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Results for “tensor ring”

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.

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14 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Solving a class of infinite-dimensional tensor eigenvalue problems by translational invariant tensor ring approximations

Here, we examine a method for solving an infinite-dimensional tensor eigenvalue problem Hx = λx, where the infinite-dimensional symmetric matrix H exhibits a translational invariant structure. We provide a formulation of this type of problem from a numerical linear algebra point of view and describe how a power method applied to e -Ht is used to obtain an approximation to the desired eigenvector. This infinite-dimensional eigenvector is represented in a compact way by a translational invariant infinite Tensor Ring (iTR). Low rank approximation is used to keep the cost of subsequent power iterations bounded while preserving the iTR structure of the approximate eigenvector. We show how the averaged Rayleigh quotient of an iTR eigenvector approximation can be efficiently computed and introduce a projected residual to monitor its convergence. In the numerical examples, we illustrate that the norm of this projected iTR residual can also be used to automatically modify the time step to ensure accurate and rapid convergence of the power method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Synthetic tensor gauge fields

Synthetic gauge fields have provided physicists with a unique tool to explore a wide range of fundamentally important phenomena. However, most experiments have focused on synthetic vector gauge fields. The very rich physics brought about by coupling tensor gauge fields to fracton phases of matter remains unexplored in laboratories. Here, we propose schemes to realize synthetic tensor gauge fields that address dipoles instead of single particles. A lattice tilted by a strong linear potential and a weak quadratic potential yields a rank-2 electric field for a dipole formed by a particle-hole pair. Such a rank-2 electric field leads to a new type of Bloch oscillations, which modulates the quadrupole moment and preserves the dipole moment of the system. In higher dimensions, the interplay between interactions and vector gauge potentials imprints a phase to the ring-exchange interaction and thus generates synthetic tensor gauge fields. Such tensor gauge fields make it possible to realize a dipolar Harper-Hofstadter model in laboratories. The resultant dipolar Chern insulators feature chiral edge currents of dipoles in the absence of net charge currents. Published by the American Physical Society 2025

Zhang, Shaoliang (ORCID:000000016635044X)↗
NASA NTRS1965

Unconventional inertial sensors.

Inertial sensors reviewing ring laser, electrostatic fluid sphere, magnetic resonance, superconductivity gyroscope, relativistic rotating tensor, vortex rate and quantum mechanical effect sensing

INERTIAL ACCELEROMETER↗
NASA NTRS1984

Relativistic dispersion, the cyclotron maser instability, and auroral kilometric radiation

It is demonstrated that relativistic effects can significantly modify the wave dispersion in auroral kilometric radiation (AKR), even for only mildly relativistic electrons, when the ratio of the square of the electron plasma frequeny omega(pe) to the square of the electron cyclotron frequency Omega(e) is much less than one, which is frequently the case in the AKR source region. The k-parallel dispersion relation for waves in a relativistic Maxwellian plasma is considered for the case of omega(pe) much less than Omega(e). The results of Shkarovsky (1966) are used to evaluate the relativistic corrections to the R-X mode cutoff. The general relativistic dispersion tensor is applied to evaluate the dispersion relation for a delta function ring distribution in p-perpendicular, again assuming omega(pe) much less than Omega(e). The effect of finite velocity spread is studied by analyzing the Dory-Guest-Harris distribution in the semirelativistic approximation. The results of computer simulations for ring and shell distributions are presented.

Pritchett, P. L.↗
NASA NTRS1985

A granular flow model for dense planetary rings

In the present study of the viscosity of a differentially rotating particle disk, in the limiting case where the particles are densely packed and their collective behavior resembles that of a liquid, the pressure tensor is derived from both the equations of hydrodynamics and a simple kinetic model of collisions due to Haff (1983). Density waves and narrow circular rings are unstable if the liquid approximation applies, and the consequent nonlinear perturbations may generate 'splashing' of the ring material in the vertical direction. These results are pertinent to the origin of the ellipticities of ringlets, the nonaxisymmetric features near the outer edge of the Saturn B ring, and unexplained residuals in kinematic models of the Saturn and Uranus rings.

Borderies, N.↗
DOE OSTI2025

Non-invertible defects from the Conway SCFT to K3 sigma models. Part I. General results

We initiate the study of supersymmetry-preserving topological defect lines (TDLs) in the Conway moonshine module V f♮ . We show that the tensor category of such defects, under suitable assumptions, admits a surjective but non-injective ring homomorphism into the ring of $\mathbb{Z}$-linear maps of the Leech lattice into itself. This puts strong constraints on possible defects and their quantum dimensions. We describe a simple construction of non-invertible TDLs from orbifolds of holomorphic (super)vertex operator algebras, which yields non-trivial examples of TDLs satisfying our main theorem. We conjecture a correspondence between four-plane-preserving TDLs in V f♮ and supersymmetry-preserving TDLs in K3 non-linear sigma models, which extends the correspondence between symmetry groups to the level of tensor category symmetry. We establish evidence for this conjecture by constructing non-invertible TDLs in special K3 non-linear sigma models.

Conformal Field Models in String Theory↗
NASA NTRS1988

Local flow structures defined by kinematic events in isotropic turbulence

The spatial structure of turbulent motion in incompressible isotropic turbulence is investigated using a conditional average in which the conditional event specifies the local deformation tensor in addition to the local velocity vector. This average gives the best estimate of the flow field around a fixed point x given the kinematic state at x. Estimates are calculated for various kinematic states in isotropic turbulence, including pure translation, pure shear, plane strain, axisymmetric strain, and pure rotation. It is demonstrated that the large-scale motion is dominated by a vortex ring structure associated with the translational component, except at critical points of the velocity vector field.

Adrian, R. J.↗
NASA NTRS1985

Particle and field stress balance within a planetary magnetosphere

A technique is developed for experimentally estimating the local tensor stresses within a planetary magnetic field configuration characterized by local spacecraft measurements. Key to the technique is the determination of the shapes of field lines using the symmetry properties of the system coupled with local and instantaneous measurements of the field line inclination angles. The technique is applied here to the inner and middle Saturnian magnetosphere using data returned by the Magnetic Field Experiment on the Voyager 1 spacecraft. It is concluded that the ring current has substantial radial structure, heretofore not shown. Outside about 13 R(s) the newly derived field stresses match remarkably well the funtional variation of the centrifugal corotation stresses of the cool particle population measured previously by the Plasma Science Experiment. Inside about 13 R(s) the key structure in the derived field stresses, a prominent local maximum, matches the approximate position of an apparent strong pressure gradient in the energetic particles characterized by the Low-Energy Charged Particle detectors.

Mauk, B. H.↗
NASA NTRS1983

Perturbed particle disks

The velocity ellipsoid in a particle disk near an isolated satellite resonance is determined by solving the Boltzmann moment equations, and solutions are obtained that are stationary functions of the azimuthal angle in a coordinate frame which rotates with the pattern speed of the perturbation potential. The magnitude of the deformation rate tensor in a perturbed particle disk is bounded from above by an expression which includes the orbital angular velocity, the optical depth, and a dimensionless constant of order unity. It is also found that, in sufficiently perturbed regions, there are ranges of azimuthal angle over which the radial component of the angular momentum flux is negative. It is also possible for the angular momentum luminosity to be negative. These results are pertinent to the understanding of sharp edges and density wave decay in planetary rings.

Borderies, N.↗
NASA NTRS1995

Critical radiation fluxes and luminosities of black holes and relativistic stars

The critial luminosity at which the outward force of radiation balances the inward force of gravity plays an important role in many astrophysical systems. We present expressions for the radiation force on particles with arbitrary cross sections and analyze the radiation field produced by radiating matter, such as a disk, ring, boundary layer, or stellar surface, that rotates slowly around a slowly rotating gravitating mass. We then use these results to investigate the critical radiation flux and, where possible, the critical luminosity of such a system in genral relativity. We demonstrate that if the radiation source is axisymmetric and emission is back-front symmetric with repect to the local direction of motion of the radiating matter, as seen in the comoving frame, then the radial component of the radiation flux and the diagonal components of the radiation stress-energy tensor outside the source are the same, to first order in the rotation rates, as they would be if the radiation source and gravitating mass were not rotating. We argue that the critical radiation flux for matter at rest in the locally nonrotating frame is often satisfactory as an astrophysical benchmark flux and show that if this benchmark is adopted, many of the complications potentially introduced by rotation of the radiation source and the gravitating mass are avoided. We show that if the radiation field in the absence of rotation would be spherically symmetric and the opacity is independent of frequency and direction, one can define a critical luminosity for the system that is independent of frequency and direction, one can define a critical luminosity for the system that is independent of the spectrum and angular size of the radiation source and is unaffected by rotation of the source and mass and orbital motion of the matter, to first order. Finally, we analyze the conditions under which the maximum possible luminosity of a star or black hole powered by steady spherically symmetric radial accretion is the same in general relativity as in the Newtonian limit.

Lamb, Frederick K.↗
DOE OSTI2024

Quantum tensor network algorithms for evaluation of spectral functions on quantum computers

We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we call a quantum tensor network (QTN), we demonstrate algorithms to prepare ground and excited states on a quantum computer and apply them to molecular nanomagnets (MNMs) as a paradigmatic example. In this setting, we develop two approaches for extracting the spectral correlation functions measured in neutron-scattering experiments: (a) a generalization of the SWAP test for computing wave function overlaps and, (b) a generalization of the notion of matrix product operators to the QTN setting which generates a linear combination of unitaries. The latter method is discussed in detail for translationally invariant spin-half systems, where it is shown to reduce the qubit resource requirements compared with the SWAP method and may be generalized to other systems. We demonstrate the versatility of our approaches by simulating spin-1/2 and spin-3/2 MNMs, with the latter being an experimentally relevant model of a Cr$^{3+}_{8}$ ring. Here, our approach has qubit requirements that are independent of the number of constituents of the many-body system and scale only logarithmically with the bond dimension of the MPS representation, making them appealing for implementation on near-term quantum hardware with mid-circuit measurement and reset.

Neutron scattering↗
NASA NTRS2005

Ring Current Dynamic in the Presence of EMIC Waves

The effect of EMIC waves, generated by a positive ion temperature anisotropy on Earth s RC ions is one of the best known examples of wave-particle interaction in the magnetosphere and the most controversial mechanism of RC losses. Under certain conditions, relativistic electrons with energy 21 MeV can be removed from the outer RB by EMIC wave scattering during a magnetic storm much faster than by any other loss mechanisms. That is why the calculation of EMIC waves is a very critical part of the NASA LWS program. The new RC model that we have developed and present for the first time has several new features that we have combine together in a one single model: (a) several lower frequency cold plasma wave modes are taken into account; (b) wave tracing of these wave has been incorporated in the energy EMIC wave equation; (c) no assumptions regarding wave shape spectra have been made; (d) no assumptions regarding the shape of particle distribution have been made to calculate the growth rate; (e) pitch- angle, energy, and mix diffusions are taken into account together for the first time; (f) the exact loss-cone RC analytical solution has been found and coupled with bounce-averaged numerical solution of kinetic equation; (g) LHW are included as an additional factor that contributes to saturation process of EMIC waves; and (h) the hot ions were included in the real part of dielectric permittivity tensor. We compare our theoretical results with the different EMIC waves models as well as RC experimental data.

Khazanov, G. V.↗
NASA NTRS2005

Ring Current-Electromagnetic Ion Cyclotron Waves Coupling

The effect of Electromagnetic Ion Cyclotron (EMIC) waves, generated by ion temperature anisotropy in Earth s ring current (RC), is the best known example of wave- particle interaction in the magnetosphere. Also, there is much controversy over the importance of EMIC waves on RC depletion. Under certain conditions, relativistic electrons, with energies 21 MeV, can be removed from the outer radiation belt (RB) by EMIC wave scattering during a magnetic storm. That is why the calculation of EMIC waves must be a very critical part of the space weather studies. The new RC model that we have developed and present for the first time has several new features that we have combine together in a one single model: (a) several lower frequency cold plasma wave modes are taken into account; (b) wave tracing of these wave has been incorporated in the energy EMIC wave equation; (c) no assumptions regarding wave shape spectra have been made; (d) no assumptions regarding the shape of particle distribution have been made to calculate the growth rate; (e) pitch-angle, energy, and mix diffusions are taken into account together for the first time; (f) the exact loss-cone RC analytical solution has been found and coupled with bounce-averaged numerical solution of kinetic equation; (g) the EMIC waves saturation due to their modulation instability and LHW generation are included as an additional factor that contributes to this process; and (h) the hot ions were included in the real part of dielectric permittivity tensor. We compare our theoretical results with the different EMIC waves models as well as RC experimental data.

Khazanov, G. V.↗
DOE OSTI2024

Harnessing complexity: Nonlinear optical phenomena in L-shapes, nanocrescents, and split-ring resonators

Here, we conduct systematic studies of the optical characteristics of plasmonic nanoparticles that exhibit C 2v symmetry. In particular, we analyze three distinct geometric configurations: an L-type shape, a crescent, and a split-ring resonator shaped like the Greek letter π. Optical properties are examined using the finite-difference time-domain method. It is demonstrated that all three shapes exhibit two prominent plasmon modes associated with the two axes of symmetry. This is in addition to a wide range of resonances observed at high frequencies corresponding to quadrupole modes and peaks due to sharp corners. Next, to facilitate nonlinear analysis, we employ a semiclassical hydrodynamic model, where the electron pressure term is explicitly accounted for. This model goes beyond the standard Drude description and enables capturing nonlocal and nonlinear effects. Employing this model enables us to rigorously examine the second-order angular resolved nonlinear optical response of these nanoparticles in each of the three configurations. Two pumping regimes are considered, namely, continuous wave (CW) and pulsed excitations. For CW pumping, we explore the properties of the second harmonic generation (SHG). Polarization and angle-resolved SHG spectra are obtained, revealing strong dependence on the nanoparticle geometry and incident wave polarization. The C 2v symmetry is shown to play a key role in determining the polarization states and selection rules of the SHG signal. For pulsed excitations, we discuss the phenomenon of broadband terahertz (THz) generation induced by the difference-frequency generation . It is shown that the THz emission spectra exhibit unique features attributed to the plasmonic resonances and symmetry of the nanoparticles. The polarization of the generated THz waves is also examined, revealing interesting patterns tied to the nanoparticle geometry. To gain deeper insight, we propose an analytical theory that agrees very well with the numerical experiments. The theory shows that the physical origin of the THz radiation is the mixing of various frequency components of the fundamental pulse by the second-order nonlinear susceptibility. An expression for the far-field THz intensity is derived in terms of the incident pulse parameters and the nonlinear response tensor of the nanoparticle. The results presented in this work offer new insights into the linear and nonlinear optical properties of nanoparticles with C 2v symmetry. The demonstrated strong SHG response and efficient broadband THz generation hold great promise for applications in nonlinear spectroscopy, nanophotonics, and optoelectronics. The proposed theoretical framework also provides a valuable tool for understanding and predicting the nonlinear behavior of other related nanostructures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗