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At least 217 records · Page 12

Dataset for manuscript "Rotational Memory Function of SPC/E water"

Memory effect are essential for dynamics of condensed materials and are responsible for non-exponential relaxation of correlation functions of dynamic variables through the memory function entering the memory equation. Memory functions of dipole rotations for polar liquids have never been calculated. We present here calculations of memory functions and single-dipole rotations and of the overall system dipole moment for SPC/E water measured by dielectric spectroscopy. The memory functions for single-particle and collective dynamics turn out to be nearly identical. This result validates theories of dielectric spectroscopy in terms of single-particle time correlation function and the connection between the collective and single-particle relaxation times in terms of the Kirkwood factor. The dataset includes single particle and system dipole moments, including their time-dependence.

74 ATOMIC AND MOLECULAR PHYSICS↗

Rotational memory function of SPC/E water

Memory effects are essential for the dynamics of condensed materials and are responsible for non-exponential relaxation of correlation functions of dynamic variables through the memory function. Memory functions of dipole rotations for water have never been calculated directly from molecular dynamics simulations. We present here calculations of memory functions for single-dipole rotations and for the overall dipole moment of the sample for SPC/E water. The normalized memory functions for single-particle and collective dipole dynamics turn out to be nearly identical. This result validates theories of dielectric spectroscopy in terms of single-particle time correlation functions and the connection between the collective and single-particle relaxation times through the Kirkwood factor. The dielectric function in this formalism contains no new dynamic information that does not exist in the single-dipole correlation function. A short memory time, ≲1 fs, justifies the use of the mathematics of rotational diffusion to describe the dynamics of a single molecular dipole moment in bulk water. Here, an analytical equation for the rotational memory time is derived.

Asthagiri, Dilipkumar N. [Oak Ridge National Labor↗

A survey of solar protons and alpha differential spectra between 1 and greater than 400 MeV/nucleon

Attempts to systematically measure and fit a large sample of flare spectra from IMP 7 and 8 satellite data to determine the spectral forms that characterize the data and the range of spectral slopes are reported. Proton spectra are constructed covering the range 0.9 to over 400 MeV, and alpha fluxes from 1.4-80 MeV/nucleon. The event spectra are composed of fluxes measured at different times at each energy, and fitting procedures were employed such as a power law in kinetic energy, an exponential in rigidity, an exponential in energy, and a Bessel function of momentum/nucleon. Best fits were obtained with the exponential in rigidity and the Bessel function, with the Bessel function having a better numerical accuracy for all 21 proton spectra considered.

Mcguire, R. E.↗

Dose-response relationship between sleep duration and human psychomotor vigilance and subjective alertness

Although it has been well documented that sleep is required for human performance and alertness to recover from low levels after prolonged periods of wakefulness, it remains unclear whether they increase in a linear or asymptotic manner during sleep. It has been postulated that there is a relation between the rate of improvement in neurobehavioral functioning and rate of decline of slow-wave sleep and/or slow-wave activity (SWS/SWA) during sleep, but this has not been verified. Thus, a cross-study comparison was conducted in which dose-response curves (DRCs) were constructed for Stanford Sleepiness Scale (SSS) and Psychomotor Vigilance Task (PVT) tests taken at 1000 hours by subjects who had been allowed to sleep 0 hours, 2 hours, 5 hours or 8 hours the previous night. We found that the DRCs to each PVT metric improved in a saturating exponential manner, with recovery rates that were similar [time constant (T) approximately 2.14 hours] for all the metrics. This recovery rate was slightly faster than, though not statistically significantly different from, the reported rate of SWS/SWA decline (T approximately 2.7 hours). The DRC to the SSS improved much more slowly than psychomotor vigilance, so that it could be fit equally well by a linear function (slope = -0.26) or a saturating exponential function (T = 9.09 hours). We conclude that although SWS/SWA, subjective alertness, and a wide variety of psychomotor vigilance metrics may all change asymptotically during sleep, it remains to be determined whether the underlying physiologic processes governing their expression are different.

Non-NASA Center↗

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗

Long-time creep behavior of the niobium alloy C-103

The creep behavior of C-103 was studied as a function of stress, temperature, and grain size for test times to 19000 hr. Over the temperature range 827 to 1204 C and the stress range 6.89 to 138 MPa, only tertiary (accelerating) creep was observed. The creep strain epsilon can be related to time t by an exponential relation epsilon = epsilon(0) + K e raised to power (st) - 1), where epsilon (0) is initial creep strain, K is the tertiary creep strain parameter, and s is the tertiary creep rate parameter. The observed stress exponent 2.87 is similar to the three power law generally observed for secondary (linear) creep of Class I solid solutions. The apparent activation energy 374 kj/g mol is close to that observed for self diffusion of pure niobium. The initial tertiary creep rate was slightly faster for fine grained than for coarse-grained material. The strain parameter K can be expressed as a combination of power functions of stress and grain size and an exponential function of temperature. Strain time curves generated by using calculated values for K and s showed reasonable agreement with observed curves to strains of at least 4 percent. The time to 1 percent strain was related to stress, temperature, and grain size in a similar manner as the initial tertiary creep rate.

Titran, R. H.↗

On the Gibbs phenomenon 3: Recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function

The investigation of overcoming Gibbs phenomenon was continued, i.e., obtaining exponential accuracy at all points including at the discontinuities themselves, from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. It was shown that if we are given the first N expansion coefficients of an L(sub 2) function f(x) in terms of either the trigonometrical polynomials or the Chebyshev or Legendre polynomials, an exponentially convergent approximation to the point values of f(x) in any sub-interval in which it is analytic can be constructed.

Gottlieb, David↗

Resolving Wave-Particle Duality Could Accelerate the Mass Production of Quantum Computers

Quantum computers, hypothesized in 1980s, use concepts of superposition and entanglement phenomena. Although theoretical propositions and associated search algorithms for accurate measurements are being generated, the development of practical quantum computers themselves are advancing very slowly requiring enormous time and investments. The underlying concepts of a quantum computer are not new to the optical domain. However, the crucial enabling concepts of Entanglement and Superposition Principle are remaining clouded under the unresolved postulates, Wave-Particle Duality (WPD), and Wave Packet Reduction (WPR), implicating incompleteness in the interpretations of the mathematical formalism behind Quantum Mechanics. The WPD debate started during late1600 between Newton and Huygens. Young’s resolution of WPD through his double-slit experiment in 1802 was effectively overturned by Einstein’s interpretation of photoelectric effect as due to “indivisible light quanta”. However, Einstein disowned his “light quanta” postulate shortly before his death in1955, even though it had earned him the Nobel Prize. We resolve WPD by synthesizing Newton’s and Maxwell’s concepts and assume atoms do emit quanta but propagate as time-finite exponential pulses. This assumption also resolves WPR for light-matter interaction with the assumption that Schrodinger’s ψ represents atom’s internal dipolar amplitude stimulations. This over-turns Born’s interpretation that ψ only represents the abstract mathematical probability amplitude, rather than the physical “internal amplitude stimulation” of the quantum entity. However, our concept of atomic pulse emission forces us to re-derive the expression for the N-slit grating-spectrometer response since the classical derivation uses CW light, which does not exist. This pulsespectrometric response function strengthens our postulate since the grating response to the exponential pulse appears to be the convolution of a Lorentzian spectrum with the classical CW response function of the grating. The Fourier Transform of an exponential function is Lorentzian and QM predicts spontaneous emission line width to be Lorentzian. Then, conceptually one can extend the grating-expression (with N=2) to get the double-slit pattern. This approach preserves the classical causality that each of the two slits, like the N-signals out of a grating, are physically real and jointly stimulate the quantum detector array at the far field to generate the “Local” cosine fringes. The detector array executes the square modulus operation on its imposed dipolar amplitude stimulation and absorbs the necessary energy to fill up their quantum cups. Hence the double-slit pattern must also be “Local”, just as the N-slit grating spectrum is generated locally at the exit spectral-plane of the spectrometer. This removes the need to believe that “single photons” mysteriously generate the double slit pattern. Quantum computers, hypothesized in 1980s, use concepts of superposition and entanglement phenomena. Although theoretical propositions and associated search algorithms for accurate measurements are being generated, the development of practical quantum computers themselves are advancing very slowly requiring enormous time and investments. The underlying concepts of a quantum computer are not new to the optical domain. However, the crucial enabling concepts of Entanglement and Superposition Principle are remaining clouded under the unresolved postulates, Wave-Particle Duality (WPD), and Wave Packet Reduction (WPR), implicating incompleteness in the interpretations of the mathematical formalism behind Quantum Mechanics. The WPD debate started during late1600 between Newton and Huygens. Young’s resolution of WPD through his double-slit experiment in 1802 was effectively overturned by Einstein’s interpretation of photoelectric effect as due to “indivisible light quanta”. However, Einstein disowned his “light quanta” postulate shortly before his death in1955, even though it had earned him the Nobel Prize. We resolve WPD by synthesizing Newton’s and Maxwell’s concepts and assume atoms do emit quanta but propagate as time-finite exponential pulses. This assumption also resolves WPR for light-matter interaction with the assumption that Schrodinger’s ψ represents atom’s internal dipolar amplitude stimulations. This over-turns Born’s interpretation that ψ only represents the abstract mathematical probability amplitude, rather than the physical “internal amplitude stimulation” of the quantum entity. However, our concept of atomic pulse emission forces us to re-derive the expression for the N-slit grating-spectrometer response since the classical derivation uses CW light, which does not exist. This pulsespectrometric response function strengthens our postulate since the grating response to the exponential pulse appears to be the convolution of a Lorentzian spectrum with the classical CW response function of the grating. The Fourier Transform of an exponential function is Lorentzian and QM predicts spontaneous emission line width to be Lorentzian. Then, conceptually one can extend the grating-expression (with N=2) to get the double-slit pattern. This approach preserves the classical causality that each of the two slits, like the N-signals out of a grating, are physically real and jointly stimulate the quantum detector array at the far field to generate the “Local” cosine fringes. The detector array executes the square modulus operation on its imposed dipolar amplitude stimulation and absorbs the necessary energy to fill up their quantum cups. Hence the double-slit pattern must also be “Local”, just as the N-slit grating spectrum is generated locally at the exit spectral-plane of the spectrometer. This removes the need to believe that “single photons” mysteriously generate the double slit pattern.

Quantum Computer↗

Parameter Transient Behavior Analysis on Fault Tolerant Control System

In a fault tolerant control (FTC) system, a parameter varying FTC law is reconfigured based on fault parameters estimated by fault detection and isolation (FDI) modules. FDI modules require some time to detect fault occurrences in aero-vehicle dynamics. This paper illustrates analysis of a FTC system based on estimated fault parameter transient behavior which may include false fault detections during a short time interval. Using Lyapunov function analysis, the upper bound of an induced-L2 norm of the FTC system performance is calculated as a function of a fault detection time and the exponential decay rate of the Lyapunov function.

Belcastro, Christine↗

Solar variation 1979-1987 estimated from an empirical model for changes with time in the sensitivity of the solar backscatter ultraviolet instrument

A model is developed that describes changes in the sensitivity of the solar backscatter UV instrument deployed with Nimbus 7 to study variations with time in solar irradiance. The exponential decay of instrument exposure to the sun and that of time are combined, and the product is used to describe the sensitivity change. Measured UV irradiances are employed to develop the values of the exponential decays, and the degradation coefficients for time dependence are found to vary with time at shorter wavelengths. Instrument sensitivity is described in terms of a functional relationship based on exponential decay with time with time-varying time dependence and on exponential decay with exposure with constant exposure dependence. The relationship provides a technique for treating data from the solar backscatter UV instrument both at short- and long-term intervals, and solar irradiance is calculated based on the approach.

Schlesinger, Barry M.↗

The reflection coefficient in stimulated parametric backscattering

The step-function approximation of the anomalous reflection coefficient in laser-induced parametric backscattering currently used in the theory of nonlinear laser plasma interactions is improved using a simple exponential derived from elliptic functions. The validity of the single-reflection analysis is reaffirmed.

Yu, C.↗

Prediction of Turbulence-Generated Noise in Unheated Jets: JeNo Technical Manual (Version 1.0) - Part 1

The model-based approach, used by the JeNo code to predict jet noise spectral directivity, is described. A linearized form of Lilley's equation governs the non-causal Green s function of interest, with the non-linear terms on the right hand side identified as the source. A Reynolds-averaged Navier-Stokes (RANS) solution yields the required mean flow for the solution of the propagation Green s function in a locally parallel flow. The RANS solution also produces time- and length-scales needed to model the non-compact source, the turbulent velocity correlation tensor, with exponential temporal and spatial functions. It is shown that while an exact non-causal Green s function accurately predicts the observed shift in the location of the spectrum peak with angle as well as the angularity of sound at low to moderate Mach numbers, the polar directivity of radiated sound is not entirely captured by this Green s function at high subsonic and supersonic acoustic Mach numbers. Results presented for unheated jets in the Mach number range of 0.51 to 1.8 suggest that near the peak radiation angle of high-speed jets, a different source/Green s function convolution integral may be required in order to capture the peak observed directivity of jet noise. A sample Mach 0.90 heated jet is also discussed that highlights the requirements for a comprehensive jet noise prediction model.

Khavaran, Abbas↗

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simple robust control laws for robot manipulators. Part 1: Non-adaptive case

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.

Wen, J. T.↗

The role of global cloud climatologies in validating numerical models

The purpose of this work is to estimate sampling errors of area-time averaged rain rate due to temporal samplings by satellites. In particular, the sampling errors of the proposed low inclination orbit satellite of the Tropical Rainfall Measuring Mission (TRMM) (35 deg inclination and 350 km altitude), one of the sun synchronous polar orbiting satellites of NOAA series (98.89 deg inclination and 833 km altitude), and two simultaneous sun synchronous polar orbiting satellites--assumed to carry a perfect passive microwave sensor for direct rainfall measurements--will be estimated. This estimate is done by performing a study of the satellite orbits and the autocovariance function of the area-averaged rain rate time series. A model based on an exponential fit of the autocovariance function is used for actual calculations. Varying visiting intervals and total coverage of averaging area on each visit by the satellites are taken into account in the model. The data are generated by a General Circulation Model (GCM). The model has a diurnal cycle and parameterized convective processes. A special run of the GCM was made at NASA/GSFC in which the rainfall and precipitable water fields were retained globally for every hour of the run for the whole year.

HARSHVARDHAN↗

Modeling of Turbulence Generated Noise in Jets

A numerically calculated Green's function is used to predict jet noise spectrum and its far-field directivity. A linearized form of Lilley's equation governs the non-causal Green s function of interest, with the non-linear terms on the right hand side identified as the source. In this paper, contributions from the so-called self- and shear-noise source terms will be discussed. A Reynolds-averaged Navier-Stokes solution yields the required mean flow as well as time- and length scales of a noise-generating turbulent eddy. A non-compact source, with exponential temporal and spatial functions, is used to describe the turbulence velocity correlation tensors. It is shown that while an exact non-causal Green's function accurately predicts the observed shift in the location of the spectrum peak with angle as well as the angularity of sound at moderate Mach numbers, at high subsonic and supersonic acoustic Mach numbers the polar directivity of radiated sound is not entirely captured by this Green's function. Results presented for Mach 0.5 and 0.9 isothermal jets, as well as a Mach 0.8 hot jet conclude that near the peak radiation angle a different source/Green's function convolution integral may be required in order to capture the peak observed directivity of jet noise.

Khavaran, Abbas↗

Asymptotic freedom in solids - A theorem

A cusp theorem is proved that relates the zero-separation value and slope of two-particle position correlation functions in quantum many-body systems with Coulombic interactions. The theorem is independent of the particle type and symmetry of the wave function. Its proof uses only the integral form of the Schroedinger equation and the continuity and exponential decay of the wave function. It is used to derive a sum rule for the electron-gas structure factor and an exact statement about the screening of point charges. Applications to atomic-orbital-based calculations for H2 and metallic H are described.

Carlsson, A. E.↗