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Results for “Exponential integrator”

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.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

A table of integrals of the error function. II - Additions and corrections.

Integrals of products of error functions with other functions are presented, taking into account a combination of the error function with powers, a combination of the error function with exponentials and powers, a combination of the error function with exponentials of more complicated arguments, definite integrals from Laplace transforms, and a combination of the error function with trigonometric functions. Other integrals considered include a combination of the error function with logarithms and powers, a combination of two error functions, and a combination of the error function with other special functions.

Geller, M.↗
NASA NTRS1984

A statistical study of active regions 1967-1981

A study is conducted of 15 years of active region data based on the Mount Wilson daily magnetograms in the interval 1967-1981. The analysis revealed the following: (1) The integral number of regions decreases exponentially with increasing region sizes, or N(A) = 4788 exp(-A/175) for the 15 years of data, where A is the area in square degrees and N(A) is the number of active regions with area equal to or greater than A; (2) the average area of active regions varies with the phase of the solar cycle. There are more larger regions during maximum than during minimum. (3) Regions in the north are 10 percent larger on average than those in the south during this interval. This coincides with a similar asymmetry in the total magnetic flux between the hemispheres. (4) Regions of all sizes and magnetic complexities show the same characteristic latitude variation with phase in the solar cycle. The largest regions, however, show a narrower latitude range.

Tang, F.↗
NASA NTRS1990

Concept For Generation Of Long Pseudorandom Sequences

Conceptual very-large-scale integrated (VLSI) digital circuit performs exponentiation in finite field. Algorithm that generates unusually long sequences of pseudorandom numbers executed by digital processor that includes such circuits. Concepts particularly advantageous for such applications as spread-spectrum communications, cryptography, and generation of ranging codes, synthetic noise, and test data, where usually desirable to make pseudorandom sequences as long as possible.

Wang, C. C.↗
NASA NTRS2004

Measurement of Initial Conditions at Nozzle Exit of High Speed Jets

The time averaged and unsteady density fields close to the nozzle exit (0.1 less than or = x/D less than or = 2, x: downstream distance, D: jet diameter) of unheated free jets at Mach numbers of 0.95, 1.4, and 1.8 were measured using a molecular Rayleigh scattering based technique. The initial thickness of shear layer and its linear growth rate were determined from time-averaged density survey and a modeling process, which utilized the Crocco-Busemann equation to relate density profiles to velocity profiles. The model also corrected for the smearing effect caused by a relatively long probe length in the measured density data. The calculated shear layer thickness was further verified from a limited hot-wire measurement. Density fluctuations spectra, measured using a two-Photomultiplier-tube technique, were used to determine evolution of turbulent fluctuations in various Strouhal frequency bands. For this purpose spectra were obtained from a large number of points inside the flow; and at every axial station spectral data from all radial positions were integrated. The radially-integrated fluctuation data show an exponential growth with downstream distance and an eventual saturation in all Strouhal frequency bands. The initial level of density fluctuations was calculated by extrapolation to nozzle exit.

Panda, J.↗
NASA NTRS1990

Discretization chaos - Feedback control and transition to chaos

Problems in the design of feedback controllers for chaotic dynamical systems are considered theoretically, focusing on two cases where chaos arises only when a nonchaotic continuous-time system is discretized into a simpler discrete-time systems (exponential discretization and pseudo-Euler integration applied to Lotka-Volterra competition and prey-predator systems). Numerical simulation results are presented in extensive graphs and discussed in detail. It is concluded that care must be taken in applying standard dynamical-systems methods to control systems that may be discontinuous or nondifferentiable.

Grantham, Walter J.↗
NASA NTRS1976

Exponential approximation for daily average solar heating or photolysis

When incorporating formulations of instantaneous solar heating or photolytic rates as functions of altitude and sun angle into long range forecasting models, it may be desirable to replace the time integrals by daily average rates that are simple functions of latitude and season. This replacement is accomplished by approximating the integral over the solar day by a pure exponential. This gives a daily average rate as a multiplication factor times the instantaneous rate evaluated at an appropriate sun angle. The accuracy of the exponential approximation is investigated by a sample calculation using an instantaneous ozone heating formulation available in the literature.

Cogley, A. C.↗
NASA NTRS1987

Dynamic topography and gravity anomalies for fluid layers whose viscosity varies exponentially with depth

Adopting the formalism of Parsons and Daly (1983), analytical integral equations (Green's function integrals) are derived which relate gravity anomalies and dynamic boundary topography with temperature as a function of wavenumber for a fluid layer whose viscosity varies exponentially with depth. In the earth, such a viscosity profile may be found in the asthenosphere, where the large thermal gradient leads to exponential decrease of viscosity with depth, the effects of a pressure increase being small in comparison. It is shown that, when viscosity varies rapidly, topography kernels for both the surface and bottom boundaries (and hence the gravity kernel) are strongly affected at all wavelengths.

Revenaugh, Justin↗
NASA NTRS1989

A method for exponential propagation of large systems of stiff nonlinear differential equations

A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.

Friesner, Richard A.↗
DOE OSTI2025

Response of Atmospheric River Width and Intensity to Aquaplanet Warming: A Detection Algorithm‐ and Background Moisture‐Independent Approach

The width of an atmospheric river (AR) is an important parameter when evaluating its impact. Although previous research suggests ARs will widen with global warming, a precise response has been muddled by the large sensitivity of width to a diverse set of AR detection techniques (ARDTs). Here, we propose a methodology that removes the influence of the ARDT by modeling AR‐integrated vapor transport (IVT) profiles as idealized exponential curves with free parameters given by background IVT, intensity above background IVT, and profile width. Notably, our definition for AR profile width does not include any explicit numerical thresholds, relative or absolute, for IVT. We apply our approach to a series of idealized aquaplanet experiments, first with a baseline sea surface temperature (SST) distribution, and then with +2K, +4K, and +6K uniform warming, so as to determine the contributions of each free parameter to AR width. We also apply our approach to high‐resolution atmosphere‐only models forced with SSTs modified to preserve historical variability but following projected warming over 2016–2050. Our results show that contributions to impacts‐relevant AR widening comes primarily from enhancements in background IVT and AR intensity, as opposed to from dynamic width changes.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1971

A method for nonlinear exponential regression analysis

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Junkin, B. G.↗
NASA NTRS1978

Radiative cooling in shock-heated hydrogen-helium plasmas

Axial and off-axis radiative cooling of cylindrical shock-heated hydrogen-helium plasmas is investigated theoretically and experimentally. The coupled fluid dynamic-radiative transfer equations are solved by a combination of approximation techniques aimed at simplifying the computation of the flux divergence term, namely, the quasi-isothermal approximation and the exponential approximation developed for the solid angle integration. The accuracy of the approximation schemes has been assessed and found acceptable for applying the methods to the rapid computation of the radiatively coupled flow problem. Radiative cooling experiments were conducted in a 6-inch annular arc accelerator shock tube (ANAA) for an initial pressure of 1 torr and shock speeds from 35 to 45 Km/sec. The results indicate that the lateral cooling is small compared with the axial cooling, and that better agreement is achieved between the data and the theoretical results by inclusion of the lateral temperature gradient.

Poon, P. T. Y.↗
NASA NTRS1982

Time-marching transonic flutter solutions including angle-of-attack effects

Transonic aeroelastic solutions based upon the transonic small perturbation potential equation were studied. Time-marching transient solutions of plunging and pitching airfoils were analyzed using a complex exponential modal identification technique, and seven alternative integration techniques for the structural equations were evaluated. The HYTRAN2 code was used to determine transonic flutter boundaries versus Mach number and angle-of-attack for NACA 64A010 and MBB A-3 airfoils. In the code, a monotone differencing method, which eliminates leading edge expansion shocks, is used to solve the potential equation. When the effect of static pitching moment upon the angle-of-attack is included, the MBB A-3 airfoil can have multiple flutter speeds at a given Mach number.

Edwards, J. W.↗
NASA NTRS1982

Time-marching transonic flutter solutions including angle-of-attack effects

Transonic aeroelastic solutions based upon the transonic small perturbation potential equation are studied. Time-marching transient solutions of plunging and pitching airfoils are analyzed using a complex exponential modal identification technique, and seven alternative integration techniques for the structural equations are evaluated. The HYTRAN2 code is used to determine transonic flutter boundaries versus Mach number and angle-of-attack for NACA 64A010 and MBB A-3 airfoils. In that code, a monotone differencing method, which eliminates leading edge expansion shocks, is used to solve the potential equation. When the effect of static pitching moment upon the angle-of-attack is included, the MBB A-3 airfoil can have multiple flutter speeds at a given Mach number.

Edwards, J. W.↗
NASA NTRS2012

Model-Based Verification and Validation of Spacecraft Avionics

Verification and Validation (V&V) at JPL is traditionally performed on flight or flight-like hardware running flight software. For some time, the complexity of avionics has increased exponentially while the time allocated for system integration and associated V&V testing has remained fixed. There is an increasing need to perform comprehensive system level V&V using modeling and simulation, and to use scarce hardware testing time to validate models; the norm for thermal and structural V&V for some time. Our approach extends model-based V&V to electronics and software through functional and structural models implemented in SysML. We develop component models of electronics and software that are validated by comparison with test results from actual equipment. The models are then simulated enabling a more complete set of test cases than possible on flight hardware. SysML simulations provide access and control of internal nodes that may not be available in physical systems. This is particularly helpful in testing fault protection behaviors when injecting faults is either not possible or potentially damaging to the hardware. We can also model both hardware and software behaviors in SysML, which allows us to simulate hardware and software interactions. With an integrated model and simulation capability we can evaluate the hardware and software interactions and identify problems sooner. The primary missing piece is validating SysML model correctness against hardware; this experiment demonstrated such an approach is possible.

MBV&V↗
DOE OSTI2025

Navigating Integration: Key Challenges for Data Centers, Nuclear Stakeholders, and Utility Operators

he exponential growth of data centers—driven by artificial intelligence and cloud computing—is reshaping the U.S. energy landscape, presenting urgent challenges and transformative opportunities for data center developers, nuclear energy providers, and utility operators. As data centers are projected to consume up to 12% of U.S. electricity by 2028, stakeholders must address rapid deployment needs, grid congestion, and the demand for reliable, high-quality power. This presentation explores the multifaceted barriers to integrating data centers with nuclear and utility infrastructure, including land use constraints, public perception, regulatory complexity, and workforce alignment. It highlights the distinct priorities and operational cultures of each sector, and the friction that arises from misaligned planning horizons and risk tolerances. We examine collaborative strategies such as co-siting, hybrid power-purchase agreements, unified community engagement, and innovative financing models.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗