Search NASA⌕ Search

SEARCH · Search NASA

Results for “Invariants”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Observation of the Spectrally Invariant Properties of Clouds in Cloudy-to-Clear Transition Zones During the MAGIC Field Campaign

We use the spectrally invariant method to study the variability of cloud optical thickness τau and droplet effective radius r(sub eff) in transition zones (between the cloudy and clear sky columns) observed from Solar Spectral Flux Radiometer (SSFR) and Shortwave Array Spectroradiometer-Zenith (SASZe) during the Marine ARM GPCI Investigation of Clouds (MAGIC) field campaign. The measurements from the SSFR and the SASZe are different, however inter-instrument differences of self-normalized measurements (divided by their own spectra at a fixed time) are small. The spectrally invariant method approximates the spectra in the cloud transition zone as a linear combination of definitely clear and cloudy spectra, where the coefficients, slope and intercept, characterize the spectrally invariant properties of the transition zone. Simulation results from the SBDART (Santa Barbara DISORT Atmospheric Radiative Transfer) model demonstrate that (1) the slope of the visible band is positively correlated with the cloud optical thickness τ while the intercept of the near-infrared band has high negative correlation with the cloud drop effective radius r(sub eff)even without the exact knowledge of τau; (2) the above relations hold for all Solar Zenith Angle (SZA) and for cloud-contaminated skies. In observations using redundant measurements from SSFR and SASZe, we find that during cloudy-to-clear transitions, (a) the slopes of the visible band decrease, and (b) the intercepts of the near-infrared band remain almost constant near cloud edges. The findings in simulations and observations suggest that, while the optical thickness decreases during the cloudy-to-clear transition, the cloud drop effective radius does not change when cloud edges are approached. These results support the hypothesis that inhomogeneous mixing dominates near cloud edges in the studied cases.

spectral invariance↗
DOE OSTI2026

Image Distinguishability Analysis Testing Through Principal Components and Its Application to Hot Spot Scale Invariance

Hot spots are spatial regions of intense energy localization that govern initiation of secondary high explosives. Studies that characterize or compare simulated hot spots are frequently either qualitatively descriptive or resort to quantitative distribution functions that neglect stochastic variations and spatial correlations—effects that are also neglected in common comparison tests like the Kolmogorov–Smirnov test. To this end, we develop an image distinguishability analysis (IDA) test based on principal component (PC) analysis that makes pixel-by-pixel comparisons between small, for example, O(<10), image data sets. The IDA test makes comparisons through a generalized distance metric in the PC space and a test statistic that is derived to calculate mathematical equation-values. Here, we derive a statistical distribution and criticality criterion to determine whether images are distinguishable from established baselines. We apply the IDA test on images generated from molecular dynamics simulations of hot spots from pore collapse in TATB to assess scale invariance in the complex patterns of hot spots that form in a representative high explosive crystal. The IDA test shows that TATB hot spot spatial temperature fields and their derived temperature histograms exhibit scale-invariant features over specific intervals of shock orientation, strength, and initial pore diameter. However, the IDA test also shows that qualitatively different conclusions regarding invariance can be reached depending on whether the hot spot is treated as a spatially correlated field as opposed to a distribution function that lacks spatial information.

organic↗
DOE OSTI2025

Semi-supervised permutation invariant particle-level anomaly detection

The development of analysis methods to distinguish potential beyond the Standard Model phenomena in a model-agnostic way can significantly enhance the discovery reach in collider experiments. However, the typical machine learning (ML) algorithms employed for this task require fixed length and ordered inputs that break the natural permutation invariance in collision events. To address this, a semi-supervised anomaly detection tool is presented that takes a variable number of particle-level inputs and leverages a signal model to encode this information into a permutation invariant, event-level representation via supervised training with a Particle Flow Network (PFN). Data events are then encoded into this representation and given as input to an autoencoder for unsupervised ANomaly deTEction on particLe flOw latent sPacE (ANTELOPE), classifying anomalous events based on a low-level and permutation invariant input modeling. Performance of the ANTELOPE architecture is evaluated on simulated samples of hadronic processes in a high energy collider experiment, showing good capability to distinguish disparate models of new physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Multi-invariants and bulk replica symmetry

In this paper, we analyze the question of replica symmetry in the bulk for multi-partite entanglement measures in the vacuum state of two dimensional holographic CFTs. We first define a class of multi-partite local unitary invariants, multi-invariants , with a given replica symmetry that acts freely and transitively on the replicas. We look for a subclass of measures such that the dual bulk geometry also preserves replica symmetry. We obtain the most general solution to this problem if we require the bulk to preserve replica symmetry for general configurations of the regions. Orbifolding the bulk solution with the replica symmetry gives us a bulk geometry with a network of conical singularities. Our approach makes it clear that there are infinitely many infinitely large families of multi-invariants such that each family evaluates identically on the holographic state. Geometrically, these are equalities involving volumes of handlebodies, possibly of different genus, at particular points in the moduli space. In certain cases, we check our bulk computation with an explicit calculation in CFT. Finally we comment on the generalization to higher dimension.

AdS-CFT Correspondence↗
DOE OSTI2024

Nonexistence of integrable nonlinear magnetic fields with invariants quadratic in momenta

Nonlinear, completely integrable Hamiltonian systems that serve as blueprints for novel particle accelerators at the intensity frontier are promising avenues for research, as Fermilab’s Integrable Optics Test Accelerator (IOTA) example clearly illustrates. Here, we show that only very limited generalizations are possible when no approximations in the underlying Hamiltonian or Maxwell equations are allowed, as was the case for IOTA. Specifically, no such systems exist with invariants quadratic in the momenta, precluding straightforward generalization of the Courant-Snyder theory of linear integrable systems in beam physics. We also conjecture that no such systems exist with invariants of higher degree in the momenta. This leaves solenoidal magnetic fields, including their nonlinear fringe fields, as the only completely integrable static magnetic fields, albeit with invariants that are linear in the momenta. The difficulties come from enforcing Maxwell equations; without constraints, we show that there are many solutions. In particular, we discover a previously unknown large family of integrable Hamiltonians.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Shearing approach to gauge-invariant Trotterization

Universal quantum simulations of gauge field theories are exposed to the risk of gauge symmetry violations when it is not known how to compile the desired operations exactly using the available gate set. In this article, we show how time evolution can be compiled in an Abelian gauge theory—if only approximately—without compromising gauge invariance, by graphically motivating a block-diagonalization procedure. When gauge-invariant interactions are associated with a “spatial network” in the space of discrete quantum numbers, it is seen that cyclically shearing the spatial network converts simultaneous updates to many quantum numbers into conditional updates of a single quantum number; ultimately, this eliminates any need to pass through (and acquire overlap onto) unphysical intermediate configurations. Shearing is explicitly applied to gauge-matter and magnetic interactions of lattice quantum electrodynamics. The features that make shearing successful at preserving Abelian gauge symmetry may also be found in non-Abelian theories, bringing one closer to gauge-invariant simulations of quantum chromodynamics.

Gauge theories↗
DOE OSTI2025

𝑇-invariance violation in neutrino oscillations and matter effects

We investigate the impact of matter effects on 𝑇 (time-reversal)-odd observables, making use of the quantum-mechanical formalism of neutrino-flavor evolution. We attempt to be comprehensive and pedagogical. Matter-induced 𝑇-invariance violation (TV) is qualitatively different from, and more subtle than, matter-induced 𝐶⁢𝑃 (charge-parity)-invariance violation. If the matter distribution is symmetric relative to the neutrino production and detection points, matter effects will not introduce any new TV. However, if there is intrinsic TV, matter effects can modify the size of the 𝑇-odd observable. On the other hand, if the matter distribution is not symmetric, there is genuine matter-induced TV. For Earth-bound long-baseline oscillation experiments, these effects are small. This remains true for unrealistically-asymmetric matter potentials (for example, we investigate the effects of “hollowing out” 50% of the DUNE neutrino trajectory). More broadly, we explore consequences, or lack thereof, of asymmetric matter potentials on oscillation probabilities. While fascinating in their own right, 𝑇-odd observables are currently of limited practical use, due in no small part to a dearth of intense, well-characterized, high-energy electron-neutrino beams. Further in the future, however, intense, high-energy muon storage rings might become available and allow for realistic studies of 𝑇-invariance in neutrino oscillations.

CP violation↗
DOE OSTI2026

Bounds on Lorentz Invariance Violation from Muon Fluctuations at the Pierre Auger Observatory

Quantum gravity theories often modify spacetime symmetries. In particular, Lorentz invariance may be violated when approaching the Planck scale. Although the scales at which interactions occur in extensive air showers induced by ultra-high-energy cosmic rays in the atmosphere are many orders of magnitude below the Planck scale, these violations might still be observable. In this Letter, the fluctuations in the number of muons in the extensive air showers measured at the Pierre Auger Observatory are exploited, for the first time, to constrain Lorentz invariance violations. The bounds derived in the hadronic sector are the strongest ever obtained, and do not rely on assumptions about the mass composition of ultra-high-energy cosmic rays. The fluctuations in the number of muons constitute a new and powerful observable to further explore Lorentz invariance in a region of the parameter space not accessible to other observables.

Abdul Halim, A. [Adelaide U.] (ORCID:0000000312181↗
DOE OSTI2026

Geometric invariants of quantum metrology

Here, we establish a conservation law for the Quantum Fisher Information Matrix (QFIM) expressed as follows; when the QFIM is constructed from a set of observables closed under commutation, i.e., a Lie algebra, the spectrum of the QFIM is invariant under unitary dynamics generated by these same operators. Each Lie algebra therefore endows any quantum state with a fixed “budget” of metrological sensitivity—an intrinsic resource that we show, like optical squeezing in interferometry, cannot be amplified by symmetry-preserving operations. The Uhlmann curvature tensor naturally inherits the same symmetry group, and so quantum incompatibility is similarly fixed. As a result, a metrological analog to Liouville's theorem appears; statistical distances, volumes, and curvatures are invariant under the evolution generated by the Lie algebra. We discuss this as it relates to the quantum analogs of classical optimality criteria. This enables one to efficiently classify useful classes of quantum states at the level of Lie algebras through geometric invariants.

Wilson, Christopher [University of Colorado, Bould↗
DOE OSTI2025

Picosecond lifetime measurements of resonances using a thick-target invariant-mass technique

Here, a new technique is presented for measuring the half-lives of resonances in the picosecond range using presently available invariant-mass apparatus and a thick target. For short-lived resonances, the energy losses of the decay fragments in the target material change their relative velocities giving rise to a poor invariant-mass resolution. However, for longer-lived resonances that travel through the remaining target material before decaying outside of the target, this dominant contribution to the resolution is eliminated. The measured invariant-mass peak will then display a narrow peak from these events which sits on a wider structure associated with the remaining events that decay in the target. The fraction of the events in the narrow peak is related to the probability that the resonance leaves the target before decaying and hence is related to the lifetime. This technique is exercised for the 2.685-MeV resonance in 33 Cl which decays by emitting an f -wave proton. A half-life of T 1/2 =5.7$^{+4.1}_{-2.5}$ ps was measured which is consistent with values inferred from other known properties of this resonance.

lifetimes & widths↗
DOE OSTI2024

Counter Data Paucity through Adversarial Invariance Encoding: A Case Study on Modeling Battery Thermal Runaway

Lithium-ion batteries, widely used for their durability and high energy storage, face the risk of internal short circuits leading to catastrophic thermal runaway events. These events, triggered by external stimuli like mechanical loads, pose safety concerns in applications such as electric vehicles. Detecting and understanding thermal runaway events is crucial, but physics-driven models struggle to explain the non-linear evolution of battery temperature during these events, considering factors like material composition and state-of-charge. Due to the rarity of these events and the cost of data collection, we propose a deep learning (DL) model to predict battery temperature responses during thermal runaway. The challenge lies in the scarcity of data, making traditional DL models prone to overfitting and learning low-quality representations of the complex process.Our approach introduces a novel few-shot architecture that incorporates an adversarially governed invariant encoding process. This architecture aims to distill "invariant" relationships by addressing distributional shifts in data across various battery properties, facilitating the detection of thermal runaway events. Specifically, our results demonstrate that deep learning models conditioned on these "invariant" representations outperform state-of-the-art baselines, achieving a remarkable 96.8% performance improvement in terms of the popular metric MAPE. This framework presents a promising direction for enhancing battery safety modeling, particularly in the context of rare and complex events like thermal runaway. Our code and code and dataset used for the paper are public1.

Tabassum, Anika [ORNL] (ORCID:0000000254600955)↗
NASA NTRS1971

Generalized invariance principles and the theory of stability.

Description of some recent extensions of the invariance principle to more generalized dynamical systems where the state space is not locally compact and the flow is unique only in the forward direction of time. A sufficient condition for asymptotic stability of an invariant set is obtained which does not require that the Liapunov function be positive-definite. A recently developed generalized invariance principle is described which is applicable to functional differential equations, partial differential equations, and, in particular, to certain stability problems arising in thermoelasticity, viscoelasticity, and distributed nonlinear networks.

Lasalle, J. P.↗
NASA NTRS1980

Restricted invariance of the Navier-Stokes equation

It is well known that the classical Navier-Stokes equation for three-dimensional incompressible viscous flow is invariant under Galilean transformations. In the present paper, it is shown that, although the general invariance group is no larger than Galilean-scale dilitation, the Navier-Stokes equation for incompressible viscous flow admits time-dependent rotational invariance for solutions of special types.

Rosen, G.↗
NASA NTRS1984

Registration of rotated images by invariant moments

A new technique for registration of rotated images using invariant moments as the similarity measure is given. If circular windows with invariant moments are used, then window search can be carried out on rotated images in the same manner cross-correlation with rectangular windows is used on translated images. Normalization of invariant moments for more accurate window similarity measurement is also given. The proposed approach is tested against two images from different satellites that have translational and rotational differences.

Goshtasby, A.↗
NASA NTRS1999

A Scale-Invariant Model of Statistical Mechanics and Modified Forms of the First and the Second Laws of Thermodynamics

A scale-invariant statistical theory of fields is presented that leads to invariant definition of density, velocity, temperature, and pressure, The definition of Boltzmann constant is introduced as k(sub k) = m(sub k)v(sub k)c = 1.381 x 10(exp -23) J x K(exp -1), suggesting that the Kelvin absolute temperature scale is equivalent to a length scale. Two new state variables called the reversible heat Q(sub rev) = TS and the reversible work W(sub rev) = PV are introduced. The modified forms of the first and second law of thermodynamics are presented. The microscopic definition of heat (work) is presented as the kinetic energy due to the random (peculiar) translational, rotational, and pulsational motions. The Gibbs free energy of an element at scale Beta is identified as the total system energy at scale (Beta-1), thus leading to an invariant form of the first law of thermodynamics U(sub Beta) = Q(sub Beta) - W(sub Beta) +N(e3)U(sub Beta-1).

Sohrab, Siavash H.↗
NASA NTRS2004

Verification of Java Programs using Symbolic Execution and Invariant Generation

Software verification is recognized as an important and difficult problem. We present a norel framework, based on symbolic execution, for the automated verification of software. The framework uses annotations in the form of method specifications an3 loop invariants. We present a novel iterative technique that uses invariant strengthening and approximation for discovering these loop invariants automatically. The technique handles different types of data (e.g. boolean and numeric constraints, dynamically allocated structures and arrays) and it allows for checking universally quantified formulas. Our framework is built on top of the Java PathFinder model checking toolset and it was used for the verification of several non-trivial Java programs.

Pasareanu, Corina↗
NASA NTRS2004

Invariant Theory for Dispersed Transverse Isotropy: An Efficient Means for Modeling Fiber Splay

Most soft tissues possess an oriented architecture of collagen fiber bundles, conferring both anisotropy and nonlinearity to their elastic behavior. Transverse isotropy has often been assumed for a subset of these tissues that have a single macroscopically-identifiable preferred fiber direction. Micro-structural studies, however, suggest that, in some tissues, collagen fibers are approximately normally distributed about a mean preferred fiber direction. Structural constitutive equations that account for this dispersion of fibers have been shown to capture the mechanical complexity of these tissues quite well. Such descriptions, however, are computationally cumbersome for two-dimensional (2D) fiber distributions, let alone for fully three-dimensional (3D) fiber populations. In this paper, we develop a new constitutive law for such tissues, based on a novel invariant theory for dispersed transverse isotropy. The invariant theory is based on a novel closed-form splay invariant that can easily handle 3D fiber populations, and that only requires a single parameter in the 2D case. The model is polyconvex and fits biaxial data for aortic valve tissue as accurately as the standard structural model. Modification of the fiber stress-strain law requires no re-formulation of the constitutive tangent matrix, making the model flexible for different types of soft tissues. Most importantly, the model is computationally expedient in a finite-element analysis.

Freed, alan D.↗
NASA NTRS2011

Spectrally-Invariant Approximation Within Atmospheric Radiative Transfer

Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These "spectrally invariant relationships" are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength independence does not hold in the atmosphere, but in cloud~dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accurately describe the extinction. and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the approximation are tested with ID radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.

Marshak, A.↗