droplets in the H2SO4+H2O system are in the range 4(10−5) to 13(10−2) ppm, a concentration which can result from photo‐oxidation of SO2 in the atmosphere Calculations are made of the growth curves for H2SO4+H2O droplets (radius versus composition) at various relative humidities from the critical size radius up to a 1000 A radius, corresponding to nuclei large enough to serve as condensation centers for heterogeneous nucleation A generalized version of the Kelvin equation which includes the composition dependence of the surface tension for a binary mixture is derived and applied in calculating these growth curves Sign errors in the second derivatives of the free energy in Doyle's paper are corrected The limitations of the binary homogeneous nucleation theory at extremely low concentrations of one of the components are discussed and it is shown that this theory becomes inapplicable if the actual vapor pressure of one component is below 10−6 torr

Predictions of arc temperature profiles using approximate emission coefficients for radiation losses

Abstract: Coefficients are calculated for the net emission of radiation per cc from the center of cylindrical isothermal plasmas of various temperatures and radii. Coefficients are given as a function of temperature and radius for the D lines of sodium vapor at 250 torr and for the continuum radiation of air at 1 and 30 atm. These coefficients are used in the Elenbaas Heller equation to derive temperature profiles of wall stabilized arcs e.g. for 4·5A with a radius of 0·35 cm in sodium vapor at 250 torr and 10,000 and 20,000A with a radius of 1 cm for air at 30 atm. Comparisons are made with calculated temperature profiles where self absorption effects and the radiation transfer are treated exactly, but still assuming thermodynamic equilibrium. It is found that the approximation using the net coefficients yields central arc temperatures and electric field strengths for a given arc current accurate to 10 per cent. Computation time for the approximate calculation is more than an order of magnitude less than for the calculation where radiation transfer is treated exactly. Thus the approximation facilitiates an account of line radiation for arc plasmas having complex spectra.

A New Interior Schwarzschild Solution

Abstract: A new interior Schwarzschild solution is presented. It is static, spherically symmetric, regular everywhere inside a sphere of coordinate radius a , and across the surface of this sphere it is joined smoothly to the exterior Schwarzschild solution. There are no radial stresses inside the sphere. The radius a is subject to the inequality a > 2 m , where m is the gravitational mass of the sphere. Under certain conditions the new solution may be interpreted as the field inside an Einstein cluster.

Calculations of Stable Domain Radii Produced by Thermomagnetic Writing

Abstract: Calculations are performed to determine the stable radius of a cylindrically symmetric domain nucleated in magneto-optical films during thermomagnetic writing with a laser beam. A critical bound on domain size is calculated which determines whether or not a domain of given radius, once nucleated, will be stable. The analysis shows that for a ferromagnetic material such as MnAlGe, the domain dimensions can grow beyond the local region of material that is heated above the Curie temperature. For ferrimagnetic thin films having a compensation point T comp , stability depends on the difference between ambient and compensation temperatures, ΔT = T a − T comp . With ΔT ≈ 0, wall energy dominates and the critical radius can be calculated from R c = σ/(2MH c ).

On Slowly Rotating Homogeneous Masses in General Relativity

Abstract: The present paper is devoted to a study of slowly rotating homogeneous masses in which the energy density E is a constant. The structure of such configurations is determined with the aid of equations derived by Hartle in the exact framework of general relativity. These configurations have a natural limit in that the static, non-rotating, configurations must have radii (R) exceeding 9/8 times the Schwarzschild radius (R s ). The derived structures, for varying R/R s , are illustrated by a series of graphs. A result of particular interest which emerges is that the ellipticity of the configuration, for varying radius but constant mass and angular momentum, exhibits a very pronounced maximum at R/R s ~2.4.

The influence of heat conduction on acoustic streaming

Abstract: The influence of heat conduction on acoustic streaming is considered including the effect of variable tube wall temperature. The calculations are carried out in the limiting case when the boundary layer is thin compared to the tube radius.

Optical antenna gain. 2: receiving antennas.

Abstract: Expressions are derived for the gain of a centrally obscured, circular optical antenna when used as the collecting and focusing optics in a laser receiver which include losses due to (1) blockage of the incoming light by the central obscuration, (2) the spillover of energy at the detector, and (3) the effect of local oscillator distribution in the case of heterodyne or homodyne detection. Numerical results are presented for direct detection and for three types of local oscillator distributions (uniform, Gaussian, and matched) in the case of heterodyne or homodyne detection. The results are presented in several graphs that allow the rapid evaluation of receiver gain for an arbitrary set of telescope and detector parameters. It is found that, for uniform illumination by the LO, the optimum SNR is obtained when the detector radius is approximately 0.74 times the Airy disk radius. The use of an optimized Gaussian (spot size = 0.46 times the Airy disk radius) improves the receiver gain by less than 1 dB. Theuse results are insensitive to the size of the central obscuration.

Turbulent flow in smooth concentric annuli with small radius ratios

Abstract: Fully developed turbulent flow through three concentric annuli was investigated experimentally for a Reynolds-number range Re = 2 × 104−2 × 105. Measurements were made of the pressure drop, the positions of zero shear stress and maximum velocity, and the velocity distribution in annuli of radius ratios α = 0.02, 0.04 and 0.1, respectively. The results for the key problem in the flow through annuli, the position of zero shear stress, showed that this position is not coincident with the position of maximum velocity. Furthermore, the investigation showed the strong influence of spacers on the velocity and shear-stress distributions. The numerous theoretical and experimental results in the literature which are based on the coincidence of the positions of zero shear stress and maximum velocity are not in agreement with reality.

Velocity autocorrelation function and dynamical structure factor of the classical one-component plasma

Abstract: We present molecular-dynamics computations of the velocity autocorrelation function and the dynamical structure factor of the classical one-component plasma. At high densities, the former exhibits marked oscillations, whereas the latter consists of very sharp peaks near the plasma frequency, up to wave vectors of order $\frac{1}{a}$, where $a$ is the ion-sphere radius. The resulting dispersion curve is discussed.

Scavenging of Aerosol Particles by a Failing Water Drop and Calculation of Washout Coefficients

Abstract: Collection efficiencies of falling water drops ranging from 0.094 to.O.254 cm in radius for silver chloride aerosol particles in nitrogen ranging from 0.15 to 0.6 μm in radius have been measured. The drops accelerated for distances ranging from 30 to 515 cm prior to entrance into the scavenging chamber. Results were extrapolated to terminal velocity. The results for the slower moving drops (30 cm acceleration distance) agreed roughly with the predictions of a theory based upon collection by Brownian diffusion. However, near terminal velocity, Brownian diffusion theory did not account for the results. Instead, for each value of particle radius a, the collection efficiency was a sharply increasing function of the impaction parameter P. Results by other workers for particles of different density agreed approximately with our values, provided comparisons were made at the same values of aρ½ where ρ is the particle density. Calculations of washout coefficient indicated that the half-life of 0.1-μm aero...

Dynamic background subtraction and the retrieval of threshold signals

Abstract: An approach is outlined for handling the general experimental problem of retrieving characteristic signals from the presence of large backgrounds. The method consists of n th‐order differentiation followed by multiple integration of the same order. It is shown that this procedure results in a function which has the form of the remainder of the (n ‐ 1)th‐order Taylor series for the background plus characteristic signals. If the function is one with a very large radius of convergence, then an order can be found such that the remainder is arbitrarily close to zero over the region of interest. Threshold functions, which are characterized by having very small convergence radii and which asymptotically approach zero on one or both sides of the point corresponding to the minimum radius of convergence, are shown to be accurately retrieved if the minimum convergence radius is contained in the region of integration. The particular advantages of the technique are demonstrated by its application to soft x‐ray appearance potential spectroscopy.

Differential PKiKP Travel Times and the Radius of the Inner Core

Abstract: Summary A value for the radius of the inner core is computed from differential PKiKP (PKiKP minus PcP) arrival time data and current Earth models. The data support an inner core radius of 1220-1230 km, the exact value depending on the model P velocity near the inner core boundary. For a model incorporating a decrease in the velocity gradient just above the boundary, in the transition zone of the core, the best value for the inner core radius is 1227.4+0.6 km. Comparison of pulse shapes and pulse durations for P, PcP, and PKiKP phases suggest that the core boundaries are sharp discontinuities relative to 1-s period waves. Complexity in explosion-related PKiKP signals is attributed to source effects.

Electrohydrodynamic capillary source of ions and charged droplets

Abstract: A semiquantitative treatment predicts that when an electrohydrodynamic capillary source produces metal droplets along with the ions that are generally observed, the charge‐to‐mass ratio will reach a maximum and the radius a minimum at about the radius at which the limit of stability against breakup into smaller drops (Rayleigh limit) becomes equal to the limit of stability against the field evaporation of ions. The maximum charge‐to‐mass ratio was found to be [inverted lazy s] 17 000 C/kg for a eutectic mixture of lead and bismuth. The semiquantitative treatment, which is supported by this experimental result, predicts that the ions should be emitted from a liquid tip having a radius of about 10 A. It is suggested that if the wobble of the tip is not too great, this type of source should have applications in ion microprobes.

Unbonded contact between a circular plate and an elastic half-space

Abstract: The paper concerns the unbonded contact between a thin circular plate of finite radius, governed by Kirchhof or Reissner theory, pressed by means of rotationally symmetric distributed load and its own weight against the surface of an elastic half-space. The contact is assumed frictionless and unbonded. A Hankel transform solution is used for the half-space and the plate deflection is found by inverting the plate equation. The coefficients in a power expansion are obtained by equating plate and half-space deflections at a number of points in the contact region. The variation of contact radius with plate radius, the radius of the uniformly applied load, and the relative stiffness of plate and foundation, is displayed in a series of figures.

Angular Correlation of Photons from Positron Annihilation in Copper-Nickel Alloys

Abstract: Angular correlation measurements of radiation from positrons annihilating in copper-nickel alloys have been carried out with crossedslit geometry using single crystals containing less than 73 at % Ni. The neck radius of the Fermi surface decreases linearly with increasing nickel content, but the neck does not detach from the hexagonal zone face even at the highest nickel content. No marked change in the composition dependence of neck radius is observed at the magnetic phase boundary near 70% Ni. The neck radius of paramagnetic nickel is estimated to be about 0.13 in unit of that for copper from the extrapolation of the observed data.

On Modelling Nucleation and Condensation Theory in Eulerian Spatial Domain

Abstract: One-dimensional, kinematical microphysical cloud models are used to study two numerical aspects associated with modelling the initial microphysical stages of cloud growth in Eulerian spatial domain. First, the high-frequency oscillations in the spatially integrated nucleation rate and maximum supersaturation which became apparent in Clark’s model calculations are reproduced in the present paper and their cause and effect studied. Second, the spatial and radius resolution requirements for calculations of the initial phases of cloud development are studied. It is found that rather high spatial as well as radius resolution are required to obtain a reasonable degree of convergence for the solution of the droplet spectrum coefficient of dispersion for a case where an eddy mixing coefficient K=2 m2 sec−1 was used. The effect of eddy mixing on droplet spectral broadening is investigated where adequate spatial and radius resolution are used. The results indicate that mixing has a rather strong effect on ...

Two Dimensional Generalization of Raizer's Analysis for the Subsonic Propagation of Laser Sparks

Abstract: An extension to two dimensions of Raizer's analysis for the steady state, subsonic propagation of laser sparks is presented. A solution in closed form is obtained for a simplified, two dimensional energy equation, yielding both axial and radial temperature profiles as well as the relationship between incident laser intensity, laser radius and propagation velocity. The propagation mechanism is assumed to be thermal conduction and radiation losses are included in a phenomenological manner. The solution is obtained for a laser spark propagating in a channel and therefore can be used to investigate the effect of a boundary on spark propagation. The solution also allows calculation of the radial heat conduction parameter A introduced by Raizer for use in one dimensional approximations. Sample calculations are presented for air sparks of .15 and .50 cm radius.

Dependence of ion acceleration on limiting current in relativistic electron beams

Abstract: A 2‐MeV 15‐kA 45‐nsec electron beam was used to obtain high‐energy deuterons when injected into a chamber filled with neutral deuterium at low pressure. It was found that ion acceleration did not occur until the electron current exceeded the space‐charge limiting current, the threshold established by the acceleration model of Olson. The limiting current was varied through its dependence on the ratio of guide tube radius to injected electron beam radius. The maximum deuteron energy was measured to be 4.5 MeV for the largest guide tube to beam radius ratio. An increasing average ion energy with an increasing radius ratio was also observed.

A Solution to the Contact of Two Rough Spherical Surfaces

Abstract: The influence of roughness on the interfacial pressure distribution in the contact of two spherical surfaces is considered. An approximate general solution is presented and it is shown that the pressure for all radii can be determined solely from a reference pressure which is, in turn, a function of two parameters - a dimensionless roughness and a dimensionless hardness. Values for the radius of contact are also presented.