Search NASA⌕ Search

SEARCH · Search NASA

Results for “Set theory”

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.

At least 469 records · Page 26

Information compression in the context model

The Context Model provides a formal framework for the representation, interpretation, and analysis of vague and uncertain data. The clear semantics of the underlying concepts make it feasible to compare well-known approaches to the modeling of imperfect knowledge like that given in Bayes Theory, Shafer's Evidence Theory, the Transferable Belief Model, and Possibility Theory. In this paper we present the basic ideas of the Context Model and show its applicability as an alternative foundation of Possibility Theory and the epistemic view of fuzzy sets.

Gebhardt, Joerg↗

Theoretical and Experimental Investigations on Droplet Evaporation and Droplet Ignition at High Pressures

The evaporation of fuel droplets under high ambient pressure and temperature in normal gravity and microgravity has been investigated experimentally. For subcritical ambient conditions, droplet evaporation after a heat-up period follows the d(exp 2)-law. For all data the evaporation constant increases as the ambient temperature increases. At identical ambient conditions the evaporation constant under microgravity is smaller compared to normal gravity. This effect can first be observed at 1 bar and increases with ambient pressure. Preliminary experiments on ignition delay for self-igniting fuel droplets have been performed. Above a 1 s delay time, at identical ambient conditions, significant differences in the results of the normal and microgravity data are observed. Self-ignition occurs within different temperature ranges due to the influence of gravity. The time dependent behavior of the droplet is examined theoretically. In the calculations two different approaches for the gas phase are applied. In the first approach the conditions at the interface are given using a quasi steady theory approximation. The second approach uses a set of time dependent governing equations for the gas phase which are then evaluated. In comparison, the second model shows a better agreement with the drop tower experiments. In both cases a time dependent gasification rate is observed.

Ristau, R.↗

The Living With a Star Space Environment Testbed Program

NASA has initiated the Living with a Star (LWS) Program to develop the scientific understanding to address the aspects of the Connected Sun-Earth system that affects life and society. The Program Architecture includes science missions, theory and modeling and Space Environment Testbeds (SET). This current paper discusses the Space Environment Testbeds. The goal of the SET program is to improve the engineering approach to accomodate and/or mitigate the effects of solar variability on spacecraft design and operations. The SET Program will infuse new technologies into the space programs through collection of data in space and subsequent design and validation of technologies. Examples of these technologies are cited and discussed.

Barth, Janet↗

Comparative Study of Impedance Eduction Methods: DLR Tests and Methodology - Part 1

The absorption efficiency of acoustic liners used in aircraft engines is characterized by the acoustic impedance. World wide, many grazing ow test rigs and eduction methods are available that provide values for that impedance. However, a direct comparison and assessment of the data of the di erent rigs and methods is often not possible because test objects and test conditions are quite di erent. Only a few papers provide a direct comparison. Therefore, this paper together with a companion paper, present data measured with a reference test object under similar conditions in the DLR and NASA grazing ow test rigs. Additionally, by applying the in-house methods Liner Impedance Non-Uniform ow Solving algorithm (LINUS, DLR) and Convected Helmhholtz Equation approach (CHE, NASA) on the data sets, similarities and differences due to underlying theory are identi ed and discussed.

Busse-Gerstengarbe, Stefan↗

High Fidelity Collision Probabilities Estimated Using Brute Force Monte Carlo Simulations

The NASA Conjunction Assessment Risk Analysis team has implemented new software to estimate the probability of collision (P (sub c)) for Earth-orbiting satellites. The algorithm employs a brute force Monte Carlo (BFMC) method which differs from most other methods because it uses orbital states and covariances propagated from their orbit determination epoch times using the full set of Astrodynamics Support Workstation higher order theory models, including the High Accuracy Satellite Drag Model. This paper de-scribes the BFMC algorithm, presents comparisons of BFMC P (sub c) estimates to those calculated using other methods, and discusses the implications for conjunction risk assessment.

Probabilities↗

Numerical Investigation of Roughness Effects on Transition on Spherical Capsules

The state of the boundary layer on space re-entry vehicles significantly affects the design of the thermal protection system. However, the physical mechanism that leads to the laminar-turbulent boundary-layer transition on blunt spherical capsules remains an open question in literature. This work numerically assesses the potential of roughness-induced non-modal disturbance growth on re-entry capsules with a spherical-section forebody by optimal transient-growth theory and direct numerical simulation. Two different sets of wind-tunnel experiments are considered. Optimal transient-growth studies have been performed for the blunt capsule experiments at Mach 5.9 in the Hypersonic Ludwieg tube Braunschweig (HLB) of the Technische Universitat Braunschweig. In some of these measurements, the capsule model was equipped with a specifically designed patch of distributed micron-sized surface roughness. The transient-growth results for the HLB capsule are compared to corresponding numerical data for a Mach 6 blunt capsule experiment in the Adjustable Contour Expansion (ACE) facility of the Texas A&M University (TAMU) at lower Reynolds number. Similar trends are observed for both configurations. In particular, a rather low maximum energy gain is noted for the surface temperature conditions of the experiments. It is shown that the surface temperature dependence of the optimal transient-growth results is very similar for both capsule configurations. Moreover, the generation of stationary disturbances by well-defined roughness patches on the capsule surface is studied for the conditions of the HLB experiment using direct numerical simulations (DNS). To help explain the observed laminar-turbulent transition downstream of the roughness patch in some of the HLB capsule experiments, additional simulations were carried out to study the evolution of unsteady perturbations within the steady disturbance flow field due to the roughness patch. However, the DNS did not provide any indication of modal or non-modal disturbance growth in the wake of the roughness patch, and hence, the physical mechanism underlying the observed onset of transition remains unknown.

Hein, Stefan↗

Multiple-Effector Control Allocation: Theory and Practice

Redundant controls are ubiquitous in many aerospace domains, including aircraft, spacecraft, and launch vehicles. Multiple control effectors having different capabilities (e.g., reaction controls, aerosurfaces, and vectored engines) must be optimally allocated to achieve high-performance and robust vehicle control, while considering different constraints, cost, or performance metrics associated with various control mixing schemes. These can include force or deflection limits, rate limits, propellant usage or drag penalties, cross-axis coupling, uncertainties, or even servoelastic interactions. This presentation introduces the fundamentals of control allocation theory, based on linear algebra and convex sets, using a handful of examples taken from the air and space vehicle domains. It is shown that even simple methods can provide verifiable and quantifiable performance benefits over ad-hoc approaches, and can support enhanced functions like fault tolerance and control reconfiguration.

Bill Benson↗

Coherent optical imaging of moving objects hidden in a heavily scattering random medium

Experimental results are presented that provide insight into the physics of statistical imaging in heavily scattering random media based on measured speckle correlations as a function of the change in position of a moving object. In this way, definitive interpretation of a rather complex and earlier theory is achieved, making this work an experimental complement to that theory paper []. Motion could be natural, where the set of positions is estimated or separately obtained, or directed, where a mechanical stage can be used to adjust the object's position. In the experiment, a coherent laser illuminates two scattering diffusers, while an object is translated between them in the resulting speckled field and images are collected in a transmission configuration. Results are shown for various objects of differing size and geometry, allowing the theory to be validated and interpreted with new understanding. This work demonstrates imaging opportunities, and applications include material characterization, environmental imaging and sensing, and deep-tissue imaging. Published by the American Physical Society 2025

Hastings, Ryan L. (ORCID:0009000095977807)↗

Ecologically-Informed Precision Conservation: A framework for increasing biodiversity in intensively managed agricultural landscapes with minimal sacrifice in crop production

Conservation actions are urgently needed to tackle biodiversity loss in intensively managed agricultural landscapes. Production lands are usually heterogeneous and contain low-yield areas that can be set aside for biodiversity conservation without serious yield losses. Here, we introduce Ecologically-Informed Precision Conservation, a framework that integrates yield mapping and ecological theory to select the best areas to create new set-asides while ensuring high crop yields at the farm/landscape level. Long-term yield maps can be generated using globally available satellite data and basic information on field/farm crop yield from farmers. Ecological principles are then used to select the subset of areas with the highest potential for biodiversity conservation by prioritising those that increase connectivity, maximise habitat heterogeneity and decrease landscape grain size. Here, the created non-crop habitats can be permanent and thus ensure biodiversity support over time. In addition, agricultural management efficiency can be enhanced by improving field shapes. The framework provides the basis for a practical, user-friendly tool that informs all interested stakeholders on how to rationalise existing agricultural landscapes using already-existing farming systems and available technologies. High cost-effectiveness from an economic and conservation perspective, along with the creation of heterogeneous non-crop habitats, make our framework a promising solution to re-design agricultural landscapes.

Precision agriculture↗

Quantum Hamilton-Jacobi theory, spectral path integrals, and exact WKB analysis

We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi (HJ) theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in quantum theory beyond approximation schemes. The canonical transformation enables one to set the new Hamiltonian to constant or zero, but keeps the information about solution in Hamilton’s characteristic function. To benefit from this in quantum theory, one must work with a formulation in which classical Hamiltonian is used. This uniquely points to phase space path integral. However, the main variable in HJ formalism is energy, not time. Thus, we are led to consider the Fourier transform of the path integral, the spectral path integral Z ˜ ( E ) . The evaluation of path integrals reduces to determining the quantum Hamilton characteristic functions (which can be achieved via an asymptotic analysis) and a discrete sum over the quantum period lattice, generalizing Gutzwiller’s sum. Published by the American Physical Society 2025

Türe, Mustafa (ORCID:0009000975968618)↗

Viscoplasticity: A thermodynamic formulation

A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity, as it applies to initially isotropic materials. Three fundamental internal state variables are admitted. They are: a tensor valued back stress for kinematic effects, and the scalar valued drag and yield strengths for isotropic effects. All three are considered to phenomenologically evolve according to competitive processes between strain hardening, strain induced dynamic recovery, and time induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is put forth. This theory allows each of the three fundamental internal variables to be composed as a sum of independently evolving constituents.

Freed, A. D.↗

Obstacles to constructing de Sitter space in string theory

There have been many attempts to construct de Sitter space-times in string theory. While arguably there have been some successes, this has proven challenging, leading to the de Sitter swampland conjecture: quantum theories of gravity do not admit stable or metastable de Sitter space. Here we explain that, within controlled approximations, one lacks the tools to construct de Sitter space in string theory. Such approximations would require the existence of a set of (arbitrarily) small parameters, subject to severe constraints. But beyond this one also needs an understanding of big-bang and big-crunch singularities that is not currently accessible to standard approximations in string theory. The existence or non-existence of metastable de Sitter space in string theory remains a matter of conjecture.

79 ASTRONOMY AND ASTROPHYSICS↗

Noise from Propellers with Symmetrical Sections at Zero Blade Angle

A theory has been deduced for the "rotation noise" from a propeller with blades of symmetrical section about the chord line and set at zero blade angle. Owing to the limitation of the theory, the equations give without appreciable error only the sound pressure for cases where the wave lengths are large compared with the blade lengths. With the aid of experimental data obtained from a two-blade arrangement, an empirical relation was introduced that permitted calculation of higher harmonics. The generality of the final relation given is indicated by the fundamental and second harmonic of a four-blade arrangement.

Deming, A F↗

Do recent observations of very large electromagnetic dissociation cross sections signify a transition towards non-perturbative QED?

The very large electromagnetic dissociation (EMD) cross section recently observed by Hill, Wohn, Schwellenbach, and Smith do not agree with Weizsacker-Williams (WW) theory or any simple modification thereof. Calculations are presented for the reaction probabilities for this experiment and the entire single and double nucleon removal EMD data set. It is found that for those few reactions where theory and experiment disagree, the probabilities are exceptionally large. This indicates that WW theory is not valid for these reactions and that one must consider higher order corrections and perhaps even a non-perturbative approach to quantum electrodynamics (QED).

Norbury, John W.↗

Langevin Dynamics modeling of gas-phase ion-ion recombination (Final Technical Report)

A self-consistent trajectory simulation approach to model MN reactions (Fig. 1) which incorporates the probability of electron transfer as a Monte Carlo operator (Fig. 2) was developed and published as Liu et al. J. Chem. Phys. 159, 114111 (2023). The electron transfer probability p ET estimated using the two-state Landau-Zener (LZ) theory was incorporated into classical trajectory simulations to elicit predictions of MN reaction cross-section σ (vacuum) or rate constant β (finite pressure). Electronic structure calculations with multireference configuration interaction (MRCI) and large correlation consistent basis sets were used to derive inputs to the LZ theory. The key advance of our trajectory simulation approach is the incorporation of electron transfer probability and the inclusion of the effect of ion-neutral interactions on MN using a Langevin representation of the effect of neutral gas on ions. For H + – H - and Li + – H(D) - pairs, our approach quantitatively agrees with measured speed-dependent cross-sections for up to ~10 5 m/s. For the ion pair Ne + – Cl - , our predictions of the MN rate constant at ~1 torr are a factor of ~2 – 3 higher than the experimentally measured value. Similarly, for Xe + – F - in the pressure range of ~20000 – 80000 Pa, our predictions of the MN rate constant are ~20% lower but are in excellent qualitative agreement with experimental data. The paradigm of using trajectory simulations to self-consistently model MN reactions is the basis for inclusion of additional non-classical, and static magnetic and electric field effects. Subsequent work, published as Roy et al. focused on modeling recombination rate constant for three ion pairs (rare gas Ar + cation and halide anions): Ar + – Cl - , Ar + – Br - , Ar + – I - , 2) considering spin-orbit couplings in the electronic structure calculations to obtain high-fidelity estimates of the electron transfer probability and incorporated within the classical trajectory simulations to elicit predictions. In addition to calculations of ion-ion recombination rate constants, a classical trajectory simulation technique (published as Roy et al. J. Chem. Phys. 162(9), 094104 (2023)) that uses quaternions to represent orientation of non-spherical particles (ions or aerosol particles) was developed to simulate the recombination of diatomic or more generally, polyatomic molecules. Finally, several other ion pairs such as Ne + – Cl - , Kr + – Cl - , were explored using the developed semi-classical trajectory simulations to understand various challenges in tackling electronic structure calculations. Using empirical approaches to parameterize the electron transfer radius, trajectory simulations were also used to probe the effect of ion number density on MN rate constant.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Scattering from randomly oriented circular discs with application to vegetation

A vegetation layer is modeled by a collection of randomly oriented circular discs over a half space. The backscattering coefficient from such a half space is computed using the radiative transfer theory. It is shown that significantly different results are obtained from this theory as compared with some earlier investigations using the same modeling approach but with restricted disc orientations. In particular, the backscattered cross polarized returns cannot have a fast increasing angular trend which is inconsistent with measurements. By setting the appropriate angle of orientation to zero the theory reduces to previously published results. Comparisons are shown with measurements taken from milo, corn and wheat and good agreements are obtained for both polarized and cross polarized returns.

Karam, M. A.↗

Hidden conformal symmetry from the lattice

We analyze newly expanded and refined data from lattice studies of an SU(3) gauge theory with eight Dirac fermions in the fundamental representation. We focus on the light composite states emerging from these studies, consisting of a set of pseudoscalars and a single light scalar. We first consider the view that this theory is just outside the conformal window. In this case, the pseudoscalars arise from spontaneous breaking of chiral symmetry. Identifying the scalar in this case as an approximate dilaton, we fit the lattice data to a dilaton effective field theory, finding that it yields a good fit even at lowest order. For comparison, we then consider the possibility that the theory is inside the conformal window. The fermion mass provides a deformation, triggering confinement. We employ simple scaling laws to fit the lattice data, and find that it is of lesser quality.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Scattering from randomly oriented circular discs with application to vegetation

A vegetation layer is modeled by a collection of randomly oriented circular discs over a half space. The backscattering coefficient from such a half space is computed using the radiative transfer theory. It is shown that significantly different results are obtained from this theory as compared with some earlier investigations using the same modeling approach but with restricted disc orientations. In particular, the backscattered cross-polarized returns cannot have a fast increasing angular trend which is inconsistent with measurements. By setting the appropriate angle of orientation to zero the theory reduces to previously published results. Comparisons are shown with measurements taken from milo, corn and wheat and good agreements are obtained for both polarized and cross-polarized returns.

Karam, M. A.↗