Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “invariant”

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 703 records · Page 39

Pursuit of paired dijet resonances in the Run 2 dataset with ATLAS

New particles with large masses that decay into hadronically interacting particles are predicted by many models of physics beyond the Standard Model. A search for a massive resonance that decays into pairs of dijet resonances is performed using 140 fb –1 of proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded by the ATLAS detector during Run 2 of the Large Hadron Collider. Resonances are searched for in the invariant mass of the tetrajet system, and in the average invariant mass of the pair of dijet systems. A data-driven background estimate is obtained by fitting the tetrajet and dijet invariant mass distributions with a four-parameter dijet function and a search for local excesses from resonant production of dijet pairs is performed. No significant excess of events beyond the Standard Model expectation is observed, and upper limits are set on the production cross sections of new physics scenarios.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for quantum black hole production in lepton + jet final states using proton-proton collisions at s = 13 TeV with the ATLAS detector

A search for quantum black holes in electron + jet and muon + jet invariant mass spectra is performed with 140 fb -1 of data collected by the ATLAS detector in proton-proton collisions at $\sqrt{s}$ =13 TeV at the Large Hadron Collider. The observed invariant mass spectrum of lepton + jet pairs is consistent with Standard Model expectations. Upper limits are set at 95% confidence level on the production cross section times branching fractions for quantum black holes decaying into a lepton and a quark in a search region with invariant mass above 2.0 TeV. The resulting quantum black hole lower mass threshold limit is 9.2 TeV in the Arkani-Hamed-Dimopoulos-Dvali model, and 6.8 TeV in the Randall-Sundrum model.

79 ASTRONOMY AND ASTROPHYSICS↗

Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: Hilbert space of a trivalent vertex

The construction of gauge-invariant states of SU(3) lattice gauge theories has garnered new interest in recent years, but implementing them is complicated by the need for SU(3) Clebsch-Gordon coefficients. In the loop-string-hadron (LSH) approach to lattice gauge theories, the elementary excitations are strictly gauge invariant, and constructing the basis requires no knowledge of Clebsch-Gordon coefficients. Originally developed for SU(2), the LSH formulation was recently generalized to SU(3), but limited to one spatial dimension. In this work, we generalize the LSH approach to constructing the basis of SU(3) gauge-invariant states at a trivalent vertex—the essential building block to multidimensional space. A direct generalization from the SU(2) vertex yields a legitimate basis; however, in certain sectors of the Hilbert space, the naive LSH basis vectors so defined suffer from being nonorthogonal. The issues with orthogonality are directly related to the “missing label” or “outer multiplicity” problem associated with SU(3) tensor products and may also be phrased in terms of Littlewood-Richardson coefficients or the need for a “seventh Casimir” operator. The states that are unaffected by the problem are orthonormalized in closed form. For the sectors that are afflicted, we discuss the nonorthogonal bases and their orthogonalization. A few candidates for seventh Casimir operators are readily constructed from the suite of LSH gauge-singlet operators. The diagonalization of a seventh Casimir represents one prescriptive solution toward obtaining a complete orthonormal basis, but a closed-form general solution remains to be found. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Energizing charged particles by an orbit instability in a slowly rotating magnetic field

In this work, the stability of charged particle motion in a uniform magnetic field with an added spatially uniform transverse rotating magnetic field (RMF) is studied analytically. It is found that the stability diagram of a single particle's orbit depends critically on the chosen boundary conditions. We show that for many boundary conditions and wide regions in the parameter space, RMFs oscillating far below the cyclotron frequency can cause linear instabilities in the motion which break μ invariance and energize particles. Such energization may appear at odds with the adiabatic invariance of μ; however, adiabatic invariance is an asymptotic result and does not preclude such heating by magnetic fields oscillating at slow frequencies. This mechanism may contribute to heating in the edge plasma of field-reversed configurations (FRCs) in rotamak-FRC experiments. Furthermore, these RMF-driven instabilities may significantly enhance azimuthal current drive during the formation of FRCs in such devices.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Transverse Momentum Distributions from Lattice QCD without Wilson Lines

The transverse-momentum-dependent distributions (TMDs), which are defined by gauge-invariant 3D parton correlators with staple-shaped lightlike Wilson lines, can be calculated from quark and gluon correlators fixed in the Coulomb gauge on a Euclidean lattice. These quantities can be expressed gauge invariantly as the correlators of Coulomb-gauge-dressed fields, which reduce to the standard TMD correlators under principal-value prescription in the infinite boost limit. In the framework of large-momentum effective theory, a quasi-TMD defined from such correlators in a large-momentum hadron state can be matched to the TMD via a factorization formula, whose exact form is derived using soft collinear effective theory and verified at one-loop order. Compared to the currently used gauge-invariant correlators, this new method can substantially improve statistical precision and simplify renormalization for the time-reversal-even TMDs, which will greatly enhance the predicative power of lattice QCD in the nonperturbative region.

Effective field theory↗

Geometric origin of the energy-momentum tensor improvement terms

In a flat background, the canonical energy momentum tensor of Lorentz and conformally invariant matter field theories can be improved to a symmetric and traceless tensor that gives the same conserved charges. We argue that the geometric origin of this improvement process is unveiled when the matter theory is coupled to metric-affine gravity. In particular, we show that the Belinfante-Rosenfeld improvement terms correspond to the matter theory’s hypermomentum. The improvement terms in conformally invariant matter theories are also related to the hypermomentum; however, a general proof would require an extended investigation. We demonstrate our results through various examples, such as the free massless scalar, the Maxwell field, Abelian p-forms, the Dirac field, and a nonunitary massless scalar field. Possible applications of our method for theories that break Lorentz or special conformal invariance are briefly discussed.

classical solutions in field theory↗

Reflections on Noether’s second theorem and the energy-momentum tensor

Through symmetry of the action under global spacetime translations, Noether’s first theorem infamously entails an energy-momentum tensor (EMT) that is neither symmetric nor gauge-invariant. In a prior work [Phys. Rev. D 106, 125012 (2022)], I had obtained a symmetric and gauge-invariant EMT by using Noether’s second theorem instead, with local spacetime translations as the symmetry group. However, the derivation therein was flawed, containing a faulty assumption about the transformation rule for spinor fields. In this work, I revisit the derivation of the previous work, both correcting the faulty step and simplifying the derivation for broader accessibility. The end result is an EMT for quantum chromodynamics that is gauge-invariant, but not symmetric.

Quantum chromodynamics↗

Refined large N duality for knots

We formulate large [Formula: see text] duality of [Formula: see text] refined Chern–Simons theory with a torus knot/link in [Formula: see text]. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the [Formula: see text]-background. This form enables us to relate refined Chern–Simons invariants of a torus knot/link in [Formula: see text] to refined BPS invariants in the resolved conifold. Assuming that the extra [Formula: see text] global symmetry acts on BPS states trivially, the duality predicts graded dimensions of cohomology groups of moduli spaces of M2–M5 bound states associated to a torus knot/link in the resolved conifold. Thus, this formulation can be also interpreted as a positivity conjecture of refined Chern–Simons invariants of torus knots/links. We also discuss about an extension to non-torus knots.

Mathematics↗

Improved measurements of nonlinear integrable optics at IOTA

Nonlinear integrable optics (NIO) are a promising novel approach at improving the stability of high intensity beams. Implementations of NIO based on specialized magnetic elements are being tested at the Integrable Optics Test Accelerator (IOTA) at Fermilab. One method of verifying proper implementation of these solutions is by measuring the analytic invariants predicted by theory. The initial measurements of nonlinear invariants were performed during IOTA run in 2019/20, however the covid-19 pandemic prevented the full-scale experimental program from being completed. Several important improvements were implemented in IOTA for the 2022/23 run, including the operation at higher beam energy of 150 MeV, improved optics control, and chromaticity correction. This report presents on the improved calibrations of the NIO for nonlinear invariant measurements.

43 PARTICLE ACCELERATORS↗

Preshot Report for the NIF DDCyl Campaign: H_Hyd_DDCyl_DRT_AAA/BBB/CCC

The first two cylinder shot days on the National Ignition Facility, allocated through the Discovery Science program, provided a successful demonstration of the cylinder platform on the NIF. Both of these shot days used cylinders that were nominally 3 times larger in radial dimension than cylinders fielded at the OMEGA laser facility, here referred to as scale-3 targets. In the first Discovery Science shot day, we demonstrated that Rayleigh-Taylor instability growth during the deceleration phase is scale-invariant between the scale-1 OMEGA experiments and similarly tailored scale-3 NIF experiments at the same convergence ratio of CR=initial radius/final radius=2.25. In the second Discovery Science shot day, we increased the convergence ratio by lowering the density of the central foam from 300 mg/cm 3 to roughly 40 mg/cm 3 with the same laser drive, resulting in a higher CR=5 at the time when the rebounding shock strikes the aluminum marker. We also greatly improved the imaging setup for the second shot day, resulting in much higher quality (greater signal-to-noise) radiographs of the implosion. This current shot day was awarded through the High Energy Density (HED) Council, following this demonstration of platform viability. It was originally scheduled for June 2020, but it was postponed several times due to the COVID-19 pandemic. It is currently scheduled for January 6, 2021. For this shot day, we will increase the radial dimension of the cylinder to four times the OMEGA-scale targets, and these will be referred to as scale-4 cylinders. Increasing the radial dimension of the target is advantageous as we push these targets to higher convergence ratio. By starting with an initially larger target, the target can push to a higher CR while maintaining the same final viewing area. Other than the larger radial dimension, the targets are very similar in design to the previous ones, consisting of an epoxy ablator, an embedded aluminum marker layer, and a low density central CH foam. These will also use a 40 mg/cm3 CH foam, reaching a CR~4.5 with the same laser energy (the added target mass reduces the final CR slightly). Note that this is NOT designed to be scale-invariant with the previous scale-1 OMEGA and scale-3 NIF shots. It was determined that the laser energy required to achieve a scale-invariant implosion was above the allowable optics damage limits (though achievable on the NIF) for these scale-4 targets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Equicontrollability and the model following problem

Equicontrollability and its application to the linear time-invariant model-following problem are discussed. The problem is presented in the form of two systems, the plant and the model. The requirement is to find a controller to apply to the plant so that the resultant compensated plant behaves, in an input-output sense, the same as the model. All systems are assumed to be linear and time-invariant. The basic approach is to find suitable equicontrollable realizations of the plant and model and to utilize feedback so as to produce a controller of minimal state dimension. The concept of equicontrollability is a generalization of control canonical (phase variable) form applied to multivariable systems. It allows one to visualize clearly the effects of feedback and to pinpoint the parameters of a multivariable system which are invariant under feedback. The basic contributions are the development of equicontrollable form; solution of the model-following problem in an entirely algorithmic way, suitable for computer programming; and resolution of questions on system decoupling.

Curran, R. T.↗

Magnetospheric whistler ducts observed by ISIS satellites

The latitudinal width of the magnetospheric whistler duct has been estimated by the first and final invariant latitudes of whistler echoes and the conservation of the magnetic flux for the centered dipole field, using 105 whistler echoes in ISIS VLF data received at Kashima, Japan for 1972-1973. The latitudinal distribution of whistler duct occurrence shows a maximum at invariant latitudes of 40-45 degrees near the maximum occurrence latitude of ground whistlers. The radial width of magnetospheric whistler duct in the geomagnetically equatorial plane increases with invariant latitude of the geomagnetic flux tube in which whistlers propagate.

Ondoh, T.↗

Estimation and correction of advection effects with single and multiple, conventional and Doppler radars

The laws of fluid motion are invariant under a Gallilean transformation. For a perfect observing system, the data analysis should, therefore, also be invariant under a Gallilean transformation. This invariance is often not preserved in practical observing systems. In this connection, it is often advisable to perform mesoscale analysis in a frame moving with respect to the earth's surface. In the present investigation the velocity of such a frame is referred to as an advection velocity. The investigation is concerned with remaining problems regarding the Gallilean transformation. The establishment of a frame of reference for the achievement of maximum coherence is considered, taking into account the case of given nonsimultaneous observations of scalars or Cartesian vectors. It is found that advection speed can be estimated objectively if a scalar or Cartesian vector can be observed directly and if, in addition, the time and position of each observation is approximately known.

Gal-Chen, T.↗

A geometric approach to failure detection and identification in linear systems

Using concepts of (C,A)-invariant and unobservability (complementary observability) subspaces, a geometric formulation of the failure detection and identification filter problem is stated. Using these geometric concepts, it is shown that it is possible to design a causal linear time-invariant processor that can be used to detect and uniquely identify a component failure in a linear time-invariant system, assuming: (1) The components can fail simultaneously, and (2) The components can fail only one at a time. In addition, a geometric formulation of Beard's failure detection filter problem is stated. This new formulation completely clarifies of output separability and mutual detectability introduced by Beard and also exploits the dual relationship between a restricted version of the failure detection and identification problem and the control decoupling problem. Moreover, the frequency domain interpretation of the results is used to relate the concepts of failure sensitive observers with the generalized parity relations introduced by Chow. This interpretation unifies the various failure detection and identification concepts and design procedures.

Massoumnia, M. A.↗

Methods for the solution of radiative transfer equation

To obtain an exact solution of the radiative-transfer equation in media where both absorption and scattering are significant, the usual approach is to use a numerical method. Three methods are known in the literature: invariant imbedding, eigenvalue-eigenfunction, and matrix doubling. This paper examines the practical application of these methods to the problem of emission from an inhomogeneous (Rayleigh) layer, the effects of layer parameters on the stability. It is found that invariant imbedding is most suitable for computing emission from an inhomogeneous layer with a temperature profile but tends to be unstable as the optical thickness of the layer increases beyond 0.5. On the other hand, the matrix-doubling method is stable for arbitrary optical thickness but is not suitable for handling multilayers. The eigenvalue-eigenfunction method is more stable than the invariant imbedding as optical thickness increases up to 2.0. It also permits temperature profile in the layer, but the computation is much more complicated. It is less stable than the matrix-doubling method when optical thickness is larger than 2.0. In general, the choice of a method is dependent on the nature of the problem.

Chen, M. F.↗

Observing rotation and deformation of sea ice with synthetic aperture radar

The ESA's ERS-1 satellite will carry SARs over the polar regions; an important component in the use of these data is an automated scheme for the extraction of sea ice velocity fields from a sequence of SAR images of the same geographical region. The image pyramid area-correlation hierarchical method is noted to be vulnerable to uncertainties for sea ice rotations greater than 10-15 deg between SAR observations. Rotation-invariant methods can successfully track isolated floes in the marginal ice zone. Hu's (1962) invariant moments are also worth considering as a possible basis for rotation-invariant tracking methods. Feature tracking is inherently robust for tracking rotating sea ice, but is limited when features are floe-lead boundaries. A variety of techniques appears neccessary.

Vesecky, J. F.↗

Covariance and the hierarchy of frame bundles

This is an essay on the general concept of covariance, and its connection with the structure of the nested set of higher frame bundles over a differentiable manifold. Examples of covariant geometric objects include not only linear tensor fields, densities and forms, but affinity fields, sectors and sector forms, higher order frame fields, etc., often having nonlinear transformation rules and Lie derivatives. The intrinsic, or invariant, sets of forms that arise on frame bundles satisfy the graded Cartan-Maurer structure equations of an infinite Lie algebra. Reduction of these gives invariant structure equations for Lie pseudogroups, and for G-structures of various orders. Some new results are introduced for prolongation of structure equations, and for treatment of Riemannian geometry with higher-order moving frames. The use of invariant form equations for nonlinear field physics is implicitly advocated.

Estabrook, Frank B.↗

Making A Circular-Harmonic Filter

Optical image-correlating system made rotationally invariant. Experiment shows circular-harmonic filter generated optically. Hologram made by phase-shifted-double-exposure procedure. Filter used in optical image-recognition system based on correlation between target (image to be recognized) and matched spatial filter. In addition to usual invariance under translation of target, circular harmonic filter invariant under rotation of target; peak intensity of illumination at origin of correlation plane does not vary when target rotated about optical axis.

Cheng, Yeou Yen↗