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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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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Bounce-Averaged Hamiltonian for Charged Particles in an Axisymmetric but Nondipolar Model Magnetosphere

In order to facilitate bounce-averaged guiding center simulations of geomagnetically trapped particles, we express the kinetic energy of a particle with magnetic coordinates (L,phi) as an analytic function of the first two adiabatic invariants (M, J) and the L value of the field line. The magnetic field model is axisymmetric, consisting of a dipolar B field plus a uniform southward magnetic field parallel to the dipole moment mu(sub E). This model magnetosphere is surrounded by a circular equatorial neutral line whose radius b is an adjustable parameter. The L value of a field line is (by definition) inversely proportional to the flux enclosed by the corresponding magnetic shell of equatorial radius r(sub 0), and the L value at the neutral line (r(sub 0) = b) is denoted L*. The azimuthal coordinate phi measures magnetic local time. The best functional representation found for the normalized difference (L(exp 3)a(exp 3)/mu(sub E))(B(sub m) - B(sub 0)) between mirror-point field B(sub m) and equatorial field B(sub 0) along any field line is a 5-term expansion in powers (2/3 through 6/3) of the quantity X equivalent to (La/mu(sub E))(exp 1/2)K, where K equivalent to (J(exp 2)/8m(sub 0)M)(exp 1/2) is an adiabatically conserved quantity independent of particle energy, m(sub 0) is the rest mass of the particle, and a is the radius of the Earth. This functional form is motivated by results for limiting cases in which particles mirror very near and very far from the magnetic equator. Expansion coefficients corresponding to various powers of X are obtained from least squares fits to numerically computed results for X as a function of L and B(sub m). These are accurately expressible as fourth-order polynomials in (r(sub 0)/b)(exp 3), hence indirectly as functions of L/L* = 3La/2b. This representation, which leads (except for a manageably small region of parameter space) to better than 1% accuracy in the specification of B(sub m) as a function of K and L, allows bounce-averaged guiding center simulations to be performed without actually tracing the bounce motions of individual particles. Bounce-averaged drifts L' (meridional) and phi' (azimuthal) are proportional to derivatives of the Hamiltonian H (sum of kinetic and potential energies) with respect to phi and L, respectively. Our formulation thus provides a computationally efficient method for tracing the bounce-averaged adiabatic motion (conserving all three invariants) and nonadiabatic transport (violating the third invariant while conserving the first two invariants) of geomagnetically trapped particles in the model magnetosphere.

Schulz, Michael↗
NASA NTRS2003

Spurious States-Free Solution of the k dot p Hamiltonian for Heterostructures

A method for eliminating spurious solution in the k dot p Hamiltonian has been proposed. Introduction of additional off-diagonal alpha k(exp 2) term converts spurious solution with large real wave vector to evanescent solution with large imaginary wave vector. This modification keeps the same effective masses at Gamma point and introduces negligible deviation from original nonparabolicity. A set of unphysical fast oscillation eigenfunctions in confined states of heterostructures are removed.

Kolokolov, Konstantin I.↗
NASA NTRSDate not supplied

Hamiltonian Optimal Control of Distributed Lagrangian Systems

This lecture presents a Hamiltonian control method and a distributed optimal control method for distributed Lagrangian systems. The distributed optimal control theory is formulated using a semi-group abstraction resulting in an integro-differential Riccati equation.

Distributed Optimal Control↗
NASA NTRSDate not supplied

Hamiltonian Control for Coupled Bending-Torsion Motion of a Swept Wing With R. T. Jones' Approximation

This paper presents distributed Hamiltonian control design approach for a Lagrangian infinite-dimensional system describing the coupled bending-torsion motion of a swept wing in unsteady airflow, which is taken into account using Theodorsen's complex valued function of reduced frequency. An implementable flutter suppressing control surface deflection commands are obtained using modes separation and R.T. Jones's approximation, and were validated in desktop simulations for flight conditions beyond the flutter airspeed.

Vahram Stepanyan↗
DOE OSTI2021

Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware

In this work we present a detailed analysis of variational quantum phase estimation (VQPE), a method based on real-time evolution for ground and excited state estimation on near-term hardware. We derive the theoretical ground on which the approach stands, and demonstrate that it provides one of the most compact variational expansions to date for solving strongly correlated Hamiltonians. At the center of VQPE lies a set of equations, with a simple geometrical interpretation, which provides conditions for the time evolution grid in order to decouple eigenstates out of the set of time evolved expansion states, and connects the method to the classical filter diagonalization algorithm. Further, we introduce what we call the unitary formulation of VQPE, in which the number of matrix elements that need to be measured scales linearly with the number of expansion states, and we provide an analysis of the effects of noise which substantially improves previous considerations. The unitary formulation allows for a direct comparison to iterative phase estimation. Our results mark VQPE as both a natural and highly efficient quantum algorithm for ground and excited state calculations of general many-body systems. We demonstrate a hardware implementation of VQPE for the transverse field Ising model. Further, we illustrate its power on a paradigmatic example of strong correlation (Cr2 in the SVP basis set), and show that it is possible to reach chemical accuracy with as few as ~50 timesteps.

Klymko, Katherine↗
DOE OSTI2026

SCF Framework, HF Stability, and RPA Correlation for Jordan–Wigner-Transformed Spin Hamiltonians on Arbitrary Coupling Topologies

Mapping spins to fermions via the Jordan–Wigner (JW) transformation can render mean-field (Hartree–Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is not limited by the nonlocal structure of JW strings or by site ordering because string operators can be absorbed into Thouless rotations of a Slater determinant, and the variational optimization of a unitary Lie-algebraic similarity transformation removes any ordering dependence. Leveraging these ideas, we develop a self-consistent field (SCF) scheme that expresses the mean-field energy as a functional of the single-particle density matrix, providing an alternative to gradient-based optimization of Thouless parameters. We derive the analytical orbital Hessian to diagnose HF stability and compute the ground-state correlation energy through the random-phase approximation (RPA). Benchmark results for the XXZ and J 1 –J 2 model on one- and two-dimensional lattices demonstrate that RPA significantly improves mean-field accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted Z -graded graphs

In this study, we consider discrete one-dimensional nonlinear equations and present the procedure of lifting them to Z -graded graphs. We identify conditions that allow one to lift one-dimensional solutions to solutions on graphs. In particular, we prove the existence of solitons for static potentials on graded fractal graphs. We also show that even for a simple example of a topologically interesting graph, the corresponding non-trivial Lax pairs and associated unitary transformations do not lift to a Lax pair on the Z -graded graph.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Geometric entropies and their Hamiltonian flows

In holographic theories, the Hubeny-Rangamani-Takayanagi (HRT) area operator plays a key role in our understanding of the emergence of semiclassical Einstein-Hilbert gravity. When higher derivative corrections are included, the role of the area is instead played by a more general functional known as the geometric entropy. It is thus of interest to understand the flow generated by the geometric entropy on the classical phase space. In particular, the fact that the associated flow in Einstein-Hilbert or Jackiw-Teitelboim (JT) gravity induces a relative boost between the left and right entanglement wedges is deeply related to the fact that gravitational dressing promotes the von Neumann algebra of local fields in each wedge to type II. This relative boost is known as a boundary-condition-preserving (BCP) kink-transformation. In a general theory of gravity (with arbitrary higher-derivative terms), it is straightforward to show that the flow continues to take the above geometric form when acting on a spacetime where the HRT surface is the bifurcation surface of a Killing horizon. However, the form of the flow on other spacetimes is less clear. In this paper, we use the manifestly-covariant Peierls bracket to explore such flows in two-dimensional theories of JT gravity coupled to matter fields with higher derivative interactions. The results no longer take a purely geometric form and, instead, demonstrate new features that should be expected of such flows in general higher derivative theories. We also show how to obtain the above flows using Poisson brackets.

AdS-CFT correspondence↗
DOE OSTI2025

A Type II Hamiltonian Variational Principle and Adjoint Systems for Lie Groups

We present a novel Type II variational principle on the cotangent bundle of a Lie group which enforces Type II boundary conditions, i.e., fixed initial position and final momentum. In general, such Type II variational principles are only globally defined on vector spaces or locally defined on general manifolds; however, by left translation, we are able to define this variational principle globally on cotangent bundles of Lie groups. Type II boundary conditions are particularly important for adjoint sensitivity analysis, which is our motivating application. As such, we additionally discuss adjoint systems on Lie groups, their properties, and how they can be used to solve optimization problems subject to dynamics on Lie groups.

97 MATHEMATICS AND COMPUTING↗