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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An analytic and complete equation of state for condensed phase materials

Analytic equations of state (EOS) are intended to reproduce theoretical and experimental data in a single phase portion of the thermodynamic space. We devise a complete and thermodynamically consistent model with four distinct features: (1) a reference isotherm that remains thermodynamically stable, (2) a flexible specific heat model based on a fourth-order rational polynomial, (3) a Grüneisen parameter that depends on specific volume and temperature, and (4) pressure and internal energy functions that can be inverted analytically in temperature. The model aims to improve the accuracy of existing equations of state while remaining computationally efficient. To demonstrate its features, we include calibrations for single-crystal pentaerythritol tetranitrate (PETN), liquid nitromethane (NM), and hexagonal close-packed beryllium (Be) metal. The parameter optimization uses the specific heat capacity, Grüneisen parameter, and static compression curves obtained from density functional theory for the crystalline solids and molecular dynamics simulations for liquid NM. We also present a velocity autocorrelation function that yields accurate phonon densities of states for the EOS calibration from the molecular dynamics trajectories. Each of the three calibrations is constrained to enforce the ambient state from experimental measurements and validated against experimental Hugoniot data from multiple sources. We also include one-dimensional hydrodynamic simulations of the isentropic compression experiments for beryllium conducted at the Z facility.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Analytical model of diffuse reflectance spectrum of skin tissue

We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions. (biophotonics)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Wavefunction stability analysis without analytical electronic Hessians: application to orbital-optimised second-order Møller–Plesset theory and VV10-containing density functionals

Wavefunction stability analysis is commonly applied to converged self-consistent field (SCF) solutions to verify whether the electronic energy is a local minimum with respect to second-order variations in the orbitals. By iterative diagonalisation, the procedure calculates the lowest eigenvalue of the stability matrix or electronic Hessian. However, analytical expressions for the electronic Hessian are unavailable for most advanced post-Hartree-Fock (HF) wave function methods and even some Kohn-Sham (KS) density functionals. To address such cases, here we formulate the Hessian-vector product within the iterative diagonalisation procedure as a finite difference of the electronic gradient with respect to orbital perturbations in the direction of the vector. As a model application, following the lowest eigenvalue of the orbital-optimised second-order Møller-Plesset perturbation theory (OOMP2) Hessian during H 2 dissociation reveals the surprising stability of the spin-restricted solution at all separations, with a second independent unrestricted solution. We show that a single stable solution can be recovered by using the regularised OOMP2 method (δ-OOMP2), which contains a level shift. Internal and external stability analyses are also performed for SCF solutions of a recently developed range-separated hybrid density functional, ωB97X-V, for which the analytical Hessian is not yet available due to the complexity of its long-range non-local VV10 correlation functional.

Brueckner orbitals↗
DOE OSTI2019

Data analytics approach for melt-pool geometries in metal additive manufacturing

Modern data analytics was employed to understand and predict physics-based melt-pool formation by fabricating Ni alloy single tracks using powder bed fusion. An extensive database of melt-pool geometries was created, including processing parameters and material characteristics as input features. Correlation analysis provided insight for relationships between process parameters and melt-pools, and enabled the development of meaningful machine learning models via the use of highly correlated features. We successfully demonstrated that data analytics facilitates understanding of the inherent physics and reliable prediction of melt-pool geometries. This approach can serve as a basis for the melt-pool control and process optimization.

36 MATERIALS SCIENCE↗
DOE OSTI2015

PROBING THE ROLE OF DYNAMICAL FRICTION IN SHAPING THE BSS RADIAL DISTRIBUTION. I. SEMI-ANALYTICAL MODELS AND PRELIMINARY N-BODY SIMULATIONS

We present semi-analytical models and simplified N-body simulations with 10{sup 4} particles aimed at probing the role of dynamical friction (DF) in determining the radial distribution of blue straggler stars (BSSs) in globular clusters. The semi-analytical models show that DF (which is the only evolutionary mechanism at work) is responsible for the formation of a bimodal distribution with a dip progressively moving toward the external regions of the cluster. However, these models fail to reproduce the formation of the long-lived central peak observed in all dynamically evolved clusters. The results of N-body simulations confirm the formation of a sharp central peak, which remains as a stable feature over time regardless of the initial concentration of the system. In spite of noisy behavior, a bimodal distribution forms in many cases, with the size of the dip increasing as a function of time. In the most advanced stages, the distribution becomes monotonic. These results are in agreement with the observations. Also, the shape of the peak and the location of the minimum (which, in most of cases, is within 10 core radii) turn out to be consistent with observational results. For a more detailed and close comparison with observations, including a proper calibration of the timescales of the dynamical processes driving the evolution of the BSS spatial distribution, more realistic simulations will be necessary.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

ANALYTIC FORMS OF THE PERPENDICULAR DIFFUSION COEFFICIENT IN NRMHD TURBULENCE

In the past different analytic limits for the perpendicular diffusion coefficient of energetic particles interacting with magnetic turbulence were discussed. These different limits or cases correspond to different transport modes describing how the particles are diffusing across the large-scale magnetic field. In the current paper we describe a new transport regime by considering the model of noisy reduced magnetohydrodynamic turbulence. We derive different analytic forms of the perpendicular diffusion coefficient, and while we do this, we focus on the aforementioned new transport mode. We show that for this turbulence model a small perpendicular diffusion coefficient can be obtained so that the latter diffusion coefficient is more than hundred times smaller than the parallel diffusion coefficient. This result is relevant to explain observations in the solar system where such small perpendicular diffusion coefficients have been reported.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

CALIBRATION OF SEMI-ANALYTIC MODELS OF GALAXY FORMATION USING PARTICLE SWARM OPTIMIZATION

We present a fast and accurate method to select an optimal set of parameters in semi-analytic models of galaxy formation and evolution (SAMs). Our approach compares the results of a model against a set of observables applying a stochastic technique called Particle Swarm Optimization (PSO), a self-learning algorithm for localizing regions of maximum likelihood in multidimensional spaces that outperforms traditional sampling methods in terms of computational cost. We apply the PSO technique to the SAG semi-analytic model combined with merger trees extracted from a standard Lambda Cold Dark Matter N-body simulation. The calibration is performed using a combination of observed galaxy properties as constraints, including the local stellar mass function and the black hole to bulge mass relation. We test the ability of the PSO algorithm to find the best set of free parameters of the model by comparing the results with those obtained using a MCMC exploration. Both methods find the same maximum likelihood region, however, the PSO method requires one order of magnitude fewer evaluations. This new approach allows a fast estimation of the best-fitting parameter set in multidimensional spaces, providing a practical tool to test the consequences of including other astrophysical processes in SAMs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

To cool is to accrete: Analytic scalings for nebular accretion of planetary atmospheres

Planets acquire atmospheres from their parent circumstellar disks. We derive a general analytic expression for how the atmospheric mass grows with time t as a function of the underlying core mass M{sub core} and nebular conditions, including the gas metallicity Z. Planets accrete as much gas as can cool: an atmosphere's doubling time is given by its Kelvin–Helmholtz time. Dusty atmospheres behave differently from atmospheres made dust-free by grain growth and sedimentation. The gas-to-core mass ratio (GCR) of a dusty atmosphere scales as GCR ∝ t{sup 0.4}M{sub core}{sup 1.7}Z{sup −0.4}μ{sub rcb}{sup 3.4}, where μ{sub rcb}∝1/(1−Z) (for Z not too close to 1) is the mean molecular weight at the innermost radiative–convective boundary. This scaling applies across all orbital distances and nebular conditions for dusty atmospheres; their radiative–convective boundaries, which regulate cooling, are not set by the external environment, but rather by the internal microphysics of dust sublimation, H{sub 2} dissociation, and the formation of H{sup −}. By contrast, dust-free atmospheres have their radiative boundaries at temperatures T{sub rcb} close to nebular temperatures T{sub out}, and grow faster at larger orbital distances where cooler temperatures, and by extension lower opacities, prevail. At 0.1 AU in a gas-poor nebula, GCR ∝ t{sup 0.4}T{sub rcb}{sup −1.9}M{sub core}{sup 1.6}Z{sup −0.4}μ{sub rcb}{sup 3.3}, while beyond 1 AU in a gas-rich nebula, GCR ∝ t{sup 0.4}T{sub rcb}{sup −1.5}M{sub core}{sup 1}Z{sup −0.4}μ{sub rcb}{sup 2.2}. We confirm our analytic scalings against detailed numerical models for objects ranging in mass from Mars (0.1M{sub ⊕}) to the most extreme super-Earths (10–20M{sub ⊕}), and explain why heating from planetesimal accretion cannot prevent the latter from undergoing runaway gas accretion.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Analytical collisionless damping rate of geodesic acoustic mode

Collisionless damping of geodesic acoustic mode (GAM) is analytically investigated by considering the finite-orbit-width (FOW) resonance effect to the 3rd order in the gyro-kinetic equations. Here, a concise and transparent expression for the damping rate is presented for the first time. Good agreement is found between the analytical damping rate and the previous TEMPEST simulation result (Xu 2008 et al Phys. Rev. Lett. 100 215001) for systematic q scans. Our result also shows that it is of sufficient accuracy and has to take into account the FOW effect to the 3rd order.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Convenient analytical solution for vibrational distribution function of molecules colliding with a wall

We study formation of the Vibrational Distribution Function (VDF) in a molecular gas at low pressure, when vibrational levels are excited by electron impact and deactivated in collisions with walls and show that this problem has a convenient analytical solution that can be used to obtain VDF and its dependence on external parameters. The VDF is determined by excitation of vibrational levels by an external source and deactivation in collisions with the wall. Deactivation in wall collisions is little known process. However, we found that the VDF is weakly dependent on the functional form of the actual form of probability ${\gamma }_{\upsilon ^{\prime} \to \upsilon }$ for a vibrational number $\upsilon ^{\prime} $ to transfer into a lower level $\upsilon $ at the wall. Because for a given excitation source of vibrational states, the problem is linear the solution for VDF involves solving linear matrix equation. The matrix equation can be easily solved if we approximate probability, in the form: ${\gamma }_{\upsilon ^{\prime} \to \upsilon }=(1/\upsilon ^{\prime} )\theta (\upsilon ^{\prime} -\upsilon ).$ In this case, the steady-state solution for VDF($\upsilon $) simply involves a sum of source rates for levels above $\upsilon ,$ with a factor of $1/(\upsilon +1).$ As an example of application, we study the vibrational kinetics in a hydrogen gas and verify the analytical solution by comparing with a full model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

An analytically tractable marked power spectrum

The increasing precision of cosmology data in the modern era is calling for methods to allow the extraction of non-Gaussian information using tools beyond two-point statistics. The marked power spectrum has the potential to extract beyond two-point information in a computationally efficient way while using much of the infrastructure already available for the power spectrum. In this work we explore the marked power spectrum from an analytical perspective. In particular, we explore a low-order polynomial for the mark that allows us to better control the theoretical uncertainties and we show that with minimal new degrees of freedom the analytical results match measurements from N-body simulations for both the matter field and biased tracers in redshift space. Finally, we show that even within the limited forms of mark that we consider, there are degeneracies that can be broken by inclusion of the marked auto-spectrum or the cross-spectrum with the unmarked field. I n conclusion, we discuss future theoretical developments that would enable us to apply this approach to survey data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Divertorlets concept for low-recycling fusion reactor divertor: experimental, analytical and numerical verification

The 'divertorlets' concept is a potential non-evaporative liquid metal solution for heat removal at low recycling regime. A toroidal divertorlets prototype was built and tested in LMX-U at Princeton Plasma Physics Laboratory to evaluate the performance of this configuration. Here, details of the design, experimental results, comparison with analytical theory and MHD numerical simulations of toroidal divertorlets are covered. Experiments, analytical model and simulations showed agreement and allowed the projection of operation properties at higher magnetic flux densities (reactor-like operation), proving the concept to be a compelling solution for divertor applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Analytic Chromaticity Formulas for the Muon g -2 experiment at fermilab

The Muon g-2 Experiment (E989) at Fermilab measured the muon anomalous magnetic moment aμ with unprecedented precision of 127 ppb using a storage ring. The experiment pushed the limits in terms of accuracy and systematic errors. Achieving the 78-ppb total systematic uncertainty required precise beam dynamics modeling and corrections for effects on the measured muon precession frequency. Here, we derived the first analytic aberration formulas up to the second order for the muon g-2 storage ring’s combined-function electrostatic quadrupoles (superimposed magnetic dipole and electric quadrupole fields) using an order-by-order perturbation method. From these, we obtained the exact chromaticity formulas for three ring models of different granularity and validated them against numerical calculations using COSY INFINITY, achieving analytic-numerical agreement to ⁠$\mathscr{O}(10^{-10})$. This work resolved discrepancies between previous approximate derivations and provided essential beam dynamics results for Runs 4-6 analyses. We also calculated nonlinear chromaticities up to ninth order. The experiment completed its final Run 6 in July 2023, collecting 21 times more data than the previous muon g-2 experiment at Brookhaven National Laboratory, with the final result announced in June 2025.

aberrations↗
DOE OSTI2022

Clump survival and migration in VDI galaxies: an analytical model versus simulations and observations

ABSTRACT We address the nature of the giant clumps in high-z galaxies that undergo violent disc instability, distinguishing between long-lived and short-lived clumps. We study the evolution of long-lived clumps during migration through the disc via an analytical model tested by simulations and confront theory with CANDELS-HST observations. The clump ‘bathtub’ model, which considers gas and stellar gain and loss, involves four parameters: the accretion efficiency α, the star formation rate (SFR) efficiency ϵd, and the outflow mass-loading factors for gas and stars, η and ηs. The corresponding time-scales are comparable to the migration time, two-three orbital times. The accretion-rate dependence on clump mass, gas, and stars, allows an analytical solution involving exponential growing and decaying modes. For the fiducial parameter values there is a main evolution phase where the SFR and gas mass are constant and the stellar mass is rising linearly with time. This makes the inverse specific SFR an observable proxy for clump age. When η or ϵd are high, or α is low, the decaying mode induces a decline of SFR and gas mass till the migration ends. Later, the masses and SFR approach an hypothetical exponential growth with a constant specific SFR. The model matches simulations with different, moderate feedbacks, both in isolated and cosmological settings. The observed clumps agree with our predictions, indicating that the massive clumps are long-lived and migrating. A challenge is to model feedback that is non-disruptive in massive clumps but suppresses SFR to match the galactic stellar-to-halo mass ratio.

Dekel, Avishai↗
DOE OSTI2026

Deep-field analytical calibration

The next generation of imaging surveys, including the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), Euclid, and the Nancy Grace Roman Space Telescope, will provide unprecedented constraints on cosmology using weak gravitational lensing. To fully exploit this statistical power, shear measurement methods must achieve sub- per cent accuracy while mitigating systematic biases from noise, the point-spread function (PSF), blending, and shear-dependent detection. The analytical calibration framework (AnaCal) has demonstrated such accuracy but requires adding noise to images, reducing effective depth. We introduce Deep-Field Analytical Calibration (DEEP-FIELD AnaCal), an extension of AnaCal that uses deep-field images to compute shear responses while preserving the statistical power of wide-field data. We validate DEEP-FIELD AnaCal on isolated and blended galaxy image simulations with LSST-like conditions, finding it meets the stringent requirement of multiplicative bias $|m| < 3\times 10^{-3}$ at 99.7 per cent confidence. Compared to standard AnaCal applied to wide-field images, DEEP-FIELD AnaCal increases the effective galaxy number density from 17 to 30 arcmin$^{-2}$ for simulated 10-yr LSST data. With deep fields $10\times$ longer than the wide field, we find pixel noise variance in shear estimation is reduced by 30 per cent and overall uncertainty by $\sim 25~{{\ \rm per\ cent}}$. Finally, using the LSST Deep Drilling Fields strategy, we assess sample variance and find an equivalent calibration uncertainty of $\lesssim 0.3~{{\ \rm per\ cent}}$. These results demonstrate that DEEP-FIELD AnaCal offers a promising path to achieve the required shear calibration for upcoming weak lensing surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Nuclear cusps and singularities in the nonadditive kinetic potential bifunctional from analytical inversion

The non-additive kinetic potential $v^{\text{NAD}}$ is a key quantity in density-functional theory (DFT) embedding methods, such as frozen density embedding theory and partition DFT. $v^{\text{NAD}}$ is a bi-functional of electron densities $\rho_{\rm B}$ and $\rho_{\rm tot} = \rho_{\rm A} + \rho_{\rm B}$. It can be evaluated using approximate kinetic-energy functionals, but accurate approximations are challenging. The behavior of $v^{\text{NAD}}$ in the vicinity of the nuclei has long been questioned, and singularities were seen in some approximate calculations. In this article, the existence of singularities in $v^{\text{NAD}}$ is analyzed analytically for various choices of $\rho_{\rm B}$ and $\rho_{\rm tot}$, using the nuclear cusp conditions for the density and Kohn-Sham potential. It is shown that no singularities arise from smoothly partitioned ground-state Kohn-Sham densities. We confirm this result by numerical calculations on diatomic test systems HeHe, HeLi$^+$, and H$_2$, using analytical inversion to obtain a numerically exact $v^{\rm NAD}$ for the local density approximation. We examine features of $v^{\rm NAD}$ which can be used for development and testing of approximations to $v^{\rm NAD}[\rho_{\rm B},\rho_{\rm tot}]$ and kinetic-energy functionals.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Analytical estimates of attosecond streaking time delay in photoionization of atoms

In this work, we present estimates of the attosecond streaking delay in photoionization of atoms based on an analytical formula. In the derivation of the formula we use that the streaking delay depends on the propagation of the photoelectron over a finite range in space. We find that the analytical estimates agree well with results of ab initio calculations. Application of the formula provides insights into the influence of the streaking field on the field-free time delay in the analysis of streaking measurements.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

Analytic generalized description of a perturbative nonparaxial elegant Laguerre-Gaussian phasor for ultrashort pulses in the time domain

An analytic expression for a polychromatic phasor representing an arbitrarily short elegant Laguerre-Gauss (eLG) laser pulse of any spot size and LG mode is presented in the time domain as a nonrecursive, closed-form perturbative expansion valid to any order of perturbative correction. Here, this phasor enables the calculation of the complex electromagnetic fields for such beams without requiring the evaluation of any Fourier integrals. It is thus straightforward to implement in analytical or numerical applications involving eLG pulses.

74 ATOMIC AND MOLECULAR PHYSICS↗