SEARCH · Engineering Papers

Results for “EXPONENTIAL FUNCTION”

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.

SourceResearch connectionFrom yearThrough year

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

At least 793 records · Page 44

All sources NASA NTRS DOE OSTI

DOE OSTI2011

Kinetics of spin relaxation in quantum wires and channels: Boundary spin echo and formation of a persistent spin helix

In this paper we use a spin kinetic equation to study spin-polarization dynamics in one-dimensional (1D) wires and 2D channels. The spin kinetic equation is valid in both diffusive and ballistic spin transport regimes and therefore is more general than the usual spin drift-diffusion equations. In particular, we demonstrate that in infinite 1D wires with Rashba spin-orbit interaction the exponential spin-relaxation decay can be modulated by an oscillating function. In the case of spin relaxation in finite length 1D wires, it is shown that an initially homogeneous spin polarization spontaneously transforms into a persistent spin helix. We find that a propagating spin-polarization profile reflects from a system boundary and returns back to its initial position similarly to the reflectance of sound waves from an obstacle. The Green's function of the spin kinetic equation is derived for both finite and infinite 1D systems. Moreover, we demonstrate explicitly that the spin relaxation in specifically oriented 2D channels with Rashba and Dresselhaus spin-orbit interactions of equal strength occurs similarly to that in 1D wires of finite length. Finally, a simple transformation mapping 1D spin kinetic equation into the Klein-Gordon equation with an imaginary mass is found thus establishing an interesting connection between semiconductor spintronics and relativistic quantum mechanics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2013

Structural short-range forces between solid-melt interfaces

We predict the structural interaction of crystalline solid-melt interfaces using amplitude equations which are derived from classical density functional theory or phase field crystal modeling. The solid ordering decays exponentially on the scale of the interface thickness at solid-melt interfaces; the overlap of two such profiles leads to a short-range interaction, which is mainly carried by the longest-range density waves, which can facilitate grain boundary premelting. Here, we calculate the tail of these interactions, depending on the relative translation of the two crystals, fully analytically and predict the interaction potential, and compare it to numerical simulations. For grain boundaries the interaction is predicted to decay twice as fast as for two crystals without misorientation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem

Simon’s problem is to find a hidden period (a bitstring) encoded into an unknown 2-to-1 function. It is one of the earliest problems for which an exponential quantum speedup was proven for ideal, noiseless quantum computers, albeit in the oracle model. Here, using two different 127-qubit IBM Quantum superconducting processors, we demonstrate an algorithmic quantum speedup for a variant of Simon’s problem where the hidden period has a restricted Hamming weight 𝑤. For sufficiently small values of 𝑤 and for circuits involving up to 58 qubits, we demonstrate an exponential speedup, albeit of a lower quality than the speedup predicted for the noiseless algorithm. The speedup exponent and the range of 𝑤 values for which an exponential speedup exists are significantly enhanced when the computation is protected by dynamical decoupling. Further enhancement is achieved with measurement error mitigation. This case constitutes a demonstration of a bona fide quantum advantage for an Abelian hidden subgroup problem.

computation↗

DOE OSTI2023

Effective fractonic behavior in a two-dimensional exactly solvable spin liquid

In this work we propose a \mathbb{Z}_N ℤ N clock model which is exactly solvable on the lattice. We find exotic properties for the low-energy physics, such as UV/IR mixing and excitations with restricted mobility, that resemble fractonic physics from higher dimensional models. We then study the continuum descriptions for the lattice system in two distinct regimes and find two qualitative distinct field theories for each one of them. A characteristic time scale that grows exponentially fast with N^2 N 2 (and diverges rapidly as function of system parameters) separates these two regimes. For times below this scale, the system is described by an effective fractonic Chern-Simons-like action, where higher-form symmetries prevent quasiparticles from hopping. In this regime, the system behaves effectively as a fracton as isolated particles, in practice, never leave their original position. Beyond the large characteristic time scale, the excitations are mobile and the effective field theory is given by a pure mutual Chern-Simons action. In this regime, the UV/IR properties of the system is captured by a peculiar realization of the translation group.

Delfino, Guilherme↗

NASA NTRS1976

Distribution of lifetimes for coronal soft X-ray bright points

The lifetime 'spectrum' of X-ray bright points (XBPs) is measured for a sample of 300 such features using soft X-ray images obtained with the S-054 X-ray spectrographic telescope aboard Skylab. 'Spectrum' here is defined as a function which gives the relative number of XBPs having a specific lifetime as a function of lifetime. The results indicate that a two-lifetime exponential can be fit to the decay curves of XBPs, that the spectrum is heavily weighted toward short lifetimes, and that the number of features lasting 20 to 30 hr or more is greater than expected. A short-lived component with an average lifetime of about 8 hr and a long-lived 1.5-day component are consistently found along with a few features lasting 50 hr or more. An examination of differences among the components shows that features lasting 2 days or less have a broad heliocentric-latitude distribution while nearly all the longer-lived features are observed within 30 deg of the solar equator.

Golub, L.↗

NASA NTRS1985

Size and DNA distributions of electrophoretically separated cultured human kidney cells

Electrophoretic purification of purifying cultured cells according to function presumes that the size of cycle phase of a cell is not an overriding determinant of its electrophoretic velocity in an electrophoretic separator. The size distributions and DNA distributions of fractions of cells purified by density gradient electrophoresis were determined. No systematic dependence of electrophoretic migration upward in a density gradient column upon either size or DNA content were found. It was found that human leukemia cell populations, which are more uniform function and found in all phases of the cell cycle during exponential growth, separated on a vertical sensity gradient electrophoresis column according to their size, which is shown to be strictly cell cycle dependent.

Kunze, M. E.↗

NASA NTRS1985

Instabilities in decelerating supersonic flows with applications to cosmic ray shocks

The nature of instabilities in cosmic ray shocks is investigated by using two distinct models for the shock wave. For wavelengths which are short relative to the thickness of the shock wave, the shock is treated as a smoothly decelerating low, and an appropriate JWKB type expansion is used to describe the perturbations to the flow. In this, the short wavelength regime, the presence of squeezing and an effective g renders strong cosmic ray shocks unstable in a way which is similar to instabilities in other supersonic flows, such as in de Laval nozzle flow or a heat conduction dominated shock wave. In the long wavelength limit, where the shock is treated as a discontinuous transition, a stability function is derived which, if negative, corresponds to unstable disturbances growing exponentially in time. In this case, it was found that if the cosmic ray fluid is relativistic (gamma sub c = 4/3) and the background plasma ideal (gamma = 5/3), then strong shocks are unstable.

Zank, A. P.↗

NASA NTRS1990

Gas flows in elliptical galaxies

In preparation for the next generation of x ray telescopes, researchers have begun a program investigating the evolving x ray properties of elliptical galaxies. Their galaxy models consist of a modified King profile for the luminous portion of the galaxy and can include an isothermal dark halo comprising 90 percent of the total mass. The stellar population is assumed to form at a rate which decreases exponentially on a dynamical time scale with a Salpeter initial mass function. Stellar mass loss occurs instantaneously as stars evolve off the main sequence. All stars more massive than 8 solar mass produce type II supernovae, while less massive stars loss mass through a planetary nebulae. The evolving rate of type I supernovae is normalized to a fraction, gamma sub sn I, of Tammann's (1974) value. All of this information is then incorporated into a one-dimensional hydrodynamics code to determine the evolving dynamical state of the interstellar medium.

David, L. P.↗

NASA NTRS1991

Free vibrations of delaminated beams

Free vibration of laminated composite beams is studied. The effect of interply delaminations on natural frequencies and mode shapes is evaluated both analytically and experimentally. The equation of motion and associated boundary conditions are derived for the free vibration of a composite beam with a delamination of arbitrary size and location. A generalized variational principle is used to formulate the equation of motion, taking into account the interlaminar stress concentration at the crack-tips. This is accomplished by introducing a 'crack function' into the beam's compatibility relations. This function has its maximum value at the crack tip and decays exponentially in the longitudinal direction. The rate of exponential decay is determined by a least-square fit with the experimental results. The effect of coupling between longitudinal vibration and bending vibration is considered in the present study. This coupling effect is found to significantly affect the natural frequencies and mode shapes of the delaminated beam.

Shen, M.-H. H.↗

NASA NTRS1996

Dynamic Light Scattering From Colloidal Gels

We present a brief, preliminary account of the interpretation of dynamic light scattering from fractal colloidal gels. For small scattering angles, and for high initial colloid particle volume fractions, the correlation functions exhibit arrested decay, reflecting the non-ergodic nature of these systems and allowing us to directly determine the elastic modulus of the gels. For smaller initial volume fractions, the correlation functions decay completely. In all cases, the initial decay is not exponential, but is instead described by a stretched exponential. We summarize the principles of a model that accounts for these data and discuss the scaling behavior of the measured parameters.

Krall, A. H.↗

NASA NTRS2013

Hubble Space Telescope Hx Imaging of Star-forming Galaxies at z approximately equal to 1-1.5: Evolution in the Size and Luminosity of Giant H II Regions

We present Hubble Space Telescope/Wide Field Camera 3 narrow-band imaging of the Hα emission in a sample of eight gravitationally lensed galaxies at z = 1-1.5. The magnification caused by the foreground clusters enables us to obtain a median source plane spatial resolution of 360 pc, as well as providing magnifications in flux ranging from approximately 10× to approximately 50×. This enables us to identify resolved star-forming HII regions at this epoch and therefore study their Hα luminosity distributions for comparisons with equivalent samples at z approximately 2 and in the local Universe. We find evolution in the both luminosity and surface brightness of HII regions with redshift. The distribution of clump properties can be quantified with an HII region luminosity function, which can be fit by a power law with an exponential break at some cut-off, and we find that the cut-off evolves with redshift. We therefore conclude that 'clumpy' galaxies are seen at high redshift because of the evolution of the cut-off mass; the galaxies themselves follow similar scaling relations to those at z = 0, but their HII regions are larger and brighter and thus appear as clumps which dominate the morphology of the galaxy. A simple theoretical argument based on gas collapsing on scales of the Jeans mass in a marginally unstable disc shows that the clumpy morphologies of high-z galaxies are driven by the competing effects of higher gas fractions causing perturbations on larger scales, partially compensated by higher epicyclic frequencies which stabilize the disc.

H imaging↗

DOE OSTI2013

Numerical computation of doppler-broadening in the resonance domain

We have implemented an accurate and fast calculation of the Doppler-broadened kernel PT(E {yields} E') for neutron elastic scattering based on a gas model. An exponential cutoff which accounts for the asymptotic behavior of the error function helps limit the range of integration while eliminating difference effects. This allows for calculating a kernel library for {sup 238}U over a very fine energy grid covering the resonance range in only a few hours in a laptop. We give an example showing the impact of {sup 238}U elastic up-scattering on the values of self shielded cross sections. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

Superposition states of ultracold bosons in rotating rings with a realistic potential barrier

In a recent paper [Phys. Rev. A 82, 063623 (2010)] Hallwood et al. argued that it is feasible to create large superposition states with strongly interacting bosons in rotating rings. Here we investigate in detail how the superposition states in rotating-ring lattices depend on interaction strength and barrier height. With respect to the latter we find a trade-off between energy gap and quality of the superposition state. Most importantly, we go beyond the {delta}-function approximation for the barrier potential and show that the energy gap decreases exponentially with the number of particles for weak barrier potentials of finite width. These are crucial issues in the design of experiments to realize superposition states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Multivariate Analogs of Classical Univariate Discrete Distributions and Their Properties

Some discrete distributions such as Bernoulli, binomial, geometric, negative binomial, Poisson, Polya–Aeppli, and others play an important role in applied problems of probability theory and mathematical statistics. We propose a variant of a multivariate distribution whose components have a given univariate discrete distribution. In fact we consider some very general variant of the so-called reduction method. We find the explicit form of the mass function and generating function of such distribution and study their properties. We prove that our construction is unique in natural exponential families of distributions. Our results are the generalization and unification of many results of other authors.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2017

Autonomous Task Management and Decision Support Tools

For some time aircraft manufacturers and researchers have been pursuing mechanisms for reducing crew workload and providing better decision support to the pilots, especially during non-normal situations. Some previous attempts to develop task managers or pilot decision support tools have not resulted in robust and fully functional systems. However, the increasing sophistication of sensors and automated reasoners, and the exponential surge in the amount of digital data that is now available create a ripe environment for the development of a robust, dynamic, task manager and decision support tool that is context sensitive and integrates information from a wide array of on-board and off aircraft sourcesa tool that monitors systems and the overall flight situation, anticipates information needs, prioritizes tasks appropriately, keeps pilots well informed, and is nimble and able to adapt to changing circumstances. This presentation will discuss the many significant challenges and issues associated with the development and functionality of such a system for use on the aircraft flight deck.

decision support↗

DOE OSTI2025

Simplifying activations with linear approximations in neural networks

A key step in Neural Networks is activation. Among the different types of activation functions, sigmoid, tanh, and others involve the usage of exponents for calculation. From a hardware perspective, exponential implementation implies the usage of Taylor series or repeated methods involving many addition, multiplication, and division steps, and as a result are power-hungry and consume many clock cycles. We implement a piecewise linear approximation of the sigmoid function as a replacement for standard sigmoid activation libraries. This approach provides a practical alternative by leveraging piecewise segmentation, which simplifies hardware implementation and improves computational efficiency. In this paper, we detail piecewise functions that can be implemented using linear approximations and their implications for overall model accuracy and performance gain. Our results show that for the DenseNet, ResNet, and GoogLeNet architectures, the piecewise linear approximation of the sigmoid function provides faster execution times compared to the standard TensorFlow sigmoid implementation while maintaining comparable accuracy. Specifically, for MNIST with DenseNet, accuracy reaches 99.91% (Piecewise) vs. 99.97% (Base) with up to 1.31x speedup in execution time. For CIFAR-10 with DenseNet, accuracy improves to 98.97% (Piecewise) vs. 99.40% (Base) while achieving 1.24x faster execution. Similarly, for CIFAR-100 with DenseNet, the accuracy is 97.93% (Piecewise) vs. 98.39% (Base), with a 1.18x execution time reduction. These results confirm the proposed method’s capability to efficiently process large-scale datasets and computationally demanding tasks, offering a practical means to accelerate deep learning models, including LSTMs, without compromising accuracy.

Activation function↗

DOE OSTI2017

A Method to Measure the Unbiased Decorrelation Timescale of the AGN Variable Signal from Structure Functions

A simple, model-independent method to quantify the stochastic variability of active galactic nuclei (AGNs) is the structure function (SF) analysis. If the SF for the timescales shorter than the decorrelation timescale τ is a single power law and for the longer ones becomes flat (i.e., white noise), then the auto-correlation function (ACF) of the signal can have the form of the power exponential (PE). We show that the signal decorrelation timescale can be measured directly from the SF as the timescale matching the amplitude 0.795 of the flat SF part (at long timescales), and only then is the measurement independent of the ACF PE power. Typically, the timescale has been measured at an arbitrarily fixed SF amplitude, but as we prove, this approach provides biased results, because the AGN SF/power spectral density slopes, and thus the ACF shape, are not constant and depend on either the AGN luminosity and/or the black hole mass. In particular, we show that using such a method for the simulated SFs that includes a combination of empirically known dependencies between the AGN luminosity L and both the SF amplitude and the PE power, and having no intrinsic τ–L dependence, produces a fake τ∝L{sup κ} relation with 0.3≲κ≲0.6, which otherwise is expected from theoretical works (κ≡0.5). Our method provides an alternative means for analyzing AGN variability to the standard SF fitting. The caveats, for both methods, are that the light curves must be sufficiently long (with a several year rest frame) and the ensemble SF assumes AGNs to have the same underlying variability process.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Exponential Increase in Relative Biological Effectiveness Along Distal Edge of a Proton Bragg Peak as Measured by Deoxyribonucleic Acid Double-Strand Breaks

Purpose: To quantify the relative biological effectiveness (RBE) of the distal edge of the proton Bragg peak, using an in vitro assay of DNA double-strand breaks (DSBs). Methods and Materials: U2OS cells were irradiated within the plateau of a spread-out Bragg peak and at each millimeter position along the distal edge using a custom slide holder, allowing for simultaneous measurement of physical dose. A reference radiation signal was generated using photons. The DNA DSBs at 3 hours (to assess for early damage) and at 24 hours (to assess for residual damage and repair) after irradiation were measured using the γH2AX assay and quantified via flow cytometry. Results were confirmed with clonogenic survival assays. A detailed map of the RBE as a function of depth along the Bragg peak was generated using γH2AX measurements as a biological endpoint. Results: At 3 hours after irradiation, DNA DSBs were higher with protons at every point along the distal edge compared with samples irradiated with photons to similar doses. This effect was even more pronounced after 24 hours, indicating that the impact of DNA repair is less after proton irradiation relative to photons. The RBE demonstrated an exponential increase as a function of depth and was measured to be as high as 4.0 after 3 hours and as high as 6.0 after 24 hours. When the RBE-corrected dose was plotted as a function of depth, the peak effective dose was extended 2-3 mm beyond what would be expected with physical measurement. Conclusions: We generated a highly comprehensive map of the RBE of the distal edge of the Bragg peak, using a direct assay of DNA DSBs in vitro. Our data show that the RBE of the distal edge increases with depth and is significantly higher than previously reported estimates.

62 RADIOLOGY AND NUCLEAR MEDICINE↗