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Results for “many body problems”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

The relativistic many body problem with an oscillator interaction

We start with the total energy E for a system of three scalar relativistic particles that, because of Einstein's relation, will have square roots of functions of the momenta. By taking powers of this relation, we finally get a fourth degree polynomial in E(exp 2), where the square roots have disappeared, and which we can convert into a type of Schroedinger equation. To be in the center of mass frame we pass to Jocobi momenta and then replace them by creation and annihilation operators. We thus get an equation in terms of the generators of a U(2) group, which, in principle, we can solve in an elementary way. Finally, we rewrite our equation in a Poincare invariant form.

Moshinsky, Marcos↗
NASA NTRS2021

Computation and Analysis of Jupiter-Europa and Jupiter-Ganymede Resonant Orbits in the Planar Concentric Circular Restricted 4-body Problem

Many unstable periodic orbits of the planar circular restricted 3-body problem (PCRTBP) persist as invariant tori when a periodic forcing is added to the equa- tions of motion. In this study, we compute tori corresponding to exterior Jupiter- Europa and interior Jupiter-Ganymede PCRTBP resonant periodic orbits in a con- centric circular restricted 4-body problem (CCR4BP). Motivated by the 2:1 Laplace resonance between Europa and Ganymede’s orbits, we then attempt the continu- ation of a Jupiter-Europa 3:4 resonant orbit from the CCR4BP into the Jupiter- Ganymede PCRTBP. We strongly believe that the resulting dynamical object is a KAM torus lying near but not on the 3:2 Jupiter-Ganymede resonance.

Gunter, Brian↗
NASA NTRS1966

Problems of stellar dynamics

Many-body problem, continuum, and statistical methods applied to dynamics of star clusters, with bibliography

STAR CLUSTER↗
NASA NTRS1979

Dominant partition method

By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails.

Dixon, R. M.↗
NASA NTRS1967

Physics

Polar substorm model on auroral effects, algebra of fermi-dirac operators applied to many-body problems, and dynamitron accelerator as thermal neutron source

MANY-BODY PROBLEM↗
NASA NTRS1983

The unitary group and the electron correlation problem

A survey is given of the background and development of the unitary group approach and its graphically-based implementations for electronic structure calculations. The nature of the unitary group and its relationship to the electronic many-body problem are briefly discussed, as well as the reasons, purpose, and methodology of its application to this problem. As much as possible, this discussion is on a mostly intuitive, non-technical level. Finally, recent accomplishments and expected future developments are briefly mentioned.

Shavitt, I.↗
NASA NTRS1989

Interaction dynamics of multiple autonomous mobile robots in bounded spatial domains

A general navigation strategy for multiple autonomous robots in a bounded domain is developed analytically. Each robot is modeled as a spherical particle (i.e., an effective spatial domain about the center of mass); its interactions with other robots or with obstacles and domain boundaries are described in terms of the classical many-body problem; and a collision-avoidance strategy is derived and combined with homing, robot-robot, and robot-obstacle collision-avoidance strategies. Results from homing simulations involving (1) a single robot in a circular domain, (2) two robots in a circular domain, and (3) one robot in a domain with an obstacle are presented in graphs and briefly characterized.

Wang, P. K. C.↗