Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “fixed point method”

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 163 records · Page 9

A feasibility study of hand kinematics for EVA analysis using magnetic resonance imaging

A new method of analyzing the kinematics of joint motion is developed. Magnetic Resonance Imaging (MRI) offers several distinct advantages. Past methods of studying anatomic joint motion have usually centered on four approaches. These methods are x-ray projection, goniometric linkage analysis, sonic digitization, and landmark measurement of photogrammetry. Of these four, only x-ray is applicable for in vivo studies. The remaining three methods utilize other types of projections of inter-joint measurements, which can cause various types of error. MRI offers accuracy in measurement due to its tomographic nature (as opposed to projection) without the problems associated with x-ray dosage. Once the data acquisition of MR images was complete, the images were processed using a 3D volume rendering workstation. The metacarpalphalangeal (MCP) joint of the left index finger was selected and reconstructed into a three-dimensional graphic display. From the reconstructed volumetric images, measurements of the angles of movement of the applicable bones were obtained and processed by analyzing the screw motion of the MCP joint. Landmark positions were chosen at distinctive locations of the joint at fixed image threshold intensity levels to ensure repeatability. The primarily two dimensional planar motion of this joint was then studied using a method of constructing coordinate systems using three (or more) points. A transformation matrix based on a world coordinate system described the location and orientation of a local target coordinate system. Future research involving volume rendering of MRI data focusing on the internal kinematics of the hand's individual ligaments, cartilage, tendons, etc. will follow. Its findings will show the applicability of MRI to joint kinematics for gaining further knowledge of the hand-glove (power assisted) design for extravehicular activity (EVA).

Dickenson, Rueben D.↗

Solar wind disturbances caused by solar flares - Equatorial plane

The propagation of solar wind disturbances caused by single, double and six successive flares in the dipolar and quadrupolar patterns of the interplanetary magnetic field (IMF) and the associated solar wind flow is studied. This study is based on a kinematic and empirical method developed by Hakamada and Akasofu (1982). Each flare is characterized by six parameters (such as the highest speed flow, its extent and duration). The successive IMF patterns in the equatorial plane of the heliosphere during a time span of 0.5-60 days after flares are presented for a variety of flares. The solar wind speed and IMF magnitude are given as a function of distance along a radial line fixed in space and also as a function of time at several points fixed in space (simulating approximately space probe observations). Some of the results are qualitatively compared with recent space probe observations, demonstrating fair similarity with the observed time profiles of solar wind speed variations over a wide range of both distances (0-10 AU) and time spans (60 days). The method provides a first-order construction, temporal and spatial, of flare-induced shocks and their multiple interactions with each other, as well as with the corotating interaction regions.

Akasofu, S.-I.↗

Treatment of atomic and molecular line blanketing by opacity sampling

An opacity sampling (OS) technique for treating the radiative opacity of large numbers of atomic and molecular lines in cool stellar atmospheres is presented. Tests were conducted and results show that the structure of atmospheric models is accurately fixed by the use of 1000 frequency points, and 500 frequency points is often adequate. The effects of atomic and molecular lines are separately studied. A test model computed by using the OS method agrees very well with a model having identical atmospheric parameters computed by the giant line (opacity distribution function) method.

Johnson, H. R.↗

Numerical study of sound propagation in a jet flow

An improved computer oriented solution method for problems involving the propagation of sound through a nonuniform jet flow is developed. The method seeks to optimize the use of computer resources such as core storage space and central memory time. Complete formulation details are presented for a jet flow model consisting of a fixed point source on the jet center line in the potential core.

Padula, S. L.↗

Nonlinear response of infinitely long circular cylindrical shells to subharmonic radial loads

The nonlinear response of infinitely long circular cylindrical shells (thin circular rings) in the presence of a two-to-one internal (autoparametric) resonance to a subharmonic excitation of order one-half of the higher mode is analyzed with the multiple-scale method. Four autonomous first-order ordinary differential equations are derived for the modulation of the amplitudes and phases of the interacting models. These modulation equations are used to determine the fixed points and their stability. The fixed points correspond to periodic oscillations of the shell, whereas the limit-cycle solutions of the modulation equations correspond to amplitude and phase-modulated oscillations of the shell. The force response curves exhibit saturation, jumps, and Hopf bifurcation. As excitation frequency changes, all limit cycles deform and lose stability through either pitchfork or cyclic-fold (saddle-node) bifurcations. Some of these saddle-node bifurcations cause a transition to chaos. The pitchfork bifurcations break the symmetry of the limit cycles.

Nayfeh, Ali H.↗

Adaptive Numerical Algorithms in Space Weather Modeling

Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different physics in different domains. A multi-physics system can be modeled by a software framework comprising of several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solar wind Roe Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamics (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical schemes. Depending on the application, we find that different time stepping methods are optimal. Several of the time integration schemes exploit the block-based granularity of the grid structure. The framework and the adaptive algorithms enable physics based space weather modeling and even forecasting.

Toth, Gabor↗

Improved Compression of Wavelet-Transformed Images

A recently developed data-compression method is an adaptive technique for coding quantized wavelet-transformed data, nominally as part of a complete image-data compressor. Unlike some other approaches, this method admits a simple implementation and does not rely on the use of large code tables. A common data compression approach, particularly for images, is to perform a wavelet transform on the input data, and then losslessly compress a quantized version of the wavelet-transformed data. Under this compression approach, it is common for the quantized data to include long sequences, or runs, of zeros. The new coding method uses prefixfree codes for the nonnegative integers as part of an adaptive algorithm for compressing the quantized wavelet-transformed data by run-length coding. In the form of run-length coding used here, the data sequence to be encoded is parsed into strings consisting of some number (possibly 0) of zeros, followed by a nonzero value. The nonzero value and the length of the run of zeros are encoded. For a data stream that contains a sufficiently high frequency of zeros, this method is known to be more effective than using a single variable length code to encode each symbol. The specific prefix-free codes used are from two classes of variable-length codes: a class known as Golomb codes, and a class known as exponential-Golomb codes. The codes within each class are indexed by a single integer parameter. The present method uses exponential-Golomb codes for the lengths of the runs of zeros, and Golomb codes for the nonzero values. The code parameters within each code class are determined adaptively on the fly as compression proceeds, on the basis of statistics from previously encoded values. In particular, a simple adaptive method has been devised to select the parameter identifying the particular exponential-Golomb code to use. The method tracks the average number of bits used to encode recent runlengths, and takes the difference between this average length and the code parameter. When this difference falls outside a fixed range, the code parameter is updated (increased or decreased). The Golomb code parameter is selected based on the average magnitude of recently encoded nonzero samples. The coding method requires no floating- point operations, and more readily adapts to local statistics than other methods. The method can also accommodate arbitrarily large input values and arbitrarily long runs of zeros. In practice, this means that changes in the dynamic range or size of the input data set would not require a change to the compressor. The algorithm has been tested in computational experiments on test images. A comparison with a previously developed algorithm that uses large code tables (generated via Huffman coding on training data) suggests that the data-compression effectiveness of the present algorithm is comparable to the best performance achievable by the previously developed algorithm.

Kiely, Aaron↗

Towards Verification of Unstructured-Grid Solvers

New methodology for verification of finite-volume computational methods using unstructured grids is presented. The discretization order properties are studied in computational windows, easily constructed within a collection of grids or a single grid. Tests are performed within each window and address a combination of problem-, solution-, and discretization/grid-related features affecting discretization error convergence. The windows can be adjusted to isolate particular elements of the computational scheme, such as the interior discretization, the boundary discretization, or singularities. Studies can use traditional grid-refinement computations within a fixed window or downscaling, a recently-introduced technique in which computations are made within windows contracting toward a focal point of interest. Grids within the windows are constrained to be consistently refined, allowing a meaningful assessment of asymptotic error convergence on unstructured grids. Demonstrations of the method are shown, including a comparative accuracy assessment of commonly-used schemes on general mixed grids and the identification of local accuracy deterioration at boundary intersections. Recommendations to enable attainment of design-order discretization errors for large-scale computational simulations are given.

Thomas, James L.↗

Treatment of atomic and molecular line blanketing by opacity sampling

A sampling technique for treating the radiative opacity of large numbers of atomic and molecular lines in cool stellar atmospheres is subjected to several tests. In this opacity sampling (OS) technique, the global opacity is sampled at only a selected set of frequencies, and at each of these frequencies the total monochromatic opacity is obtained by summing the contribution of every relevant atomic and molecular line. In accord with previous results, we find that the structure of atmospheric models is accurately fixed by the use of 1000 frequency points, and 100 frequency points are adequate for many purposes. The effects of atomic and molecular lines are separately studied. A test model computed using the OS method agrees very well with a model having identical atmospheric parameters, but computed with the giant line (opacity distribution function) method.

Johnson, H. R.↗

Noise constraints effecting optimal propeller designs

A preliminary design tool for advanced propellers was developed combining a fast vortex lattice aerodynamic analysis, a fast subsonic point source noise analysis, and an optimization scheme using a conjugate directions method. Twist, chord and sweep distributions are optimized to simultaneously improve both the aerodynamic performance and the noise observed at a fixed relative position. The optimal noise/performance tradeoffs for straight and advanced concept blades are presented. The techniques used include increasing the blade number, blade sweep, reducing the rotational speed, shifting the spanwise loading and diameter changes.

Miller, C. J.↗

Noise constraints effecting optimal propeller designs

A preliminary design tool for advanced propellers was developed combining a fast vortex lattice aerodynamic analysis, a fast subsonic point source noise analysis, and an optimization scheme using a conjugate directions method. Twist, chord and sweep distributions are optimized to simultaneously improve both the aerodynamic performance and the noise observed at a fixed relative position. The optimal noise/performance tradeoffs for straight and advanced concept blades are presented. The techniques used include increasing the blade number, blade sweep, reducing the rotational speed, shifting the spanwise loading and diameter changes.

Miller, C. J.↗

X-ray fluorescence microscopy methods for biological tissues

Abstract Synchrotron-based X-ray fluorescence microscopy is a flexible tool for identifying the distribution of trace elements in biological specimens across a broad range of sample sizes. The technique is not particularly limited by sample type and can be performed on ancient fossils, fixed or fresh tissue specimens, and in some cases even live tissue and live cells can be studied. The technique can also be expanded to provide chemical specificity to elemental maps, either at individual points of interest in a map or across a large field of view. While virtually any sample type can be characterized with X-ray fluorescence microscopy, common biological sample preparation methods (often borrowed from other fields, such as histology) can lead to unforeseen pitfalls, resulting in altered element distributions and concentrations. A general overview of sample preparation and data-acquisition methods for X-ray fluorescence microscopy is presented, along with outlining the general approach for applying this technique to a new field of investigation for prospective new users. Considerations for improving data acquisition and quality are reviewed as well as the effects of sample preparation, with a particular focus on soft tissues. The effects of common sample pretreatment steps as well as the underlying factors that govern which, and to what extent, specific elements are likely to be altered are reviewed along with common artifacts observed in X-ray fluorescence microscopy data.

Pushie, M. Jake (ORCID:0000000174945427)↗

Phases of 2D massless QCD with qubit regularization

We investigate the possibility of reproducing the continuum physics of 2D S U ( N ) gauge theory coupled to a single flavor of massless Dirac fermion using qubit regularization. The continuum theory is described by N free fermions in the ultraviolet (UV) and a coset Wess-Zumino-Witten (WZW) model in the infrared (IR). In this work, we first explore how well these features can be reproduced using the Kogut-Susskind (KS) Hamiltonian with a finite-dimensional link Hilbert space and a generalized Hubbard coupling. We do this by analyzing the renormalization group (RG) flow diagram of the continuum theory and identifying important phases of the theory. Using strong coupling expansions, we show that our lattice model exhibits a gapped dimer phase and a spin-chain phase. Furthermore, for N = 2 , using tensor network methods, we show that there is a second-order phase transition between these two phases, which we identify as the critical surface of the continuum theory that connects the IR and UV fixed points. In the IR, we identify the critical theory at the transition as the expected S U ( 2 ) 1 WZW model. Lastly, we argue that modifications of our model may allow the study of the UV physics of free fermions. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Nonlinear systems approach to control system design

Consider some of the control system design methods for plants with nonlinear dynamics. If the nonlinearity is weak relative to the size of the operating region, then the linear methods apply directly. Fixed-gain design may be feasible even for significant nonlinearities. It may be possible to find a single gain which provides adequate control of the linear models at several perturbation points. If the nonlinearity is restricted to a sector, that fact may be used to obtain a fixed-gain controller. Otherwise, a gain may have to be associated with each perturbation point Pi. A gain schedule K(p(v)) is obtained by connecting the perturbation points by a function, say p(v), of the scheduling parameter v (i.e., speed). When the scheduling parameter must be multidimensional, this approach is difficult; the objective is to develop an easier procedure.

Meyer, G.↗

Overview of magnetic bearing control and linearization approaches for annular magnetically suspended devices

An overview of magnetic bearing control and linearization approaches which have been considered for annular magnetically suspended devices is presented. These devices include the Annular Momentum Control Device and the Annular Suspension and Pointing System. Two approaches were investigated for controlling the magnetic actuator. One approach involves controlling the upper and lower electromagnets differentially about a bias flux. The bias flux can either be supplied by permanent magnets in the magnetic circuit or by bias currents. In the other approach, either the upper electromagnet or the lower electromagnet is controlled depending on the direction of force required. One advantage of the bias flux is that for small gap perturbations about a fixed operating point, the force-current characteristic is linear. Linearization approaches investigated for individual element control include an analog solution of the nonlinear electromagnet force equation and a microprocessor-based table lookup method.

Groom, N. J.↗

Efficient numerical simulation of electron states in quantum wires

A new algorithm is presented for the numerical simulation of electrons in a quantum wire as described by a two-dimensional eigenvalue problem for Schroedinger's equation coupled with Poisson's equation. Initially, the algorithm employs an underrelaxed fixed point iteration to generate an approximation which is reasonably close to the solution. Subsequently, this approximate solution is employed as an initial guess for a Jacobian-free implementation of an approximate Newton method. In this manner the nonlinearity in the model is dealt with effectively. The effectiveness of this approach is demonstrated in a set of numerical experiments which study the electron states on the cross section of a quantum wire structure based on III-V semiconductors at 4.2 and 77 K.

Kerkhoven, Thomas↗

Echocardiographic measurements of left ventricular mass by a non-geometric method

The accuracy of a new nongeometric method for calculating left ventricular myocardial volumes from two-dimensional echocardiographic images was assessed in vitro using 20 formalin-fixed normal human hearts. Serial oblique short-axis images were acquired from one point at 5-deg intervals, for a total of 10-12 cross sections. Echocardiographic myocardial volumes were calculated as the difference between the volumes defined by the epi- and endocardial surfaces. Actual myocardial volumes were determined by water displacement. Volumes ranged from 80 to 174 ml (mean 130.8 ml). Linear regression analysis demonstrated excellent agreement between the echocardiographic and direct measurements.

Parra, Beatriz↗

Variable Step Integration Coupled with the Method of Characteristics Solution for Water-Hammer Analysis, A Case Study

One-dimensional water-hammer modeling involves the solution of two coupled non-linear hyperbolic partial differential equations (PDEs). These equations result from applying the principles of conservation of mass and momentum to flow through a pipe, and usually the assumption that the speed at which pressure waves propagate through the pipe is constant. In order to solve these equations for the interested quantities (i.e. pressures and flow rates), they must first be converted to a system of ordinary differential equations (ODEs) by either approximating the spatial derivative terms with numerical techniques or using the Method of Characteristics (MOC). The MOC approach is ideal in that no numerical approximation errors are introduced in converting the original system of PDEs into an equivalent system of ODEs. Unfortunately this resulting system of ODEs is bound by a time step constraint so that when integrating the equations the solution can only be obtained at fixed time intervals. If the fluid system to be modeled also contains dynamic components (i.e. components that are best modeled by a system of ODEs), it may be necessary to take extremely small time steps during certain points of the model simulation in order to achieve stability and/or accuracy in the solution. Coupled together, the fixed time step constraint invoked by the MOC, and the occasional need for extremely small time steps in order to obtain stability and/or accuracy, can greatly increase simulation run times. As one solution to this problem, a method for combining variable step integration (VSI) algorithms with the MOC was developed for modeling water-hammer in systems with highly dynamic components. A case study is presented in which reverse flow through a dual-flapper check valve introduces a water-hammer event. The predicted pressure responses upstream of the check-valve are compared with test data.

Turpin, Jason B.↗