Search NASA⌕ Search

SEARCH · Search NASA

Results for “LOGARITHM”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Logarithmic spiral grids for image processing

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.

Weiman, C. F. R.↗
NASA NTRS1981

A numerical solution for two-dimensional Fredholm integral equations of the second kind with kernels of the logarithmic potential form

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.

Gabrielsen, R. E.↗
NASA NTRS1984

An improved logarithmic amplifier circuit for PDS microdensitometers

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.

Anderson, C. M.↗
NASA NTRS1983

An improved logarithmic amplifier circuit for PDS microdensitometers

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.

Anderson, C. M.↗
NASA NTRS1993

Computation of unsteady shock-induced combustion using logarithmic species conservation equations

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.

Wilson, Gregory J.↗
NASA NTRS1993

Pseudospectral simulation of compressible turbulence using logarithmic variables

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.

Shebalin, John V.↗
NASA NTRS1924

The logarithmic polar curve-it's theory and application to the predetermination of airplane performance

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.

Cronstedt, Val↗
NASA NTRS1995

Optical Logarithmic Transformation of Speckle Images with Bacteriorhodopsin Films

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.

Downie, John D.↗
NASA NTRS1998

Acceleration of Logarithmic Convergence

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.

Gaskin, J. G.↗
NASA NTRS2003

Evaporation Loss of Light Elements as a Function of Cooling Rate: Logarithmic Law

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.

Xiong, Yong-Liang↗
NASA NTRS2016

Introducing a Degree of Freedom in the Family of Generalized Logarithmic Spirals

The versatility of the family of generalized logarithmic spirals is improved by introducing a degree of freedom in the solution. The low-thrust acceleration profile now includes a control term that affects both the magnitude and the direction of the thrust. Exact and fully analytic solutions to the trajectory, the velocity, the time of flight, etc. are made available. Two integrals of motion are preserved. The first one is a generalization of the equation of the energy and depends on the values of the control parameter. The second one relates to the equation of the angular momentum. The problem of finding spiral transfers between two arbitrary state vectors reduces to solving one algebraic equation with one unknown. The degree of freedom allows fixing the time of flight of the transfer. If the time of flight is fixed, then there are two equations with two unknowns. No other iterative procedures are required. Coast arcs can be introduced in the solution naturally. An explicit expression for the maximum acceleration reached along the transfer is provided. Thanks to the symmetry properties of the solution a simple algorithm for generating periodic orbits is presented. An arbitrary number of intermediate nodes can be introduced to improve the flexibility of the solution when facing optimization problems. An example of a low-thrust gravity-assist Earth-Mars-Ceres trajectory shows that the solution is comparable to that obtained with other preliminary design techniques.

Roa, Javier↗
NASA NTRS2022

Asymmetric Warming/Cooling Response to CO2 Increase/Decrease Mainly Due to Non-Logarithmic Forcing, not Feedbacks

We explore the CO2 dependence of effective climate sensitivity (SG) with symmetric abrupt and transient CO2 forcing, spanning the range 1/8×, 1/4×, 1/2×, 2×, 4×, and 8×CO2, using two state-of-the-art fully coupled atmosphere-ocean-sea-ice-land models. In both models, under abrupt CO2 forcing, we find an asymmetric response in surface temperature and SG. The surface global warming at 8×CO2 is more than one third larger than the corresponding cooling at 1/8×CO2, and SG is CO2 dependent, increasing non-monotonically from 1/8×CO2 to 8×CO2. We find similar CO2 dependence in the transient runs, forced with -1%yr−1CO2 and +1%yr−1CO2 up to 1/8×CO2 and 8×CO2, respectively. The non-logarithmic radiative forcing – not the changing feedbacks – primarily explains the dependence of SG on CO2, particularly at low CO2 levels. The changing feedbacks, however, explain SG’s non-monotonic behavior.

climate sensitivity↗
NASA NTRS1971

High current compensation network for dc logarithmic amplifiers

Circuit voltage output is reduced by voltage equivalent to ampere resistance drop of nonlogarithmic resistances of practical diodes; therefore, output is same as circuit using ideal diode. Circuit applies to meter and electronic recorder movements, and improves performance of radiation detectors and several microbiological monitoring devices

Wilson, J. H.↗
NASA NTRS1971

Low cost, logarithmic mass flow computer

Computer solves the equation relating gas flow through a nozzle, venturi, or orifice to the absolute temperature, absolute pressure, and differential pressure of the fluid. Inexpensive method has high frequency response and provides true analog output.

Dolce, J. L.↗