Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Continuous derivative”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

The pattern speed of the Milky Way bar from transverse velocities

ABSTRACT We use the continuity equation to derive a method for measuring the pattern speed of the Milky Way’s bar/bulge from proper motion data. The method has minimal assumptions but requires complete coverage of the non-axisymmetric component in two of the three Galactic coordinates. We apply our method to the proper motion data from a combination of Gaia DR2 and VISTA Variables in the Via Lactea (VVV) to measure the pattern speed of the bar as $\Omega _\mathrm{p}=(41\pm 3)\, \mathrm{km\, s^{-1}\, kpc^{-1}}$ (where the error is statistical). This puts the corotation radius at $(5.7\pm 0.4)\, \mathrm{kpc}$, under the assumptions of the standard peculiar motion of the Sun and the absence of non-axisymmetric streaming in the Solar neighbourhood. The obtained result uses only data on the near side of the bar which produces consistent measurements of the distance and velocity of the centre of the Galaxy. Addition of the data on the far side of the bar pulls the pattern speed down to $\Omega _\mathrm{p}=(31\pm 1)\, \mathrm{km\, s^{-1}\, kpc^{-1}}$ but requires a lower transverse velocity for the Galactic centre than observed. This suggests systematics of $5-10\, \mathrm{km\, s^{-1}kpc^{-1}}$ dominate the uncertainty. We demonstrate using a dynamically formed bar/bulge simulation that even with the limited field of view of the VVV survey our method robustly recovers the pattern speed.

Sanders, Jason L.↗
DOE OSTI2026

Time Correlations from Steady-State Expectation Values

Recovering properties of correlation functions is typically challenging. On the one hand, experimentally, it requires measurements with a temporal resolution finer than the system’s dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a system parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable, and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to the experimental characterization of ultrafast systems and to the theoretical analysis of many-body models whose dynamics are hard to compute.

Górecki, Wojciech [INFN, Pavia] (ORCID:00000001991↗
DOE OSTI2022

Thermodynamics of quantum measurement and Maxwell's demon's arrow of time

Here, we discuss the thermodynamic aspects of a single qubit based device, powered by weak quantum measurements, and feedback controlled by a quantum Maxwell's demon. We discuss both discrete and time-continuous operation of the measurement based device at finite temperature of the reservoir. In the discrete example where a demon acquires information via discrete weak measurements, we find that the thermodynamic variables including the heat exchanged, extractable work, and the entropy produced are completely determined by an information theoretic measure of the demon's perceived arrow of time. We also discuss a realistic time-continuous operation of the device where the feedback is applied after a sequence of weak measurements. In the time-continuous limit, we derive the exact finite-time statistics of work, heat and entropy changes along individual quantum trajectories of the quantum measurement process, and relate them to the demon's arrow of time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Dark matter catalyzed baryon destruction

WIMP-type dark matter may have additional interactions that break baryon number, leading to induced nucleon decays which are subject to direct experimental constraints from proton decay experiments. In this work, we analyze the possibility of continuous baryon destruction, deriving strong limits from the dark matter accumulating inside old neutron stars, as such a process leads to excess heat generation. We construct the simplest particle dark matter model that breaks the baryon and lepton numbers separately but conserves B - L. Virtual exchange by DM particles in this model results in dinucleon decay via nn → $n\overline{v}$ and np → ne⁺ processes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Charge Conservation beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024

Physics↗
DOE OSTI2022

Path Integrals for Nonadiabatic Dynamics: Multistate Ring Polymer Molecular Dynamics

This review focuses on a recent class of path-integral-based methods for the simulation of nonadiabatic dynamics in the condensed phase using only classical molecular dynamics trajectories in an extended phase space. Specifically, a semiclassical mapping protocol is used to derive an exact, continuous, Cartesian variable path-integral representation for the canonical partition function of a system in which multiple electronic states are coupled to nuclear degrees of freedom. Building on this exact statistical foundation, multistate ring polymer molecular dynamics methods are developed for the approximate calculation of real-time thermal correlation functions. As a result, the remarkable promise of these multistate ring polymer methods, their successful applications, and their limitations are discussed in detail.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Mixing Cell Model: A One-Dimensional Numerical Model for Assessment of Water Flow and Contaminant Transport in the Unsaturated Zone

This report describes the Mixing Cell Model code, a one dimensional model for water flow and solute transport in the unsaturated zone under steady state or transient flow conditions. The model is based on the principles and assumptions underlying mixing-cell model formulations. The unsaturated zone is discretized into a series of independent mixing cells. Each cell may have unique hydrologic, lithologic, and sorptive properties. Ordinary differential equations describe the material (water and solute) balance within each cell. Water-flow equations are derived from the continuity equation, assuming that unit gradient conditions exist at all times in each cell. Pressure gradients are considered implicitly through model discretization. Unsaturated hydraulic conductivity and moisture contents are determined by the material specific moisture-characteristic curves. Solute-transport processes include explicit treatment of advective processes, first order chain decay, and linear sorption reactions. Dispersion is addressed through implicit and explicit dispersion. Implicit dispersion is an inherent feature of all mixing-cell models and originates from the formulation of the problem in terms of mass balance around fully mixed volume elements. Expressions are provided that relate implicit dispersion to the physical dispersion of the system. Two FORTRAN codes were developed to solve the water flow and solute-transport equations: (1) the Mixing Cell Model for Flow (MCMF) solves transient water-flow problems and (2) the Mixing Cell Model for Transport (MCMT) solves the solute-transport problem. The transient water-flow problem is typically solved first by estimating the water flux through each cell in the model domain as a function of time using the MCMF code. These data are stored in either ASCII or binary files that are later read by the solute transport code (MCMT). Code output includes solute pore water concentrations, water and solute inventories in each cell and at each specified output time, and water and solute fluxes through each cell and specified output time. Computer run times for coupled transient water flow and solute transport were typically several seconds on a 2 GHz Intel Pentium IV desktop computer. The model was benchmarked against analytical solutions and finite element approximations to the partial differential equations (PDE) describing unsaturated flow and transport. Differences between the maximum solute flux estimated by the mixing cell model and the PDE models were typically less than two percent. This revision includes an option for a fixed concentration lower boundary condition for diffusive fluxes for versions 020321 and later.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Extending and Smoothing Two-dimension Equation of State Simulation Data

The Multiphase Equation of State (MEOS) project works to produce high quality equation of state tables which are used in computationally intensive simulations of materials in different conditions. An equation of state table describes the state of matter under certain physical conditions such as pressure, volume, temperature, or internal energy. MEOS uses many different models and combinations thereof to produce accurate tables consisting of continuous smooth data, derivatives, and higher-order derivatives. Accurate and smooth data are important factors in producing precise simulations. This report focuses on improving the electron tables produced from Purgatorio and Thomas-Fermi data. Purgatorio data is extremely accurate but often jagged and discontinuous in the lower temperature and density region. Thomas-Fermi is a model that provides smooth data throughout. Together, this produces an EOS data table that is both accurate and smooth. This report describes the implementation of a new feature that allows users to define more detailed regions in the Purgatorio table to be replaced with Thomas-Fermi. As a result, MEOS can generate a table that is both more smooth and still accurate.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

Coordinated adaptive filters for motion simulators.

A new approach to providing motion drive signals to a flight simulator utilizing coordinated adaptive filters is presented. Some motivation for the use of coordinated washout is discussed, along with conditions that determine the burden of coordination. The coordinated adaptive filters are derived, based on continuous steepest descent, and the application of the filters to simulated flight data is demonstrated.

Parrish, R. V.↗
NASA NTRS1982

C-1 surface interpolation for scattered data on a sphere

An algorithm is described for constructing a smooth computable function, f, defined over the surface of a sphere and interpolating a set of n data values, u sub i, associated with n locations, P sub i, on the surface of the sphere. The interpolation function, f, will be continuous and have continuous first partial derivatives. The locations, p sub i, are not required to lie on any type of regular grid.

Lawson, C. L.↗
NASA NTRS1984

Variational objective analyses for cyclone studies

The basic analysis equations, i.e., the two horizontal momentum equations, the hydrostatic equation, and the integrated continuity equation were derived for the nonlinear vertical coordinate, nondimensionalized, and expressed in finite differences on a staggered grid. Special care was taken to transform the hydrostatic equation and the pressure gradient terms of the horizontal momentum equations to nearly eliminate truncation error over steeply sloping terrain. This formulation also eliminated explicit reference to orographically induced variations in the thermodynamic variables so that the variational adjustments are on the scale of the meteorological perturbations. The analysis equations were subjected to the Euler-Lagrange operations as expressed for finite differences and an additional set of five partial differential equations was derived, bringing to nine the number of equations in Model I. Higher order terms, terms containing observed quantities, and terms containing none of the variables to be adjusted were grouped into forcing functions and the equations were solved for the zero order terms. Zero order variables were eliminated between these equations and there resulted two diagnostic equations which take the form of general linear second order partial differential equations with nonconstant coefficients.

Achtemeier, G. L.↗
NASA NTRS1986

The X-ray background and the evolution of quasars

The contribution of QSOs and active galaxies to the 2-10-keV X-ray background is calculated theoretically, assuming that the X-ray luminosity of each GSO has a power-law time evolution (dL/dt = AL exp alpha) and applying the continuity equation to derive the X-ray luminosity function at arbitrary redshift. The observed X-ray background is shown to require alpha greater than 1.2, ruling out pure luminosity evolution (alpha = 1).

Tucker, W. H.↗
NASA NTRS1989

A space-time discretization procedure for wave propagation problems

Higher order compact algorithms are developed for the numerical simulation of wave propagation by using the concept of a discrete dispersion relation. The dispersion relation is the imprint of any linear operator in space-time. The discrete dispersion relation is derived from the continuous dispersion relation by examining the process by which locally plane waves propagate through a chosen grid. The exponential structure of the discrete dispersion relation suggests an efficient splitting of convective and diffusive terms for dissipative waves. Fourth- and eighth-order convection schemes are examined that involve only three or five spatial grid points. These algorithms are subject to the same restrictions that govern the use of dispersion relations in the constructions of asymptotic expansions to nonlinear evolution equations. A new eighth-order scheme is developed that is exact for Courant numbers of 1, 2, 3, and 4. Examples are given of a pulse and step wave with a small amount of physical diffusion.

Davis, Sanford↗
NASA NTRS1991

State-Variable Representations For Moving-Average Sampling

Two state-variable representations derived for continuous-time plant driven by control algorithm including zero-order hold and measurements sampled at mutliple rates by multiple-input/multiple-output moving-average processes. New representations enhance observability and controllability of plant. Applications include mathematical modeling of navigation systems including star trackers, gyroscopes, and accelerometers.

Polites, Michael E.↗
NASA NTRS1991

Analytical relationships of nuclear field and microdosimetric quantities for target fragmentation in tissue systems

A simple analytic formula for the nuclear fields formed by target fragmentation in tissue systems is derived using the continuous slowing down approximation (CSDA). The energy fluctuations in sensitive localized sites within the tissue system caused by these nuclear events are defined by microdosimetry. In that CSDA is used, the energy fluctuations exclude the role of secondary electrons. The relations also relate to the response of microdosimetric devices to nuclear fragmentation fields.

Wilson, John W.↗
NASA NTRS1992

Aeronautical research in the United States: Challenges for the 1990's

New opportunities for greater performance civil air transportation aircraft derive from the continuing advancements in the aeronautical disciplines: advancements in aerodynamics, structures and materials, propulsion, and flight control technologies. These opportunities impact future subsonic transports, high speed civil transports, and hypersonic vehicles. There are, however, new constraints within which progress will be made, including stringent environmental constraints on engine emissions and noise, old and new safety constraints on operations (especially in severe weather), aging airframes, and changing transportation marketplace demands affecting all of these vehicle classes. Some of the NASA aeronautical research programs will be discussed in four areas: (1) advanced subsonic airplanes; (2) next generation high speed civil transport aircraft (SST's); (3) high performance military aircraft; and (4) next century hypersonic vehicles. This presentation overviews the exciting progress which is possible in aeronautics during the 1990's.

Holmes, Bruce J.↗
NASA NTRS1992

Onboard configuration and operation of the TDRSS onboard navigation system (TONS)

This paper presents an overview of onboard navigation via TDRSS for both the EP/EUVE (Explorer Platform/Extreme Ultraviolet Explorer) experiment and for future users of TONS. System goals and objectives are discussed, and the operations concept for the three stages of TONS development is presented. A description is given of the first stage of the TONS development, the experiment implementation on EP, including the hardware characteristics, signal acquisition process, onboard data acquisition, and ground data processing in the flight emulation environment of the TONS Ground Support System (TGSS). Evaluation of the experiment implementation is presented and improvements described in terms of the second development stage, a full TONS I system, which uses Doppler data derived from scheduled forward-link S-band services to provide onboard orbit and frequency determination. A method for onboard time maintenance commensurate with TONS I is also presented. TONS II, the third stage, will use Doppler and pseudorange data derived from a continuous, nonscheduled forward-link S-band beacon service to provide onboard orbit, time, and frequency determination.

Gramling, Cheryl J.↗