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NASA NTRS1985

Bounding solutions of geometrically nonlinear viscoelastic problems

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Stubstad, J. M.↗

NASA NTRS1986

Bounding solutions of geometrically nonlinear viscoelastic problems

Stubstad, J. M.↗

DOE OSTI2020

In Situ X-Ray Absorption Spectroscopy Disentangles the Roles of Copper and Silver in a Bimetallic Catalyst for the Oxygen Reduction Reaction

Silver-based bimetallic catalysts for the oxygen reduction reaction (ORR) are promising for a wide variety of renewable energy technologies, including alkaline fuel cells and metal-air batteries. The activity of bimetallic catalysts can sometimes surpass that of either constituent element, but the origin of the enhanced performance is still debated. At a given active site, two complementary mechanisms are proposed to explain the performance improvements: the binding energy of intermediate adsorbates can be tuned by direct electronic contributions from the alloying element or by changes in the bond lengths from lattice distortion. To distinguish between these effects and elucidate the respective roles of each element in the bimetallic, it is critical to study catalysts at the molecular scale under reaction conditions. In this work, we use in situ X-ray absorption spectroscopy (XAS) alongside density functional theory (DFT) to show that direct electronic rather than geometric effects are the primary cause of improved ORR activity in a bimetallic CuAg catalyst. Our results indicate that the local bonding as well as the electronic structure of Ag are virtually unchanged by the presence of Cu, whereas the electronic states of Cu in CuAg are significantly altered. DFT calculations support these experimental findings. We show strong evidence that the activity of the bimetallic CuAg catalyst exceeds the sum of the activities of Cu and Ag, not by incremental improvement of the active Ag sites, but by creating highly active Cu-centered catalytic sites. The insight that the main role of Ag in bimetallic catalysts may be to promote its fellow element through local electronic interactions provides a new design principle for engineering the next generation of bimetallic catalysts for the ORR and beyond.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1984

Investigation of the external flow analysis for density measurements at high altitude

The results of analysis performed on the external flow around the shuttle orbiter nose regions at the Shuttle Upper Atmosphere Mass Spectrometer (SUMS) inlet orifice are presented. The purpose of the analysis is to quantitatively characterize the flow conditions to facilitate SUMS flight data reduction and subsequent determination of orbiter aerodynamic force coefficients in the hypersonic rarefied flow regime. Experimental determination of aerodynamic force coefficients requires accurate simultaneous measurement of forces (or acceleration) and dynamic pressure along with independent knowledge of density and velocity. The SUMS provides independent measurement of dynamic pressure; however, it does so indirectly and requires knowledge of the relationship between measured orifice conditions and the dynamic pressure which can only be determined on the basis of molecule or theory for a winged configuration. Monte Carlo direct simulation computer codes were developed for both the flow field solution at the orifice and for the internal orifice flow. These codes were used to study issues associated with geometric modeling of the orbiter nose geometry and the modeling of intermolecular collisions including rotational energy exchange and a preliminary analysis of vibrational excitation and dissociation effects. Data obtained from preliminary simulation runs are presented.

Bienkowski, G. K.↗

NASA NTRS1974

A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface

A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edge formed by perfectly conducting curved or plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresnel integrals, which ensure that the total field is continuous at shadow and reflection boundaries.

Kouyoumjian, R. G.↗

DOE OSTI2024

Null Raychaudhuri: canonical structure and the dressing time

Abstract We initiate a study of gravity focusing on generic null hypersurfaces, non-perturbatively in the Newton coupling. We present an off-shell account of the extended phase space of the theory, which includes the expected spin-2 data as well as spin-0, spin-1 and arbitrary matter degrees of freedom. We construct the charges and the corresponding kinematic Poisson brackets, employing a Beltrami parameterization of the spin-2 modes. We explicitly show that the constraint algebra closes, the details of which depend on the non-perturbative mixing between spin-0 and spin-2 modes. Finally we show that the spin zero sector encodes a notion of a clock, called dressing time, which is dynamical and conjugate to the constraint. It is well-known that the null Raychaudhuri equation describes how the geometric data of a null hypersurface evolve in null time in response to gravitational radiation and external matter. Our analysis leads to three complementary viewpoints on this equation. First, it can be understood as a Carrollian stress tensor conservation equation. Second, we construct spin-0, spin-2 and matter stress tensors that act as generators of null time reparametrizations for each sector. This leads to the perspective that the null Raychaudhuri equation can be understood as imposing that the sum of CFT-like stress tensors vanishes. Third, we solve the Raychaudhuri constraint non-perturbatively. The solution relates the dressing time to the spin-2 and matter boost charge operators. Finally we establish that the corner charge corresponding to the boost operator in the dressing time frame is monotonic. These results show that the notion of an observer can be thought of as emerging from the gravitational degrees of freedom themselves. We briefly mention that the construction offers new insights into focusing conjectures.

Physics↗

NASA NTRS2001

Applicability of the single equivalent point dipole model to represent a spatially distributed bio-electrical source

Although the single equivalent point dipole model has been used to represent well-localised bio-electrical sources, in realistic situations the source is distributed. Consequently, position estimates of point dipoles determined by inverse algorithms suffer from systematic error due to the non-exact applicability of the inverse model. In realistic situations, this systematic error cannot be avoided, a limitation that is independent of the complexity of the torso model used. This study quantitatively investigates the intrinsic limitations in the assignment of a location to the equivalent dipole due to distributed electrical source. To simulate arrhythmic activity in the heart, a model of a wave of depolarisation spreading from a focal source over the surface of a spherical shell is used. The activity is represented by a sequence of concentric belt sources (obtained by slicing the shell with a sequence of parallel plane pairs), with constant dipole moment per unit length (circumferentially) directed parallel to the propagation direction. The distributed source is represented by N dipoles at equal arc lengths along the belt. The sum of the dipole potentials is calculated at predefined electrode locations. The inverse problem involves finding a single equivalent point dipole that best reproduces the electrode potentials due to the distributed source. The inverse problem is implemented by minimising the chi2 per degree of freedom. It is found that the trajectory traced by the equivalent dipole is sensitive to the location of the spherical shell relative to the fixed electrodes. It is shown that this trajectory does not coincide with the sequence of geometrical centres of the consecutive belt sources. For distributed sources within a bounded spherical medium, displaced from the sphere's centre by 40% of the sphere's radius, it is found that the error in the equivalent dipole location varies from 3 to 20% for sources with size between 5 and 50% of the sphere's radius. Finally, a method is devised to obtain the size of the distributed source during the cardiac cycle.

NASA Discipline Cardiopulmonary↗

NASA NTRS1975

Light aircraft lift, drag, and moment prediction: A review and analysis

The historical development of analytical methods for predicting the lift, drag, and pitching moment of complete light aircraft configurations in cruising flight is reviewed. Theoretical methods, based in part on techniques described in the literature and in part on original work, are developed. These methods form the basis for understanding the computer programs given to: (1) compute the lift, drag, and moment of conventional airfoils, (2) extend these two-dimensional characteristics to three dimensions for moderate-to-high aspect ratio unswept wings, (3) plot complete configurations, (4) convert the fuselage geometric data to the correct input format, (5) compute the fuselage lift and drag, (6) compute the lift and moment of symmetrical airfoils to M = 1.0 by a simplified semi-empirical procedure, and (7) compute, in closed form, the pressure distribution over a prolate spheroid at alpha = 0. Comparisons of the predictions with experiment indicate excellent lift and drag agreement for conventional airfoils and wings. Limited comparisons of body-alone drag characteristics yield reasonable agreement. Also included are discussions for interference effects and techniques for summing the results above to obtain predictions for complete configurations.

Smetana, F. O.↗

DOE OSTI2025

Low-Density Parity-Check Stabilizer Codes as Gapped Quantum Phases: Stability under Graph-Local Perturbations

We generalize the proof of stability of topological order, due to Bravyi, Hastings, and Michalakis, to stabilizer Hamiltonians corresponding to low-density parity-check (LDPC) codes without the restriction of geometric locality in Euclidean space. We consider Hamiltonians 𝐻 0 defined by ⟦𝑁,𝐾,𝑑⟧ LDPC codes, which obey certain topological quantum order conditions: (i) code distance 𝑑 ≥ 𝑐⁢log (𝑁), implying local indistinguishability of ground states, and (ii) a mild condition on local and global compatibility of ground states—these include good quantum LDPC codes and the toric code on a hyperbolic lattice, among others. We consider stability under weak perturbations that are quasilocal on the interaction graph defined by 𝐻 0 and that can be represented as sums of bounded-norm terms. As long as the local perturbation strength is smaller than a finite constant, we show that the perturbed Hamiltonian has well-defined spectral bands originating from the 𝑂⁡(1) smallest eigenvalues of 𝐻 0 . The band originating from the smallest eigenvalue has 2 𝐾 states, is separated from the rest of the spectrum by a finite energy gap, and has exponentially narrow bandwidth 𝛿 =𝐶⁢𝑁⁢𝑒 −Θ⁡(𝑑) , which is tighter than the best-known bounds even in the Euclidean case. We also obtain that the new ground-state subspace is related to the initial-code subspace by a quasilocal unitary, allowing one to relate their physical properties. Our proof uses an iterative procedure that performs successive rotations to eliminate non-frustration-free terms in the Hamiltonian. Our results extend to quantum Hamiltonians built from classical LDPC codes, which give rise to stable symmetry-breaking phases. These results show that LDPC codes very generally define stable gapped quantum phases, even in the non-Euclidean setting, initiating a systematic study of such phases of matter.

mathematical physics↗

NASA NTRS1997

Calculation of Heavy Ion Inactivation and Mutation Rates in Radial Dose Model of Track Structure

In the track structure model, the inactivation cross section is found by summing an inactivation probability over all impact parameters from the ion to the sensitive sites within the cell nucleus. The inactivation probability is evaluated by using the dose response of the system to gamma rays and the radial dose of the ions and may be equal to unity at small impact parameters. We apply the track structure model to recent data with heavy ion beams irradiating biological samples of E. Coli, B. Subtilis spores, and Chinese hamster (V79) cells. Heavy ions have observed cross sections for inactivation that approach and sometimes exceed the geometric size of the cell nucleus. We show how the effects of inactivation may be taken into account in the evaluation of the mutation cross sections in the track structure model through correlation of sites for gene mutation and cell inactivation. The model is fit to available data for HPRT (hypoxanthine guanine phosphoribosyl transferase) mutations in V79 cells, and good agreement is found. Calculations show the high probability for mutation by relativistic ions due to the radial extension of ions track from delta rays. The effects of inactivation on mutation rates make it very unlikely that a single parameter such as LET (linear energy transfer) can be used to specify radiation quality for heavy ion bombardment.

Cucinotta, Francis A.↗

NASA NTRS1980

Computer prediction of large reflector antenna radiation properties

A FORTRAN program for calculating reflector antenna radiation patterns was rewritten and extended to include reflectors composed of a number of panels. These individual panels must be analytic surfaces. The theoretical foundation for the program is as follows: Geometrical optics techniques are used to trace rays from a feed antenna to the reflector surface and back to a mathematical plane just in front of the reflector. The resulting tangential electric field distribution, assumed to be the only source of forward radiation, is integrated numerically to calculate the radiation pattern for a desired set of angles. When the reflector is composed of more than one panel, each panel is treated as a separated antenna, the ray-tracing procedure and integration being repeated for each panel. The results of the individual aperture plane integrations are stored and summed to yield the relative electric field strength over the angles of interest. An example and several test cases are included to demonstrate the use of the program and verify the new method of computation.

Botula, A.↗

DOE OSTI2025

Multistate Geometry of Shift Current and Polarization

The quantum metric and Berry curvature capture essential properties of nontrivial Bloch states and underpin many fascinating phenomena. However, it becomes increasingly evident that a more comprehensive understanding of quantum state geometry is necessary to explain properties involving Bloch states of multiple bands, such as optical transitions. To this end, we employ quantum state projectors to develop an explicitly gauge-invariant formalism and demonstrate its power with applications to nonlinear optics and the theory of electronic polarization. We provide a simple expression for the shift current that resolves its precise relation to the moments of electronic polarization, clarifies the treatment of band degeneracies, and reveals its decomposition into the sum of the skewness of the occupied states and intrinsically multistate geometry. The projector approach is applied to calculate nonlinear optical properties of transition metal dichalcogenides (TMDs) layers, using previously calculated minimal tight-binding models, and demonstrated analytically on a three-band generalization of the Rice-Mele chain to elucidate the different contributions. We close with comments on further applications of the projector operator approach to multistate geometry.

electric polarization↗

DOE OSTI2022

Self-equilibrated backstresses induce compensation between hardening and softening: Micromechanical and microstructural features

For crystal plasticity formulation neglecting the strain gradients at the dislocation scale, backstresses are necessary to satisfy the mesoscopic stress equilibrium and strain compatibility requirements. Backstresses in a material point and those between neighboring points are treated separately. Physically backstresses can dynamically induce either hardening or softening effects to adjust the dislocation hardening of slip systems, whereas the sum of the stresses resulting in backstresses in the representative volume element (RVE) is zero. Backstress hardening suppresses certain slip activities, while backstress softening triggers excess dislocations. A two-phase brass is studied. Backstresses make the hard phase deform smaller and the soft phase deform more than those without employing backstresses in a model. In the former, more homogeneous lattice strain and higher yield stress are obtained. Backstress has limited effects on the evolution of the critical resolved shear stress and crystallographic texture. Furthermore, it is a major cause of the banded structures featuring sharp crystallographic contrasts which are not parallel to the slip planes. Tests indicate that backstress induces a serrated behavior at the early stages of deformation and induces the geometrically necessary bands (GNBs), which are parallel to the macroscopic axes.

36 MATERIALS SCIENCE↗

NASA NTRS2003

Using Correlated Photons to Suppress Background Noise

A proposed method of suppressing the effect of background noise in an optical communication system would exploit the transmission and reception of correlated photons at the receiver. The method would not afford any advantage in a system in which performance is limited by shot noise. However, if the performance of the system is limited by background noise (e.g., sunlight in the case of a free-space optical communication system or incoherently scattered in-band photons in the case of a fiber-optic communication system), then the proposed method could offer an advantage: the proposed method would make it possible to achieve a signal-to-noise ratio (S/N) significantly greater than that of an otherwise equivalent background- noise-limited optical communication system based on the classical transmission and reception of uncorrelated photons. The figure schematically depicts a classical optical-communication system and a system according to the proposed method. In the classical system, a modulated laser beam is transmitted along an optical path to a receiver, the optics of which include a narrow-band-pass filter that suppresses some of the background noise. A photodetector in the receiver detects the laser-beam and background photons, most or all of which are uncorrelated. In the proposed system, correlated photons would be generated at the transmitter by making a modulated laser beam pass through a nonlinear parametric down-conversion crystal. The sum of frequencies of the correlated photons in each pair would equal the frequency of the incident photon from which they were generated. As in the classical system, the correlated photons would travel along an optical path to a receiver, where they would be band-pass filtered and detected. Unlike in the classical system, the photodetector in the receiver in this system would be one that intrinsically favors the detection of pairs of correlated photons over the detection of uncorrelated photons. Even though there would be no way of knowing the precise location and time of creation of a given pair of correlated signal photons in the nonlinear down-conversion crystal, the fact that the photons are necessarily created at the same time and place makes it possible to utilize conventional geometrical imaging optics to reunite the photons in coincidence in the receiving photodetector. Because most or all of the signal photons would be correlated while most or all of the noise photons would be uncorrelated, the S/N would be correspondingly enhanced in the photodetector output. An additional advantage to be gained by use of a correlated-photon detector is that it could be capable of recovering the signal even in the presence of background light so bright that a classical uncorrelated-photon detector would be saturated. A blocked-impurity-band (BIB) photodetector that preferentially detects pairs of correlated photons over uncorrelated ones and that operates at a quantum efficiency of 88 percent is commercially available. This detector must be cooled to the temperature of liquid helium to obtain the desired low-noise performance. It is planned to use this detector in a proof-of-principle demonstration. In addition, it may be possible to develop GaN-based photodetectors that could offer the desired low-noise performance at room temperature.

Jackson, Deborah↗

DOE OSTI2023

A spectral metric for collider geometry

By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an idealized celestial sphere and then define the metric in terms of optimal transport in two dimensions. In this paper, we advocate for representing events in terms of a spectral function that encodes pairwise particle angles and products of particle energies, which enables a metric distance defined in terms of one-dimensional optimal transport. This approach has the advantage of automatically incorporating obvious isometries of the data, like rotations about the colliding beam axis. It also facilitates first-principles calculations, since there are simple closed-form expressions for optimal transport in one dimension. Up to isometries and event sets of measure zero, the spectral representation is unique, so the metric on the space of spectral functions is a metric on the space of events. At lowest order in perturbation theory in electron-positron collisions, our metric is simply the summed squared invariant masses of the two event hemispheres. Going to higher orders, we present predictions for the distribution of metric distances between jets in fixed-order and resummed perturbation theory as well as in parton-shower generators. Finally, we speculate on whether the spectral approach could furnish a useful metric on the space of quantum field theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2006

System Finds Horizontal Location of Center of Gravity

An instrumentation system rapidly and repeatedly determines the horizontal location of the center of gravity of a laboratory vehicle that slides horizontally on three air bearings (see Figure 1). Typically, knowledge of the horizontal center-of-mass location of such a vehicle is needed in order to balance the vehicle properly for an experiment and/or to assess the dynamic behavior of the vehicle. The system includes a load cell above each air bearing, electronic circuits that generate digital readings of the weight on each load cell, and a computer equipped with software that processes the readings. The total weight and, hence, the mass of the vehicle are computed from the sum of the load-cell weight readings. Then the horizontal position of the center of gravity is calculated straightforwardly as the weighted sum of the known position vectors of the air bearings, the contribution of each bearing being proportional to the weight on that bearing. In the initial application for which this system was devised, the center- of-mass calculation is particularly simple because the air bearings are located at corners of an equilateral triangle. However, the system is not restricted to this simple geometry. The system acquires and processes weight readings at a rate of 800 Hz for each load cell. The total weight and the horizontal location of the center of gravity are updated at a rate of 800/3 approx. equals 267 Hz. In a typical application, a technician would use the center-of-mass output of this instrumentation system as a guide to the manual placement of small weights on the vehicle to shift the center of gravity to a desired horizontal position. Usually, the desired horizontal position is that of the geometric center. Alternatively, this instrumentation system could be used to provide position feedback for a control system that would cause weights to be shifted automatically (see Figure 2) in an effort to keep the center of gravity at the geometric center.

Johnston, Albert S.↗

NASA NTRS1995

Contact and pressure balance structures in two-fluid cosmic-ray hydrodynamics

The role of cosmic-ray-modified contact discontinuities and pressure balance structures in two-fluid cosmic-ray hydrodynamics in one Cartesian space dimension are investigated by means of analytic and numerical solution examples, as well as by weakly nonlinear asymptotics. The fundamental wave modes of the two-fluid cosmic-ray hydrodynamic equations in the long-wavelength limit consist of the backward and forward propagating cosmic-ray-modified sound waves, with sound speed dependent on both the cosmic-ray and thermal gas pressures; the contact discontinuity; and a pressure balance mode in which the sum ofthe cosmic ray and thermal gas pressure perturbations is zero. The pressure balance mode, like the contact discontinuity is advected with the background flow. The interaction of the pressure balance mode with the contact discontinuity is investigated by means of the method of multiple scales. The thermal gas and cosmic-ray pressure perturbations satisfy a linear diffusion equation, and entropy perturbations arising from nonisentropic initial conditions for the thermal gas are frozen into the fluid. The contact discontinuity and pressure balance eigenmodes both admit nonzero perturbations in the thermal gas, whereas the cosmic-ray-modified sound waves are isentropic. The total entropy perturbation is shared between the contact discontinuity and pressure balance eigenmodes, and examples are given in which there is a transfer of entropy between the two modes. In particular, N-wave type density disturbances are obtained which arise as a result of the entropy transfer between the two modes. A weakly nonlinear geometric optics perturbation expansion is used to study the long timescale evolution of the short-wavelength entropy wave and the thermal gas sound waves in a slowly varying, large-scale background flow. The weakly nonlinear geometric optics expansion is also used to generalize previous studies of squeezing instability for short-wavelength sound waves in the two fluid model, by including a weakly nonlinear wave steepening term that leads to shock formation, as well as the effect of long time and space dependence of the background flow. Implications of cosmic-ray-modified pressure balance structures and contact discontinuities in models of the interaction of traveling interplanetary shocks and compression and rarefraction waves with the solar wind termination shock are briefly discussed.

Webb, G. M.↗

NASA NTRS2008

Model of Image Artifacts from Dust Particles

A mathematical model of image artifacts produced by dust particles on lenses has been derived. Machine-vision systems often have to work with camera lenses that become dusty during use. Dust particles on the front surface of a lens produce image artifacts that can potentially affect the performance of a machine-vision algorithm. The present model satisfies a need for a means of synthesizing dust image artifacts for testing machine-vision algorithms for robustness (or the lack thereof) in the presence of dust on lenses. A dust particle can absorb light or scatter light out of some pixels, thereby giving rise to a dark dust artifact. It can also scatter light into other pixels, thereby giving rise to a bright dust artifact. For the sake of simplicity, this model deals only with dark dust artifacts. The model effectively represents dark dust artifacts as an attenuation image consisting of an array of diffuse darkened spots centered at image locations corresponding to the locations of dust particles. The dust artifacts are computationally incorporated into a given test image by simply multiplying the brightness value of each pixel by a transmission factor that incorporates the factor of attenuation, by dust particles, of the light incident on that pixel. With respect to computation of the attenuation and transmission factors, the model is based on a first-order geometric (ray)-optics treatment of the shadows cast by dust particles on the image detector. In this model, the light collected by a pixel is deemed to be confined to a pair of cones defined by the location of the pixel s image in object space, the entrance pupil of the lens, and the location of the pixel in the image plane (see Figure 1). For simplicity, it is assumed that the size of a dust particle is somewhat less than the diameter, at the front surface of the lens, of any collection cone containing all or part of that dust particle. Under this assumption, the shape of any individual dust particle artifact is the shape (typically, circular) of the aperture, and the contribution of the particle to the attenuation factor for a given pixel is the fraction of the cross-sectional area of the collection cone occupied by the particle. Assuming that dust particles do not overlap, the net transmission factor for a given pixel is calculated as one minus the sum of attenuation factors contributed by all dust particles affecting that pixel. In a test, the model was used to synthesize attenuation images for random distributions of dust particles on the front surface of a lens at various relative aperture (F-number) settings. As shown in Figure 2, the attenuation images resembled dust artifacts in real test images recorded while the lens was aimed at a white target.

Willson, Reg↗