scholarly journals Vision-aided inertial navigation: Closed-form determination of absolute scale, speed and attitude

2011 ◽  
Author(s):  
Agostino Martinelli ◽  
Chiara Troiani ◽  
Alessandro Renzaglia
Keyword(s):  
Closed Form ◽  
Inertial Navigation ◽  
Absolute Scale

Solutions to the Vector Tetrahedron Equation

1965 ◽  
Vol 87 (2) ◽  
pp. 228-234 ◽  
Author(s):  
Milton A. Chace
Keyword(s):  
Closed Form ◽  
Digital Computer ◽  
Three Dimensional ◽  
Dimensional Vector ◽  
Spherical Coordinates ◽  
Tetrahedron Equation ◽  
Position Determination ◽  
Closed Form Solutions

A set of nine closed-form solutions are presented to the single, three-dimensional vector tetrahedron equation, sum of vectors equals zero. The set represents all possible combinations of unknown spherical coordinates among the vectors, assuming the coordinates are functionally independent. Optimum use is made of symmetry. The solutions are interpretable and can be evaluated reliably by digital computer in milliseconds. They have been successfully applied to position determination of many three-dimensional mechanisms.

scholarly journals Simple and Exact Closed-Form Expression for Determination of a Penetrated Ray Path in a Ray Tracing

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hyun Wook Moon ◽  
Woojoong Kim ◽  
Sewoong Kwon ◽  
Jaeheung Kim ◽  
Young Joong Yoon
Keyword(s):  
Closed Form ◽  
Approximate Method ◽  
Ray Tracing ◽  
Conventional Method ◽  
Closed Form Expression ◽  
Indoor Environments ◽  
Straight Line ◽  
Ray Path ◽  
Ray Tracing Simulation

A simple and exact closed-form equation to determine a penetrated ray path in a ray tracing is proposed for an accurate channel prediction in indoor environments. Whereas the penetrated ray path in a conventional ray tracing is treated as a straight line without refraction, the proposed method is able to consider refraction through the wall in the penetrated ray path. Hence, it improves the accuracy in ray tracing simulation. To verify the validation of the proposed method, the simulated results of conventional method, approximate method, and proposed method are compared with the measured results. The comparison shows that the proposed method is in better agreement with the measured results than the conventional method and approximate method, especially in high frequency bands.

scholarly journals Size and Concentration Determination of Colloidal Nanocrystals by Small-Angle X-Ray Scattering

2018 ◽  
Author(s):  
Jorick Maes ◽  
Nicolo Castro ◽  
Kim De Nolf ◽  
Willem Walravens ◽  
Benjamin Abécassis ◽  
...  
Keyword(s):  
Band Gap ◽  
Small Angle ◽  
Accurate Determination ◽  
Band Gap Energy ◽  
Colloidal Nanocrystals ◽  
X Ray ◽  
Absolute Scale ◽  
X Ray Scattering ◽  
Ray Scattering

<div> <div> <div> <p>The accurate determination of the dimensions of a nano-object is paramount to the de- velopment of nanoscience and technology. Here, we provide procedures for sizing quasi- spherical colloidal nanocrystals (NCs) by means of small-angle x-ray scattering (SAXS). Using PbS NCs as a model system, the protocols outline the extraction of the net NC SAXS pattern by background correction and address the calibration of scattered x-ray intensity to an absolute scale. Different data analysis methods are compared, and we show that they yield nearly identical estimates of the NC diameter in the case of a NC ensemble with a monodisperse and monomodal size distribution. Extending the analysis to PbSe, CdSe </p> </div> </div> <div> <div> <p>and CdS NCs, we provide SAXS calibrated sizing curves, which relate the NC diameter and the NC band-gap energy as determined using absorbance spectroscopy. In compari- son with sizing curves calibrated by means of transmission electron microscopy (TEM), we systematically find that SAXS calibration assigns a larger diameter than TEM calibration to NCs with a given band gap. We attribute this difference to the difficulty of accurately sizing small objects in TEM images. To close, we demonstrate that NC concentrations can be directly extracted from SAXS patterns normalized to an absolute scale, and we show that SAXS-based concentrations agree with concentration estimates based on absorption spectroscopy.</p></div></div></div>

Stress Intensity Factor Coefficients for Circumferential ID Surface Flaws in Cylinders for Appendix A of ASME Section XI

2013 ◽  
Author(s):  
Russell C. Cipolla ◽  
Darrell R. Lee
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Flat Plate ◽  
Closed Form ◽  
Fourth Order ◽  
Surface Crack ◽  
Crack Size ◽  
Plate Geometry

The stress intensity factor (KI) equations for a surface crack in ASME Section XI, Appendix A are based on non-dimensional coefficients (Gi) that allow for the calculation of stress intensity factors for a cubic varying stress field. Currently, the coefficients are in tabular format for the case of a surface crack in a flat plate geometry. The tabular form makes the computation of KI tedious when determination of KI for various crack sizes is required and a flat plate geometry is conservative when applied to a cylindrical geometry. In this paper, closed-form equations are developed based on tabular data from API 579 (2007 Edition) [1] for circumferential cracks on the ID surface of cylinders. The equations presented, represent a complete set of Ri/t, a/t, and a/l ratios and include those presented in the 2012 PVP paper [8]. The closed-form equations provide G0 and G1 coefficients while G2 through G4 are obtained using a weight function representation for the KI solutions for a surface crack. These equations permit the calculation of the Gi coefficients without the need to perform tabular interpolation. The equations are complete up to a fourth order polynomial representation of applied stress, so that the procedures in Appendix A have been expanded. The fourth-order representation for stress will allow for more accurate fitting of highly non-linear stress distributions, such as those depicting high thermal gradients and weld residual stress fields. The equations developed in this paper will be added to the Appendix A procedures in the next major revision to ASME Section XI. With the inclusion of equations to represent Gi, the procedures of Appendix A for the determination of KI can be performed more efficiently without the conservatism of using flat plate solutions. This is especially useful when performing flaw growth evaluations where repetitive calculations are required in the computations of crack size versus time. The equations are relatively simple in format so that the KI computations can be performed by either spreadsheet analysis or by simple computer programming. The format of the equations is generic in that KI solutions for other geometries can be added to Appendix A relatively easily.

scholarly journals Closed-form rocking overturning conditions for a family of pulse ground motions

2016 ◽  
Vol 472 (2196) ◽  
pp. 20160662 ◽  
Author(s):  
Elias G. Dimitrakopoulos ◽  
Edwin Dat Win Fung
Keyword(s):  
Lower Bound ◽  
Finite Number ◽  
Closed Form ◽  
Physical Mechanism ◽  
Ground Motions ◽  
Critical Conditions ◽  
Rocking Block ◽  
Approximate Analytical Solutions ◽  
The Stability

This paper characterizes the stability of a rigid rocking block subjected to a family of multi-lobe pulse ground motions. It unveils a counter to intuition plurality of overturning (OT) modes despite the short duration and bounded energy of the examined ground motions. Accordingly, it describes with original closed-form expressions the critical conditions of all OT modes involving a finite number of impacts. It also proposes pertinent semi-analytical, exact analytical and approximate analytical solutions with respect to the determination of the (unknown) times of impact, as appropriate. The analysis reveals that the first , or lower bound , critical OT mode is in most cases toppling during free rocking after one impact specifically before the end of the pulse. For this case, it elucidates the physical mechanism behind the timing of impact that produces minimum amplitude and maximum amplitude critical OT, respectively, and proposes pertinent closed-form approximations. Finally, the study derives, in ‘universal’ terms, global ‘safety walls’ against rocking OT considering a large number of different pulse shapes.

Explicit formulation for the axial collapse of a pipe during drilling

2010 ◽  
Vol 224 (8) ◽  
pp. 1547-1549
Author(s):  
A Almasi
Keyword(s):  
Closed Form ◽  
Plastic Hinge ◽  
Variable Length ◽  
Experimental Results ◽  
Displacement Curve ◽  
Explicit Formulation ◽  
Theoretical Predictions ◽  
Hinge Zone ◽  
Good Agreement

New closed-form expressions are introduced for ax-symmetric progressive axial collapse of pipes that use a plastic folding mechanism based on variable length of an active plastic hinge zone. A procedure for determination of a load—displacement curve of axial pipe collapse is presented. Theoretical predictions give a good agreement with the experimental results owing to the influence of presented new refinements.

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