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DOE OSTI2020

Matter couplings and equivalence principles for soft scalars

Scalar effective field theories with enhanced soft limits behave in many ways like gauge theories and gravity. In particular, symmetries fix the structure of interactions and the tree-level S-matrix in both types of theories. We explore how this analogy persists in the presence of matter by considering theories with additional fields coupled to the Dirac-Born-Infeld (DBI) scalar or the special galileon in a way that is consistent with their symmetries. Using purely on-shell arguments, we show that these theories obey analogues of the S-matrix equivalence principle whereby all matter fields must couple to the DBI scalar or the special galileon through a particular quartic vertex with a universal coupling. These equivalence principles imply the universality of the leading double soft theorems in these theories, which are scalar analogues of Weinberg’s gravitational soft theorem, and can be used to rule out interactions with massless higher-spin fields when combined with analogues of the generalized Weinberg-Witten theorem. We verify in several examples that amplitudes with external matter fields nontrivially exhibit enhanced single soft limits and we show that such amplitudes can be constructed using soft recursion relations when they have sufficiently many external DBI or special galileon legs, including amplitudes with massive higher-spin fields. As part of our analysis we construct a recently conjectured special galileon-vector effective field theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1984

Thermal emission of nonspherical particles

The thermal emission of nonspherical particles is studied by applying the fluctuation dissipation theorem to calculate the Stokes' vector source terms in radiative transfer theory. Generally, all the four Stokes' parameters in the source term are nonzero and are proportional to the absorption coefficient in the backward direction. The measurements of active and passive remote sensing are related by showing that within the framework of radiative transfer theory, the emissivity of vertically and horizontally polarized waves can be expressed in terms of the bistatic scattering coefficients in the usual manner. In addition, the emissions of the third and fourth Stokes' parameters are also expressed in terms of bistatic scattering coefficients.

Tsang, L.↗

DOE OSTI2020

Perspective on Kramers symmetry breaking and restoration in relativistic electronic structure methods for open-shell systems

Without rigorous symmetry constraints, solutions to approximate electronic structure methods may artificially break symmetry. In the case of the relativistic electronic structure, if time-reversal symmetry is not enforced in calculations of molecules not subject to a magnetic field, it is possible to artificially break Kramers degeneracy in open shell systems. This leads to a description of excited states that may be qualitatively incorrect. Despite this, different electronic structure methods to incorporate correlation and excited states can partially restore Kramers degeneracy from a broken symmetry solution. For single-reference techniques, the inclusion of double and possibly triple excitations in the ground state provides much of the needed correction. Formally, however, this imbalanced treatment of the Kramers-paired spaces is a multi-reference problem, and so methods such as complete-active-space methods perform much better at recovering much of the correct symmetry by state averaging. Using multi-reference configuration interaction, any additional corrections can be obtained as the solution approaches the full configuration interaction limit. A recently proposed “Kramers contamination” value is also used to assess the magnitude of symmetry breaking.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2001

Crack Turning Mechanics of Composite Wing Skin Panels

The safety of future composite wing skin integral stiffener panels requires a full understanding of failure mechanisms of these damage tolerance critical structures under both in-plane and bending loads. Of primary interest is to derive mathematical models using fracture mechanics in anisotropic cracked plate structures, to assess the crack turning mechanisms, and thereby to enhance the residual strength in the integral stiffener composite structures. The use of fracture mechanics to assess the failure behavior in a cracked structure requires the identification of critical fracture parameters which govern the severity of stress and deformation field ahead of the flaw, and which can be evaluated using information obtained from the flaw tip. In the three-year grant, the crack-tip fields under plane deformation, crack-tip fields for anisotropic plates and anisotropic shells have been obtained. In addition, methods for determining the stress intensity factors, energy release rate, and the T-stresses have been proposed and verified. The research accomplishments can be summarized as follows: (1) Under plane deformation in anisotropic solids, the asymptotic crack-tip fields have been obtained using Stroh formalism; (2) The T-stress and the coefficient of the second term for sigma(sub y), g(sub 32), have been obtained using path-independent integral, the J-integral and Betti's reciprocal theorem together with auxiliary fields; (3) With experimental data performed by NASA, analyses indicated that the mode-I critical stress intensity factor K(sub Q) provides a satisfactory characterization of fracture initiation for a given laminate thickness, provided the failure is fiber-dominated and crack extends in a self-similar manner; (4) The high constraint specimens, especially for CT specimens, due to large T-stress and large magnitude of negative g(sub 32) term may be expected to inhibit the crack extension in the same plane and promote crack turning; (5) Crack turning out of crack plane in generally anisotropic solids under plane deformation has been studied; (6) The role of T-stress and the higher-order term of sigma(sub y) on the crack turning and stability of the kinked crack has been quantified; (7) Asymptotic crack-tip fields including the effect of transverse shear deformation (Reissner plate theory) in an anisotropic plate under bending, twisting moments, and transverse shear loads has been presented; (8) The expression of the path-independent J-integral in terms of the generalized stress and strain has been derived; (9) Asymptotic crack-tip fields including the effect of transverse shear deformation (Reissner shallow shell theory) in a general anisotropic shell has been developed; (10) The Stroh formalism was used to characterize the crack tip fields in shells up to the second term and the energy release rate was expressed in a very compact form.

Yuan, F. G.↗

NASA NTRS2000

An Improved Elastic and Nonelastic Neutron Transport Algorithm for Space Radiation

A neutron transport algorithm including both elastic and nonelastic particle interaction processes for use in space radiation protection for arbitrary shield material is developed. The algorithm is based upon a multiple energy grouping and analysis of the straight-ahead Boltzmann equation by using a mean value theorem for integrals. The algorithm is then coupled to the Langley HZETRN code through a bidirectional neutron evaporation source term. Evaluation of the neutron fluence generated by the solar particle event of February 23, 1956, for an aluminum water shield-target configuration is then compared with MCNPX and LAHET Monte Carlo calculations for the same shield-target configuration. With the Monte Carlo calculation as a benchmark, the algorithm developed in this paper showed a great improvement in results over the unmodified HZETRN solution. In addition, a high-energy bidirectional neutron source based on a formula by Ranft showed even further improvement of the fluence results over previous results near the front of the water target where diffusion out the front surface is important. Effects of improved interaction cross sections are modest compared with the addition of the high-energy bidirectional source terms.

Clowdsley, Martha S.↗

NASA NTRS1975

A Theoretical Investigation of the Input Characteristics of a Rectangular Cavity-Backed Slot Antenna

Equations which represent the magnetic and electric stored energies are derived for an infinite section of rectangular waveguide and a rectangular cavity. These representations which are referred to as being physically observable are obtained by considering the difference in the volume integrals appearing in the complex Poynting theorem. It is shown that the physically observable stored energies are determined by the field components that vanish in a reference plane outside the aperture. These physically observable representations are used to compute the input admittance of a rectangular cavity-backed slot antenna in which a single propagating wave is assumed to exist in the cavity. The slot is excited by a voltage source connected across its center; a sinusoidal distribution is assumed in the slot. Input-admittance calculations are compared with measured data. In addition, input-admittance curves as a function of electrical slot length are presented for several size cavities. For the rectangular cavity backed slot antenna, the quality factor and relative bandwidth were computed independently by using these energy relationships. It is shown that the asymptotic relationship which is usually assumed to exist between the quality bandwidth and the reciprocal of relative bandwidth is equally valid for the rectangular cavity backed slot antenna.

Cockrell, C. R.↗

NASA NTRS2007

Symmetry, Statistics and Structure in MHD Turbulence

Here, we examine homogeneous MHD turbulence in terms of truncated Fourier series. The ideal MHD equations and the associated statistical theory of absolute equilibrium ensembles are symmetric under P, C and T. However, the presence of invariant helicities, which are pseudoscalars under P and C, dynamically breaks this symmetry. This occurs because the surface of constant energy in phase space has disjoint parts, called components: while ensemble averages are taken over all components, a dynamical phase trajectory is confined to only one component. As the Birkhoff-Khinchin theorem tells us, ideal MHD turbulence is thus non-ergodic. This non-ergodicity manifests itself in low-wave number Fourier modes that have large mean values (while absolute ensemble theory predicts mean values of zero). Therefore, we have coherent structure in ideal MHD turbulence. The level of non-ergodicity and amount of energy contained in the associated coherent structure depends on the values of the helicities, as well as on the presence, or not, of a mean magnetic field and/or overall rotation. In addition to the well known cross and magnetic helicities, we also present a new invariant, which we call the parallel helicity, since it occurs when mean field and rotation axis are aligned. The question of applicability of these results to real (i.e., dissipative) MHD turbulence is also examined. Several long-time numerical simulations on a 64(exp 3) grid are given as examples. It is seen that coherent structure begins to form before decay dominates over nonlinearity. The connection of these results with inverse spectral cascades, selective decay, and magnetic dynamos is also discussed.

Shebalin, John V.↗

NASA NTRS2002

Self-Consistent Magnetosphere-Ionosphere Coupling and Associated Plasma Energization Processes

Magnetosphere-Ionosphere (MI) coupling and associated with this process electron and ion energization processes have interested scientists for decades and, in spite of experimental and theoretical research efforts, are still ones of the least well known dynamic processes in space plasma physics. The reason for this is that the numerous physical processes associated with MI coupling occur over multiple spatial lengths and temporal scales. One typical example of MI coupling is large scale ring current (RC) electrodynamic coupling that includes calculation of the magnetospheric electric field that is consistent with the ring current (RC) distribution. A general scheme for numerical simulation of such large-scale magnetosphere-ionosphere coupling processes has been presented earlier in many works. The mathematical formulation of these models are based on "modified frozen-in flux theorem" for an ensemble of adiabatically drifting particles in the magnetosphere. By tracking the flow of particles through the inner magnetosphere, the bounce-averaged phase space density of the hot ions and electrons can be reconstructed and the magnetospheric electric field can be calculated such that it is consistent with the particle distribution in the magnetosphere. The new a self-consistent ring current model has been developed that couples electron and ion magnetospheric dynamics with calculation of electric field. Two new features were taken into account in addition to the RC ions, we solve an electron kinetic equation in our model, self-consistently including these results in the solution. Second, using different analytical relationships, we calculate the height integrated ionospheric conductances as the function of precipitated high energy magnetospheric electrons and ions as produced by our model. This results in fundamental changes to the electric potential pattern in the inner magnetosphere, with a smaller Alfven boundary than previous potential formulations would predict but one consistent with recent satellite observations. This leads to deeper penetration of the plasma sheet ions and electrons into the inner magnetosphere and more effective ring current ions and electron energization.

Khazanov, G. V.↗

NASA NTRSDate not supplied

Towards Formalization of Advanced Linear Algebra with Applications to Dynamical Systems using PVS

Linear Algebra is essential for numerous aerospace problems of interest. Formal reasoning about hybrid systems that contain variables modeled by differential equations rely on concepts from Linear Algebra such as eigenvalues, matrix decompositions, and matrix valued functions. For example, the long-term dynamics of a system of differential equations depend on the stability/instability of its equilibrium points, which often reduces to an eigenvalue problem. This talk will embark on a quest to formalize theorems and results about eigenvalues and eigenvectors using PVS. We shall start our journey with 2 x 2 complex matrices, where we will apply our PVS code to a simple example of a dynamical system. Since it can be difficult or impossible to give simple expressions of eigenvalues for larger matrices (i.e. 5 x 5 or higher), we then move towards specifying the power method for verified computation of eigenvalue approximations in PVS. This effort requires development of multivariate complex arithmetic. At the end of the day, having such additions to the PVS NASA libraries will help move towards the use of formal methods to verify concepts of control theory and system level verification.

Linear Algebra↗

DOE OSTI2024

Modeling powder spreadability in powder-based processes using the discrete element method

Powder-bed fusion (PBF) processes refer to a subset of Additive Manufacturing (AM) techniques where powder is spread on the build-plate before melting (by a laser or electron beam). While PBF processes are attractive due to their ability for realizing complex structures that are either difficult or impossible to create through conventional means, the parts fabricated with these techniques can exhibit defects such as pores, inclusions, and excessive surface roughness. To minimize these defects, much research has been dedicated towards process maturation by optimizing laser or electron beam parameters. However, these developmental efforts typically do not address the recoating process where achieving dense and uniform layers of powder is a necessity for ensuring process repeatability and part quality. While the recoating process can be studied through experimentation, the dynamics of particle movement are difficult to analyze experimentally. Therefore, here, in this study, powder spreading in PBF was simulated through the Discrete Element Method (DEM) to elucidate the mechanisms that control powder-bed quality. Utilizing the Buckingham Pi theorem, a dimensionless metric referred to as the spreading index is developed that combines powder-bed density, roughness, and particle size to assess the quality of powder layers. The formulated spreading index is then related to several dimensionless quantities that provide insight into the mechanisms dominating powder spreading in PBF. The DEM simulations conducted in this work focused on the scenario where powder is spread onto an existing powder bed and revealed that a reduction in the recoating velocity causes an increase in the spreading index while little to no impact on the spreading index was observed when varying layer thickness from 30 μm to 75 μm.Particle size effects on the powder-bed quality were also investigated.

36 MATERIALS SCIENCE↗

NASA NTRS1985

Geocoronal structure - The effects of solar radiation pressure and the plasmasphere interaction

The theory of planetary exospheres is extended to incorporate solar radiation pressure in a rigorous manner, and an evaporative geocoronal prototype (classical, motionless exobase) is constructed using Liouville's theorem. Model calculations for density and kinetic temperature at points along the earth-sun axis (solar and antisolar directions) reveal an extensive satellite component, comprising approximately 2/3 of the total hydrogen density near 10 earth radii, and a temperature profile suggestive of an isotropic quasi-Maxwellian velocity distribution for the bound component. A geotail is also evident as an enhancement of the density at local midnight compared to local noon that increases outward (from approximately 25 percent at 10 earth radii to over 60 percent at 20 earth radii). Additional mechanisms acting upon the geocorona alter the basic evaporative case in notable ways. Solar ionization has been included in a simple fashion; the effect is to partially deplete the density without otherwise altering the structure. Interaction with a simple plasmasphere via the Boltzmann equation results in 'heating' the geocorona and enhancing the escape flux at the expense of the density of the bound component, an effect not appreciated in earlier studies; the geotail survives this interaction.

Bishop, J.↗

DOE OSTI2020

Data-Consistent Inversion for Stochastic Input-to-Output Maps

Data-consistent inversion is a recently developed measure-theoretic framework for solving a stochastic inverse problem involving models of physical systems. The goal is to construct a probability measure on model inputs (i.e., parameters of interest) whose associated push-forward measure matches (i.e., is consistent with) a probability measure on the observable outputs of the model (i.e., quantities of interest). Previous implementations required the map from parameters of interest to quantities of interest to be deterministic. This work generalizes this framework for maps that are stochastic, i.e., contain uncertainties and variation not explainable by variations in uncertain parameters of interest. Generalizations of previous theorems of existence, uniqueness, and stability of the data-consistent solution are provided while new theoretical results address the stability of marginals on parameters of interest. A notable aspect of the algorithmic generalization is the ability to query the solution to generate independent identically distributed samples of the parameters of interest without requiring knowledge of the so-called stochastic parameters. This work therefore extends the applicability of the data-consistent inversion framework to a much wider class of problems. This includes those based on purely experimental and field data where only a subset of conditions are either controllable or can be documented between experiments while the underlying physics, measurement errors, and any additional covariates are either uncertain or not accounted for by the researcher. Finally, numerical examples demonstrate application of this approach to systems with stochastic sources of uncertainties embedded within the modeling of a system and a numerical diagnostic is summarized that is useful for determining if a key assumption is verified among competing choices of stochastic maps.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Anti-symmetric representation of the extended magnetohydrodynamic equations

We introduce the anti-symmetric representation of the extended magnetohydrodynamic (MHD) equations. In this representation, the use of the anti-symmetric flux operator (∇·ν+ν·∇) results in conservation theorems with discrete analogs. Inherently robust numerical applications are achieved with little effort, and conservation to machine precision is possible with simple numerical schemes. Starting from the two-fluid equations, we construct a single-fluid MHD model based on generalized center-of-mass variables for the mass (√ρ), momentum (√ρν), and pressure (√ p ). This model is shown to possess identical conservation properties to the two-fluid system, with the only restriction being the use of a single temperature. Common approximations to the Braginskii heat fluxes and to the gyroviscous stress tensor are cast into our representation for convenience. The discrete conservation properties are verified using the classic Orszag–Tang vortex problem. In addition to the favorable mass, momentum, and energy conservation properties, the time reversibility of the simulations is demonstrated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1992

Conservative-variable average states for equilibrium gas multi-dimensional fluxes

Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average Jacobian, and it is shown that the average eigenvalues, Mach number, and eigenvectors may not coincide with their classical pointwise counterparts. A general equilibrium-gas equation of state is then discussed for conservative-variable computational fluid dynamics (CFD) Euler formulations. The associated derivations lead to unique compatibility relations that constrain the pressure Jacobian derivatives. Thereafter, alternative forms for the pressure variation and average sound speed are developed in terms of two average pressure Jacobian derivatives. Significantly, no additional degree of freedom exists in the determination of these two average partial derivatives of pressure. Therefore, they are simultaneously computed exactly without any auxiliary relation, hence without any geometric solution projection or arbitrary scale factors. Several alternative formulations are then compared and key differences highlighted with emphasis on the determination of the pressure variation and average sound speed. The relevant underlying assumptions are identified, including some subtle approximations that are inherently employed in published average-state procedures. Finally, a representative test case is discussed for which an intrinsically exact average state is determined. This exact state is then compared with the predictions of recent methods, and their inherent approximations are appropriately quantified.

Iannelli, G. S.↗

DOE OSTI2026

Boundary-induced classical generalized Gibbs ensemble with angular momentum

We investigate how confinement geometry leads to the emergence of a Generalized Gibbs Ensemble (GGE) in classical systems. Unlike the standard Gibbs ensemble, the GGE includes additional conserved quantities, such as angular momentum, that arise from boundary-induced symmetries. Using analytical arguments based on the maximum entropy principle, we show that circular boundaries preserve angular momentum and drive the system toward a chiral, non-ergodic GGE that violates time-reversal symmetry. This ensemble differs fundamentally from the Gibbs case, producing near-boundary condensation and revealing how geometry alone can alter thermal equilibration. To quantify these effects, we introduce an order parameter measuring deviations from Gibbs behavior and demonstrate that conventional Monte Carlo methods must incorporate angular momentum conservation under such conditions. Our study highlights how geometric constraints shape non-equilibrium statistical ensembles and lead to subtle departures from the Bohr-van Leeuwen theorem. These predictions are validated through detailed simulations of confined classical hard-disk gases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2005

Bayesian Retrieval of Complete Posterior PDFs of Oceanic Rain Rate From Microwave Observations

This paper presents a new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measurements Mission (TRMM) Microwave Imager (TMI) over the ocean, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes Theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance our understanding of theoretical benefits of the Bayesian approach, we have conducted sensitivity analyses based on two synthetic datasets for which the true conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak, due to saturation effects. It is also suggested that the choice of the estimators and the prior information are both crucial to the retrieval. In addition, the performance of our Bayesian algorithm is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate.

Chiu, J. Christine↗

DOE OSTI2023

Tuning nonequilibrium phase transitions with inertia

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation–dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. Further, this density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

The coset construction for particles of arbitrary spin

When a Poincaré-invariant system spontaneously breaks continuous internal symmetries, Goldstones’ theorem demands the existence of massless, spin-zero excitations in a one-to-one correspondence with the broken symmetry generators. When a system spontaneously breaks Poincaré symmetry, however, the kinds of excitations that satisfy Goldstone’s theorem can be quite unusual. In particular, they may have any spin and need not be particles or even quasiparticles. The standard coset construction used to formulate effective actions of Goldstones, however, is rather restrictive and is incapable of generating the full spectrum of possibilities allowed by Goldstone’s theorem. We propose a (partial) remedy to this problem by postulating a novel coset construction for systems that spontaneously break Poincaré symmetry. This new construction is capable of generating effective actions with a wide range of Goldstone excitations — including fermionic degrees of freedom — even when all symmetries are bosonic. To demonstrate its utility, we focus on constructing effective actions for point particles of various spins. We recover the known result that a particle of spin s requires an \( \mathcal{N} \) = 2 s supersymmetric worldline reparameterization gauge symmetry, which we implement at the level of the coset construction. In the process, we discover that massless particles require a novel kind of inverse Higgs constraint that bears some resemblance to the dynamical inverse Higgs constraints that appear in certain fermi liquid effective field theories. We then consider particles that, in addition to quantum spin, have finite spatial extent and are free to rotate. We derive a novel action for such particles and find a ‘spin-orbital’ coupling between the intrinsic quantum spin and the physical-rotation degrees of freedom.

79 ASTRONOMY AND ASTROPHYSICS↗