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Correction factors for small values of logarithm of Debye length ratio to mean impact parameter in electrical conductivity of fully ionized plasma
Detailed analysis of an analog-to-digital conversion system consisting of a linear converter and a logarithmic amplifier containing nonlinear elements. It is shown that the small-signal resolution of such a system is much greater than that of linear systems used under the same conditions. A design for a low-power analog-to-digital converter operating at medium speed with a large input signal variation field is outlined.
Solid-state logarithmic-function generator is compact and provides improved accuracy. Generator includes a stable multivibrator feeding into RC circuit. Resulting exponentially decaying voltage is compared with input signal. Generator output is proportional to time required for exponential voltage to decay from preset reference level to level of input signal.
An algorithm for symbolic integration of functions built up from the rational functions by repeatedly applying either the exponential or logarithm functions is discussed. This algorithm does not require polynomial factorization nor partial fraction decomposition and requires solutions of linear systems with only a small number of unknowns. It is proven that if this algorithm is applied to rational functions over the integers, a computing time bound for the algorithm can be obtained which is a polynomial in a bound on the integer length of the coefficients, and in the degrees of the numerator and denominator of the rational function involved.
A logarithmic-singularity correction factor is derived for use in kernel function methods associated with Multhopp's subsonic lifting-surface theory. Because of the form of the factor, a relation was formulated between the numbers of chordwise and spanwise control points needed for good accuracy. This formulation is developed and discussed. Numerical results are given to show the improvement of the computation with the new correction factor.
An improved high-voltage stepping supply, for space instrumentation is described where low power consumption and fast settling time between steps are required. The high-voltage stepping supply, utilizing an average power of 750 milliwatts, delivers a pair of mirror images with 64 level logarithmic outputs. It covers a four decade range of + or - 2500 to + or - 0.29 volts having an output stability of + or - 0.5 percent or + or - 20 millivolts for all line load and temperature variations. The supply provides a typical step setting time of 1 millisecond with 100 microseconds for the lower two decades. The versatile design features of the high-voltage stepping supply provides a quick response staircase generator as described or a fixed voltage with the option to change levels as required over large dynamic ranges without circuit modifications. The concept can be implemented up to + or - 5000 volts. With these design features, the high-voltage stepping supply should find numerous applications where charged particle detection, electro-optical systems, and high voltage scientific instruments are used.
A circuit deriving an output voltage that is proportional to the logarithm of a dc input voltage susceptible to wide variations in amplitude includes a constant current source which forward biases a diode so that the diode operates in the exponential portion of its voltage versus current characteristic, above its saturation current. The constant current source includes first and second, cascaded feedback, dc operational amplifiers connected in negative feedback circuit. An input terminal of the first amplifier is responsive to the input voltage. A circuit shunting the first amplifier output terminal includes a resistor in series with the diode. The voltage across the resistor is sensed at the input of the second dc operational feedback amplifier. The current flowing through the resistor is proportional to the input voltage over the wide range of variations in amplitude of the input voltage.
A logarithmic current-measuring instrument was developed to measure plasma coupling currents at a common mode voltage of 5 kilovolts. Positive or negative currents can be measured from 10 to the -9th power to .001 ampere direct current. Optical isolation is used to control input switching and to provide data referenced to ground potential. Analog meter readouts as well as zero to five volt outputs are provided for peripheral data collection. Six independent channels are provided. Three measure positive currents, and three measure negative currents. Although designed for vacuum operation, it can be used equally well in air to measure low currents at high common mode voltages.
A picture digitization grid based on logarithmic spirals rather than Cartesian coordinates is presented. Expressing this curvilinear grid as a conformal exponential mapping reveals useful image processing properties. The mapping induces a computational simplification that suggests parallel architectures in which most geometric transformations are effected by data shifting in memory rather than arithmetic on coordinates. These include fast, parallel noise-free rotation, scaling, and some projective transformations of pixel defined images. Conformality of the mapping preserves local picture-processing operations such as edge detection.
Two dimensional Fredholm integral equations with logarithmic potential kernels are numerically solved. The explicit consequence of these solutions to their true solutions is demonstrated. The results are based on a previous work in which numerical solutions were obtained for Fredholm integral equations of the second kind with continuous kernels.
A high speed logarithmic amplifier circuit for the Perkin-Elmer PDS microdensitometer is discussed. The circuit is designed around an Analog Devices 757p log-amp module. The amplifier produces undistorted profiles of rapidly changing, dense ( 4) images over the available range of scanning speeds. The circuit board was designed to replace directly the manufacturer supplied unit; neither electrical nor mechanical modifications of the basic PDS are required. The performance of the circuit is illustrated through its effects on the overall modulation transfer function of the instrument and by scans of a well exposed stellar image. Circuit diagrams and parts lists a mechanism for obtaining either circuit board layout art work or finished circuit boards are presented.
A high-speed logarithmic-amplifier circuit for a PDS microdensitometer is discussed. The circuit is designed around a 757P log-amp module which replaces the FMI 531 'Negative Log/Anti-log' device of the original. The new amplifier is capable of producing undistorted profiles of rapidly changing, dense images over the available range of scanning speeds. The circuit board has been designed to directly replace the manufacturer supplied unit; neither electrical nor mechanical modifications of the basic PDS are required. The performance of the circuit is illustrated through its effects on the overall Modulation Transfer Function of the instrument and by scans of a well-exposed stellar image. Circuit diagrams and parts lists are presented.
Numerical simulations are used to investigate periodic combustion instabilities observed in ballistic-range experiments of blunt bodies flying at supersonic speeds through hydrogen-air mixtures. The computations are validated by comparing experimental shadowgraphs with shadowgraphs created from the computed flowfields and by comparing the experimentally measured instability frequencies with computed frequencies. The numerical simulations use a logarithmic transformation of the species conservation equations as a way to reduce the grid requirements for computing shock-induced combustion. The transformation is applied to the Euler equations coupled to a detailed hydrogen-air chemical reaction mechanism with 13 species and 33 reactions. The resulting differential equations are solved using a finite volume formulation and a two-step predictor-corrector scheme to advance the solution in time. Results are presented and compared for both a flux-vector splitting scheme and an upwind TVD scheme. The computations add insight to the physical processes observed in the experiments and the numerical methods needed to simulate them. The usefulness of the ballistic-range experiments for the validation of numerical techniques and chemical kinetic models is also demonstrated.
The direct numerical simulation of dissipative, highly compressible turbulent flow is performed using a pseudospectral Fourier technique. The governing equations are cast in a form where the important physical variables are the fluid velocity and the natural logarithms of the fluid density and temperature. Bulk viscosity is utilized to model polyatomic gases more accurately and to ensure numerical stability in the presence of strong shocks. Numerical examples include three-dimensional supersonic homogeneous turbulence and two-dimensional shock-turbulence interactions.
The logarithmic polar curve has for several years been used by the most prominent aerodynamical laboratories as well as by airplane manufacturers in Europe. To show more clearly the practical application of the polar curve, a series of examples are given with suggestions for solution. After a discussion of the theory and the practical application of the polar curve, the following problems are discussed: climbing flight, speed at various altitudes, and the characteristics of two seater observation airplanes of recent design.
The application of logarithmic transformations to speckle images is sometimes desirable in converting the speckle noise distribution into an additive, constant-variance noise distribution. The optical transmission properties of some bacteriorhodopsin films are well suited to implement such a transformation optically in a parallel fashion. I present experimental results of the optical conversion of a speckle image into a transformed image with signal-independent noise statistics, using the real-time photochromic properties of bacteriorhodopsin. The original and transformed noise statistics are confirmed by histogram analysis.
In this paper, we shall give a characterization of all monotonically decreasing sequence of positive terms, whose sum converge and then introduce a Transformation which can be used to accelerate the convergence of a large class of logarithmically convergent series.
Knowledge about the evaporation loss of light elements is important to our understanding of chondrule formation processes. The evaporative loss of light elements (such as B and Li) as a function of cooling rate is of special interest because recent investigations of the distribution of Li, Be and B in meteoritic chondrules have revealed that Li varies by 25 times, and B and Be varies by about 10 times. Therefore, if we can extrapolate and interpolate with confidence the evaporation loss of B and Li (and other light elements such as K, Na) at a wide range of cooling rates of interest based upon limited experimental data, we would be able to assess the full range of scenarios relating to chondrule formation processes. Here, we propose that evaporation loss of light elements as a function of cooling rate should obey the logarithmic law.