SEARCH · Engineering Papers

Results for “Integrable field theories”

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 487 records · Page 27

All sources NASA NTRS DOE OSTI

DOE OSTI2021

Geometry and entanglement in the scattering matrix

A formulation of nucleon–nucleon scattering is developed in which the S-matrix, rather than an effective-field theory (EFT) action, is the fundamental object. Spacetime plays no role in this description: the S-matrix is a trajectory that moves between RG fixed points in a compact theory space defined by unitarity. This theory space has a natural operator definition, and a geometric embedding of the unitarity constraints in four-dimensional Euclidean space yields a flat torus, which serves as the stage on which the S-matrix propagates. Trajectories with vanishing entanglement are special geodesics between RG fixed points on the flat torus, while entanglement is driven by an external potential. The system of equations describing S-matrix trajectories is in general complicated, however the very-low-energy S-matrix –that appears at leading-order in the EFT description– possesses a UV/IR conformal invariance which renders the system of equations integrable, and completely determines the potential. In this geometric viewpoint, inelasticity is in correspondence with the radius of a three-dimensional hyperbolic space whose two-dimensional boundary is the flat torus. This space has a singularity at vanishing radius, corresponding to maximal violation of unitarity. The trajectory on the flat torus boundary can be explicitly constructed from a bulk trajectory with a quantifiable error, providing a simple example of a holographic quantum error correcting code.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Electronic density response of warm dense matter

Matter at extreme temperatures and pressures—commonly known as warm dense matter (WDM)—is ubiquitous throughout our Universe and occurs in astrophysical objects such as giant planet interiors and brown dwarfs. Moreover, WDM is very important for technological applications such as inertial confinement fusion and is realized in the laboratory using different techniques. A particularly important property for the understanding of WDM is given by its electronic density response to an external perturbation. Such response properties are probed in x-ray Thomson scattering (XRTS) experiments and are central for the theoretical description of WDM. In this work, we give an overview of a number of recent developments in this field. To this end, we summarize the relevant theoretical background, covering the regime of linear response theory and nonlinear effects, the fully dynamic response and its static, time-independent limit, and the connection between density response properties and imaginary-time correlation functions (ITCF). In addition, we introduce the most important numerical simulation techniques, including path-integral Monte Carlo simulations and different thermal density functional theory (DFT) approaches. From a practical perspective, we present a variety of simulation results for different density response properties, covering the archetypal model of the uniform electron gas and realistic WDM systems such as hydrogen. Moreover, we show how the concept of ITCFs can be used to infer the temperature from XRTS measurements of arbitrary complex systems without the need for any models or approximations. Finally, we outline a strategy for future developments based on the close interplay between simulations and experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

hi_class background evolution, initial conditions and approximation schemes

Cosmological datasets have great potential to elucidate the nature of dark energy and test gravity on the largest scales available to observation. Theoretical predictions can be computed with hi_class (www.hiclass-code.net), an accurate, fast and flexible code for linear cosmology, incorporating a wide range of dark energy theories and modifications to general relativity. We introduce three new functionalities into hi_class: (1) Support for models based on covariant Lagrangians, including a constraint-preserving integration scheme for the background evolution and a series of worked-out examples: Galileon, nKGB, quintessence (monomial, tracker) and Brans-Dicke. (2) Consistent initial conditions for the scalar-field perturbations in the deep radiation era, identifying the conditions under which modified-gravity isocurvature perturbations may grow faster than adiabatic modes leading to a loss of predictivity. (3) An automated quasistatic approximation scheme allowing order-of-magnitude improvement in computing performance without sacrificing accuracy for wide classes of models. These enhancements bring the treatment of dark energy and modified gravity models to the level of detail comparable to software tools restricted to standard $\Lambda$CDM cosmologies. Finally, the hi_class code is publicly available (https://github.com/miguelzuma/hi_class_public), ready to explore current data and prepare for next-generation experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1977

A statistical formulation of one-dimensional electron fluid turbulence

A one-dimensional electron fluid model is investigated using the mathematical methods of modern fluid turbulence theory. Non-dissipative equilibrium canonical distributions are determined in a phase space whose co-ordinates are the real and imaginary parts of the Fourier coefficients for the field variables. Spectral densities are calculated, yielding a wavenumber electric field energy spectrum proportional to k to the negative second power for large wavenumbers. The equations of motion are numerically integrated and the resulting spectra are found to compare well with the theoretical predictions.

Fyfe, D.↗

NASA NTRS1991

Coherent laser radar performance for general atmospheric refractive turbulence

A general theory for the signal-to-noise ratio (SNR) of a coherent detection laser radar is developed using the path-integral formulation (Fresnel approximation), which is valid for any typical path-integrated atmospheric refractive turbulence. The principal effects of refractive turbulence are discussed, and analytical expressions are presented for the case of untruncated Gaussians for the transmitted field, local oscillator field, and transmitter/receiver optics. The physical mechanisms that reduce heterodyne efficiency are identified.

Frehlich, Rod G.↗

NASA NTRS2015

Zernike Wavefront Sensor Modeling Development for LOWFS on WFIRST-AFTA

WFIRST-AFTA design makes use of an existing 2.4m telescope for direct imaging of exoplanets. To maintain the high contrast needed for the coronagraph, wavefront error (WFE) of the optical system needs to be continuously sensed and controlled. Low Order Wavefront Sensing (LOWFS) uses the rejected starlight from an immediate focal plane to sense wavefront changes (mostly thermally induced low order WFE) by combining the LOWFS mask (a phase plate located at the small center region with reflective layer) with the starlight rejection masks, i.e. Hybrid Lyot Coronagraph (HLC)'s occulter or Shaped Pupil Coronagraph (SPC)'s field stop. Zernike wavefront sensor (ZWFS) measures phase via the phase-contrast method and is known to be photon noise optimal for measuring low order aberrations. Recently, ZWFS was selected as the baseline LOWFS technology on WFIST/AFTA for its good sensitivity, accuracy, and its easy integration with the starlight rejection mask. In this paper, we review the theory of ZWFS operation, describe the ZWFS algorithm development, and summarize various numerical sensitivity studies on the sensor performance. In the end, the predicted sensor performance on SPC and HLC configurations are presented.

Zernike phase contrast↗

NASA NTRS1993

Theory for noise of propellers in angular inflow with parametric studies and experimental verification

This report presents the derivation of a frequency domain theory and working equations for radiation of propeller harmonic noise in the presence of angular inflow. In applying the acoustic analogy, integration over the tangential coordinate of the source region is performed numerically, permitting the equations to be solved without approximation for any degree of angular inflow. Inflow angle is specified in terms of yaw, pitch, and roll angles of the aircraft. Since these can be arbitrarily large, the analysis applies with equal accuracy to propellers and helicopter rotors. For thickness and loading, the derivation is given in complete detail with working equations for near and far field. However, the quadrupole derivation has been carried only far enough to show feasibility of the numerical approach. Explicit formulas are presented for computation of source elements, evaluation of Green's functions, and location of observer points in various visual and retarded coordinate systems. The resulting computer program, called WOBBLE has been written in FORTRAN and follows the notation of this report very closely. The new theory is explored to establish the effects of varying inflow angle on axial and circumferential directivity. Also, parametric studies were performed to evaluate various phenomena outside the capabilities of earlier theories, such as an unsteady thickness effect. Validity of the theory was established by comparison with test data from conventional propellers and Prop Fans in flight and in wind tunnels under a variety of operating conditions and inflow angles.

Propeller acoustics↗

DOE OSTI2020

Bootstrap bounds on closed Einstein manifolds

A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy certain consistency conditions that follow from associativity and the completeness of eigenmodes. We show that it is possible to obtain nontrivial bounds on the geometric data of closed Einstein manifolds by using semidefinite programming to study these consistency conditions, in analogy to the conformal bootstrap bounds on conformal field theories. These bootstrap bounds translate to constraints on the tree-level masses and cubic couplings of Kaluza-Klein modes in theories with compact extra dimensions. We show that in some cases the bounds are saturated by known manifolds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Extending GPU-accelerated Gaussian integrals in the TeraChem software package to f type orbitals: Implementation and applications

Here, the increasing availability of graphics processing units (GPUs) for scientific computing has prompted interest in accelerating quantum chemical calculations through their use. However, the complexity of integral kernels for high angular momentum basis functions often limits the utility of GPU implementations with large basis sets or for metal containing systems. In this work, we report the implementation of f function support in the GPU-accelerated TeraChem software package through the development of efficient kernels for the evaluation of Hamiltonian integrals. The high efficiency of the resulting code is demonstrated through density functional theory (DFT) calculations on increasingly large organic molecules and transition metal complexes, as well as coupled cluster singles and doubles calculations on water clusters. Preliminary investigations into Ni(I) catalysis with DFT and the photochemistry of MnH(CH 3 ) with complete active space self-consistent field are also carried out. Overall, our GPU-accelerated software appears to be well-suited for fast simulation of large transition metal containing systems, as well as organic molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1985

On the coupling of fluid dynamics and electromagnetism at the top of the earth's core

A kinematic approach to short-term geomagnetism has recently been based upon pre-Maxwell frozen-flux electromagnetism. A complete dynamic theory requires coupling fluid dynamics to electromagnetism. A geophysically plausible simplifying assumption for the vertical vorticity balance, namely that the vertical Lorentz torque is negligible, is introduced and its consequences are developed. The simplified coupled magnetohydrodynamic system is shown to conserve a variety of magnetic and vorticity flux integrals. These provide constraints on eligible models for the geomagnetic main field, its secular variation, and the horizontal fluid motions at the top of the core, and so permit a number of tests of the underlying assumptions.

Benton, E. R.↗

NASA NTRS1993

Ion mixing in the plasma sheet boundary layer by drift instabilities

The linear stability properties of collisionless drift instabilities are analyzed in a Harris equilibrium model of the plasma sheet boundary layer (PSBL). The strearmng ions with drift-type instabilities driven in the PSBL are considered. The fluid approximation leads to growth but predicts that the mode width approaches the gyroradius of the energetic ions. Thus an integral equation theory for the modes is developed taking into account that in the PSBL the curvature drift is weak compared with the grad-B drift. The exact wave particle resonance is kept in the nonlocal response functions. Plasma density, temperature, and magnetic gradient drift motions are taken into account. The drift modes produce an anomalous cross-field momentum transport mixing the PSBL ions on the time scale of tens of seconds. A nonlinear simulation is performed which shows the coalescence of the small scale, fast growing modes into large-scale vortices. The relation between these collective modes and plasma sheet transport phenomena is discussed including the comparison with the competing plasma mixing from single-particle stochasticity.

Horton, W.↗

NASA NTRS1946

Investigation of Turbulent Mixing Processes

With water as driving medium and delivered medium in a device similar to a simple jet apparatus, the pressure and velocity fields of the mixing zone were explored with a pitot bar; the ratio of delivered to driving volume ranged between the values 0, 1, 2, and 4. An attempt was also made to analyze the mixing flow mathematically by integration of the equation of motion, with the aid of conventional formulas for the turbulent shearing stress, but this succeeded only approximately for the very simplified case that a driving jet is introduced in an unlimited parallel flow, while the pressure over the whole mixing field is assumed to be constant. In spite of these dissimilar assumptions for the theory and the experiment, the form of the measured and the computed velocity profiles indicates a very high degree of approximation. The pressure rise, which was approximated by Flugel's formulas, disclosed good agreement with the measured values.

Viktorin, K.↗

NASA NTRS1988

Generalized adiabatic theory applied to the magnetotail current sheet

The generalized first adiabatic invariant, an extension of the magnetic moment for regions of large field gradients, has been applied to the study of particles in the magnetotail current sheet. Boundaries in phase space are obtained which form a generalized loss cone and separate particles drifting into and out of the layer from particles trapped within the layer, and the boundaries can be employed in the moment integrals for densities and currents when the drifting particles differ in temperature. It is shown that the parallel pressure of the drifting particles must exceed the transverse pressure for self-consistent solutions to exist. Fully self-consistent solutions are obtained using bi-Maxwellian ion and Maxwellian electron distributions.

Rogers, Shelley H.↗

DOE OSTI2025

Bridging the gap between molecules and materials in quantum chemistry with localized active spaces

The number of materials that “bridge the gap” between single molecules and extended solids, such as metal-organic frameworks and organic semiconductors, has been increasing. Consequently, there is a growing need for modeling approaches that effectively integrate the real-space molecular perspective employed by computational chemists and the reciprocal-space dispersive perspective employed by computational physicists. Here, we propose the localized active space (LAS) approach as a promising method to successfully bridge this gap. The LAS approach extends the active space concept from multiconfigurational methods such as complete active space self-consistent field theory to multiple molecular fragments via a product-form wave function ansatz. Here, we apply this method to solid state phenomena by treating each unit cell as a fragment with different sets of local quantum numbers (e.g., charge and excitation number). State interaction between these LAS states (LASSI) thus provides a comprehensive basis for the study of charge and energy transfer, meeting and surpassing the capabilities of single-reference fragmentation approaches such as constrained density functional theory (cDFT). Most centrally, we show how combining this LASSI approach with multiconfigurational pair-density functional theory (MC-PDFT) provides an elegant and efficient method to compute band structures that capture multiconfigurational character. We apply the LASSI band structure approach to the computation of band gaps in stretched hydrogen chain, polyacetylene, and bulk nickel oxide (NiO), finding good or excellent quantitative agreement with reference values in all cases. Additionally, we use the LAS basis in one-dimensional model systems to demonstrate its ability to treat difficult solid-state phenomena such as exciton transfer and excitation at p-n junctions.

method development↗

NASA NTRS1984

High altitude chemically reacting gas particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution

The overall contractual effort and the theory and numerical solution for the Reacting and Multi-Phase (RAMP2) computer code are described. The code can be used to model the dominant phenomena which affect the prediction of liquid and solid rocket nozzle and orbital plume flow fields. Fundamental equations for steady flow of reacting gas-particle mixtures, method of characteristics, mesh point construction, and numerical integration of the conservation equations are considered herein.

Smith, S. D.↗

NASA NTRS1985

Polar convection patterns under quiet conditions

Convection electric field patterns at high latitudes appropriate to periods of low geomagnetic activity are presented. The postulate that the global Joule dissipation rate is a minimum is employed to derive characteristic field distributions for the situation when ring current ohmic losses are negligible and the auroral oval enhancement of height-integrated Hall conductivity is small. The fast Fourier transform is introduced to compute Fourier coefficients of discrete field-aligned current data, and the method is shown to be quite useful in this context as a least squares fitting routine. The model calculations demonstrate the approach of the high-latitude ionosphere toward the perfect shielding configuration predicted by the theory for quiet times.

Barbosa, D. D.↗

NASA NTRS2001

Estimates of M2 Tidal Energy Dissipation from TOPEX/Poseidon Altimeter Data

Most of the tidal energy dissipation in the ocean occurs in shallow seas, as has long been recognized. However, recent work has suggested that a significant fraction of the dissipation, perhaps 1 TW or more, occurs in the deep ocean. This paper builds further evidence for that conclusion. More than 6 years of data from the TOPEX/Poseidon satellite altimeter are used to map the tidal dissipation rate throughout the world ocean. The dissipation rate is estimated as a balance between the rate of working by tidal forces and the energy flux divergence, computed using currents derived by least squares fitting of the altimeter data and the shallow water equations. Such calculations require dynamical assumptions, in particular about the nature of dissipation. To assess sensitivity of dissipation estimates to input assumptions, a large suite of tidal inversions based on a wide range of drag parameterizations and employing both real and synthetic altimeter data are compared. These experiments and Monte Carlo error fields from a generalized inverse model are used to establish error uncertainties for the dissipation estimates. Owing to the tight constraints on tidal elevation fields provided by the altimeter, area integrals of the energy balance are remarkably insensitive to required dynamical assumptions. Tidal energy dissipation is estimated for all major shallow seas (excluding individual polar seas) and compared with previous model and data-based estimates. Dissipation in the open ocean is significantly tnhanced around major bathymetric features, in a manner consistent with simple theories the generation of baroclinic tides.

Egbert, Gary D.↗

DOE OSTI2023

Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics

In Born–Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born–Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born–Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born–Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born–Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original “zeroth-level” shadow energy functionals and potentials used in extended Lagrangian BOMD. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree–Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗