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This letter describes an active RC network which realizes a fourth-order low-pass Butterworth characteristic. It requires one active element and has the practical advantage that all capacitors have the same value. A design chart is included.
A measurement system using a deceleration probe was designed for determining the local values of gas and liquid mass flux in various gas/liquid droplet sprayfields. The system was used to characterize two-phase flowfields generated by gas/liquid rocket-motor injectors. Measurements were made at static pressures up to 500 psia and injected mass flow ratios up to 20. The measurement system can also be used at higher pressures and in gas/solid flowfields.
A new iterative scheme for solving boundary value problems is presented. It consists of the introduction of an artificial time dependence into a modified version of the system of equations. Then explicit forward integrations in time are followed by explicit integrations backwards in time. The method converges under much more general conditions than schemes based in forward time integrations (false transient schemes). In particular it can attain a steady state solution of an elliptical system of equations even if the solution is unstable, in which case other iterative schemes fail to converge. The simplicity of its use makes it attractive for solving large systems of nonlinear equations.
The Du Fort-Frankel difference scheme is generalized to difference operators of arbitrary high order accuracy in space and to arbitrary order of the parabolic differential operator. Spectral methods can also be used to approximate the spatial part of the differential operator. The scheme is explicit, and it is unconditionally stable for the initial value problem. Stable boundary conditions are given for two different fourth order accurate space approximations.
Electronic analog divider circuit employs, over certain range, current-exponential voltage characteristics of diode to obtain better accuracy at low denominator values.
During the summer of 1974 and spring of 1975, measurements of attenuation of propagation through rain were made at Wallops Island, VA, using 13 and 18 GHz transmitters operating in the uplink mode toward the ATS-6 satellite. Simultaneously, rain reflectivity levels were measured along the earth-satellite path using a high resolution (0.4 deg beamwidth) S-band radar having a scanning antenna. Four rain-gages and two disdrometers were also located in the vicinity of the transmitters. The radar and disdrometer data were used in a modelling program to predict attenuation levels which were subsequently compared to the directly measured fades over nearly simultaneous time intervals. Predicted attenuation levels were obtained for three drop size distributions. Comparisons between predicted and measured attenuation levels showed the APL dropsize distribution gave the smallest rms difference of 1.3 dB at 13 and 18 GHz although the rms difference corresponding to Marshall-Palmer was close to this value. The good agreement suggests the validity of using radar to model path attenuation to obtain attenuation statistics.
Absolute gf-values were obtained for 98 transitions in neutral scandium by the hook method using an inductively coupled heat-pipe oven. Of the 98 lines, 51 are classified, 33 are unclassified lines that occur in pairs with the lower energy level identified, and 14 are unclassified but are believed to originate from one of the two lower levels of the ground state. The results are compared with semiempirical and other measurement results in the literature.
Correlations between Ar-40 and Ar-36 from size fractions of three Apollo 15 fines (15071, 15421, 15501) have been obtained. The Ar-40 intercept values of these fines and of 15091 and 15601 are generally lower than what one would expect for fines resulting from the comminution of rocks having ages of about 3.3 billion yr, typical for basalts of the landing site. This is interpreted to be the result of contamination by ray material from the Copernican age (equal or less than about 1 billion yr) craters, Autolycus and Aristillus, north of the landing site.
Most existing deconvolution techniques are incapable of determining phase properties of wavelets from time series data; to assure a unique solution, minimum phase is usually assumed. It is demonstrated, for moving average processes of order one, that deconvolution filtering using the absolute value norm provides an estimate of the wavelet shape that has the correct phase character when the random driving process is nonnormal. Numerical tests show that this result probably applies to more general processes.
We solve in closed form the boundary-value problem for the partial differential equations which describe the (azimuthal) rotation velocity and induced magnetic fields in a cylindrical plasma centrifuge with ring electrodes of different radii and an external, axial magnetic field. The electric field, current density, and velocity distributions are discussed in terms of the Hartmann number H and the magnetic Reynolds number R. For small Hall coefficients, the induced magnetic field does not affect the plasma rotation. As a result of the Lorentz forces, the plasma rotates with speeds as high as 100,000 cm/sec around its axis of symmetry at typical conditions, so that the lighter (heavier) ion and atom components are enriched at (off) the center of the discharge cylinder.
The stability of approximating the solution of mixed initial-boundary value problems for hyperbolic systems by semidiscrete Galerkin methods is studied. It is shown that a particular straightforward Galerkin method yields an unstable approximation, and that this numerical instability is caused by an improper treatment of the boundary. Stable schemes are then presented, one of which differs from the unstable scheme only insofar as the treatment of the boundary is concerned. These stable schemes make use of a particular matrix which symmetrizes the differential system. It is therefore shown that the use of this matrix is crucial to the stability of the computations as well as for obtaining a priori bounds on the energy of the continuous system. This symmetrizing matrix is also related to the diagonalizing matrix for the system of hyperbolic equations and to the Liapunov matrix for the system of ordinary differential equations resulting from the application of Galerkin's method.
An electrical discharge between two ring electrodes embedded in the mantle of a cylindrical chamber is considered, in which the plasma in the anode and cathode regions rotates in opposite directions under the influence of an external axial magnetic field. The associated boundary-value problem for the coupled partial differential equations describing the azimuthal velocity and radial current-density fields is solved in closed form. The velocity, current density, induced magnetic induction, and electric fields are presented for typical Hartmann numbers, magnetic Reynolds numbers, and geometry parameters. The discharge is shown to produce anodic and cathodic plasma sections rotating at speeds of the order 1,000,000 cm/sec for conventional magnetic field intensities. Possible application of the magnetoactive discharge as a plasma centrifuge for isotope separation is discussed.
A Galerkin-Ritz procedure for any arbitrary system of field equations is shown to follow generically from 'two-functional' variational conditions. The initial-value problem for boundary-free incompressible Navier-Stokes flow is solved analytically in the two-parameter-function approximation.
Definitions in the case of multiple series equations and multiple integral equations are examined. In considering the solution of a given mixed boundary value problem perhaps the simplest technique is the direct application of the method of complex potentials provided the problem admits such potentials and the domain and the boundary conditions are suitable for such an application. The direct application of complex potentials is described with the aid of examples, taking into account a problem in potential theory, the case of periodic cuts, and an elasticity problem for a nonhomogeneous plane. The reduction to singular integral equations is discussed along with the numerical solution of singular integral equations of the first kind, integral equations with generalized Cauchy kernels, and singular integral equations of the second kind.
Apparent lethal concentrations for 50 per cent of the test animals within a 30-min exposure period (ALC/50/) were determined for seventeen samples of polymeric materials, using the screening test method. The materials evaluated included resin-glass composites, film composites, and miscellaneous resins. ALC(50) values, based on weight of original sample charged, ranged from 24 to 110 mg/l. Modified phenolic resins seemed to exhibit less toxicity than the baseline epoxy resins. Among the film composites evaluated, only flame modified polyvinyl fluoride appeared to exhibit less toxicity than the baseline polyvinyl fluoride film.
Discharge-flow experiments at 295 K of the OH + HO2 reaction are described in which excess O3 is added to OH through a movable injector; OH concentration is measured downstream by resonance fluorescence with and without addition of excess NO just upstream of the detector so that both OH concentration and OH concentration + HO2 concentration are determined independently. The data are compared with a computer model involving 12 reaction steps. A simple sensitivity analysis is carried out to establish how errors in the other 'known' rate constants affect the data fit. Best agreement is obtained between computer calculations and experiments when k1 for the OH + HO2 reaction is in the range 2-3 x 10 to the -11th cu cm/s. Values above about 5 x 10 to the -11th are very unlikely whereas those below about 1 x 10 to the -11th are less strongly excluded.
Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.
The first integral of x-double prime = - V prime (x) yields an integral for the period of a periodic solution, if such exists. In general, this integral cannot be evaluated. By means of an approximate solution along with the minimization of a mean-square error, one can obtain an approximate value for the period in terms of the amplitude of the motion. The calculated period agrees very well with the period obtained by means of numerical integration for the case of orbit-orbit resonance involving the motion of two satellites of a planet. The same method is applied to obtain an alternative derivation of the first Krylov-Bogoliuboff averaging method in nonlinear mechanics.