Approximation of the restricted problem by the two-fixed-center problem second semi- annual report, part i
Perturbation theory of two-fixed-center problem leading to restricted three-body approximation
PERTURBATION THEORY↗
SEARCH · Engineering Papers
Results for “three body”
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.
Lectures on regularization
Regularization of relative many-body equations of celestial mechanics and relative three-body equations in case of binary collisions
MANY-BODY PROBLEM↗
Some periodic solutions of elliptical and restricted four-body problems.
Periodic solutions of elliptical and restricted four-body problems about libration points of restricted three-body problem
FOUR-BODY METHOD↗
Close encounters of the third-body kind
We simulated encounters involving binaries of two eccentricities: e = 0 (i.e., circular binaries) and e = 0.5. In both cases the binary contained a point mass of 1.4 solar masses (i.e., a neutron star) and a 0.8 solar masses main-sequence star modeled as a polytrope. The semimajor axes of both binaries were set to 60 solar radii (0.28 AU). We considered intruders of three masses: 1.4 solar masses (a neutron star), 0.8 solar masses (a main-sequence star or a higher mass white dwarf), and 0.64 solar masses (a more typical mass white dwarf). Our strategy was to perform a large number (40,000) of encounters using a three-body code, then to rerun a small number of cases with a three-dimensional smoothed particle hydrodynamics (SPH) code to determine the importance of hydrodynamical effects. Using the results of the three-body runs, we computed the exchange across sections, sigma(sub ex). From the results of the SPH runs, we computed the cross sections for clean exchange, denoted by sigma(sub cx); the formation of a triple system, denoted by sigma(sub trp); and the formation of a merged binary with an object formed from the merger of two of the stars left in orbit around the third star, denoted by sigma(sub mb). For encounters between either binary and a 1.4 solar masses neutron star, sigma(sub cx) approx. 0.7 sigma(sub ex) and sigma(sub mb) + sigma(sub trp) approx. 0.3 sigma(sub ex). For encounters between either binary and the 0.8 solar masses main-sequence star, sigma(sub cx) approx. 0.50 sigma(sub ex) and sigma(sub mb) + sigma(sub trp) approx. 1.0 sigma(sub ex). If the main sequence star is replaced by a main-sequence star of the same mass, we have sigma(sub cx) approx. 0.5 sigma(sub ex) and sigma(sub mb) + sigma(sub trp) approx. 1.6 sigma(sub ex). Although the exchange cross section is a sensitive function of intruder mass, we see that the cross section to produce merged binaries is roughly independent of intruder mass. The merged binaries produced have semi-major axes much larger than either those of the original binaries or those of binaries produced in clean exchanges. Coupled with their lower kick velocities, received from the encounters, their larger size will enhance their cross section, shortening the waiting time to a subsequent encounter with another single star.
Davies, M. B.↗
Clustering reactions of H2CN(+) ions with HCN
The rate coefficients for the first and second steps in the clustering sequence of H2CN(+) ions with HCN, H2CN(+) + HCN + M - H2CN(+) (HCN) + M and H2CN(+) (HCN) + HCN + M - H2CN(+) (HCN)2 + M, have been measured at temperatures from 189 to 296 K for M = He. The three-body association rate coefficients for both reactions are least-squares fitted for a power dependence on gas temperature. The temperature dependences of the three-body association reaction rate coefficients fitted in the range 200 to 300 K are given. The absolute values and temperature dependences are rather similar.
Chatterjee, B. K.↗
Metallic Environmentally Resistant Coating Rapid Innovation Initiative
Lightweight alloys such as aluminum (Al) and titanium (Ti) are often specified for space systems to minimize mass while maintaining structural integrity [1,2]. Such alloys however, have poor tribological response (high friction and wear), especially in extreme space environments, which becomes worse with the additional presence of lunar regolith. This leads to short lifetimes and premature failures that will ultimately limit long term operations on the lunar surface [2]. This project is addressing this technology gap by developing advanced wear- and radiation-resistant coatings for lightweight parts to extend the life-time and sustainability of both lunar and Martian assets. Ceramics were considered for their high wear resistance, but were rejected because of their low fracture toughness, which would be especially problematic for structural components. The novel and existing coating technologies and deposition methods are being tested in this project. The coating materials are Boron Nitride-Aluminum (BN-Al), Nickle Titanium (NiTi), Aluminum Oxide (AlO3), Ti64 with hBN at 2 and 10 vol percent (Ti-2vol%hBN and Ti-10vol%hBN), and the deposition techniques are high pressure cold-spray (CS) and ambient and vacuum plasma-spray (APS and VPS) [3,4,5]. BN-Al, NiTi, Ti-2vol%hBN, and Ti-10vol%hBN were applied with all three deposition techniques, and AlO3 was applied only using the APS deposition technique. A tungstenite (WS2) film was applied to the NiTi VPS coating. The coating and deposition technique configurations are being tested against several key end-use performance parameters. The parameters include the capabilities of the coatings under wear environments such as regolith simulant, thermal cycling from high (120°C) to cryogenic (-173°C), high vacuum (~10-7 torr), and pre- and post-exposure to ionizing particle radiation. Wear tests include pin on disk, three-body abrasion, and surface erosion by high velocity regolith impacts. The initial down selection is being performed using on virgin and environmental exposure samples using pin on disk and three body abrasion wear tests. From preliminary assessment of this testing, a few configurations were eliminated. Ti-10vol%hBN could not be applied using CS application and NiTi could not be applied using APS or CS application so these configurations did not get tested. Early pin on disk wear tests showed poor wear performance of BN-Al so this coating was eliminated early in the testing process. AlO3 on Al substrate did not survive thermal cycling, but wear testing is continuing for AlO3 on Ti substrate. A more detailed analysis is being con-ducted to further reduce the number of configuration for phase II and III. Phase II testing will include conventionally and additively manufactured substrates with surface erosion testing. In phase III, the coatings will be applied to three mechanism types: channel and slot, ball and socket, and a hinge joint. Each will demonstrate a different type of wear incidence. The mechanisms and their base materials are of direct interest to the end users and infusion points: the Human Landing System (HLS) and the Lunar Surface Innovation Initiative (sustained lunar surface operations). The technology development project is based out of Marshall Space Flight Center, has partnered with Florida International University (Miami, FL) and Plasma Processes (Huntsville, Al), and is supported by a group of NASA mentors from different centers.
dust mitigation↗
Many-Body Potential for Simulating Self-Assembly of Polymer-Grafted Nanoparticles in a Polymer Matrix
Many-body interactions between polymer-grafted nanoparticles (NPs) play a key role in promoting their assembly into low-dimensional structures within polymer melts, even when the particles are spherical and isotropically grafted. However, capturing such interactions in simulations of NP assembly is very challenging because explicit modeling of the polymer grafts and melt chains is highly computationally expensive, even using coarse-grained models. Here, we develop a many-body potential for describing the effective interactions between spherical polymer-grafted NPs in a polymer matrix through a machine-learning approach. The approach involves using permutationally invariant polynomials to fit two- and three-body interactions derived from the potential of mean force calculations. The potential developed here reduces the computational cost by several orders of magnitude, thereby, allowing us to explore assembly behavior over large length and time scales. We show that the potential not only reproduces previously known assembled phases such as 1D strings and 2D hexagonal sheets, which generally cannot be achieved using isotropic two-body potentials, but can also help discover interesting phases such as networks, clusters, and gels. We demonstrate how each of these assembly morphologies intrinsically arises from a competition between two- and three-body interactions. Our approach for deriving many-body effective potentials can be readily extended to other colloidal systems, enabling researchers to make accurate predictions of their behavior and dissect the role of individual interaction energy terms of the overall potential in the observed behavior.
36 MATERIALS SCIENCE↗
How to renormalize coupled cluster theory
Coupled cluster theory is an attractive tool to solve the quantum many-body problem because its singles and doubles (CCSD) approximation is computationally affordable and yields about 90% of the correlation energy. Capturing the remaining 10%, e.g., via including triples, is numerically expensive. In this work, we assume that short-range three-body correlations dominate and—following Lepage (arXiv:nucl-th/9706029)—that their effects can be included within CCSD by renormalizing the three-body contact interaction. We renormalize this contact in 16 O and obtain systematically improved CCSD results for 24 O, 20–34 Ne, 40,48 Ca, 78 Ni, 90 Zr, and 100 Sn.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Implementing the finite-volume three-pion scattering formalism across all non-maximal isospins
We present a numerical exploration of the relativistic-field-theory (RFT) formalism for three pions with all possible values of non-maximal isospin, I πππ = 2, 1 and 0. Using the generic-isospin extension of the RFT formalism [1] and applying our open-source Python library to implement the framework, we predict a range of three-pion energies for illustrative values of the two-to-two scattering amplitudes for various finite-volume irreps also with non-zero total momentum P in the finite-volume frame. The results restrict attention to the case of a vanishing intrinsic three-body interaction so that the spectra can be understood as a baseline. In future lattice QCD calculations, deviations from these values will be translated into evidence for intrinsic three-body effects in the various scattering channels.
hadronic spectroscopy↗
Procedure for estimating aerodynamics of three-dimensional bodies in transitional flow
Based on considerations of fluid dynamic simulation appropriate to hypersonic, viscous flow over blunt-nosed lifting bodies, a method was presented earlier for estimating drag coefficients in the transitional-flow regime. The extension of the same method to prediction of lift coefficients is presented in this paper. Correlation of available experimental data by a simulation parameter appropriate for this purpose is the basis of the procedure described. Under low-density, hypersonic flow conditions, the overriding importance of projected and wetted areas, rather than details of body configuration, support this approach for finding aerodynamic forces. The ease of application of the method makes it useful for preliminary studies that involve a wide variety of three-dimensional vehicle configurations or a range of angles of attack of a given vehicle. It is also easy to examine the influence of different assumptions regarding gas/surface interaction parameters.
Potter, J. Leith↗
Computer simulation of surface and film processes
All the investigations which were performed employed in one way or another a computer simulation technique based on atomistic level considerations. In general, three types of simulation methods were used for modeling systems with discrete particles that interact via well defined potential functions: molecular dynamics (a general method for solving the classical equations of motion of a model system); Monte Carlo (the use of Markov chain ensemble averaging technique to model equilibrium properties of a system); and molecular statics (provides properties of a system at T = 0 K). The effects of three-body forces on the vibrational frequencies of triatomic cluster were investigated. The multilayer relaxation phenomena for low index planes of an fcc crystal was analyzed also as a function of the three-body interactions. Various surface properties for Si and SiC system were calculated. Results obtained from static simulation calculations for slip formation were presented. The more elaborate molecular dynamics calculations on the propagation of cracks in two-dimensional systems were outlined.
Tiller, W. A.↗
Harmonic oscillator representation in the theory of scattering and nuclear reactions
The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.
Smirnov, Yuri F.↗
Application of dynamical systems theory to a very low energy transfer
We use lobe dynamics in the restricted three-body problem to design orbits with prescribed itineraries with respect to the resonance regions within a Hill's region. the application we envision is the design of a low energy trajectory to orbit three of Jupiter's moons using the patched three-body approximation. We introduce the "switching region," the P2BA analogue to the "spere of influence."
Marsden, J. E.↗
Long-term evolution of a planetesimal swarm in the vicinity of a protoplanet
Many models of planet formation involve scenarios in which one or a few large protoplanets interact with a swarm of much smaller planetesimals. In such scenarios, three-body perturbations by the protoplanet as well as mutual collisions and gravitational interactions between the swarm bodies are important in determining the velocity distribution of the swarm. We are developing a model to examine the effects of these processes on the evolution of a planetesimal swarm. The model consists of a combination of numerical integrations of the gravitational influence of one (or a few) massive protoplanets on swarm bodies together with a statistical treatment of the interactions between the planetesimals. Integrating the planetesimal orbits allows us to take into account effects that are difficult to model analytically or statistically, such as three-body collision cross-sections and resonant perturbations by the protoplanet, while using a statistical treatment for the particle-particle interactions allows us to use a large enough sample to obtain meaningful results.
Kary, David M.↗
Ion-atom association reactions in the rare gases.
A simple resonance theory of three-body ion-atom association reactions is presented. The reaction is considered as proceeding through the formation of a long lived orbiting resonance complex between the atom and the ion. The population of these quasi-bound states is estimated assuming thermal equilibrium. A stable molecular ion may then be formed upon deactivation of the complex by collision with a third body. Various simplifying approximations to the potential curves and surfaces are employed. Furthermore, the deactivation cross sections for the relevant complexes are estimated from the corresponding atomic 'sizes.' A simple analytical formula for the three-body rate constant is thus derived. Reasonable agreement with experiment is obtained for He(+) in He and fair agreement for other light systems.
Dickinson, A. S.↗
Simulation of Binary-single Interactions in AGN Disk. I. Gas-enhanced Binary Orbital Hardening
Stellar-mass binary black hole (BBH) mergers within the accretion disks of active galactic nuclei may contribute to gravitational wave (GW) events detected by ground-based GW detectors. In particular, the interaction between a BBH and a single stellar-mass black hole (sBH), known as the binary-single interaction (BSI) process, can potentially lead to GW events with detectable nonzero eccentricity. Previous studies of the BSI process, which neglected the effects of gas, showed that BSIs contribute non-negligibly to GW events in a coplanar disk environment. In this work, we conduct a series of two-dimensional hydrodynamical and N-body simulations to explore the BSI in a gas environment by coupling REBOUND with Athena++. We perform 360 simulation runs, spanning parameters in disk surface density Σ 0 and impact parameter b. We find that the gas-induced energy dissipation within the three-body system becomes significant if the encounter velocity between the sBHs is sufficiently large (≫c s ). Our simulation results indicate that approximately half of the end states of the BSI are changed by gas. Furthermore, at higher gas density, the number of close encounters during the BSI process will increase, and the end-state BBHs tend to be more compact. Consequently, the presence of gas may shorten the GW merger timescale for end-state BBHs and increase the three-body merger rate.
79 ASTRONOMY AND ASTROPHYSICS↗
Chaotic behavior and the origin of the 3/1 Kirkwood gap
The sudden eccentricity increases discovered by Wisdom (1982) are reproduced in numerical integrations of the planar ecliptic restricted three-body problem, verifying that this phenomenon is real. Mapping derivations are qualitatively reviewed and the maximum Liapunov characteristic exponent and its importance for determining the character of a trajectory are explained. The results of a number of calculations of this exponent using the differential equations for the unaveraged three-body problem are shown and compared to equivalent calculations using a mapping. In all cases the two approaches agree whether the orbits are chaotic or quasiperiodic. The mappings are used to trace out the chaotic zone near the 3/1 commensurability, both in the planar-ecliptic problem and in the three-dimensional elliptic problem. The outer boundary of the chaotic zone coincides with the boundary of the 3/1 Kirkwood gap in the actual distribution of asteroids within the errors of the asteroid orbital elements.
Wisdom, J.↗
On the capture of the Moon
This paper studies the possibility of lunar capture depending on variations of the solar mass under certain well specified conditions and assumptions regarding the behaviour of the three-body dynamical system formed by the Sun, Earth and Moon. It is found that a large amount of decrease in the solar mass (approximately 37%) would be required to allow capture if the model of the planar restricted problem of three bodies is assumed, if the masses of the Earth and Moon did not change and if the angular momentum of the Sun-Earth system did not change. Such large mass-changes of the Sun can not be associated with radiation mass losses only with catastrophic events, such as stellar close approaches.
Szebehely, V.↗