Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Differentiable physics”

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 613 records · Page 34

Scattering and collapse of Langmuir waves driven by a weak electron beam

Wave-wave interactions are examined, particularly for significance in relation to Langmuir turbulence associated with type III solar radio emissions. The Zakharov equations are considered as two coupled nonlinear partial differential equations for the low-frequency density and the Langmuir envelope, and the electron and ion temperatures are regarded as equal. The Zhakharov equations are solved in one dimension, and display no collapse of a driven broadband pump, indicating that scattering instabilities are important in the saturation of a beam-plasma instability. A two-dimensional numerical simulation is developed to interpret the role of parametric instabilities, and it is concluded that the distortion of a wave packet is due to scattering instability, and not a change in the physics of direct collapse due to an artificial numerical damping. Further discussions are presented for comparisons of models of Langmuir turbulence in type III bursts.

Hafizi, B.↗

A computer program for the simulation of heat and moisture flow in soils

A computer program that simulates the flow of heat and moisture in soils is described. The space-time dependence of temperature and moisture content is described by a set of diffusion-type partial differential equations. The simulator uses a predictor/corrector to numerically integrate them, giving wetness and temperature profiles as a function of time. The simulator was used to generate solutions to diffusion-type partial differential equations for which analytical solutions are known. These equations include both constant and variable diffusivities, and both flux and constant concentration boundary conditions. In all cases, the simulated and analytic solutions agreed to within the error bounds which were imposed on the integrator. Simulations of heat and moisture flow under actual field conditions were also performed. Ground truth data were used for the boundary conditions and soil transport properties. The qualitative agreement between simulated and measured profiles is an indication that the model equations are reasonably accurate representations of the physical processes involved.

Camillo, P.↗

Multiple periodicities in the solar magnetic field - Possible origin in a multiple-mode solar dynamo

The solar magnetic field is generated in an oscillatory mode with a 22 yr full period and gives rise to the 11 yr sunspot cycle. However, analyses of contemporary solar records, as well as other surrogate indicators of solar activity, suggest the presence also of longer term periodicities in the solar magnetic cycle. This paper suggests that the solar dynamo can operate in a multiply periodic state, with several periodicites being generated simultaneously at different depths in the convection zone. A simple two-layer model of the solar convection zone is used to illustrate the physical mechanism of spatially localized, multiple-periodicity-mode dynamo regeneration. The two layers are characterized by differences in their respective turbulent magnetic diffusivities. Although the magnetic modes interact with one another, each mode is produced large in one layer or the other, and has an oscillation period approximately equal to the time characteristic of magnetic diffusion across the layer. The observed complicated periodicity pattern in the solar magnetic field could be a combination of two (or more) dynamo modes generated in this manner. The calculations are carried out using a differential rotation model consistent with recent helioseismological measurements, illustrating the challenge to dynamo theory raised by those observational results.

Boyer, D. W.↗

Two-fluid simulations of galaxy formation

We investigate the formation of galaxies and larger structure with a simulation modeling two gravitationally coupled fluids representing dark matter and baryons. The baryon gas dynamics are calculated with a smoothed particle hydrodynamics (SPH) method, and the physics modeled includes thermal pressure, shock heating, and radiative cooling. We simulate a 16 Mpc periodic cube with 64(exp 3) particles in each fluid and 10% baryon mass fraction. We confirm, for the first time experimentally, disk formation as a natural consequence of hierarchical clustering in a large-scale cosmological environment. The majority of isolated galaxies exhibit centrifugally supported disks. A power-law relation between cold baryonic mass and maximum rotation velocity is found, M varies as nu(sub rot)(exp alpha) with alpha = 2.5 after correcting for differential numerical resolution. Both the spatial and velocity distributions of the simulated galaxies are biased with respect to the dark matter. A counts-in-cells analysis indicates that an unphysical degree of merging in the central cluster is likely responsible for the antibias signal in the correlation function. A robust, scale-dependent velocity bias is measured. The ratio of galaxy to dark matter pairwise velocity dispersions on a scale of 1 Mpc is 0.7. The amplitude is only mildly dependent on redshift or mass cutoff and scales with separation as r(exp 0.2). The degree to which these results depend on numerical parameters is discussed. Mass resolution plays a key role in controlling the resulting fraction of cold, dense baryons. The mass fraction associated with galaxies decreases by a factor of approximately greater than 3 when the mass per particle is increased by a factor 8. Photoionization and energy input from supernova will have to be included to determine more carefully the fraction of highly dissipated material and the characteristics of the stellar component of galaxies.

Evrard, August E.↗

Analysis of composite ablators using massively parallel computation

In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

Shia, David↗

Evolution of planetesimals. I - Dynamics: Relaxation in a thin disk. II - Numerical simulations

The study examines the effects of density inhomogeneity and differential rotation as well as inelastic collisions on the dynamical evolution of planetesimals. Consideration is given to a three-step analysis: the dynamical evolution of the planetesimals, collisions and mass accumulation, and interaction with gas. It is shown that the velocity dispersion of a cold system of planetesimals increases rapidly due to elastic gravitational scattering. When the dispersion in the epicycle amplitude becomes comparable to the planetesimals' Roche radius, energy is transferred from the systematic Keplerian shear to the dispersive motion. With a numerical N-body scheme, gravitational scattering and physical collisions among a system of planetesimals is simulated. It is shown that dynamical equilibrium is attained with a velocity dispersion comparable to the surface escape velocity of those planetesimals which contribute most of the system mass.

Palmer, P. L.↗

Feedback Control of Plasma Instabilities with Charged Particle Beams and Study of Plasma Turbulence

A new non-perturbing technique for feedback control of plasma instabilities has been developed in the Columbia Linear Machine (CLM). The feedback control scheme involves the injection of a feedback modulated ion beam as a remote suppressor. The ion beam was obtained from a compact ion beam source which was developed for this purpose. A Langmuir probe was used as the feedback sensor. The feedback controller consisted of a phase-shifter and amplifiers. This technique was demonstrated by stabilizing various plasma instabilities to the background noise level, like the trapped particle instability, the ExB instability and the ion-temperature-gradient (ITG) driven instability. An important feature of this scheme is that the injected ion beam is non-perturbing to the plasma equilibrium parameters. The robustness of this feedback stabilization scheme was also investigated. The principal result is that the scheme is fairly robust, tolerating about 100% variation about the nominal parameter values. Next, this scheme is extended to the unsolved general problem of controlling multimode plasma instabilities simultaneously with a single sensor-suppressor pair. A single sensor-suppressor pair of feedback probes is desirable to reduce the perturbation caused by the probes. Two plasma instabilities the ExB and the ITG modes, were simultaneously stabilized. A simple 'state' feedback type method was used where more state information was generated from the single sensor Langmuir probe by appropriate signal processing, in this case, by differentiation. This proof-of-principle experiment demonstrated for the first time that by designing a more sophisticated electronic feedback controller, many plasma instabilities may be simultaneously controlled. Simple theoretical models showed generally good agreement with the feedback experimental results. On a parallel research front, a better understanding of the saturated state of a plasma instability was sought partly with the help of feedback. A plasma instability is usually observed in its saturated state and appears as a single feature in the frequency spectrum with a single azimuthal and parallel wavenumbers. The physics of the non-zero spectral width was investigated in detail because the finite spectral width can cause "turbulent" transport. One aspect of the "turbulence" was investigated by obtaining the scaling of the linear growth rate of the instabilities with the fluctuation levels. The linear growth rates were measured with the established gated feedback technique. The research showed that the ExB instability evolves into a quasi-coherent state when the fluctuation level is high. The coherent aspects were studied with a bispectral analysis. Moreover, the single spectral feature was discovered to be actually composed of a few radial harmonics. The radial harmonics play a role in the nonlinear saturation of the instability via three-wave coupling.

Tham, Philip Kin-Wah↗

A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach

A new formulation of electromagnetic wave scattering by convex, two-dimensional conducting bodies is reported. This formulation, called the on-surface radiation condition (OSRC) approach, is based upon an expansion of the radiation condition applied directly on the surface of a scatterer. It is now shown that application of a suitable radiation condition directly on the surface of a convex conducting scatterer can lead to substantial simplification of the frequency-domain integral equation for the scattered field, which is reduced to just a line integral. For the transverse magnetic case, the integrand is known explicitly. For the transverse electric case, the integrand can be easily constructed by solving an ordinary differential equation around the scatterer surface contour. Examples are provided which show that OSRC yields computed near and far fields which approach the exact results for canonical shapes such as the circular cylinder, square cylinder, and strip. Electrical sizes for the examples are ka = 5 and ka = 10. The new OSRC formulation of scattering may present a useful alternative to present integral equation and uniform high-frequency approaches for convex cylinders larger than ka = 1. Structures with edges or corners can also be analyzed, although more work is needed to incorporate the physics of singular currents at these discontinuities. Convex dielectric structures can also be treated using OSRC.

Kriegsmann, Gregory A.↗

An Investigation of Differential Deposition for Figure Corrections in Full-Shell Grazing-Incidents X-Ray Optics

We are investigating differential deposition as a way of correcting small figure errors inside full-shell grazing-incidence x-ray optics. The optics in our study are fabricated using the electroformed-nickel-replication technique, and the figure errors arise from fabrication errors in the mandrel, from which the shells are replicated, as well as errors induced during the electroforming process. Combined, these give sub-micron-scale figure deviations which limit the angular resolution of the optics to approx. 10 arcsec. Sub-micron figure errors can be corrected by selectively depositing (physical vapor deposition) material inside the shell. The requirements for this filler material are that it must not degrade the ultra-smooth surface finish necessary for efficient x-ray reflection (approx. 5 A rms), and must not be highly stressed. In addition, a technique must be found to produce well controlled and defined beams within highly constrained geometries, as some of our mirror shells are less than 3 cm in diameter.

Gubarev, Mikhail V.↗

Evolution of molecular clouds

The evolution of interstellar molecular hydrogen was studied, with a special interest for the formation and evolution of molecular clouds and star formation within them, by a two-dimensional hydrodynamical simulation performed on a rectangular grid of physical sizes on the order of 100 pc. It is filled with an initial density of approx. 1 cm(exp -3), except for one cell (approx. 1 pc(exp 2)) at the center of the grid where an accretion core of 1-10(exp 3) solar masses is placed. The grid is co-moving with the gridcenter that is on a circular orbit around the Galactic center and that also is the guiding center of epicyclic approximation of orbits of the matter surrounding it. The initial radial velocity is zero; to account for differential rotation the initial tangential velocity (i.e. the movement around the galactic center) is proportional to the radial distance to the grid center. The rate is comparable to the rotation rate at the Local Standard of Rest. The influence of galactic rotation is noticed by spiral or elliptical forms, but on much longer time scales than self gravitation and cooling processes. Density and temperature are kept constant at the boundaries and no inflow is allowed along the tangential boundaries.

Sevenster, M.↗

Application of differential similarity to finding nondimensional groups important in tests of cooled engine components

The method of differential similarity is applied to the partial differential equations and boundary conditions which govern the temperature, velocity, and pressure fields in the flowing gases and the solid stationary components in air-cooled engines. This procedure yields the nondimensional groups which must have the same value in both the test rig and the engine to produce similarity between the test results and the engine performance. These results guide the experimentalist in the design and selection of test equipment that properly scales quantities to actual engine conditions. They also provide a firm fundamental foundation for substantiation of previous similarity analyses which employed heuristic, physical reasoning arguments to arrive at the nondimensional groups.

Sucec, J.↗

A suggestion concerning the generation of the physical state of stellar mantles

The physical state of the winds of B supergiants varies from one of a high level of ionization and rapid outflow to one of relatively low ionization and a moderate rate of outflow as one goes from type B0 to type A0. It is proposed here that this is the result of magnetodynamic energy being released in the mantles of these stars, much as occurs in the sun. Data are presented to show that this idea is plausible. It is noted that the release of magnetodynamic energy as the result of interaction between magnetic fields and differential motion in an inhomogeneous structure is probably the cause of the heating in all outer stellar atmospheres (mantles). In the late-type stars, the material in the mantle must first be ionized by the deposition of energy from acoustic waves; in the early-type stars, the material is already ionized at least once in the photosphere, as a result of the normal transfer of radiative energy, so no priming process is necessary for these stars.

Underhill, A. B.↗

Theory of radio occultation by Saturn's rings

The radio occultation technique, as applied to Saturn's rings, is developed as a new method for the study of the physical properties of planetary ring systems. The rings are treated as a Doppler-spread radar target composed of an ensemble of discrete scatterers. The mathematical formulation of the received signal as a random-phasor-sum process is carried out following a conventional radar theory approach, providing a convenient starting point for deriving coherent signal parameters. A classical result is rederived for the equivalent refractive index of the medium. The analysis is generalized to include ringlets of arbitrary width and it is shown that when the width is such that two adjacent rays are differentially perturbed in phase, ray bending that causes focusing of the coherent signal may result. The diffuse component is also treated in detail.

Marouf, E. A.↗

Dynamic Nonlinear Elastic Stability of Helicopter Rotor Blades in Hover and in Forward Flight

Equations for large coupled flap-lag motion of hingeless elastic helicopter blades are consistently derived. Only torsionally-rigid blades excited by quasi-steady aerodynamic loads are considered. The nonlinear equations of motion in the time and space variables are reduced to a system of coupled nonlinear ordinary differential equations with periodic coefficients, using Galerkin's method for the space variables. The nonlinearities present in the equations are those arising from the inclusion of moderately large deflections in the inertia and aerodynamic loading terms. The resulting system of nonlinear equations has been solved, using an asymptotic expansion procedure in multiple time scales. The stability boundaries, amplitudes of nonlinear response, and conditions for existence of limit cycles are obtained analytically. Thus, the different roles played by the forcing function, parametric excitation, and nonlinear coupling in affecting the solution can be easily identified, and the basic physical mechanism of coupled flap-lag response becomes clear. The effect of forward flight is obtained with the requirement of trimmed flight at fixed values of the thrust coefficient.

Friedmann, P.↗

The Primordial Inflation Explorer (PIXIE)

The Primordial Inflation Explorer is an Explorer-class mission to measure the gravity-wave signature of primordial inflation through its distinctive imprint on the linear polarization of the cosmic microwave background. PIXIE uses an innovative optical design to achieve background-limited sensitivity in 400 spectral channels spanning 2.5 decades in frequency from 30 GHz to 6 THz (1 cm to 50 micron wavelength). Multi-moded non-imaging optics feed a polarizing Fourier Transform Spectrometer to produce a set of interference fringes, proportional to the difference spectrum between orthogonal linear polarizations from the two input beams. The differential design and multiple signal modulations spanning 11 orders of magnitude in time combine to reduce the instrumental signature and confusion from unpolarized sources to negligible levels. PIXIE will map the full sky in Stokes I, Q, and U parameters with angular resolution 2.6 deg and sensitivity 0.2 uK per 1 deg square pixel. The principal science goal is the detection and characterization of linear polarization from an inflationary epoch in the early universe, with tensor-to-scalar ratio r <10(exp -3) at 5 standard deviations. In addition, the rich PIXIE data will constrain physical processes ranging from Big Bang cosmology to the nature of the first stars to the physical conditions within the interstellar medium of the Galaxy. We describe the PIXIE instrument and mission architecture needed to detect the signature of an inflationary epoch in the early universe using only 4 semiconductor bolometers.

Kogut, Alan J.↗

Deciphering the Effects of Microgravity Cell by Cell

Forces generated by gravity have a profound impact on the behavior of cells in tissues affecting the course of the cell cycle and differentiation fate of progenitors in mammalian tissues. These cells are contributing to normal tissue regenerative health and defence against disease. In Human space exploration context, it is extremely important to determine spaceflight provoked changes in tissue's regenerational capabilities. Microgravity experienced during spaceflight causes unloading and mechanical disuse on all orthostatic support tissues, therefore impacting stem cell fate and lineage commitment decisions. Investigating how ESCs respond to mechanical stimulation is a platform for fundamental developmental and regeneration research applicable for spaceflight. However, the gene expression programs associatiated with early committment stem cell pathways in response to physical stimulation are not readily known. Single-cell RNA-seq technologies have recently revolutionized the world of molecular biology by providing the capability to assess gene expression pattern within a single cell. Our method isolates and separately barcodes mRNAs from thousands of single cells and sequences their expressomes. Understanding regenerative processes on a molecular level would not only help reduce long-term spaceflight impact on health, but also may enable the development of novel tissue regenerative approaches to tissue degeneration on Earth.

Single cell sequencing↗

Comparative Magma Oceanography

The question of whether the Earth ever passed through a magma ocean stage is of considerable interest. Geochemical evidence strongly suggests that the Moon had a magma ocean and the evidence is mounting that the same was true for Mars. Analyses of martian (SNC) meteorites have yielded insights into the differentiation history of Mars, and consequently, it is interesting to compare that planet to the Earth. Three primary features of Mars contrast strongly to those of the Earth: (i) the extremely ancient ages of the martian core, mantle, and crust (about 4.55 b.y.); (ii) the highly depleted nature of the martian mantle; and (iii) the extreme ranges of Nd isotopic compositions that arise within the crust and depleted mantle. The easiest way to explain the ages and diverse isotopic compositions of martian basalts is to postulate that Mars had an early magma ocean. Cumulates of this magma ocean were later remelted to form the SNC meteorite suite and some of these melts assimilated crustal materials enriched in incompatible elements. The REE pattern of the crust assimilated by these SNC magmas was LREE enriched. If this pattern is typical of the crust as a whole, the martian crust is probably similar in composition to melts generated by small degrees of partial melting (about 5%) of a primitive source. Higher degrees of partial melting would cause the crustal LREE pattern to be essentially flat. In the context of a magma ocean model, where large degrees of partial melting presumably prevailed, the crust would have to be dominated by late-stage, LREE-enriched residual liquids. Regardless of the exact physical setting, Nd and W isotopic evidence indicates that martian geochemical reservoirs must have formed early and that they have not been efficiently remixed since. The important point is that in both the Moon and Mars we see evidence of a magma ocean phase and that we recognize it as such. Several lines of theoretical inference point to an early Earth that was also hot and, perhaps, mostly molten. The Giant Impact hypothesis for the origin of the Moon offers a tremendous input of thermal energy and the same could be true for core formation. And current solar system models favor the formation of a limited number of large (about 1000 km) planetesimals that, upon accreting to Earth, would cause great heating, being lesser versions of the Giant Impact. Several lines of geochemical evidence do not favor this hot early Earth scenario. (i) Terrestrial man-tle xenoliths are sometimes nearly chondritic in their major element compositions, suggesting that these rocks have never been much molten. Large degrees of partial melting probably promote differentiation rather than homogenization. (ii) Unlike the case of Mars, the continental crust probably did not form as a highly fractionated residual liquid from a magma ocean (about 99% crystallization), but, rather, formed in multiple steps. [The simplest model for the formation of continental crust is complicated: (a) about 10% melting of a primitive mantle, making basalt; (b) hydrothermal alteration of that basalt, converting it to greenstone; and (c) 10% partial melting of that greenstone, producing tonalite.] This model is reinforced by the recent observation from old (about 4.1 b.y.) zircons that the early crust formed from an undepleted mantle having a chondritic Lu/Hf ratio. (iii) If the mantle were once differentiated by a magma ocean, the mantle xenolith suite requires that it subsequently be homogenized. The Os isotopic compositions of fertile spinel lherzolites place constraints on the timing of that homogenization. The Os isotopic composition of spinel lherzolites approaches that of chondrites and correlates with elements such as Lu and Al. As Lu and Al concentrations approach those of the primitive mantle, Os isotopic compositions approach chondritic. The Re and Os in these xenoliths were probably added as a late veneer. Thus, the mantle that received the late veneer must have been nearly chondritic in terms of its major elements (excluding Fe). If the mantle that the veneer was mixed into was not al-ready homogenized, then Os isotopes should not correlate with incompatible elements such as Al. Consequently, either early differentiation of the mantle did not occur or the homogenization of this differentiation must have occurred before the late veneer was added. The timing of the late veneer is itself uncertain but presumably postdated core formation at about 4.45 b.y. and did not postdate the 3.8-3.9 b.y. late bombardment of the Moon. This timing based on siderophile elements is consistent with the Hf isotopic evidence cited above. If the Earth, Moon and Mars had magma oceans, the Earth subsequently rehomogenized whereas the Moon and Mars did not. The simplest solution to this observation is that homogenization of igneous differentiates was never necessary on Earth, either because the hypothetical magma ocean never occurred or because this event did not produce mantle differentiation.

Jones, J. H.↗

The general Lie group and similarity solutions for the one-dimensional Vlasov-Maxwell equations

The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov-Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multispecies case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution for a one-species, one-dimensional plasma is one of the general similarity solutions.

Roberts, D.↗