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The analytical solution presented is based on the assumption that the deformed thickness of the plate is approximately constant. The nonlinear equations governing finite axisymmetric deformations of a circular plate made of neo-Hookean material are used in the analysis. The variation of circumferential extension ratio and the variation of deformed thickness are shown in graphs.
Analytical and semi-empirical methods for determining the transmission of sound through isolated panels and predicting panel transmission loss are described. Test results presented include the influence of plate stiffness and mass and the effects of pressurization and vibration damping materials on sound transmission characteristics. Measured and predicted results are presented in tables and graphs.
A key science goal of the NASA “Moon to Mars” campaign is to understand how biology responds to the Lunar, Martian, and deep space environments in order to advance fundamental knowledge, reduce risk, and support safe, productive human space missions. Through the powerful emerging computer science approaches of artificial intelligence (AI) and machine learning (ML), a paradigm shift has begun in biomedical science and engineered astronaut health systems, to enable Earth-independence and autonomy of mission operations. We present a decadal view of AI/ML architecture to support deep space mission goals, developed in concert with leaders in the field. We describe current AI/ML methods to support 1) fundamental biology, 2) in situ analytics, 3) high performance computing hardware, 4) automated science, 5) self-driving labs, 6) remote data management, 7) integrated real-time mission biomonitoring, and 8) a Precision Space Health system. Cutting-edge AI/ML approaches that can be integrated to support these domains include active learning, explainable AI, adaptive learning, causal inference, knowledge graphs, federated learning, transfer learning, and large language models. Finally, we present results from several current ML projects that are underway in the field to address key challenges of small sample n, high feature count, heterogeneity, and sparse data. These include 1) connecting omics data to phenotypic data using an ensemble model to infer causality of spaceflight rodent liver health disruption, 2) usage of explainable ML to interrogate the muscular underpinnings of spaceflight muscle atrophy, 3) ML models analyzing and determining directed acyclic graphs of human space health risk leveraging rodent bone datasets, 4) usage of large pre-trained models connecting biomedical knowledgebases with small spaceflight datasets to understand gene-to-gene interaction networks, and 5) a suite of benchmarked open science datasets (spaceflight mouse liver; radiation DNA damage) enabling programmers to identify the best ML algorithms to answer space biological science questions.
A key science goal of the NASA “Moon to Mars” campaign is to understand how biology responds to the Lunar, Martian, and deep space environments in order to advance fundamental knowledge, reduce risk, and support safe, productive human space missions. Through the powerful emerging computer science approaches of artificial intelligence (AI) and machine learning (ML), a paradigm shift has begun in biomedical science and engineered astronaut health systems, to enable Earth-independence and autonomy of mission operations. We present a decadal view of AI/ML architecture to support deep space mission goals, developed in concert with leaders in the field. We describe current AI/ML methods to support 1) fundamental biology, 2) in situ analytics, 3) high performance computing hardware, 4) automated science, 5) self-driving labs, 6) remote data management, 7) integrated real-time mission biomonitoring, and 8) a Precision Space Health system. Cutting-edge AI/ML approaches that can be integrated to support these domains include active learning, explainable AI, adaptive learning, causal inference, knowledge graphs, federated learning, transfer learning, and large language models. Finally, we present results from several current ML projects that are underway in the field to address key challenges of small sample n, high feature count, heterogeneity, and sparse data. These include 1) connecting omics data to phenotypic data using an ensemble model to infer causality of spaceflight rodent liver health disruption, 2) usage of explainable ML to interrogate the muscular underpinnings of spaceflight muscle atrophy, 3) ML models analyzing and determining directed acyclic graphs of human space health risk leveraging rodent bone datasets, 4) usage of large pre-trained models connecting biomedical knowledgebases with small spaceflight datasets to understand gene-to-gene interaction networks, and 5) a suite of benchmarked open science datasets (spaceflight mouse liver; radiation DNA damage) enabling programmers to identify the best ML algorithms to answer space biological science questions.
The progressive ionization and subsequent dynamical evolution of nonhomogeneously distributed low-metal-abundance diffuse gas after star formation in globular clusters are investigated analytically, taking the gravitational acceleration due to the stars into account. The basic equations are derived; the underlying assumptions, input parameters, and solution methods are explained; and numerical results for three standard cases (ionization during star formation, ionization during expansion, and evolution resulting in a stable H II region at its equilibrium Stromgren radius) are presented in graphs and characterized in detail. The time scale of residual-gas loss in typical clusters is found to be about the same as the lifetime of a massive star on the main sequence.
In the field of metamaterial research, random structures offer a novel and less conventional approach compared to traditional periodic designs. Designing random metamaterials is challenging when it comes to ensuring intercon- nectivity, which is essential for manufacturability. This study introduces an innovative framework for generating random metamaterials using graph al- gorithms, ensuring connectivity and adaptability across various base shapes, including cylinders, triangles, pyramids, and cubes. By employing graph algorithms, our framework enhances the intuitiveness and efficiency of de- sign representation and manipulation, streamlining the design process. The framework generates families of designs that exhibit a wide range of prop- erty magnitudes that can be adjusted intuitively by modifying the input parameters. The rapid design process allows many designs to be generated, offering the user a multitude of solutions around the target property range. The designs can be effectively implemented in various fields and subjected to diverse analytical studies, including static, dynamic, and eigenfrequency assessments. We illustrate computational results for two key properties (stiff- ness and acoustic impedance), showcasing the method’s effectiveness through examples ranging from rod-based to cube-based designs. Here, the framework not only advances metamaterial research but also creates new opportunities for innovation in fields requiring customized material properties.
The measurement of reflected solar radiation by spacecraft wide-field-of-view radiometers is considered analytically, and the method proposed by Smith (1987) for the solution of the discretized governing equations is described and demonstrated. The theoretical basis of the singular-value decomposition method (partitioning the albedo field into observable and unobservable components) is outlined; its application to Nimbus 7 ERB data is explained in detail; and numerical results are presented in graphs and maps and briefly characterized.
The legacy communications link analysis software currently used at Wallops Flight Facility involves processes that are different for command destruct, radar, and telemetry. There is a clear advantage to developing an easy-to-use tool that combines all the processes in one application. Link Analysis in the Mission Planning Lab (MPL) uses custom software and algorithms integrated with Analytical Graphics Inc. Satellite Toolkit (AGI STK). The MPL link analysis tool uses pre/post-mission data to conduct a dynamic link analysis between ground assets and the launch vehicle. Just as the legacy methods do, the MPL link analysis tool calculates signal strength and signal- to-noise according to the accepted processes for command destruct, radar, and telemetry assets. Graphs and other custom data are generated rapidly in formats for reports and presentations. STK is used for analysis as well as to depict plume angles and antenna gain patterns in 3D. The MPL has developed two interfaces with the STK software (see figure). The first interface is an HTML utility, which was developed in Visual Basic to enhance analysis for plume modeling and to offer a more user friendly, flexible tool. A graphical user interface (GUI) written in MATLAB (see figure upper right-hand corner) is also used to quickly depict link budget information for multiple ground assets. This new method yields a dramatic decrease in the time it takes to provide launch managers with the required link budgets to make critical pre-mission decisions. The software code used for these two custom utilities is a product of NASA's MPL.
The ranges of validity of approximations of P(l), the penetration factor which appears in the parameterization of nuclear-reaction cross sections at low energies and is employed in the extrapolation of laboratory data to even lower energies of astrophysical interest, are investigated analytically. Consideration is given to the WKB approximation, P(l) at the energy of the total barrier, approximations derived from the asymptotic expansion of G(l) for large eta, approximations for small values of the parameter x, applications of P(l) to nuclear reactions, and the dependence of P(l) on channel radius. Numerical results are presented in tables and graphs, and parameter ranges where the danger of serious errors is high are identified.
A direct method for determining the effective elastic stiffnesses and deformation behavior of composite box-beam (BB) structures is developed analytically, validated, and demonstrated. The BB walls are modeled as orthotropic-ply laminated plates, so that the elastic properties vary both through the thickness and around the BB contour; deformation is described in terms of extension, bending, twisting, shearing, and torsion-related out-of-plane warping. Numerical results for several BB configurations are presented in tables and graphs and compared with experimental data and FEM computations (Stemple and Lee, 1989): good general agreement is obtained for cross-ply, antisymmetric, and symmetric layups, except for symmetric layups with ply orientation angles theta greater than 30 deg. Both out-of-plane warping and transverse shear coupling are found to have significant effects on BB elastic response.
The dynamic behavior of a spinning linear-elastic paraboloid subject to nonaxisymmetric deformation is investigated analytically, applying the Rayleigh-Ritz procedure described by Utku et al. (1983). Energy-density, strain-displacement, and velocity-displacement expressions are generated; expressions for the generalized strain and position vector are derived; and the discretized dynamic equations are obtained. Numerical results obtained with a computer-program implementation of the method are presented in extensive tables and graphs. The effects of spin rate and bending rigidity and results for the special case of a spinning disk are included.
While standardized ontologies like the Brick schema address data heterogeneity in Building Automation Systems (BAS), accessing this semantic data remains a challenge as domain experts often lack the expertise to formulate complex SPARQL queries. To bridge this gap, we present BrickQA, a Large Language Model (LLM)-based framework that translates natural language into executable SPARQL queries through structured query decomposition, dynamic schema exploration, and inline validation. BrickQA utilizes an iterative reasoning agent to actively navigate graph topology through dynamic exploration actions without requiring exhaustive context injection or model fine-tuning. This approach effectively mitigates hallucinations, particularly in large-scale building knowledge graphs. Empirical evaluation on BuildingQA, a standardized benchmark, demonstrates that BrickQA significantly outperforms ReAct baselines, delivering a 0.291–0.355 absolute F1 improvement while achieving 3 × –12.7 × higher token cost-efficiency. Beyond these metrics, the framework maintains structural fidelity across heterogeneous buildings and remains resilient to ambiguous queries without requiring site-specific fine-tuning. Furthermore, a case study on operational analytics validates the framework’s capability to handle temporal and aggregation constraints, effectively transforming abstract semantic models into actionable facility management insights.1
The applicability of current finite-volume CFD algorithms based on the Euler equations to the vortex flow over a helicopter in forward flight is investigated analytically. The general characteristics of the flow are reviewed; existing Euler, Navier-Stokes, perturbation, high-order, and adaptive methods are briefly characterized; and a novel Eulerian/Lagrangian approach with entropy and vorticity corrections is presented in detail. Numerical results for simple convection of a finite-core Lamb vortex moving downstream with its axis perpendicular to the flow are presented in graphs, and the possibility of extending the method to three-dimensional, viscous, and shock flows is discussed.
The corrections to the transport cross-sections and collision integrals for Coulomb interactions arising from the application of realistic interaction energies of the ions of nitrogen and oxygen are investigated. Accurate potential-energy curves from an ab initio electronic-structure calculation and a semiclassical description of the scattering are used to determine the difference between the cross-sections for the real interaction forces and a Coulomb force for large values of the Debye shielding parameter. Graphs of the correction to the diffusion and viscosity-collision integrals are presented for temperatures from about 10,000 K to 150,000 K. This correction can be combined with tabulations of the collision integrals for shielded Coulomb potentials to determine the contribution of N(+)-N(+), N(+)-O(+), and O(+)-O(+) interactions to the transport properties of high-temperature air. Analytical forms are fitted to the calculated results to assist this application.
The Stakeholder-guided holistic, Adaptive Framework for enhancing community Energy Resilience (SAFER) project advances resilience science and engineering by addressing challenges in rural Kansas communities where aging infrastructure, extreme weather, and socioeconomic disparities heighten vulnerability to energy disruptions. Traditional approaches often focus on technical performance while overlooking community concerns and priorities. SAFER responds by integrating community perspectives with advanced analytical frameworks to create a holistic model for measuring and improving resilience. Project objectives included developing novel resilience metrics, advancing modeling frameworks that capture interdependencies across infrastructures, and embedding community-centric indicators directly into planning processes for distributed energy resources. The key technical innovations included the creation of self-organizing map (SOM)-based indices for objective resilience quantification, hetero-functional graph theory (HFGT) models linking power, water, transportation, and community assets, and graph neural network (GNN) tools for identifying critical nodes in complex systems. Community-centric energy planning was demonstrated through optimal siting and sizing of (photovoltaic) PV and battery storage, ensuring resilience enhancements also addressed energy burden and energy insecurity. SAFER engaged community partners in Dodge City and Ford County through surveys, focus groups, and workshops, generating more than 600 responses that established baseline measures of energy burden, financial insecurity, and willingness-to-pay to avoid outages. This data, organized in terms of a community capitals framework, informed the development of weighted reliability indices that better reflect community costs than traditional utility metrics. SAFER’s GNN-based critical node identification framework identified expert-labelled critical nodes with over 99% accuracy, while also uncovering additional functionalities essential for proactive resilience planning. The project’s models demonstrated that optimal PV and storage deployment could improve resilience indices by over 11 percent, with dispatch strategies further enhancing outcomes, confirming both the technical effectiveness and economic feasibility of these approaches. Through its combined emphasis on rigorous modeling, community-focused planning, and community engagement, SAFER advances the state of resilience research while delivering direct benefits to rural communities. The project provides tools, guidelines, and resilience heatmaps that help utilities, local governments, and residents better anticipate disruptions, prioritize investments, and strengthen the capacity to withstand and recover from energy-related hazards. Furthermore, the developed HFG and GNN frameworks are designed for transferability, allowing them to be adapted for resilience planning in other communities with minimal retraining. This inductive learning capability provides a scalable pathway to extend the SAFER project’s impact. Thus, creating a foundation for a nationally applicable model of infrastructure resilience. Additionally, the HFG can also be extended to include other FEMA community lifelines.
The onset of vortex breakdown in compressible flows is investigated analytically for the case in which the flow is axially symmetric, the vortex is isolated, its axis is parallel to the main flow, and the vortex radius is small compared to the breakdown length. The conservation equations for mass, momentum, and energy are formulated and solved numerically using a finite-difference scheme, as described by Krause (1985); numerical results are presented in graphs and briefly characterized.
An analytical model was developed that can be used to establish certain parameters of a thermal vacuum environmental test program based on an optimization of program costs. This model is in the form of a computer program that interacts with a user insofar as the input of certain parameters. The program provides the user a list of pertinent information regarding an optimized test program and graphs of some of the parameters. The model is a first attempt in this area and includes numerous simplifications. The model appears useful as a general guide and provides a way for extrapolating past performance to future missions.
The effects of mean-flow incidence, airfoil camber, and airfoil thickness on the incompressible aerodynamics of an oscillating airfoil are investigated theoretically, developing and applying a first-order FEM based on locally analytical solutions (LASs). Laplace equations are used to describe the steady and unsteady harmonic velocity potentials; a body-fitted computational grid is employed; grid-element solutions for both potentials are determined using a numerical LAS method; and the LASs are then assembled to obtain a complete solution. Results for a series of flat-plate and Joukowski airfoils are presented in extensive graphs and discussed in detail.