Engineering Papers⌕ Search

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.

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

At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Resonances in positron-hydrogen scattering in dense quantum plasmas

We have investigated the S-wave resonance states in positron-hydrogen system embedded in dense quantum plasmas using Hylleraas-type wave functions within the framework of the stabilization method. The effect of quantum plasmas has been incorporated using the exponential-cosine-screened Coulomb (modified Yukawa-type) potential. Resonance parameters (both position and width) below the Ps n = 2 threshold are reported as functions of plasma screening parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Probing the nonexponential decay regime in open quantum systems

The most important law of radioactivity is that of the exponential decay. In the realm of quantum mechanics, however, this decay law is neither rigorous nor fundamental. The deviations from the exponential decay have been observed experimentally at the early stage of a decay process, but there is little evidence for non-exponential behavior at long times. Yet such long-term non-exponentiality is expected theoretically to probe the non-resonant background components of the initial wave function which preserve the structural interference and the memory of how the state was created. In this paper, we propose new observables that can be used for experimental investigations of the post-exponential decay regime, including the decay of threshold resonances, particle correlations in three-body decays, and interference between near-lying resonances. While the specific examples presented in this work pertain to atomic nuclei, the properties of non-exponential decay are generic, i.e., they apply to other many-body open quantum systems, such as hadrons, atoms, molecules, and nanostructures.

6 ≤ A ≤ 19↗
DOE OSTI2018

Universality Classes of Interaction Structures for NK Fitness Landscapes

Kauffman’s NK-model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems. Genotypes are represented as sequences of L binary loci. The fitness assigned to a genotype is a sum of contributions, each of which is a random function defined on a subset of k≤L loci. These subsets or neighborhoods determine the genetic interactions of the model. Whereas earlier work on the NK model suggested that most of its properties are robust with regard to the choice of neighborhoods, recent work has revealed an important and sometimes counter-intuitive influence of the interaction structure on the properties of NK fitness landscapes. Here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible (that is, fitness-monotonic) mutational pathways. In particular, we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of L, and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large k. Moreover, we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in L for a large class of interaction structures that we characterize as locally bounded. Finally, we discuss the impact of the NK interaction structures on the dynamics of evolution using adaptive walk models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach

This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Uncovering the binding nature of thiocyanate in contact ion pairs with lithium ions

Ion pair formation is a fundamental molecular process that occurs in a wide variety of systems, including electrolytes, biological systems, and materials. In solution, the thiocyanate (SCN–) anion interacts with cations to form contact ion pairs (CIPs). Due to its ambidentate nature, thiocyanate can bind through either its sulfur or nitrogen atoms, depending on the solvent. This study focuses on the binding nature of thiocyanate with lithium ions as a function of the solvents using FTIR, 2D infrared spectroscopy (2DIR) spectroscopies, and theoretical calculations. The study reveals that the SCN– binding mode (S or N end) in CIPs can be identified through 2DIR spectroscopy but not by linear IR spectroscopy. Linear IR spectroscopy shows that the CN stretch frequencies are too close to one another to separate N- and S-bound CIPs. Moreover, the IR spectrum shows that the S–C stretch presents different frequencies for the salt in different solvents, but it is related to the anion speciation rather than to its binding mode. A similar trend is observed for the anion bend. 2DIR spectra show different dynamics for N-bound and S-bound thiocyanate. In particular, the frequency–frequency correlation function (FFCF) dynamics extracted from the 2DIR spectra have a single picosecond exponential decay for N-bound thiocyanate and a biexponential decay for S-bound thiocyanate, consistent with the binding mode of the anion. Lastly, it is also observed that the binding mode also affects the line shape parameters, probably due to the different molecular mechanisms of the FFCF for N- and S-bound CIPs.

25 ENERGY STORAGE↗
DOE OSTI2014

Dynamic fracture of functionally graded magnetoelectroelastic composite materials

The stress, magnetic and electric field analysis of multifunctional composites, weakened by impermeable cracks, is of fundamental importance for their structural integrity and reliable service performance. The aim is to study dynamic behavior of a plane of functionally graded magnetoelectroelastic composite with more than one crack. The coupled material properties vary exponentially in an arbitrary direction. The plane is subjected to anti-plane mechanical and in-plane electric and magnetic load. The boundary value problem described by the partial differential equations with variable coefficients is reduced to a non-hypersingular traction boundary integral equation based on the appropriate functional transform and frequency-dependent fundamental solution derived in a closed form by Radon transform. Software code based on the boundary integral equation method (BIEM) is developed, validated and inserted in numerical simulations. The obtained results show the sensitivity of the dynamic stress, magnetic and electric field concentration in the cracked plane to the type and characteristics of the dynamic load, to the location and cracks disposition, to the wave-crack-crack interactions and to the magnitude and direction of the material gradient.

36 MATERIALS SCIENCE↗
DOE OSTI2011

A COMPLETE SAMPLE OF ULTRALUMINOUS X-RAY SOURCE HOST GALAXIES

One hundred seven ultraluminous X-ray sources (ULXs) with 0.3-10.0 keV luminosities in excess of 10{sup 39} erg s{sup -1} are identified in a complete sample of 127 nearby galaxies. The sample includes all galaxies within 14.5 Mpc above the completeness limits of both the Uppsala Galaxy Catalogue and the Infrared Astronomical Satellite survey. The galaxy sample spans all Hubble types, a four-decade range in mass, 7.5 < log (M/M{sub sun}) < 11.4, and in star formation rate, 0.0002 < SFR(M{sub sun} yr{sup -1}) {<=} 3.6. ULXs are detected in this sample at rates of one per 3.2 Multiplication-Sign 10{sup 10} M{sub sun}, one per {approx}0.5 M{sub sun} yr{sup -1} star formation rate, and one per 57 Mpc{sup 3} corresponding to a luminosity density of {approx}2 Multiplication-Sign 10{sup 37} erg s{sup -1} Mpc{sup -3}. At these rates we estimate as many as 19 additional ULXs remain undetected in fainter dwarf galaxies within the survey volume. An estimated 14 objects, or 13%, of the 107 ULX candidates are expected to be background sources. The differential ULX luminosity function shows a power-law slope {alpha} {approx} -0.8 to -2.0 with an exponential cutoff at {approx}20 Multiplication-Sign 10{sup 39} erg s{sup -1} with precise values depending on the model and on whether the ULX luminosities are estimated from their observed numbers of counts or, for a subset of candidates, from their spectral shapes. Extrapolating the observed luminosity function predicts at most one very luminous ULX, L{sub X} {approx} 10{sup 41} erg s{sup -1}, within a distance as small as 100 Mpc. The luminosity distribution of ULXs within the local universe cannot account for the recent claims of luminosities in excess of 2 Multiplication-Sign 10{sup 41} erg s{sup -1}, requiring a new population class to explain these extreme objects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Grand canonical electronic density-functional theory: Algorithms and applications to electrochemistry

First-principles calculations combining density-functional theory and continuum solvation models enable realistic theoretical modeling and design of electrochemical systems. When a reaction proceeds in such systems, the number of electrons in the portion of the system treated quantum mechanically changes continuously, with a balancing charge appearing in the continuum electrolyte. A grand-canonical ensemble of electrons at a chemical potential set by the electrode potential is therefore the ideal description of such systems that directly mimics the experimental condition. We present two distinct algorithms: a self-consistent field method and a direct variational free energy minimization method using auxiliary Hamiltonians (GC-AuxH), to solve the Kohn-Sham equations of electronic density-functional theory directly in the grand canonical ensemble at fixed potential. Both methods substantially improve performance compared to a sequence of conventional fixed-number calculations targeting the desired potential, with the GC-AuxH method additionally exhibiting reliable and smooth exponential convergence of the grand free energy. Lastly, we apply grand-canonical density-functional theory to the under-potential deposition of copper on platinum from chloride-containing electrolytes and show that chloride desorption, not partial copper monolayer formation, is responsible for the second voltammetric peak.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Measurement of the central exclusive production of charged particle pairs in proton-proton collisions at $\sqrt{s}$ = 200 GeV with the STAR detector at RHIC

We report on the measurement of the Central Exclusive Production of charged particle pairs h+h- (h = π, K, p) with the STAR detector at RHIC in proton-proton collisions at $\sqrt{s}$ = 200 GeV. The charged particle pairs produced in the reaction pp → p' + h + h - + p' are reconstructed from the tracks in the central detector and identified using the specific energy loss and the time of flight method, while the forward-scattered protons are measured in the Roman Pot system. Exclusivity of the event is guaranteed by requiring the transverse momentum balance of all four final-state particles. Differential cross sections are measured as functions of observables related to the central hadronic final state and to the forward-scattered protons. They are measured in a fiducial region corresponding to the acceptance of the STAR detector and determined by the central particles’ transverse momenta and pseudorapidities as well as by the forward-scattered protons’ momenta. This fiducial region roughly corresponds to the square of the four-momentum transfers at the proton vertices in the range 0.04 GeV 2 < -t 1 , -t 2 < 0.2 GeV 2 , invariant masses of the charged particle pairs up to a few GeV and pseudorapidities of the centrally-produced hadrons in the range |η| < 0.7. The measured cross sections are compared to phenomenological predictions based on the Double Pomeron Exchange (DPE) model. Structures observed in the mass spectra of π + π - and K + K - pairs are consistent with the DPE model, while angular distributions of pions suggest a dominant spin-0 contribution to π + π - production. For π + π - production, the fiducial cross section is extrapolated to the Lorentz-invariant region, which allows decomposition of the invariant mass spectrum into continuum and resonant contributions. The extrapolated cross section is well described by the continuum production and at least three resonances, the f 0 (980), f 2 (1270) and f 0 (1500), with a possible small contribution from the f 0 (1370). Fits to the extrapolated differential cross section as a function of t 1 and t 2 enable extraction of the exponential slope parameters in several bins of the invariant mass of π + π - pairs. These parameters are sensitive to the size of the interaction region.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Event-shape and multiplicity dependence of freeze-out radii in pp collisions at $\sqrt{s}$= 7 TeV

Two-particle correlations in high-energy collision experiments enable the extraction of particle source radii by using the Bose-Einstein enhancement of pion production at low relative momentum q ∝ 1/R. It was previously observed that in pp collisions at $\sqrt{s}$ = 7TeV the average pair transverse momentum k T range of such analyses is limited due to large background correlations which were attributed to mini-jet phenomena. To investigate this further, an event-shape dependent analysis of Bose-Einstein correlations for pion pairs is performed in this work. By categorizing the events by their transverse sphericity S T into spherical (S T > 0:7) and jet-like (S T < 0:3) events a method was developed that allows for the determination of source radii for much larger values of k T for the first time. Spherical events demonstrate little or no background correlations while jet-like events are dominated by them. This observation agrees with the hypothesis of a mini-jet origin of the non-femtoscopic background correlations and gives new insight into the physics interpretation of the k T dependence of the radii. The emission source size in spherical events shows a substantially diminished k T dependence, while jet-like events show indications of a negative trend with respect to k T in the highest multiplicity events. Regarding the emission source shape, the correlation functions for both event sphericity classes show good agreement with an exponential shape, rather than a Gaussian one.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Random Knotting in Fractal Ring Polymers

Many ring polymer systems of physical and biological interest exhibit both pronounced topological effects and nontrivial self-similarity, but the relationship between these two phenomena has not yet been clearly established. Here, we use theory and simulation to formulate such a connection by studying a fundamental topological property—the random knotting probability—for ring polymers with varying fractal dimension, d f . Using straightforward scaling arguments, we generalize a classic mathematical result, showing that the probability of a trivial knot decays exponentially with chain size, N, for all fractal dimensions: P 0 (N) ∝ exp(–N/N 0 ). However, no such simple considerations can account for the dependence of the knotting length, N 0 , on d f , necessitating a more involved analytical calculation. This analysis reveals a complicated double-exponential dependence, which is well supported by numerical data. By contrast, functional forms typical of simple scaling theories fail to adequately describe the observations. These findings are equally valid for two-dimensional ring polymer systems, where “knotting” is defined as the intersection of any two segments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Continuum electromagnetic gyrokinetic simulations of turbulence in the tokamak scrape-off layer and laboratory devices

Here, we present algorithms and results from Gkeyll, a full-f continuum, electromagnetic gyrokinetic code, designed to study turbulence in the edge region of fusion devices. The edge is computationally very challenging, requiring robust algorithms that can handle large-amplitude fluctuations and stable interactions with plasma sheaths. We present an energy-conserving high-order discontinuous Galerkin scheme that solves gyrokinetic equations in Hamiltonian form. Efficiency is improved by a careful choice of basis functions and automatically generated computation kernels. Previous verification tests were performed in the straight-field-line large plasma device [Shi et al., J. Plasma Phys. 83, 905830304 (2017)] and the Texas Helimak, a simple magnetized torus [Bernard et al., Phys. Plasmas 26, 042301 (2019)], including the effect of end-plate biasing on turbulence. Results for the scrape-off layer for NSTX parameters with a model helical magnetic geometry with bad curvature have been obtained [Shi et al., Phys. Plasmas 26, 012307 (2019)]. In this paper, we present algorithms for the two formulations of electromagnetic gyrokinetics: the Hamiltonian and the symplectic. We describe each formulation and show results of benchmark tests. Although our scheme works for the Hamiltonian formulation, the presence of spurious numerical modes for high-β and large $k^2_⊥ρ^2_s$ regimes shows that the symplectic formulation is more robust. We then review our recent algorithm for the symplectic formulation [Mandell et al., J. Plasma Phys. 86, 905860109 (2020)], along with example application of this new capability. Maintaining positivity of the distribution function can be challenging, and we describe a new and novel exponential recovery based algorithm to address this.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Radiative dynamics and delayed emission in pure and doped InP/ZnSe/ZnS quantum dots

We have used time-correlated single photon counting to elucidate the radiative dynamics of InP/ZnSe/ZnS core/shell/shell quantum dots (QDs) that differ in the amount and distribution of excess indium. Stoichiometric QDs having an In:P atom ratio very near unity exhibit simple luminescence kinetics. The photoluminescence (PL) rises with the 40 ps instrument response function and exhibits a decay that is close to a single exponential with a time constant that decreases from 32 to 28 ns with increasing shell thickness. QDs having excess indium (In:P ratio of 1.15–1.63) show a significant component of a slower rise time assigned to transient population of indium-based hole traps in the ZnSe shell. They also have a slower PL decay, attributed to an equilibrium between these traps, which are optically dark, and the emissive valence-band state. This results in a radiative lifetime that increases from 32 to 48 ns with increasing shell thickness. Different treatments of the InP cores prior to shell deposition result in different core/shell interfaces as indicated by resonance Raman spectroscopy, as well as differences in the amplitude and timescale of the slow PL rise and the PL decay time. These are interpreted in terms of different radial distributions of the indium-based hole traps, which can be related to differences in the interfacial lattice strain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Theory and modeling of molecular modes in the NMR relaxation of fluids

Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. Here, we recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker–Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole–dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé–Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

SHORT-TERM VARIABILITY OF X-RAYS FROM ACCRETING NEUTRON STAR VELA X-1. I. SUZAKU OBSERVATIONS

We have analyzed the time variability of the wide-band X-ray spectrum of Vela X-1, the brightest wind-fed accreting neutron star, on a short timescale of 2 ks by using Suzaku observations with an exposure of 100 ks. During the observation, the object showed strong variability, including several flares and so-called 'low states', in which the X-ray luminosity decreases by an order of magnitude. Although the spectral hardness increases with the X-ray luminosity, the majority of the recorded flares do not show any significant changes in circumstellar absorption. However, a sign of heavy absorption was registered immediately before one short flare that showed a significant spectral hardening. In the low states, the flux level is modulated with the pulsar spin period, indicating that even at this state the accretion flow reaches the close proximity of the neutron star. Phenomenologically, the broadband X-ray spectra, which are integrated over the entire spin phase, are well represented by the 'NPEX' function (a combination of negative and positive power laws with an exponential cutoff by a common folding energy) with a cyclotron resonance scattering feature at 50 keV. Fitting of the data allowed us to infer a correlation between the photon index and X-ray luminosity. Finally, the circumstellar absorption shows a gradual increase in the orbital phase interval 0.25-0.3, which can be interpreted as an impact of a bow shock imposed by the motion of the compact object in the supersonic stellar wind.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

PLANET OCCURRENCE WITHIN 0.25 AU OF SOLAR-TYPE STARS FROM KEPLER

We report the distribution of planets as a function of planet radius, orbital period, and stellar effective temperature for orbital periods less than 50 days around solar-type (GK) stars. These results are based on the 1235 planets (formally 'planet candidates') from the Kepler mission that include a nearly complete set of detected planets as small as 2 R{sub Circled-Plus }. For each of the 156,000 target stars, we assess the detectability of planets as a function of planet radius, R{sub p}, and orbital period, P, using a measure of the detection efficiency for each star. We also correct for the geometric probability of transit, R{sub *}/a. We consider first Kepler target stars within the 'solar subset' having T{sub eff} = 4100-6100 K, log g 4.0-4.9, and Kepler magnitude Kp < 15 mag, i.e., bright, main-sequence GK stars. We include only those stars having photometric noise low enough to permit detection of planets down to 2 R{sub Circled-Plus }. We count planets in small domains of R{sub p} and P and divide by the included target stars to calculate planet occurrence in each domain. The resulting occurrence of planets varies by more than three orders of magnitude in the radius-orbital period plane and increases substantially down to the smallest radius (2 R{sub Circled-Plus }) and out to the longest orbital period (50 days, {approx}0.25 AU) in our study. For P < 50 days, the distribution of planet radii is given by a power law, df/dlog R = k{sub R}R{sup {alpha}} with k{sub R} = 2.9{sup +0.5}{sub -0.4}, {alpha} = -1.92 {+-} 0.11, and R {identical_to} R{sub p}/R{sub Circled-Plus }. This rapid increase in planet occurrence with decreasing planet size agrees with the prediction of core-accretion formation but disagrees with population synthesis models that predict a desert at super-Earth and Neptune sizes for close-in orbits. Planets with orbital periods shorter than 2 days are extremely rare; for R{sub p} > 2 R{sub Circled-Plus} we measure an occurrence of less than 0.001 planets per star. For all planets with orbital periods less than 50 days, we measure occurrence of 0.130 {+-} 0.008, 0.023 {+-} 0.003, and 0.013 {+-} 0.002 planets per star for planets with radii 2-4, 4-8, and 8-32 R{sub Circled-Plus }, in agreement with Doppler surveys. We fit occurrence as a function of P to a power-law model with an exponential cutoff below a critical period P{sub 0}. For smaller planets, P{sub 0} has larger values, suggesting that the 'parking distance' for migrating planets moves outward with decreasing planet size. We also measured planet occurrence over a broader stellar T{sub eff} range of 3600-7100 K, spanning M0 to F2 dwarfs. Over this range, the occurrence of 2-4 R{sub Circled-Plus} planets in the Kepler field increases with decreasing T{sub eff}, with these small planets being seven times more abundant around cool stars (3600-4100 K) than the hottest stars in our sample (6600-7100 K).

79 ASTRONOMY AND ASTROPHYSICS↗