SEARCH · Search NASA
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.
In a normal coordinate system { y 𝑎 } , the identity 𝜕 2 𝑥 𝑝 /∂y 𝑛 ∂y 𝑚 = ∂ 2 𝑥 𝑝 /∂y 𝑚 ∂y 𝑛 is used to obtain expressions, involving the components of the metric tensor in this coordinate system, for the derivatives of the unit tangent vectors to the parametric curves. An example is given for a normal coordinate system in the De Sitter universe.
We explore the feasibility of using nominally-orthogonal jets as active aerodynamic load control for multi-element high-lift systems, and whether the nominally-orthogonal jets can offer a variety of performance improvements. These nominally-orthogonal jets inject momentum normal to the airfoil surface near the flap trailing edge, where they create a vortex that entrains flow from the opposing side and change the airfoil circulation. Lift-enhancement opportunities of trailing edge nominally-orthogonal jets have previously been studied by Malavard et al. and Blaylock et al. on single-element airfoils; however, their effect on drag was not thoroughly investigated. In this study, we investigate two- dimensional nominally-orthogonal jet effects on both lift and drag on a two-element airfoil, NLR7301. We utilize Chimera Grid Tools to generate structured curvilinear overset grids, and the Reynolds-averaged Navier-Stokes solver OVERFLOW-2 to solve for the flow field around the airfoil. We perform various computational sensitivity studies on the baseline airfoil without a jet to validate computational results against benchmark experimental data. Using a Chimera overset grid topology, we demonstrate a similar lift-enhancement effect between a nominally-orthogonal jet and a nominally-orthogonal physical tab employed at the same location on the studied airfoil. After we introduce the nominally-orthogonal jet concept, we investigate nominally-orthogonal jets with various momentum coefficient settings, C(sub µ) = 0.00 − 0.04 and present a lift-enhancement relationship ∆C(sub l) ≃ 3.59 (C(sub µ)) for this airfoil. We discuss that utilizing a nominally-orthogonal jet with C(sub µ) = 0.01 can shift the linear region of the lift curve by a ∆C(sub l) = 0.36 for the pressure side jet and by a ∆C(sub l) = −0.27 for the suction side jet. Employing a nominally-orthogonal jet is also shown effective in altering the drag. To study the impact, we carry out a drag decomposition study in the form of drag polars. We show for a given C(sub l) = 2.50, a nominally-orthogonal jet with C(sub µ) = 0.01 on the pressure and suction side of the airfoil results in 113 drag count decrements and 41 drag count increments, respectively, compared to the baseline airfoil with no jet. These results show that large and controllable changes in aerodynamic performance can be achieved by relatively small active flow control inputs using the nominally-orthogonal jets presented in this study.
In many bacteria, the location of the mRNA start codon is determined by a short ribosome binding site sequence that base pairs with the 3'-end of 16S rRNA (rRNA) in the 30S subunit. Many groups have changed these short sequences, termed the Shine-Dalgarno (SD) sequence in the mRNA and the anti-Shine-Dalgarno (ASD) sequence in 16S rRNA, to create "orthogonal" ribosomes to enable the synthesis of orthogonal polymers in the presence of the endogenous translation machinery. However, orthogonal ribosomes are prone to SD-independent translation. Ribosomal protein bS1, which binds to the 30S ribosomal subunit, is thought to promote translation initiation by shuttling the mRNA to the ribosome. Thus, a better understanding of how the SD and bS1 contribute to start codon selection could help efforts to improve the orthogonality of ribosomes. Here, we engineered the Escherichia coli ribosome to prevent binding of bS1 to the 30S subunit and separate the activity of bS1 binding to the ribosome from the role of the mRNA SD sequence in start codon selection. We find that ribosomes lacking bS1 are slightly less active than wild-type ribosomes in vitro. Furthermore, orthogonal 30S subunits lacking bS1 do not have an improved orthogonality. Our findings suggest that mRNA features outside the SD sequence and independent of binding of bS1 to the ribosome likely contribute to start codon selection and the lack of orthogonality of present orthogonal ribosomes.
This paper presents an alternative to the correlation of individual components of a mode shape vectors by directly examining the sensitivity of the cross-orthogonality between test and analytical mode shapes. If the test and analysis mode shapes are identical, the diagonal elements of the cross-orthogonality will be identical to the test orthogonality matrix, so the cross-orthogonality matrix provides a concise measure of the 'closeness' between test and analysis mode shapes. There are two major advantages to the cross-orthogonality correlation approach. The first is that a direct correlation of this matrix will more directly meet the goal of the correlation effort (measured by cross-orthogonality). Secondly, and more importantly, the correlation of cross-orthogonality greatly reduces the amount of data that needs to be handled when compared to the correlation of mode shapes.
Investigation of the detailed capabilities and performance characterization of systems that employ L-orthogonal signaling techniques. L-orthogonal signals represent a unified set of signals wherein the polyphase and orthogonal (bi-orthogonal) signal sets are included as special cases. This fact is important, since orthogonal (bi-orthogonal) and polyphase signaling sets represent opposing forces as far as tradeoffs between error probability, energy-to-noise ratio, and bandwidth requirements are concerned. Bounds on the performance of the optimum receiver and the performance of various suboptimum (practical) receiver structures are given. Coherent and differentially coherent detection of differentially encoded signals are also pursued. Various comparisons and tradeoffs are made by means of numerical evaluation of the error probability expressions.
The purpose was to investigate a new simultaneous expansion/orthogonalization method in comparison with two previously published expansion methods and a widely used orthogonalization technique. Each expansion method uses data from an analytical model of the structure to complete the estimate of the mode shape vectors. Berman and Nagy used Guyan expansion in their work with improving analytical models. In this method, modes are expanded one at a time, producing a set not orthogonal with respect to the mass matrix. Baruch and Bar Itzhack's optimal orthogonalization procedure was used to subsequently adjust the expanded modes. A second expansion technique was presented by O'Callahan, Avitabile, and Reimer and separately by Kammer. Again, modes are expanded individually and orthogonalized after expansion with the same optimal technique as above. Finally, a simultaneous expansion/orthogonalization method was developed from the orthogonal Procrustes problem of computational mathematics. In this method modes are optimally expanded as a set and orthogonal with respect to the mass matrix as a result. Two demonstation problems were selected for the comparison of the methods described. The first problem is an 8 degree of freedom spring-mass problem first presented by Kabe. Several conditions were examined for expansion method including the presence of errors in the measured data and in the analysis models. As a second demonstration problem, data from tests of laboratory scale model truss structures was expanded for system identification. Tests with a complete structure produced a correlated analysis model and the stiffness and mass matrices. Tests of various damaged configurations produced measured data for 6 modes at 14 dof locations.
An experiment was conducted to assess the relative influence of several factors on performance with orthogonal stimulus-response arrays. Subjects responded to the onset of one of three aligned light circles with a press of one of three aligned response keys. The response array was aligned parallel, angled, or orthogonal to the stimulus array. The results indicated that performance with orthogonal arrays is worse than with parallel or angled S-R arrays. For the orthogonal arrangements, the results also indicate that each hand prefers a mapping directly opposite to the other hand, and that this mapping reverses when the orientation of the stimulus and response arrays are transposed. In addition, the results also revealed that the relative costs of orthogonal S-R arrangements are somewhat attenuated when the assigned mapping associates (i.e., colocates) a given display with its closest control.
The no-cloning theorem leads to information-theoretic security in various quantum cryptographic protocols. However, this security typically derives from a possibly weaker property that classical information encoded in certain quantum states cannot be broadcast. To formally capture this property, we introduce the study of ‘orthogonality broadcasting.’ When attempting to broadcast the orthogonality of two different qubit bases, we establish that the power of classical and quantum communication is equivalent. However, quantum communication is shown to be strictly more powerful for broadcasting orthogonality in higher dimensions. We then relate orthogonality broadcasting to quantum position verification and provide a new method for establishing error bounds in the no pre-shared entanglement model that can address protocols previous methods could not. Our key technical contribution is an uncertainty relation that uses the geometric relation of the states that undergo broadcasting rather than the non-commutative aspect of the final measurements.
A study of L-orthogonal signal performance represents an approach wherein the performance of polyphase and orthogonal signal sets stand out as the extreme special cases. The L-orthogonal signal model and its associated bandwidth properties are briefly discussed. System performance is investigated by presenting tight upper and lower bounds on the error probability performance of the maximum-likelihood receiver of L-orthogonal signals suggested by Reed and Scholtz (1966). A study of the error probability performance of the suboptimum receiver in the presence of noisy reference signals is also conducted.
A two-dimensional (one space and time) scalar adaptation of the proper orthogonal decomposition was applied to streamwise velocity data obtained in a lobed mixer flowfield, using a rake of 15 single-component hot wires. Through the application of the proper orthogonal decomposition, the amount of streamwise turbulent kinetic energy contained in the various proper orthogonal modes was examined for two different downstream locations (z/h = 2.6 and 3.9). The large eddy or dominant mode was shown to have a measurable decrease in the relative streamwise component of the kinetic energy between these two downstream locations. This indicates that the large eddy, as defined by the proper orthogonal decomposition, breaks down, and the flow becomes more homogeneous. A pseudoflow visualization technique was then employed to help visualize this process.
A wind tunnel experiment for characterizing the aerodynamic and propulsion forces and moments acting on a research model airplane is described. The model airplane called the Free-flying Airplane for Sub-scale Experimental Research (FASER), is a modified off-the-shelf radio-controlled model airplane, with 7 ft wingspan, a tractor propeller driven by an electric motor, and aerobatic capability. FASER was tested in the NASA Langley 12-foot Low-Speed Wind Tunnel, using a combination of traditional sweeps and modern experiment design. Power level was included as an independent variable in the wind tunnel test, to allow characterization of power effects on aerodynamic forces and moments. A modeling technique that employs multivariate orthogonal functions was used to develop accurate analytic models for the aerodynamic and propulsion force and moment coefficient dependencies from the wind tunnel data. Efficient methods for generating orthogonal modeling functions, expanding the orthogonal modeling functions in terms of ordinary polynomial functions, and analytical orthogonal blocking were developed and discussed. The resulting models comprise a set of smooth, differentiable functions for the non-dimensional aerodynamic force and moment coefficients in terms of ordinary polynomials in the independent variables, suitable for nonlinear aircraft simulation.
Abstract Uric acid (UA) is a vital biomarker for the diagnosis and management of various health conditions, including cardiovascular diseases, gout, kidney disorders, metabolic syndrome, and wound healing. Despite significant advances in wearable sensor technology, challenges persist in developing wearable sensors that are capable of maintaining high sensitivity, selectivity, and stability. In this study, we present an epidermal sensing platform enhanced with single-atom materials (SAMs) designed for flexible and orthogonal electrochemical detection of UA. We designed and synthesized an SAM with Fe-N 5 active sites to boost the electrochemical sensing signals, integrating it with laser-engraved graphene (LEG) to fabricate a wearable SAM-based UA patch sensor. This design provides superior UA detection performance compared to sensors based on conventional nanomaterials. In addition, we enhanced the detection accuracy and range by using an orthogonal approach that combines direct oxidation through differential pulse voltammetry (DPV) along with parallel biocatalytic amperometric detection. The resulting SAM-based UA orthogonal sensor patch demonstrated exceptional performance in wearable applications through tests measuring sweat UA levels in subjects before and after consuming a purine-rich diet. Graphical Abstract
An application of a simple numerical technique which allows for the rapid construction of orthogonal coordinate systems about axisymmetric blunt bodies is presented. This technique can generate orthogonal meshes which have unequally spaced points in two directions. Relations are given for the numerical generation of the metric coefficients. Body shapes ranging from simple analytical bodies to complex reverse curvature bodies are presented together with their orthogonal coordinate systems. The relatively good accuracy of the technique is shown in tabular data describing coordinate line slopes and metric coefficients. The predictor-corrector numerical method used to generate these results is both simple in concept and easy to program, so that the application of the technique should be broader than the results presented.
Orthogonality relations are obtained for the spherical harmonic coefficients of functions defined on the surface of a sphere. Following a brief discussion of the orthogonality of Fourier series coefficients, consideration is given to the values averaged over all orientations of the coordinate system of the spherical harmonic coefficients of a function defined on the surface of a sphere that can be expressed in terms of Legendre polynomials for the special case where the function is the sum of two delta functions located at two different points on the sphere, and for the case of an essentially arbitrary function. It is noted that the orthogonality relations derived have found applications in statistical studies of the geomagnetic field.
An application of a simple numerical technique which allows for the rapid construction of orthogonal coordinate systems about two dimensional and axisymmetric bodies is presented. The technique is based on a predictor corrector numerical method. It can be used to generate orthogonal meshes which have unequally spaced points in two directions. These orthogonal meshes in their transformed computational plane are, however, equally spaced so that the differencing for the metric coefficients and the fluid dynamic equation terms can be easily determined using equally spaced central finite differences. Solutions to the Navier-Stokes equations for flow over blunt bodies with reverse curvature are presented. The coupling of the time dependent fluid dynamic equations and the coordinate generator worked well with no undesirable effects noted.
As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.
As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.
Tests of large structures on-orbit will be performed with measurements at a relatively few structure points. Values for the unmeasured degrees of freedom (dofs) can be estimated based on measured dofs and analytical model dynamic information. These 'expanded' mode shapes are useful for optimal-update identification and damage location as well as test/analysis correlation. A new method of expansion for test mode shape vectors is developed from the orthogonal Procrustes problem from computational linear algebra. A subspace defined by the set of measured dofs is compared to a subspace defined by mode shapes from an analytical model of the structure. The method simultaneously expands and orthogonalizes the mode shape vectors. Two demonstration problems are used to compare the new method to current expansion techniques. One demonstration uses test data from a laboratory scale-model truss structure. Performance of the new method is comparable or superior to that of the previous expansion methods which require separate orthogonalization.