Passive Approximation with High-Order B-Splines

2019 ◽  
pp. 83-94
Author(s):  
Yevhen Ivanenko ◽  
Sven Nordebo
Keyword(s):  
High Order ◽  
B Splines

A Stabilized B-Splines FEM Formulation for the Solution of an Inverse Elasticity Problem Arising in Medical Imaging

2008 ◽  
Author(s):  
Carlos E. Rivas ◽  
Paul E. Barbone ◽  
Assad A. Oberai
Keyword(s):  
Mechanical Properties ◽  
Diagnostic Value ◽  
Incompressible Material ◽  
High Order ◽  
Elasticity Problem ◽  
Parameter Distribution ◽  
Order Continuity ◽  
B Splines ◽  
Inverse Elasticity ◽  
Continuous Problem

Soft tissue pathologies are often associated with changes in mechanical properties. For example, breast and other tumors usually present as stiff lumps. Imaging the spatial distribution of the mechanical properties of tissues thus reveals information of diagnostic value. Doing so, however, typically requires the solution of an inverse elasticity problem. In this work we consider the inverse elasticity problem for an incompressible material in plane stress, formulated and solved as a constrained optimization problem. We formulate this inverse problem enforcing high order continuity for our variables. Driven by the requirements for the strong and weak solutions to this problem, we assume that our data field (i.e. the measured displacement) is in H2 and our parameter distribution (i.e. the sought shear modulus distribution) is in H1. This high order regularity requirement for the data is incompatible with standard FEM. We solve this problem using a FEM formulation that is novel in two respects. First, we employ quadratic b-splines that enforce C1 continuity in our displacement field, consistent with the variational requirements of the continuous problem. Second, we include Galerkin-least-squares (GLS) stabilization in the iterative optimization formulation. GLS adds consistent stability to the discrete formulation that otherwise violates an ellipticity condition that is satisfied by the continuous problem. Computational examples validate this formulation and demonstrate numerical convergence with mesh refinement.

High order interpolation and differentiation using B-splines

2004 ◽  
Vol 197 (1) ◽  
pp. 253-274 ◽  
Author(s):  
A.K. Chaniotis ◽  
D. Poulikakos
Keyword(s):  
High Order ◽  
B Splines ◽  
High Order Interpolation

Determination of the Burgers vector of a dislocation in a Fe-Mn alloy by weak-beam image in HVEM

1978 ◽  
Vol 36 (1) ◽  
pp. 330-331
Author(s):  
Y. Ishida ◽  
H. Ishida ◽  
K. Kohra ◽  
H. Ichinose
Keyword(s):  
High Order ◽  
Simulation Technique ◽  
The Other ◽  
Image Simulation ◽  
Diffraction Vector ◽  
Burgers Vector ◽  
Weak Beam ◽  
Beam Image ◽  
Edge Component

IntroductionA simple and accurate technique to determine the Burgers vector of a dislocation has become feasible with the advent of HVEM. The conventional image vanishing technique(1) using Bragg conditions with the diffraction vector perpendicular to the Burgers vector suffers from various drawbacks; The dislocation image appears even when the g.b = 0 criterion is satisfied, if the edge component of the dislocation is large. On the other hand, the image disappears for certain high order diffractions even when g.b ≠ 0. Furthermore, the determination of the magnitude of the Burgers vector is not easy with the criterion. Recent image simulation technique is free from the ambiguities but require too many parameters for the computation. The weak-beam “fringe counting” technique investigated in the present study is immune from the problems. Even the magnitude of the Burgers vector is determined from the number of the terminating thickness fringes at the exit of the dislocation in wedge shaped foil surfaces.

The usefulness of high index low symmetry zone axes for holz line analysis

1987 ◽  
Vol 45 ◽  
pp. 384-385
Author(s):  
C. M. Sung ◽  
D. B. Williams
Keyword(s):  
Lattice Parameter ◽  
High Order ◽  
Zone Axis ◽  
High Index ◽  
High Symmetry ◽  
Second Phases ◽  
Line Patterns ◽  
Low Symmetry ◽  
Line Analysis

Researchers have tended to use high symmetry zone axes (e.g. <111> <114>) for High Order Laue Zone (HOLZ) line analysis since Jones et al reported the origin of HOLZ lines and described some of their applications. But it is not always easy to find HOLZ lines from a specific high symmetry zone axis during microscope operation, especially from second phases on a scale of tens of nanometers. Therefore it would be very convenient if we can use HOLZ lines from low symmetry zone axes and simulate these patterns in order to measure lattice parameter changes through HOLZ line shifts. HOLZ patterns of high index low symmetry zone axes are shown in Fig. 1, which were obtained from pure Al at -186°C using a double tilt cooling holder. Their corresponding simulated HOLZ line patterns are shown along with ten other low symmetry orientations in Fig. 2. The simulations were based upon kinematical diffraction conditions.

Are HOLZ lines kinematic in off-zone-axis orientation?

1993 ◽  
Vol 51 ◽  
pp. 692-693
Author(s):  
J. M. Zuo ◽  
A. L. Weickenmeier ◽  
R. Holmestad ◽  
J. C. H. Spence
Keyword(s):  
Structure Determination ◽  
Standard Procedure ◽  
High Order ◽  
Zone Axis ◽  
Great Promise ◽  
Line Position ◽  
Measured Intensity ◽  
Constant Intensity ◽  
Axis Orientation ◽  
Diffraction Condition

The application of high order reflections in a weak diffraction condition off the zone axis center, including those in high order laue zones (HOLZ), holds great promise for structure determination using convergent beam electron diffraction (CBED). It is believed that in this case the intensities of high order reflections are kinematic or two-beam like. Hence, the measured intensity can be related to the structure factor amplitude. Then the standard procedure of structure determination in crystallography may be used for solving unknown structures. The dynamic effect on HOLZ line position and intensity in a strongly diffracting zone axis is well known. In a weak diffraction condition, the HOLZ line position may be approximated by the kinematic position, however, it is not clear whether this is also true for HOLZ intensities. The HOLZ lines, as they appear in CBED patterns, do show strong intensity variations along the line especially near the crossing of two lines, rather than constant intensity along the Bragg condition as predicted by kinematic or two beam theory.

Relativistic high-order harmonic generation

2003 ◽  
Vol 50 (3-4) ◽  
pp. 375-386
Author(s):  
D. B. MilosÕeviĆ ◽  
W. Becker
Keyword(s):  
Harmonic Generation ◽  
High Order ◽  
High Order Harmonic Generation ◽  
High Order Harmonic
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