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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2024

Universality in logarithmic temperature corrections to near-extremal rotating black hole thermodynamics in various dimensions

The low-temperature thermodynamics of near-extremal rotating black holes has recently been revisited to incorporate one-loop contributions that are dominant in this regime. We discuss these quantum corrections to the gravitational path integral for asymptotically Anti de-Sitter black holes in four and five dimensions. In four dimensions we explicitly consider Kerr-AdS 4 , Kerr-Newman-AdS 4 and the rotating black hole in $\mathcal{N}$ = 4 gauged supergravity with two scalars and two electric charges turned on. In five dimensions we explicitly address the asymptotically flat Myers-Perry black hole and the Kerr-AdS5 black hole. In every case we find that tensor modes contribute $\frac{3}{2}$logT Hawking to the low-temperature thermodynamics. We identify the root cause of this universality in two facts: (i) the universal presence of a SL(2, $\mathbb{R}$) subgroup of isometries in the near-horizon geometry and (ii) a set of cancellations in the Lichnerowicz operator. We show that these two conditions hold for near-extremal black holes in asymptotically flat and asymptotically AdS spacetimes of various dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Logarithmic Corrections to Kerr Thermodynamics

Recent work has shown that loop corrections from massless particles generate $\frac{3}{2}$ ⁢log⁡𝑇 Hawking corrections to black hole entropy which dominate the thermodynamics of cold near-extreme charged black holes. Here we adapt this analysis to near-extreme Kerr black holes. Like AdS 2 ×𝑆 2 , the near-horizon extreme Kerr (NHEK) metric has a family of normalizable zero modes corresponding to reparametrizations of boundary time. The path integral over these zero modes leads to an infrared divergence in the one-loop approximation to the Euclidean NHEK partition function. We regulate this divergence by retaining the leading finite temperature correction in the NHEK scaling limit. This “not-NHEK” geometry lifts the eigenvalues of the zero modes, rendering the path integral infrared finite. The quantum-corrected near-extremal entropy exhibits $\frac{3}{2}$ ⁢log⁡𝑇 Hawking behavior characteristic of the Schwarzian model and predicts a lifting of the ground state degeneracy for the extremal Kerr black hole.

General relativity↗
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.↗
NASA NTRS1985

Analysis of aircraft spectrometer data with logarithmic residuals

Spectra from airborne systems must be analyzed in terms of their mineral-related absorption features. Methods for removing backgrounds and extracting these features one at a time from reflectance spectra are discussed. Methods for converting radiance spectra into a form similar to reflectance spectra so that the feature extraction procedures can be implemented on aircraft spectrometer data are also discussed.

Green, A. A.↗
NASA NTRS1937

Universal logarithmic law of velocity distribution as applied to the investigation of boundary layer and drag of streamline bodies at large Reynolds number

In the present paper we shall consider a figure of revolution, so that the formulas applicable to the more simple cases as, for example, a wing or flat plate will follow from our equations as corollaries. For checking the results of our theory, we made use of the data derived from the tests of Freeman on a 1/40-scale model of the airship "Akron" conducted in the large NACA wind tunnel. In the first part we shall derive the fundamental equation for a body of revolution according to the Karman theory in its original form, and in the second part we shall give all the comparisons of the results of tests with the modified theory.

Gurjienko, G↗
NASA NTRS2016

Characterization of DBD Plasma Actuators Performance without External Flow : Thrust-Voltage Quadratic Relationship in Logarithmic Space for Sinusoidal Excitation - Part I

We present results of thrust measurements of Dielectric Barrier Discharge (DBD) plasma actuators. We have used a test setup, measurement, and data processing methodology that we developed in prior work. The tests were conducted with High Density Polyethylene (HDPE) actuators of three thicknesses. The applied voltage driving the actuators was a pure sinusoidal waveform. The test setup was suspended actuators with a partial liquid interface. The tests were conducted at low ambient humidity. The thrust was measured with an analytical balance and the results were corrected for anti-thrust to isolate the plasma generated thrust. Applying this approach resulted in smooth and repeatable data. It also enabled curve fitting that yielded quadratic relations between the plasma thrust and voltage in log-log space at constant frequencies. The results contrast power law relationships developed in literature that appear to be a rough approximation over a limited voltage range.

Dielectric Barrier Discharge↗
NASA NTRS2016

Characterization of DBD Plasma Actuators Performance Without External Flow - Part I: Thrust-Voltage Quadratic Relationship in Logarithmic Space for Sinusoidal Excitation

Results of characterization of Dielectric Barrier Discharge (DBD) plasma actuators without external flow are presented. The results include aerodynamic and electric performance of the actuators without external flow for different geometrical parameters, dielectric materials and applied voltage level and wave form.

Dielectric Barrier Discharge↗