An Analysis of Insar Displacement Vector Decomposition Fallacies and the Strap-Down Solution

2021 ◽  
Author(s):  
Wietske S. Brouwer ◽  
Ramon F. Hanssen
Keyword(s):  
Displacement Vector ◽  
Vector Decomposition

Simulation and Contrast Analysis of tem Images of Cracks

1990 ◽  
Vol 48 (1) ◽  
pp. 578-579
Author(s):  
D. Goyal ◽  
A. H. King
Keyword(s):  
Displacement Vector ◽  
Crack Tip ◽  
Perfect Crystal ◽  
Operating Conditions ◽  
Displacement Fields ◽  
Fringe Contrast ◽  
Orthogonal Geometry ◽  
Moire Fringe ◽  
Moiré Fringe

TEM images of cracks have been found to give rise to a moiré fringe type of contrast. It is apparent that the moire fringe contrast is observed because of the presence of a fault in a perfect crystal, and is characteristic of the fault geometry and the diffracting conditions in the TEM. Various studies have reported that the moire fringe contrast observed due to the presence of a crack in an otherwise perfect crystal is distinctive of the mode of crack. This paper describes a technique to study the geometry and mode of the cracks by comparing the images they produce in the TEM because of the effect that their displacement fields have on the diffraction of electrons by the crystal (containing a crack) with the corresponding theoretical images. In order to formulate a means of matching experimental images with theoretical ones, displacement fields of dislocations present (if any) in the vicinity of the crack are not considered, only the effect of the displacement field of the crack is considered.The theoretical images are obtained using a computer program based on the two beam approximation of the dynamical theory of diffraction contrast for an imperfect crystal. The procedures for the determination of the various parameters involved in these computations have been well documented. There are three basic modes of crack. Preliminary studies were carried out considering the simplest form of crack geometries, i. e., mode I, II, III and the mixed modes, with orthogonal crack geometries. It was found that the contrast obtained from each mode is very distinct. The effect of variation of operating conditions such as diffracting vector (), the deviation parameter (ω), the electron beam direction () and the displacement vector were studied. It has been found that any small change in the above parameters can result in a drastic change in the contrast. The most important parameter for the matching of the theoretical and the experimental images was found to be the determination of the geometry of the crack under consideration. In order to be able to simulate the crack image shown in Figure 1, the crack geometry was modified from a orthogonal geometry to one with a crack tip inclined to the original crack front. The variation in the crack tip direction resulted in the variation of the displacement vector also. Figure 1 is a cross-sectional micrograph of a silicon wafer with a chromium film on top, showing a crack in the silicon.

Method of first integrals and interface, surface waves

2010 ◽  
Vol 32 (2) ◽  
pp. 107-120
Author(s):  
Pham Chi Vinh ◽  
Trinh Thi Thanh Hue ◽  
Dinh Van Quang ◽  
Nguyen Thi Khanh Linh ◽  
Nguyen Thi Nam
Keyword(s):  
Rayleigh Waves ◽  
Displacement Vector ◽  
Attenuation Factor ◽  
Electrical Potential ◽  
Polarization Vector ◽  
First Integrals ◽  
Dispersion Equations ◽  
Interface Surface ◽  
Electric Induction ◽  
The One

The method of first integrals (MFI) based on the equation of motion for the displacement vector, or  based on the one for the traction vector was introduced  recently in order to find explicit secular equations of Rayleigh waves whose characteristic equations (i.e the equations determining the attenuation factor) are fully quartic or are of higher order (then the classical approach is not applicable). In this paper it is shown that, not only to Rayleigh waves,  the MFI can be applicable also to other waves by running it on the equations for mixed vectors. In particular: (i) By applying the MFI  to the equations for the displacement-traction vector we get the explicit dispersion equations of Stoneley waves in twinned crystals (ii)  Running the MFI on the equations for the traction-electric induction vector and the traction-electrical potential vector provides the explicit dispersion equations of SH-waves in piezoelastic materials. The obtained dispersion equations are identical with the ones previously derived using the method of polarization vector, but the procedure of driving them is more simple.

An Eight-Node Hexahedral Finite Element with Rotational DOFs for Elastoplastic Applications

2019 ◽  
Vol 11 (1) ◽  
pp. 54-66
Author(s):  
Ayoub Ayadi ◽  
Kamel Meftah ◽  
Lakhdar Sedira ◽  
Hossam Djahara
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Plastic Zone ◽  
Displacement Vector ◽  
Small Strain ◽  
Benchmark Problems ◽  
Plasticity Model ◽  
Vector Approximation ◽  
Calculation Code

Abstract In this paper, the earlier formulation of the eight-node hexahedral SFR8 element is extended in order to analyze material nonlinearities. This element stems from the so-called Space Fiber Rotation (SFR) concept which considers virtual rotations of a nodal fiber within the element that enhances the displacement vector approximation. The resulting mathematical model of the proposed SFR8 element and the classical associative plasticity model are implemented into a Fortran calculation code to account for small strain elastoplastic problems. The performance of this element is assessed by means of a set of nonlinear benchmark problems in which the development of the plastic zone has been investigated. The accuracy of the obtained results is principally evaluated with some reference solutions.

Spacetime Geometry

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Coordinate System ◽  
Special Relativity ◽  
Displacement Vector ◽  
Proper Time ◽  
Plane Geometry ◽  
Spatial Displacement ◽  
Spacetime Geometry ◽  
Space And Time ◽  
Displacement Vectors

This chapter shows that the counterintuitive aspects of special relativity are due to the geometry of spacetime. We begin by showing, in the familiar context of plane geometry, how a metric equation separates frame‐dependent quantities from invariant ones. The components of a displacement vector depend on the coordinate system you choose, but its magnitude (the distance between two points, which is more physically meaningful) is invariant. Similarly, space and time components of a spacetime displacement are frame‐dependent, but the magnitude (proper time) is invariant and more physically meaningful. In plane geometry displacements in both x and y contribute positively to the distance, but in spacetime geometry the spatial displacement contributes negatively to the proper time. This is the source of counterintuitive aspects of special relativity. We develop spacetime intuition by practicing with a graphic stretching‐triangle representation of spacetime displacement vectors.

scholarly journals Organ motion in linac-based SBRT for glottic cancer

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Annarita Perillo ◽  
Valeria Landoni ◽  
Alessia Farneti ◽  
Giuseppe Sanguineti
Keyword(s):  
Early Stage ◽  
Displacement Vector ◽  
Thyroid Cartilage ◽  
Three Dimensional ◽  
Target Volume ◽  
Glottic Cancer ◽  
Organ Motion ◽  
Delivery Times ◽  
Significant Difference ◽  
Pre Treatment

Abstract Purpose The purpose of this study is to evaluate inter- and intra-fraction organ motion as well as to quantify clinical target volume (CTV) to planning target volume (PTV) margins to be adopted in the stereotactic treatment of early stage glottic cancer. Methods and materials Stereotactic body radiotherapy (SBRT) to 36 Gy in 3 fractions was administered to 23 patients with early glottic cancer T1N0M0. Patients were irradiated with a volumetric intensity modulated arc technique delivered with 6 MV FFF energy. Each patient underwent a pre-treatment cone beam computed tomography (CBCT) to correct the setup based on the thyroid cartilage position. Imaging was repeated if displacement exceeded 2 mm in any direction. CBCT imaging was also performed after each treatment arc as well as at the end of the delivery. Swallowing was allowed only during the beam-off time between arcs. CBCT images were reviewed to evaluate inter- and intra-fraction organ motion. The relationships between selected treatment characteristics, both beam-on and delivery times as well as organ motion were investigated. Results For the population systematic (Ʃ) and random (σ) inter-fraction errors were 0.9, 1.3 and 0.6 mm and 1.1, 1.3 and 0.7 mm in the left-right (X), cranio-caudal (Y) and antero-posterior (Z) directions, respectively. From the analysis of CBCT images acquired after treatment, systematic (Ʃ) and random (σ) intra-fraction errors resulted 0.7, 1.6 and 0.7 mm and 1.0, 1.5 and 0.6 mm in the X, Y and Z directions, respectively. Margins calculated from the intra-fraction errors were 2.4, 5.1 and 2.2 mm in the X, Y and Z directions respectively. A statistically significant difference was found for the displacement in the Z direction between patients irradiated with > 2 arcs versus ≤ 2 arcs, (MW test, p = 0.038). When analyzing mean data from CBCT images for the whole treatment, a significant correlation was found between the time of delivery and the three dimensional displacement vector (r = 0.489, p = 0.055), the displacement in the Y direction (r = 0.553, p = 0.026) and the subsequent margins to be adopted (r = 0.626, p = 0.009). Finally, displacements and the subsequent margins to be adopted in Y direction were significantly greater for treatments with more than 2 arcs (MW test p = 0.037 and p = 0.019, respectively). Conclusions In the setting of controlled swallowing during treatment delivery, intra-fraction motion still needs to be taken into account when planning with estimated CTV to PTV margins of 3, 5 and 3 mm in the X, Y and Z directions, respectively. Selected treatments may require additional margins.

scholarly journals Retrieving Sun-Induced Chlorophyll Fluorescence from Hyperspectral Data with TanSat Satellite

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4886
Author(s):  
Shilei Li ◽  
Maofang Gao ◽  
Zhao-Liang Li
Keyword(s):  
Chlorophyll Fluorescence ◽  
Fluorescence Spectrum ◽  
Singular Vector ◽  
Low Frequency ◽  
Information Criterion ◽  
Hyperspectral Data ◽  
High Spectral Resolution ◽  
Remotely Sensed Data ◽  
Spectral Window ◽  
Vector Decomposition

A series of algorithms for satellite retrievals of sun-induced chlorophyll fluorescence (SIF) have been developed and applied to different sensors. However, research on SIF retrieval using hyperspectral data is performed in narrow spectral windows, assuming that SIF remains constant. In this paper, based on the singular vector decomposition (SVD) technique, we present an approach for retrieving SIF, which can be applied to remotely sensed data with ultra-high spectral resolution and in a broad spectral window without assuming that the SIF remains constant. The idea is to combine the first singular vector, the pivotal information of the non-fluorescence spectrum, with the low-frequency contribution of the atmosphere, plus a linear combination of the remaining singular vectors to express the non-fluorescence spectrum. Subject to instrument settings, the retrieval was performed within a spectral window of approximately 7 nm that contained only Fraunhofer lines. In our retrieval, hyperspectral data of the O2-A band from the first Chinese carbon dioxide observation satellite (TanSat) was used. The Bayesian Information Criterion (BIC) was introduced to self-adaptively determine the number of free parameters and reduce retrieval noise. SIF retrievals were compared with TanSat SIF and OCO-2 SIF. The results showed good consistency and rationality. A sensitivity analysis was also conducted to verify the performance of this approach. To summarize, the approach would provide more possibilities for retrieving SIF from hyperspectral data.

scholarly journals A Whole-Field Interferometric Scheme for Measuring strain and Flow Rates of Glacier and Other Natural Surfaces

1983 ◽  
Vol 29 (103) ◽  
pp. 492-497
Author(s):  
Gary Cloud ◽  
Edgar Conley
Keyword(s):  
Displacement Vector ◽  
Surface Displacement ◽  
Time Lapse ◽  
Speckle Interferometry ◽  
Narrow Beam ◽  
Coherent Light ◽  
Ice Surface ◽  
Glacier Ice ◽  
Fringe Patterns ◽  
Small Overlap

AbstractThe flow of glacier ice is mapped using high-resolution photography and non-coherent-light speckle interferometry. Young’s fringe patterns result when a double-exposed photoplate image of the straining surface is illuminated by a narrow beam of coherent light. Geometry gives a relationship between the ice surface displacement vector and the interference fringe patterns. This displacement vector is corrected for rigid-body (camera) movement and projected onto the ice surface using topological maps. The strain during the time-lapse interval is thus known. Comparison with data acquired by surveying techniques at Nisqually Glacier, Washington, U.S.A., is limited because of small overlap of the surface studied. In the areas for which results can be compared, our experiments yield a flow of 0.6 m/d where conventional methods yield about 0.4 m/d.

Efficient Scalable Video Coding Method Using Discrete Bandelet Transform

2020 ◽  
Vol 34 (14) ◽  
pp. 2055023
Author(s):  
Yogananda Patnaik ◽  
Dipti Patra
Keyword(s):  
Video Coding ◽  
Scalable Video Coding ◽  
Research Area ◽  
Set Partitioning ◽  
Scalable Video ◽  
Vector Decomposition ◽  
Coding Method ◽  
Benchmark Datasets ◽  
Spatio Temporal ◽  
Ordered Data

Video coding is an imperative part of the modern day communication system. Furthermore, it has vital roles in the fields of video streaming, multimedia, video conferencing and much more. Scalable Video Coding (SVC) is an emerging research area, due to its extensive application in most of the multimedia devices as well as public demand. The proposed coding technique is capable of eliminating the Spatio-temporal regularity of a video sequence. In Discrete Bandelet Transform (DBT), the directions are modeled by a three-directional vector field, known as structural flow. Regularity is decided by this flow where the data entropy is low. The wavelet vector decomposition of geometrically ordered data results in a lesser extent of significant coefficients. The directions of geometrical regularity are interpreted with a two-dimensional vector, and the approximation of these directions is found with spline functions. This paper deals with a novel SVC technique by exploiting the DBT. The bandelet coefficients are further encoded by utilizing Set Partitioning in Hierarchical Trees (SPIHT) encoder, followed by global thresholding mechanism. The proposed method is verified with several benchmark datasets using the performance measures which gives enhanced performance. Thus, the experimental results bring out the superiority of the proposed technique over the state-of-arts.

Micro and Macromechanical Study of Stress-Induced Martensitic Transformation in a Cu-Al-Be Polycrystalline Shape Memory Alloy

2006 ◽  
Vol 509 ◽  
pp. 87-92 ◽  
Author(s):  
F.M. Sánchez ◽  
G. Pulos
Keyword(s):  
Martensitic Transformation ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Vector Fields ◽  
Displacement Vector ◽  
Optical Microscope ◽  
Image Sequences ◽  
Tension Test ◽  
Loading Device ◽  
Stress States

An experimental investigation of the micro and macromechanical stress-induced martensitic transformation in a Cu-Al-Be polycrystalline shape memory alloy is undertaken using a uniaxial tension test. Digital images are acquired at different stress states. The image sequences are analyzed to estimate the optical flow to get displacement vector fields. The experiments are carried out on a miniature hydraulic loading device mounted under an optical microscope. The stress-strain curves and associated images show stress-induced martensitic transformation in specific grains. Displacement vector fields for the polycrystalline shape memory alloy are obtained. They are inhomogeneous due to the martensitic transformation and inter-granular interactions.

Sign in / Sign up

Export Citation Format

Share Document