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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

A micro-scale cutting model for UD CFRP composites with thermo-mechanical coupling

Cutting a unidirectional carbon fiber-reinforced polymer (UD CFRP) structure is the basic unit for CFRP machining, which is a complex thermal-mechanically coupled process. To reveal the deformation mechanism and predict cutting force in UD CFRP micro cutting, a micro-scale fracture model for UD CFRP cutting with thermal-mechanical coupling is demonstrated in this paper, which captures the failure modes for fibers, matrix and the interface based on a micro-level RVE using a relatively simple damage based fracture method. The thermal-mechanical coupling model at the micro scale is developed on the basis of the plastic energy dissipation and frictional heating during cutting. Failure models for the fiber, matrix and interface region are applied depending on the material properties of each of these three phases. Numerical simulations based on the above model with different fiber orientations were performed to predict the deformation and forces of different components in UD CFRP. Cutting experiments with the same fiber orientations as considered in the simulations were carried out to validate the force and deformation results. The predicted force and deformation patterns match well with evidence from our experiments. In general, the cutting force is larger than the thrust force regardless of fiber orientation. The cutting force reaches a maximum as the fiber orientation approaches 90 , but thrust forces do not vary substantially across cases. When the fiber orientation is acute, the deformation of fibers is much smaller than when the cutting angle is obtuse. Surface roughness follows the same trend with cutting angle as fiber deformation.

42 ENGINEERING↗
DOE OSTI2017

Brownian dynamics of confined suspensions of active microrollers

In this study, we develop efficient numerical methods for performing many-body Brownian dynamics simulations of a recently observed fingering instability in an active suspension of colloidal rollers sedimented above a wall [M. Driscoll, B. Delmotte, M. Youssef, S. Sacanna, A. Donev, and P. Chaikin, Nat. Phys. (2016), preprint arXiv:1609.08673. We present a stochastic Adams-Bashforth integrator for the equations of Brownian dynamics, which has the same cost but is more accurate than the widely used Euler-Maruyama scheme, and use a random finite difference to capture the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. We generate the Brownian increments using a Krylov method and show that for particles confined to remain in the vicinity of a no-slip wall by gravity or active flows, the number of iterations is independent of the number of particles. Our numerical experiments with active rollers show that the thermal fluctuations set the characteristic height of the colloids above the wall, both in the initial condition and the subsequent evolution dominated by active flows. Finally, the characteristic height in turn controls the time scale and wavelength for the development of the fingering instability

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A moment-based kinetic theory model for polydisperse gas–particle flows

Starting from a generalized population balance equation and the Boltzmann–Enskog collision model for hard spheres, a kinetic theory model for polydisperse gas–particle flows is introduced. Here, polydispersity results from spherical particles with the same material density but different diameters. The particle size distribution (PSD) of the particles is allowed to evolve in space and time due to physical processes such as mixing. In order to treat a continuous PSD, the particle-phase model is formulated in terms of the moments of the PSD, and velocity moments conditioned on the particle size. Velocity moments up to second order are included, resulting in transport equations for the mass, momentum and granular temperature, all conditioned on the particle size. In the numerical implementation, the PSD is represented using quadrature-based moment methods (QBMM). With QBMM, a continuous PSD can be treated using a relatively small number of moments as compared to class or sectional methods. In this work, a realizable numerical algorithm for solving the moment system in a finite-volume code is proposed, valid for dilute systems wherein frictional forces are negligible. The ability of the proposed model to describe polydisperse gas–particle systems is demonstrated using cluster-induced turbulence and riser flow.

42 ENGINEERING↗
DOE OSTI2025

A Comparative Study of Physics‐Informed and Data‐Driven Neural Networks for Compound Flood Simulation at River‐Ocean Interfaces: A Case Study of Hurricane Irene

Simulating compound flooding (CF) at the river-ocean interface within large-scale Earth System Models (ESMs) presents significant challenges due to complex interactions between river discharge, storm surge, and tides. This study assesses the comparative advantages of physics-informed and data-driven machine learning (ML) approaches for enhancing local ESM performance. We systematically compare data-driven neural network models (i.e., CNNs, U-Net, Long Short-Term Memory (LSTM), Gated Recurrent Unit), and physics-informed neural network (PINN) models, including vanilla PINN and a finite-difference-based PINN (FD-PINN). Specifically, FD-PINN is introduced to enhance computational efficiency, accelerating vanilla PINNs by ∼6.5 times while improving accuracy. To enhance data-driven model training, a new data-generation approach is developed to sample historical fluvial and coastal flood events, which ensures a robust data set for extreme event prediction. The models are evaluated using a realistic one-dimensional river domain extracted from an ESM's river mesh and the Hurricane Irene event as an independent test case. Results show that FD-PINN achieves accurate predictions with significantly reduced computational costs relative to vanilla PINNs. Among data-driven models, the best overall performance is achieved by a CNN-LSTM hybrid, which balances accuracy and efficiency. While a fully connected CNN (CNN-FC) provides the best accuracy, it incurs high computational cost. Architectures lacking strong temporal modeling tend to underperform on unseen events. These findings highlight the importance of sequence-aware designs for robust generalization. This study reveals the trade-offs between physics-informed and data-driven models and proposes an adaptive hybrid framework for integrating ML into ESMs to enhance local flood simulations.

Earth Systems Modeling↗
DOE OSTI2022

Commensuration effects on skyrmion Hall angle and drag for manipulation of skyrmions on two-dimensional periodic substrates

Here, we examine the dynamics of an individually driven skyrmion moving through a background lattice of skyrmions coupled to a 2D periodic substrate as we vary the ratio of the number of skyrmions to the number of pinning sites across commensurate and incommensurate conditions. As the skyrmion density increases, the skyrmion Hall angle is nonmonotonic, dropping to low or zero values in commensurate states and rising to an enhanced value in incommensurate states. Under commensuration, the driven skyrmion is channeled by a symmetry direction of the pinning array and exhibits an increased velocity. At fillings for which the skyrmion Hall angle is zero, the velocity has a narrow band noise signature, while for incommensurate fillings, the skyrmion motion is disordered and the velocity noise is broad band. Under commensurate conditions, multi-step depinning transitions appear and the skyrmion Hall angle is zero at low drives but becomes finite at higher drives, while at incommensurate fillings there is only a single depinning transition. As the gyrotropic component of the skyrmion dynamics, called the Magnus force, increases, peaks in the velocity that appear in commensurate regimes cross over to dips, and new types of directional locking effects can arise in which the skyrmion travels along other symmetry directions of the background lattice. At large Magnus forces, and particularly at commensurate fillings, the driven skyrmion can experience a velocity boost in which the skyrmion moves faster than the applied drive due to the alignment of the Magnus-induced velocity with the driving direction. In some cases, an increase of the Magnus force can produce regimes of enhanced pinning when the skyrmion is forced to move along a nonsymmetry direction of the periodic pinning array. This is in contrast to systems with random pinning, where increasing the Magnus force generally reduces the pinning effect. We demonstrate these dynamics for both square and triangular substrates and map out the different regimes as a function of filling fraction, pinning force, and the strength of the Magnus force in a series of dynamic phase diagrams.

36 MATERIALS SCIENCE↗
NASA NTRS2005

Inference of Ice Cloud Properties from High-spectral Resolution Infrared Observations

The theoretical basis is explored for inferring the microphysical properties of ice crystal from high-spectral resolution infrared observations. A radiative transfer model is employed to simulate spectral radiances to address relevant issues. The extinction and absorption efficiencies of individual ice crystals, assumed as hexagonal columns for large particles and droxtals for small particles, are computed from a combination of the finite- difference time-domain (FDTD) technique and a composite method. The corresponding phase functions are computed from a combination of FDTD and an improved geometric optics method (IGOM). Bulk scattering properties are derived by averaging the single- scattering properties of individual particles for 30 particle size distributions developed from in situ measurements and for additional four analytical Gamma size distributions for small particles. The non-sphericity of ice crystals is shown to have a significant impact on the radiative signatures in the infrared (IR) spectrum; the spherical particle approximation for inferring ice cloud properties may result in an overest&ation of the optical thickness and an inaccurate retrieval of effective particle size. Furthermore, we show that the error associated with the use of the Henyey-Greenstein phase function can be as larger as 1 K in terms of brightness temperature for larger particle effective size at some strong scattering wavenumbers. For small particles, the difference between the two phase functions is much less, with brightness temperatures generally differing by less than 0.4 K. The simulations undertaken in this study show that the slope of the IR brightness temperature spectrum between 790-960/cm is sensitive to the effective particle size. Furthermore, a strong sensitivity of IR brightness temperature to cloud optical thickness is noted within the l050-1250/cm region. Based on this spectral feature, a technique is presented for the simultaneous retrieval of the visible optical thickness and effective particle size from high spectral resolution infrared data under ice cloudy con&tion. The error analysis shows that the uncertainty of the retrieved optical thickness and effective particle size has a small range of variation. The error for retrieving particle size in conjunction with an uncertainty of 5 K in cloud'temperature, or a surface temperature uncertainty of 2.5 K, is less than 15%. The corresponding e m r in the uncertainty of optical thickness is within 5-2096, depending on the value of cloud optical thickness. The applicability of the technique is demonstrated using the aircraft-based High- resolution Interferometer Sounder (HIS) data from the Subsonic Aircraft: Contrail and Cloud Effects Special Study (SUCCESS) in 1996 and the First ISCCP Regional Experiment - Arctic Clouds Experiment (FIRE-ACE) in 1998.

Huang, Hung-Lung↗
DOE OSTI2023

Assessing parallel path cooling tower performance via artificial neural networks

Real-time monitoring of a research nuclear reactor, a system in which all generated power is dissipated to the environment, can be performed via analysis of the heat rejection from the cooling system. Given an inlet water temperature and flow rate, the reactor power can be well-approximated from the outlet water temperature; however, the instrumentation to measure outlet conditions may not be robust or accurate. If we know how a cooling tower performs from historical data, but cannot measure the outlet temperature, a mathematical representation of the system can be inverted to obtain the outlet water temperature that describes the cooling capacity. Unfortunately, model inversion processes are computationally expensive. To address this, an artificial neural network (ANN) is implemented to assess the performance of a multi-cell cooling tower for a nuclear reactor. This approach leverages the Merkel model to obtain an extensive data set describing performance of the cooling tower cells throughout a wide array of potential operating conditions. The Merkel model is expressed as a function of four parameters: the inlet and outlet water temperatures, inlet air wet bulb temperature, and ratio of liquid-to-gas mass flow rates (L/G), which together provide a non-dimensional number indicative of cooling tower performance, called the Merkel integral. Computing a 4-dimensional data structure that describes finite combinations of the Merkel integral, an inverse model is then generated using an ANN to determine the cell outlet water temperature from the other three model parameters along with the computed Merkel integral. Compared to traditional model inversion methods, the ANN reduces the computational time by approximately 4 orders of magnitude, with effectively no sacrifice to solution accuracy, and could be applied for different cooling towers in the event the performance curve is known. Finally, three use cases of the ANN are then reviewed: (1) determining the cell outlet water temperatures when gas flow at rated conditions (GFRC) is known, (2) performing the prior case without knowledge of the GRFC, and (3) assessing performance differences between the individual tower cells.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

An Eulerian projection method for quasi-static elastoplasticity

A well-established numerical approach to solve the Navier-Stokes equations for incompressible fluids is Chorin's projection method, whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved, which is used to orthogonally project the velocity field to maintain the incompressibility constraint. In this paper, we develop a mathematical correspondence between Newtonian fluids in the incompressible limit and hypo-elastoplastic solids in the slow, quasi-static limit. Using this correspondence, we formulate a new fixed-grid, Eulerian numerical method for simulating quasi-static hypo-elastoplastic solids, whereby the stress is explicitly updated, and then an elliptic problem for the velocity is solved, which is used to orthogonally project the stress to maintain the quasi-staticity constraint. We develop a finite-difference implementation of the method and apply it to an elasto-viscoplastic model of a bulk metallic glass based on the shear transformation zone theory. We show that in a two-dimensional plane strain simple shear simulation, the method is in quantitative agreement with an explicit method. Like the fluid projection method, it is efficient and numerically robust, making it practical for a wide variety of applications. We also demonstrate that the method can be extended to simulate objects with evolving boundaries. Here, we highlight a number of correspondences between incompressible fluid mechanics and quasi-static elastoplasticity, creating possibilities for translating other numerical methods between the two classes of physical problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Bose-Luttinger liquids

In this report we study systems of bosons whose low-energy excitations are located along a spherical submanifold of momentum space. We argue for the existence of gapless phases which we dub “Bose-Luttinger liquids,” which in some respects can be regarded as bosonic versions of Fermi liquids, while in other respects they exhibit striking differences. These phases have bosonic analogues of Fermi surfaces, and like Fermi liquids they possess a large number of emergent conservation laws. Unlike Fermi liquids, however, these phases lack quasiparticles, possess different RG flows, and have correlation functions controlled by a continuously varying exponent η, which characterizes the anomalous dimension of the bosonic field. We show that when η > 1, these phases are stable with respect to all symmetric perturbations. These theories may be of relevance to several physical situations, including frustrated quantum magnets, rotons in superfluid He, and superconductors with finite-momentum pairing. As a concrete application, we show that coupling a Bose-Luttinger liquid to a conventional Fermi liquid produces a resistivity scaling with temperature as T η . We argue that this may provide an explanation for the non-Fermi liquid resistivity observed in the paramagnetic phase of MnSi.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Towards a generalized computational fluid dynamics technique for all Mach numbers

Currently there exists no single unified approach for efficiently and accurately solving computational fluid dynamics (CFD) problems across the Mach number regime, from truly low speed incompressible flows to hypersonic speeds. There are several CFD codes that have evolved into sophisticated prediction tools with a wide variety of features including multiblock capabilities, generalized chemistry and thermodynamics models among other features. However, as these codes evolve, the demand placed on the end user also increases simply because of the myriad of features that are incorporated into these codes. In order for a user to be able to solve a wide range of problems, several codes may be needed requiring the user to be familiar with the intricacies of each code and their rather complicated input files. Moreover, the cost of training users and maintaining several codes becomes prohibitive. The objective of the current work is to extend the compressible, characteristic-based, thermochemical nonequilibrium Navier-Stokes code GASP to very low speed flows and simultaneously improve convergence at all speeds. Before this work began, the practical speed range of GASP was Mach numbers on the order of 0.1 and higher. In addition, a number of new techniques have been developed for more accurate physical and numerical modeling. The primary focus has been on the development of optimal preconditioning techniques for the Euler and the Navier-Stokes equations with general finite-rate chemistry models and both equilibrium and nonequilibrium thermodynamics models. We began with the work of Van Leer, Lee, and Roe for inviscid, one-dimensional perfect gases and extended their approach to include three-dimensional reacting flows. The basic steps required to accomplish this task were a transformation to stream-aligned coordinates, the formulation of the preconditioning matrix, incorporation into both explicit and implicit temporal integration schemes, and modification of the numerical flux formulae. In addition, we improved the convergence rate of the implicit time integration schemes in GASP through the use of inner iteration strategies and the use of the GMRES (General Minimized Resisual) which belongs to the class of algorithms referred to as Krylov subspace iteration. Finally, we significantly improved the practical utility of GASP through the addition of mesh sequencing, a technique in which computations begin on a coarse grid and get interpolated onto successively finer grids. The fluid dynamic problems of interest to the propulsion community involve complex flow physics spanning different velocity regimes and possibly involving chemical reactions. This class of problems results in widely disparate time scales causing numerical stiffness. Even in the absence of chemical reactions, eigenvalue stiffness manifests itself at transonic and very low speed flows which can be quantified by the large condition number of the system and evidenced by slow convergence rates. This results in the need for thorough numerical analysis and subsequent implementation of sophisticated numerical techniques for these difficult yet practical problems. As a result of this work, we have been able to extend the range of applicability of compressible codes to very low speed inviscid flows (M = .001) and reacting flows.

Walters, R. W.↗
DOE OSTI2016

Radiative decay rate of excitons in square quantum wells: Microscopic modeling and experiment

The binding energy and the corresponding wave function of excitons in GaAs-based finite square quantum wells (QWs) are calculated by the direct numerical solution of the three-dimensional Schrödinger equation. The precise results for the lowest exciton state are obtained by the Hamiltonian discretization using the high-order finite-difference scheme. The microscopic calculations are compared with the results obtained by the standard variational approach. The exciton binding energies found by two methods coincide within 0.1 meV for the wide range of QW widths. The radiative decay rate is calculated for QWs of various widths using the exciton wave functions obtained by direct and variational methods. The radiative decay rates are confronted with the experimental data measured for high-quality GaAs/AlGaAs and InGaAs/GaAs QW heterostructures grown by molecular beam epitaxy. The calculated and measured values are in good agreement, though slight differences with earlier calculations of the radiative decay rate are observed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Fano resonances based on plasmonic square resonator with high figure of merits and its application in glucose concentrations sensing

A compact plasmonic structure is proposed employing symmetrical metal–insulator-metal (MIM) waveguides coupled to the square resonator for nano-sensing applications, especially for water glucose sensing. Finite difference time domain method is chosen to derivate the output characteristics and magnetic-field distributions. Outcomes illustrate the Fano resonance in the output characteristics can be simply managed by varying the inner and outer lengths and the refractive index of the square cavity. Also, between Fano resonance wavelength and resonator length, a linear behavior exists. These features suggest that physical parameters provide flexibility to propose the structure. Our plasmonic device produces a sensitivity and figure of merit of about 6400 nm/RIU and 1 × 10{sup 4}, respectively. By utilizing the mathematical model for water refractive index, we aim to develop a sensor structure to detect the glucose concentration in water. This designed sensor may discover significant applications in future nanosensing domain.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2019

Discovery of Activities via Statistical Clustering of Fixation Patterns

Human behavior often consists of a series of distinct activities, each characterized by a unique pattern of interaction with the visual environment. This is true even in a restricted domain, such as a pilot flying an airplane; in this case, activities with distinct visual signatures might be things like communicating, navigating, monitoring, etc. We propose a novel analysis method for gaze-tracking data, to perform blind discovery of these hypothetical activities. We compare, not individual fixations, but groups of fixations aggregated over a fixed time interval (Tau). We assume that the environment has been divided into a finite set of discrete areas-of-interest (AOIs). For a given time interval, we compute the proportion of time spent fixating each AOI, resulting in an N-dimensional vector, where N is the number of AOIs. These proportions can be converted to integer counts by multiplying by Tau divided by the average fixation duration, a parameter that we fix at 283 milliseconds. We compare different intervals by computing the chi-squared statistic. The p-value associated with the statistic is the likelihood of observing the data under the hypothesis that the data in the two intervals were generated by a single process with a single set of probabilities governing the fixation of each AOI. We cluster the intervals, first by merging adjacent intervals that are sufficiently similar, optionally shifting the boundary between non-merged intervals to maximize the difference. Then we compare and cluster non-adjacent intervals. The method is evaluated using synthetic data generated by a hand-crafted set of activities. While the method generally finds more activities than put into the simulation, we have obtained agreement as high as 80 percent between the inferred activity labels and ground truth.

Eye Movements↗
DOE OSTI2021

Momentum distribution of the uniform electron gas at finite temperature: Effects of spin polarization

We carry out extensive direct path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) at finite temperature for different values of the spin-polarization ξ. This allows us to unambiguously quantify the impact of spin effects on the momentum distribution function n(k) and related properties. We find that interesting physical effects like the interaction-induced increase in the occupation of the zero-momentum state n(0) substantially depend on ξ. Our results further advance the current understanding of the UEG as a fundamental model system, and are of practical relevance for the description of transport properties of warm dense matter in an external magnetic field. All PIMC results are freely available online and can be used as a benchmark for the development of methods and applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium

Abstract Singular currents typically appear on rational surfaces in non-axisymmetric ideal magnetohydrodynamic (MHD) equilibria with a continuum of nested flux surfaces and a continuous rotational transition. These currents have two components: a surface current (Dirac δ -function in flux surface labeling) that prevents the formation of magnetic islands, and an algebraically divergent Pfirsch–Schlüter current density when a pressure gradient is present across the rational surface. On flux surfaces adjacent to the rational surface, the traditional treatment gives the Pfirsch–Schlüter current density scaling as J ∼ 1 / Δ ι , where Δ ι is the difference of the rotational transform relative to the rational surface. If the distance s between flux surfaces is proportional to Δ ι , the scaling relation J ∼ 1 / Δ ι ∼ 1 / s will lead to a paradox that the Pfirsch–Schlüter current is not integrable. In this work, we investigate this issue by considering the pressure-gradient-driven singular current in the Hahm–Kulsrud–Taylor problem, which is a prototype for singular currents arising from resonant magnetic perturbations. We show that not only the Pfirsch–Schlüter current density but also the diamagnetic current density are divergent as ∼ 1 / Δ ι . However, due to the formation of a Dirac δ -function current sheet at the rational surface, the neighboring flux surfaces are strongly packed with s ∼ ( Δ ι ) 2 . Consequently, the singular current density J ∼ 1 / s , making the total current finite, thus resolving the paradox. Furthermore, the strong packing of flux surfaces causes a steepening of the pressure gradient near the rational surface, with ∇ p ∼ d p / d s ∼ 1 / s . In general non-axisymmetric MHD equilibrium, contrary to Grad’s conjecture that the pressure profile is flat around densely distributed rational surfaces, our result suggests a pressure profile that densely steepens around them.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1994

Kinetic and thermodynamic properties of a convecting plasma in a two-dimensional dipole field

Charged particle guiding center motion is considered in the magnetic field of a two-dimensional ('line') dipole on which is superimposed a small, static, perpendicular electric field. The parallel equation of motion is that of a simple harmonic oscillator for cos theta, the cosine of magnetic colatitude theta. Equations for the perpendicular electric and magnetic drifts are derived as well as their bounce-averaged forms. The latter are solved to yield a bounce-averaged guiding center trajectory, which is the same as that obtained from conversation of magnetic moment mu, longitudinal invariant J, and total (kinetic plus electrostatic) energy K. The algebraic simplicity of the trajectory equations is also manifest in the forms of the invariants. An interesting result is that guiding centers drift in such a way that they preserve the values of their equatorial pitch angles and (equivalently) mirror latitudes. The most general Maxwellian form of the equilibrium one-particle distribution function f is constructed from the invariants, and spatially varying density and pressure moments, parallel and perpendicular to the magnetic field, are identified. Much of the paper deals with the more restricted problem in which f is specified as a bi-Maxwellian over a straight line of finite length in the equatorial plane of the dipole and perpendicular to field lines. This might be thought of as specifying a cross-tail ion injection source; our formalism then describes the subsequent spatial development. The distribution away from the source is a scaled bi-Maxwellian but one that is cut off at large and small kinetic energies, which depend on position. Density and pressure components are reduced from the values they would have if the total content of individual flux tubes convected intact. The equatorial and meridional variations of density and pressure components are examined and compared systematically for the isotropic and highly anisotropic situations. There appears to be little qualitative difference due to anisotropy. An anisotropy measure is defined, and its spatial variation determined as a signature of possible MHD instability. Extreme values are found, larger than at the source, but the plasma beta in such regions is probably so low as to render the effect inconsequential energetically. Finally, the possible consequence of 'nonadia- batic' pressure profiles on electrostatic interchanges is considered, and a boundary delineating stabilizing and destabilizing regions determined.

Huang, T. S.↗
DOE OSTI2017

Extended Hamiltonians and shift, ladder functions and operators

In recent years, many natural Hamiltonian systems, classical and quantum, with constants of motion of high degree, or symmetry operators of high order, have been found and studied. Most of these Hamiltonians, in the classical case, can be included in the family of extended Hamiltonians, geometrically characterized by the structure of warped manifold of their configuration manifold. For the extended Hamiltonians, the characteristic constants of motion of high degree are polynomial in the momenta of determined form. We consider here a different form of the constants of motion, based on the factorization procedure developed for systems of two degrees of freedom by S. Kuru, J. Negro and others. We show that an important subclass of the extended Hamiltonians, with arbitrary dimension, admits factorized constants of motion and we determine their expression. The classical constants can be polynomial or non-polynomial in the momenta, but the factorization procedure allows, in a type of extended Hamiltonians, their quantization via shift and ladder operators, for systems of any finite dimension. - Highlights: • A factorization procedure is proposed for first integrals of high degree of extended Hamiltonian systems. • The extended Hamiltonians are defined on warped manifolds of any finite dimension. • Polynomial first integrals are quantized into factorized polynomial symmetry operators of Laplace–Beltrami-type quantum Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗