Blade: A package for block-triangular form improved Feynman integrals decomposition
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Guan, Xin↗
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Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's
If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.
Geddes, K. O.↗
Friction-less low-profile hinge system and method
The present disclosure relates to a reduced friction torsion component system that makes use of a first frame portion adapted to be coupled to, or integrally formed with, a first object, and forming a first bore, and a second frame portion adapted to be coupled to, or integrally formed with, a second object, and forming a second bore. The two bores are axially aligned and receive at least one elongated hinge component. The elongated hinge component operates to both couple the first and second frame portions together for pivoting movement relative to one another, and also provides a torsional biasing force to enable pivotal deployment from a first position to a second position of one of the first or second frame portions.
Riot, Vincent J.↗
On the formulation of the aerodynamic characteristics in aircraft dynamics
The theory of functionals is used to reformulate the notions of aerodynamic indicial functions and superposition. Integral forms for the aerodynamic response to arbitrary motions are derived that are free of dependence on a linearity assumption. Simplifications of the integral forms lead to practicable nonlinear generalizations of the linear superpositions and stability derivative formulations. Applied to arbitrary nonplanar motions, the generalization yields a form for the aerodynamic response that can be compounded of the contributions from a limited number of well-defined characteristic motions, in principle reproducible in the wind tunnel. Further generalizations that would enable the consideration of random fluctuations and multivalued aerodynamic responses are indicated.
Tobak, M.↗
Enabling energy‐efficient manufacturing of pharmaceutical solid oral dosage forms via integrated techno‐economic analysis and advanced process modeling
Abstract The global pharmaceutical industry is a trillion‐dollar market. However, the pharmaceutical sector often lags in manufacturing innovation and automation which limits its potential to maximize energy efficiency. The integration of techno‐economic analysis (TEA) with advanced process models as part of an overarching smart manufacturing platform, can help industries create business models, which can be adapted for manufacturing to reduce energy consumption and operating costs while ensuring product quality which can further enable a more sustainable process operation. In this study, a rational design of experiment on three unit‐operations (wet granulation, drying, and milling) was performed on a batch (case 1) and continuous (case 2) pharmaceutical process to obtain experimental data. Process models for predicting product quality and energy efficiency of each of the three‐unit operations were developed. The experimental data were used to validate the models and good agreement was observed. The energy consumption of each unit operation was calculated using statistical models relating the power consumption and the process parameters. The developed process models and energy models were further integrated into a TEA framework, which quantified the energy and monetary cost of manufacturing for both batch and continuous manufacturing cases. With this integrated framework, energy costs savings of ~33% was obtained in the continuous manufacturing process (case 2) over the batch process (case 1).
Sampat, Chaitanya↗
Accurate numerical, integral methods for computing drift-kinetic Trubnikov-Rosenbluth potentials
A novel numerical method is employed to compute the integral form of the axi-symmetric Trubnikov-Rosenbluth potentials. Two methods for quadrature in pitch-angle are described and their convergence properties are studied. Careful attention is given to quadrature over a singular Green's function. Here it is shown that an infinite series representation of the Green's function can be used more efficiently than its closed form involving complete elliptic integrals. Then a collocation method in speed, with its associated quadrature scheme, is laid out and its convergence properties are studied. Using the proposed scheme, accurate low-order moments of the field collision operator are obtained using relatively few velocity space degrees of freedom. The scheme is showcased by solving for the equilibrium, axi-symmetric bootstrap current in tokamaks. A C 0 Gauss-Lobatto-Legendre finite element pitch-angle basis with vertex nodes at the trapped/passing boundary is shown, in the context of the integral methods used, to be much more efficient than the more common Legendre polynomial expansion.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Integrated particles sensor formed on single substrate using fringes formed by diffractive elements
Integrated sensors are described using lasers on substrates. In one embodiment, a first sensor forms a laser beam and uses a quartz substrate to sense particle motion by interference of the particles with a diffraction beam caused by a laser beam. A second sensor uses gradings to produce an interference. In another embodiment, an integrated sensor includes a laser element, producing a diverging beam, and a single substrate which includes a first diffractive optical element placed to receive the diverging beam and produce a fringe based thereon, a scattering element which scatters said fringe beam based on particles being detected, and a second diffractive element receiving scattered light.
Gharib, Morteza↗
An Improved Theoretical Aerodynamic Derivatives Computer Program for Sounding Rockets
The paper outlines a Theoretical Aerodynamic Derivatives (TAD) computer program for computing the aerodynamics of sounding rockets. TAD outputs include normal force, pitching moment and rolling moment coefficient derivatives as well as center-of-pressure locations as a function of the flight Mach number. TAD is applicable to slender finned axisymmetric vehicles at small angles of attack in subsonic and supersonic flows. TAD improvement efforts include extending Mach number regions of applicability, improving accuracy, and replacement of some numerical integration algorithms with closed-form integrations. Key equations used in TAD are summarized and typical TAD outputs are illustrated for a second-stage Tomahawk configuration.
Barrowman, J. S.↗
Structural Benchmark Testing of Superalloy Lattice Block Subelements Completed
Superalloy lattice block panels, which are produced directly by investment casting, are composed of thin ligaments arranged in three-dimensional triangulated trusslike structures (see the preceding figure). Optionally, solid panel face sheets can be formed integrally during casting. In either form, lattice block panels can easily be produced with weights less than 25 percent of the mass of a solid panel. Inconel 718 (IN 718) and MarM-247 superalloy lattice block panels have been developed under NASA's Ultra-Efficient Engine Technology Project and Higher Operating Temperature Propulsion Components Project to take advantage of the superalloys' high strength and elevated temperature capability with the inherent light weight and high stiffness of the lattice architecture (ref. 1). These characteristics are important in the future development of turbine engine components. Casting quality and structural efficiency were evaluated experimentally using small beam specimens machined from the cast and heat treated 140- by 300- by 11-mm panels. The matrix of specimens included samples of each superalloy in both open-celled and single-face-sheet configurations, machined from longitudinal, transverse, and diagonal panel orientations. Thirty-five beam subelements were tested in Glenn's Life Prediction Branch's material test machine at room temperature and 650 C under both static (see the following photograph) and cyclic load conditions. Surprisingly, test results exceeded initial linear elastic analytical predictions. This was likely a result of the formation of plastic hinges and redundancies inherent in lattice block geometry, which was not considered in the finite element models. The value of a single face sheet was demonstrated by increased bending moment capacity, where the face sheet simultaneously increased the gross section modulus and braced the compression ligaments against early buckling as seen in open-cell specimens. Preexisting flaws in specimens were not a discriminator in flexural, shear, or stiffness measurements, again because of redundant load paths available in the lattice block structure. Early test results are available in references 2 and 3; more complete analyses are scheduled for publication in 2004.
Source record↗
Time-domain analysis of planar microstrip devices using a generalized Yee-algorithm based on unstructured grids
The generalized Yee-algorithm is presented for the temporal full-wave analysis of planar microstrip devices. This algorithm has the significant advantage over the traditional Yee-algorithm in that it is based on unstructured and irregular grids. The robustness of the generalized Yee-algorithm is that structures that contain curved conductors or complex three-dimensional geometries can be more accurately, and much more conveniently modeled using standard automatic grid generation techniques. This generalized Yee-algorithm is based on the the time-marching solution of the discrete form of Maxwell's equations in their integral form. To this end, the electric and magnetic fields are discretized over a dual, irregular, and unstructured grid. The primary grid is assumed to be composed of general fitted polyhedra distributed throughout the volume. The secondary grid (or dual grid) is built up of the closed polyhedra whose edges connect the centroid's of adjacent primary cells, penetrating shared faces. Faraday's law and Ampere's law are used to update the fields normal to the primary and secondary grid faces, respectively. Subsequently, a correction scheme is introduced to project the normal fields onto the grid edges. It is shown that this scheme is stable, maintains second-order accuracy, and preserves the divergenceless nature of the flux densities. Finally, for computational efficiency the algorithm is structured as a series of sparse matrix-vector multiplications. Based on this scheme, the generalized Yee-algorithm has been implemented on vector and parallel high performance computers in a highly efficient manner.
Gedney, Stephen D.↗
Dehydroxylation kinetics of kaolinite and montmorillonite examined using isoconversional methods
The use of calcined clays as supplementary cementitious materials (SCMs) in concrete is a promising strategy towards decarbonizing the cement and concrete industry. This is especially relevant considering the ever-increasing demand for concrete. Comprehensive understanding of the kinetics of calcination is essential towards maximizing the potential reactivity of clay minerals while ensuring energy efficiency. In this study, the kinetics of the dehydroxylation of kaolinite and montmorillonite are investigated under non-isothermal conditions at constant heating rate. Activation energies ( E a ) are determined via Friedman differential and advanced Vyazovkin incremental methods over the isoconversional range; these are devoid of computational approximations, thus allowing kinetic analysis without assuming a specific reaction model. Kinetic equations—in the differential form as well as a combination of differential and integral forms are compared against the experimentally determined reaction models to identify the most probable dehydroxylation mechanism for kaolinite and montmorillonite. A reaction order mechanism is established for dehydroxylation of kaolinite, while montmorillonite is noted to undergo dehydroxylation via a single-step reversible diffusion-controlled process. Kinetic triplet—comprising activation energy, reaction model and pre-exponential factor—is used to predict isothermal calcination conditions, which is further verified using analytical techniques. Heat release rates of clay-portlandite blends from isothermal calorimetry are used within a thermodynamic framework to quantify reactivity of the calcined clays. Here, the study demonstrates a general approach based on isoconversional methods to predict calcination conditions for different clays that can be used in efficient and optimized production of blended cements or SCMs.
36 MATERIALS SCIENCE↗
Plug-type heat flux gauge
A plug-type heat flux gauge formed in a material specimen and having a thermoplug integrally formed in the material specimen, and a method for making the same are disclosed. The thermoplug is surrounded by a concentric annulus, through which thermocouple wires are routed. The end of each thermocouple wire is welded to the thermoplug, with each thermocouple wire welded at a different location along the length of the thermoplug. The thermoplug and concentric annulus may be formed in the material specimen by electrical discharge machining and trepanning procedures.
Liebert, Curt H.↗
On Formulations of Discontinuous Galerkin and Related Methods for Conservation Laws
A formulation for the discontinuous Galerkin (DG) method that leads to solutions using the differential form of the equation (as opposed to the standard integral form) is presented. The formulation includes (a) a derivative calculation that involves only data within each cell with no data interaction among cells, and (b) for each cell, corrections to this derivative that deal with the jumps in fluxes at the cell boundaries and allow data across cells to interact. The derivative with no interaction is obtained by a projection, but for nodal-type methods, evaluating this derivative by interpolation at the nodal points is more economical. The corrections are derived using the approximate (Dirac) delta functions. The formulation results in a family of schemes: different approximate delta functions give rise to different methods. It is shown that the current formulation is essentially equivalent to the flux reconstruction (FR) formulation. Due to the use of approximate delta functions, an energy stability proof simpler than that of Vincent, Castonguay, and Jameson (2011) for a family of schemes is derived. Accuracy and stability of resulting schemes are discussed via Fourier analyses. Similar to FR, the current formulation provides a unifying framework for high-order methods by recovering the DG, spectral difference (SD), and spectral volume (SV) schemes. It also yields stable, accurate, and economical methods.
Huynh, H. T.↗
Conservative high-order-accurate finite-difference methods for curvilinear grids
Two fourth-order-accurate finite-difference methods for numerically solving hyperbolic systems of conservation equations on smooth curvilinear grids are presented. The first method uses the differential form of the conservation equations; the second method uses the integral form of the conservation equations. Modifications to these schemes, which are required near boundaries to maintain overall high-order accuracy, are discussed. An analysis that demonstrates the stability of the modified schemes is also provided. Modifications to one of the schemes to make it total variation diminishing (TVD) are also discussed. Results that demonstrate the high-order accuracy of both schemes are included in the paper. In particular, a Ringleb-flow computation demonstrates the high-order accuracy and the stability of the boundary and near-boundary procedures. A second computation of supersonic flow over a cylinder demonstrates the shock-capturing capability of the TVD methodology. An important contribution of this paper is the dear demonstration that higher order accuracy leads to increased computational efficiency.
Rai, Man M.↗
Quadrature Based Neural Network Learning of Stochastic Hamiltonian Systems
Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic Hamiltonian systems (SHSs) from observational data. We propose the quadrature-based models according to the integral form of the SHSs’ solutions, where we denoise the loss-by-moment calculations of the solutions. The integral pattern of the models transforms the source of the essential learning error from the discrepancy between the modified Hamiltonian and the true Hamiltonian in the classical HNN models into that between the integrals and their quadrature approximations. This transforms the challenging task of deriving the relation between the modified and the true Hamiltonians from the (stochastic) Hamilton–Jacobi PDEs, into the one that only requires invoking results from the numerical quadrature theory. Meanwhile, denoising via moments calculations gives a simpler data fitting method than, e.g., via probability density fitting, which may imply better generalization ability in certain circumstances. Numerical experiments validate the proposed learning strategy on several concrete Hamiltonian systems. The experimental results show that both the learned Hamiltonian function and the predicted solution of our quadrature-based model are more accurate than that of the corrected symplectic HNN method on a harmonic oscillator, and the three-point Gaussian quadrature-based model produces higher accuracy in long-time prediction than the Kramers–Moyal method and the numerics-informed likelihood method on the stochastic Kubo oscillator as well as other two stochastic systems with non-polynomial Hamiltonian functions. Moreover, the Hamiltonian learning error εH arising from the Gaussian quadrature-based model is lower than that from Simpson’s quadrature-based model. These demonstrate the superiority of our approach in learning accuracy and long-time prediction ability compared to certain existing methods and exhibit its potential to improve learning accuracy via applying precise quadrature formulae.
Mathematics↗
Diode assembly and method of forming a diode assembly for pulsed fusion events
A diode assembly for producing a pulsed fusion event in a z-pinch driver. The diode assembly includes an inner core formed of a fusionable fuel source material including a lithium compound formed of one or more lithium isotopes and one or more hydrogen isotopes. A lithium metal outer sheath is integrally formed around the inner core by decomposing a surface of the fusionable fuel source material.
Brown, Sam W.↗
Vacuum Plasma Spray of CuCrNb Alloy for Advanced Liquid - Fuel Combustion Chambers
The copper-8 atomic percent chromium-4 atomic percent niobium (CuCrNb) alloy was developed by Glenn Research Center (formally Lewis Research Center) as an improved alloy for combustion chamber liners. In comparison to NARloy-Z, the baseline (as in Space Shuttle Main Engine) alloy for such liners, CuCrNb demonstrates mechanical and thermophysical properties equivalent to NARloy-Z, but at temperatures 100 C to 150 C (180 F to 270 F) higher. Anticipated materials related benefits include decreasing the thrust cell liner weight 5% to 20%, increasing the service life at least two fold over current combustion chamber design, and increasing the safety margins available to designers. By adding an oxidation and thermal barrier coating to the liner, the combustion chamber can operate at even higher temperatures. For all these benefits, however, this alloy cannot be formed using conventional casting and forging methods because of the levels of chromium and niobium, which exceed their solubility limit in copper. Until recently, the only forming process that maintains the required microstructure of CrNb intermetallics is powder metallurgy formation of a billet from powder stock, followed by extrusion. This severely limits its usefulness in structural applications, particularly the complex shapes required for combustion chamber liners. Vacuum plasma spray (VPS) has been demonstrated as a method to form structural articles including small combustion chambers from the CuCrNb alloy. In addition, an oxidation and thermal barrier layer can be formed integrally on the hot wall of the liner that improve performance and extend service life. This paper discusses the metallurgy and thermomechanical properties of VPS formed CuCrNb versus the baseline powder metallurgy process, and the manufacturing of small combustion chamber liners at Marshall Space Flight Center using the VPS process. The benefits to advanced propulsion initiatives of using VPS to fabricate combustion chamber liners while maintaining the superior CuCrNb properties are also presented.
Zimmerman, Frank↗