Some applications of the theory of unbounded operators to ordinary differential equations.
Kato perturbation theorems applied to ordinary differential equations in Banach space
DIFFERENTIAL EQUATION↗
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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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Earth-Moon Libration Point Orbit Stationkeeping: Theory, Modeling and Operations
Collinear Earth-Moon libration points have emerged as locations with immediate applications. These libration point orbits are inherently unstable and must be maintained regularly which constrains operations and maneuver locations. Stationkeeping is challenging due to relatively short time scales for divergence effects of large orbital eccentricity of the secondary body, and third-body perturbations. Using the Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) mission orbit as a platform, the fundamental behavior of the trajectories is explored using Poincare maps in the circular restricted three-body problem. Operational stationkeeping results obtained using the Optimal Continuation Strategy are presented and compared to orbit stability information generated from mode analysis based in dynamical systems theory.
Folta, David C.↗
The theory, design, and operation of the suppressed carrier data-aided tracking receiver
A viable, efficient, and easily mechanized carrier regenerating receiver for use in suppressed carrier-tracking system is described. The receiver referred to as a data-aided receiver (DAR) incorporates a data-aided loop (DAL) which provides the required carrier reference signal. The DAL employs the principle of decision feedback and as such is more efficient than other forms of suppressed carrier-tracking loops. The analysis, design, and implementation of the DAR are covered in detail. Performance comparisons and mechanization tradeoffs are made, wherever possible, with discrete carrier systems and other suppressed carrier systems presently in use. Experimental performance verification is given throughout in support of the theory presented.
Simon, M. K.↗
A review of peridynamic theory and nonlocal operators along with their computer implementations
Not Available
97 MATHEMATICS AND COMPUTING↗
Stability theory of nonlinear operational differential equations in Hilbert space
Existence, uniqueness, and stability criteria for linear and nonlinear operational differential equations in Banach and Hilbert spaces
Pao, C.-V.↗
An extension of lifting rotor theory to cover operation at large angles of attack and high inflow conditions
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Gessow, Alfred↗
The Application of Modeling and Simulation in Capacity Management within the ITIL Framework
Tightly integrating modeling and simulation techniques into Information Technology Infrastructure Library (ITIL) practices can be one of the driving factors behind a successful and cost-effective capacity management effort for any Information Technology (IT) system. ITIL is a best practices framework for managing IT infrastructure, development and operations. Translating ITIL theory into operational reality can be a challenge. This paper aims to highlight how to best integrate modeling and simulation into an ITIL implementation. For cases where the project team initially has difficulty gaining consensus on investing in modeling and simulation resources, a clear definition for M&S implementation into the ITIL framework, specifically its role in supporting Capacity Management, is critical to gaining the support required to garner these resources. This implementation should also help to clearly define M&S support to the overall system mission. This paper will describe the development of an integrated modeling approach and how best to tie M&S to definitive goals for evaluating system capacity and performance requirements. Specifically the paper will discuss best practices for implementing modeling and simulation into ITIL. These practices hinge on implementing integrated M&S methods that 1) encompass at least two or more predictive modeling techniques, 2) complement each one's respective strengths and weaknesses to support the validation of predicted results, and 3) are tied to the system's performance and workload monitoring efforts. How to structure two forms of modeling: statistical and simUlation in the development of "As Is" and "To Be" efforts will be used to exemplify the integrated M&S methods. The paper will show how these methods can better support the project's overall capacity management efforts.
Rahmani, Sonya↗
Continuous Family of Conformal Field Theories and Exactly Marginal Operators
Does a conformal manifold imply the existence of exactly marginal operators? We answer this question affirmatively under the assumption that there exists a conformal interface with certain properties connecting nearby conformal field theories. We show that the exactly marginal operator that connects the conformal field theories can be reconstructed from the interface displacement operator. Our construction is model independent and based on the general principles of conformal symmetry.
conformal field theory↗
Operation and maintenance, fire rescue air-pack. Volume 2: Communications
The operation and maintenance procedures are described for the development model of the fire rescue air pack (FRAP) voice amplifier assembly, including the battery charger. Operational instructions include a general description of the assembly, specifications, and installation and operation. Maintenance instructions include theory of operation, preventive maintenance, repair, adjustment, and a parts list. The FRAP is intended to permit fire rescue personnel to enter a smoke-filled, toxic or oxygen depleted environment carrying their own source of breathing air. The voice amplifier assembly permits the wearer to communicate by voice with other persons in the vicinity. The battery charger assembly provides a means of keeping the amplifier batteries fully charged.
Source record↗
Graph Theory Roots of Spatial Operators for Kinematics and Dynamics
Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.
Jain, Abhinandan↗
SimSup's Loop: A Control Theory Approach to Spacecraft Operator Training
Immersive simulation is a staple of training for many complex system operators, including astronauts and ground operators of spacecraft. However, while much has been written about simulators, simulation facilities, and operator certification programs, the topic of how one develops simulation scenarios to train a spacecraft operator is relatively understated in the literature. In this paper, an approach is presented for using control theory as the basis for developing the immersive simulation scenarios for a spacecraft operator training program. The operator is effectively modeled as a high level controller of lower level hardware and software control loops that affect a select set of system state variables. Simulation scenarios are derived from a STAMP-based hazard analysis of the operator's high and low level control loops. The immersive simulation aspect of the overall training program is characterized by selecting a set of scenarios that expose the operator to the various inadequate control actions that stem from control flaws and inadequate control executions in the different sections of the typical control loop. Results from the application of this approach to the Lunar Atmosphere and Dust Environment Explorer (LADEE) mission are provided through an analysis of the simulation scenarios used for operator training and the actual anomalies that occurred during the mission. The simulation scenarios and inflight anomalies are mapped to specific control flaws and inadequate control executions in the different sections of the typical control loop to illustrate the characteristics of anomalies arising from the different sections of the typical control loop (and why it is important for operators to have exposure to these characteristics). Additionally, similarities between the simulation scenarios and inflight anomalies are highlighted to make the case that the simulation scenarios prepared the operators for the mission.
LADEE↗
Perturbative quantum evolution of the gravitational state and dressing in general backgrounds
This paper sets up a perturbative treatment of the evolving quantum state of a gravitational system, in a Schrödinger-like picture, working about a general background. This connects gauge symmetry, the constraints, gravitational dressing, and evolution. Starting with a general time slicing, we give a simple derivation of the relation between the constraints, the Hamiltonian, and its well-known boundary term. Among different approaches to quantization with constraints, we focus on a “gauge-invariant canonical quantization,” which is developed perturbatively in the gravitational coupling. The leading-order solution of the constraints (including the Wheeler-DeWitt equation) for perturbations about the background is given in terms of an explicit construction of gravitational dressings built using certain generalized Green’s functions; different such dressings corresponding to adding propagating gravitational waves to a particular solution of the constraints. Dressed operators commute with the constraints, expressing their gauge invariance, and have an algebraic structure differing significantly from the undressed operators of the underlying field theory. These operators can act on the vacuum to create dressed states, and evolution of general such states is then generated by the boundary Hamiltonian, and alternately may be characterized using other relational observables. This provides a concrete approach to studying perturbative time evolution, including the leading gravitational backreaction, of quantum states of black holes with flat or anti–de-Sitter asymptotics, for example on horizon-crossing slices. This description of evolution in turn provides a starting point for investigating possibly important corrections to quantum evolution, that go beyond quantized general relativity. Published by the American Physical Society 2024
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Renormalization of asymmetric staple-shaped Wilson-line operators in lattice and continuum perturbation theory
In this work, we study the renormalization of nonlocal quark bilinear operators containing an asymmetric staple-shaped Wilson line at the one-loop level in both lattice and continuum perturbation theory. These operators enter the first-principle calculation of transverse momentum-dependent parton distribution functions (TMDPDFs) in lattice QCD using the formulation of large momentum effective theory. We provide appropriate RI ′ -type conditions that address the power and logarithmic divergences, as well as the mixing among staple operators of different Dirac structures, using a number of different possible projectors. A variant of RI ′ , including calculations of rectangular Wilson loops, which cancel the pinch-pole singularities of the staple operators at infinite length and reduce residual power divergences, is also employed. We calculate at one-loop order the conversion matrix, which relates the quasi-TMDPDFs in the RI ′ -type schemes to the reference scheme MS ¯ for arbitrary values of the renormalization momentum scale and of the dimensions of the staple. Published by the American Physical Society 2024
Astronomy & Astrophysics↗
Inert gas thrusters
Inert gases, particularly argon and xenon, are of interest as possible alternatives to the usual electric thruster propellants of mercury and cesium. Hollow cathode data were obtained for a wide range of operating conditions. Some test conditions gave plasma coupling voltages at or below the sputtering threshold, hence should permit long operating lifetimes. All observations of hollow cathode operation were consistent with a single theory of operation, in which a significant amount of the total electron emission is from localized areas within the orifice. This mode of emission is also supported by scanning electron microscope photographs that indicate local temperatures at or near the melting temperature of the tungsten tip. Experimental hollow cathode performance was correlated for two orifice diameters, three inert gas propellants, and a range of flow rates for each propellant. The basic theory for the production of doubly ionized argon and xenon was completed. Experimental measurements of the doubly ionized fraction agree with theory within about plus or minus 20 percent. High voltage isolators were studied for the propellant feed line. The breakdown voltage per segment ranged from 300 to over 500 V with argon.
Kaufman, H. R.↗
Linear-scaling quadruple excitations in local pair natural orbital coupled-cluster theory
Here, we present a fast, asymptotically linear-scaling implementation of the perturbative quadruples energy correction in coupled-cluster theory using local natural orbitals. Our work follows the domain-based local pair natural orbital (DLPNO) approach previously applied to lower levels of excitations in coupled-cluster theory. Our DLPNO-CCSDT(Q) algorithm uses converged doubles and triples amplitudes from a preceding DLPNO-CCSDT computation to compute the quadruples amplitude and energy in the quadruples natural orbital (QNO) basis. We demonstrate the compactness of the QNO space, showing that more than 95% of the (Q) correction can be recovered using relatively loose natural orbital cutoffs, compared to the tighter cutoffs used in pair and triples natural orbitals at lower levels of coupled-cluster theory. We also highlight the accuracy of our algorithm in the computation of relative energies, which yields deviations of sub-kJ mol −1 in relative energy compared to the canonical CCSDT(Q). Timings are conducted on a series of growing linear alkanes (up to 10 carbons and 608 basis functions) and water clusters (up to 49 water molecules and 2842 basis functions) to establish the asymptotic linear-scaling of our DLPNO-(Q) algorithm.
Auxiliary functions↗
Koopman and Transfer Operator Techniques from the Perspective of Quantum Theory
Review article on connections between Koopman/transfer operator methods and quantum theory
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Extended Aging Theories for Predictions of Safe Operational Life of Critical Airborne Structural Components
The previously developed Ko closed-form aging theory has been reformulated into a more compact mathematical form for easier application. A new equivalent loading theory and empirical loading theories have also been developed and incorporated into the revised Ko aging theory for the prediction of a safe operational life of airborne failure-critical structural components. The new set of aging and loading theories were applied to predict the safe number of flights for the B-52B aircraft to carry a launch vehicle, the structural life of critical components consumed by load excursion to proof load value, and the ground-sitting life of B-52B pylon failure-critical structural components. A special life prediction method was developed for the preflight predictions of operational life of failure-critical structural components of the B-52H pylon system, for which no flight data are available.
Ko, William L.↗
Theory and application of radiation boundary operators
A succinct unified review is provided of the theory of radiation boundary operators. With the recent introduction of the on-surface radiation condition (OSRC) method and the continued growth of finite-difference and finite-element techniques for modeling electromagnetic wave scattering problems, the understanding and use of radiation boundary operators has become increasingly important. Results are presented to illustrate the application of radiation boundary operators in both these areas. Recent OSRC results include analysis of the scattering behavior of both electrically small and large cylinders, a reactively loaded acoustic sphere, and a simple reentrant duct. Radiation boundary operator results include the demonstration of the effectiveness of higher-order operators in truncating finite-difference time-domain grids.
Moore, Thomas G.↗