scholarly journals Identification and stability of small-sized dislocations using a direct algorithm

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Batoul Abdelaziz ◽  
Abdellatif El Badia ◽  
Ahmad El Hajj
Keyword(s):  
Inverse Problem ◽  
Three Dimensional ◽  
Initial Position ◽  
Direct Algorithm ◽  
Test Functions ◽  
Boundary Measurements ◽  
Hölder Stability

<p style='text-indent:20px;'>This paper considers the problem of identifying dislocation lines of curvilinear form in three-dimensional materials from boundary measurements, when the areas surrounded by the dislocation lines are assumed to be small-sized. The objective of this inverse problem is to reconstruct the number, the initial position and certain characteristics of these dislocations and establish, using certain test functions, a Hölder stability of the centers. This paper can be considered as a generalization of [<xref ref-type="bibr" rid="b9">9</xref>], where instead of reconstructing point-wise dislocations, as done in the latter paper, our aim is to recover the parameters of line dislocations by employing a direct algebraic algorithm.</p>

Stability and the inverse gravimetry problem with minimal data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Victor Isakov ◽  
Aseel Titi
Keyword(s):  
Inverse Problem ◽  
Gravitational Force ◽  
Three Dimensional ◽  
Minimal Amount ◽  
Algebraic Equations ◽  
Inverse Gravimetry ◽  
Reference Domain ◽  
Boundary Measurements ◽  
Minimal Data ◽  
Simple Systems

AbstractThe inverse problem in gravimetry is to find a domain 𝐷 inside the reference domain Ω from boundary measurements of gravitational force outside Ω. We found that about five parameters of the unknown 𝐷 can be stably determined given data noise in practical situations. An ellipse is uniquely determined by five parameters. We prove uniqueness and stability of recovering an ellipse for the inverse problem from minimal amount of data which are the gravitational force at three boundary points. In the proofs, we derive and use simple systems of linear and nonlinear algebraic equations for natural parameters of an ellipse. To illustrate the technique, we use these equations in numerical examples with various location of measurements points on \partial\Omega. Similarly, a rectangular 𝐷 is considered. We consider the problem in the plane as a model for the three-dimensional problem due to simplicity.

Acceleration of the EM-like reconstruction method for diffuse optical tomography with ordered-subsets method

2014 ◽  
Vol 22 (3) ◽  
Author(s):  
Caifang Wang
Keyword(s):  
Numerical Experiments ◽  
Imaging Modality ◽  
Random Medium ◽  
Optical Tomography ◽  
Back Propagation ◽  
Three Dimensional ◽  
Diffuse Optical Tomography ◽  
Optical Parameters ◽  
Reconstruction Method ◽  
Boundary Measurements

Abstract.Diffuse optical tomography (DOT) is an optical imaging modality, which provides the spatial distribution of the optical parameters inside a random medium. A propagation back-propagation method named EM-like reconstruction method for stationary DOT problem has been proposed yet. This method is really time consuming. Hence the ordered-subsets (OS) technique for this reconstruction method is studied in this paper. The boundary measurements of DOT are grouped into nonoverlapping and overlapping ordered sequence of subsets with random partition, sequential partition and periodic partition, respectively. The performance of OS methods is compared with the standard EM-like reconstruction method with two-dimensional and three-dimensional numerical experiments. The numerical experiments indicate that reconstruction of nonoverlapping subsets with periodic partition, overlapping subsets with periodic partition and standard EM-like method provide very similar acceptable reconstruction results. However, reconstruction of nonoverlapping subsets with periodic partition spends a minimum of time to get proper results.

Trajectory planning for coordinately operating robots

1990 ◽  
Vol 4 (3) ◽  
pp. 165-177 ◽  
Author(s):  
Y. P. Chien ◽  
Qing Xue
Keyword(s):  
Trajectory Planning ◽  
Three Dimensional ◽  
Initial Position ◽  
Minimum Time ◽  
Future Research ◽  
Rigid Object ◽  
Redundant Robots ◽  
Planning Algorithm ◽  
The Common ◽  
Joint Velocity

An efficient locally minimum-time trajectory planning algorithm for coordinately operating multiple robots is introduced. The task of the robots is to carry a common rigid object from an initial position to a final position along a given path in three-dimensional workspace in minimum time. The number of robots in the system is arbitrary. In the proposed algorithm, the desired motion of the common object carried by the robots is used as the key to planning of the trajectories of all the non-redundant robots involved. The search method is used in the trajectory planning. The planned robot trajectories satisfy the joint velocity, acceleration and torque constraints as well as the path constraints. The other constraints such as collision-free constraints, can be easily incorporated into the trajectory planning in future research.

An inversion formula for the transport equation in ℝ3 using complex analysis in several variables

2019 ◽  
Vol 27 (3) ◽  
pp. 341-352
Author(s):  
Seyed Majid Saberi Fathi
Keyword(s):  
Inverse Problem ◽  
Transport Equation ◽  
Inversion Formula ◽  
Complex Analysis ◽  
Three Dimensional ◽  
Analytical Continuation ◽  
Radon Transforms ◽  
Photon Transport ◽  
X Ray ◽  
Several Variables

Abstract In this paper, the stationary photon transport equation has been extended by analytical continuation from {\mathbb{R}^{3}} to {\mathbb{C}^{3}} . A solution to the inverse problem posed by this equation is obtained on a hyper-sphere and a hyper-cylinder as X-ray and Radon transforms, respectively. We show that these results can be transformed into each other, and they agree with known results. Numerical reconstructions of a three-dimensional Shepp–Logan head phantom using the obtained inverse formula illustrate the analytical results obtained in this manuscript.

scholarly journals The Localization of Activity Sources in a Three-Dimensional Model of the Human Brain Using the Joint Analysis of EEG / sMRI Data

2019 ◽  
Vol 17 (3) ◽  
pp. 18-28
Author(s):  
E. Bykova ◽  
A. Savostyanov
Keyword(s):  
Inverse Problem ◽  
Brain Activity ◽  
Three Dimensional ◽  
Human Head ◽  
Joint Analysis ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Use Of Data ◽  
The Individual ◽  
The Brain

Despite the large number of existing methods of the diagnosis of the brain, brain remains the least studied part of the human body. Electroencephalography (EEG) is one of the most popular methods of studying of brain activity due to its relative cheapness, harmless, and mobility of equipment. While analyzing the EEG data of the brain, the problem of solving of the inverse problem of electroencephalography, the localization of the sources of electrical activity of the brain, arises. This problem can be formulated as follows: according to the signals recorded on the surface of the head, it is necessary to determine the location of sources of these signals in the brain. The purpose of my research is to develop a software system for localization of brain activity sources based on the joint analysis of EEG and sMRI data. There are various approaches to solving of the inverse problem of EEG. To obtain the most exact results, some of them involve the use of data on the individual anatomy of the human head – structural magnetic resonance imaging (sMRI data). In this paper, one of these approaches is supposed to be used – Electromagnetic Spatiotemporal Independent Component Analysis (EMSICA) proposed by A. Tsai. The article describes the main stages of the system, such as preprocessing of the initial data; the calculation of the special matrix of the EMSICA approach, the values of which show the level of activity of a certain part of the brain; visualization of brain activity sources on its three-dimensional model.

Seismic Rays

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Inverse Problem ◽  
Seismic Tomography ◽  
Seismic Waves ◽  
Seismic Station ◽  
Three Dimensional ◽  
Arrival Times ◽  
The Earth ◽  
Straight Lines ◽  
Ray Path ◽  
Uniform Composition

This chapter focuses on the underlying mathematics of seismic rays. Seismic waves caused by earthquakes and explosions are used in seismic tomography to create computer-generated, three-dimensional images of Earth's interior. If the Earth had a uniform composition and density, seismic rays would travel in straight lines. However, it is broadly layered, causing seismic rays to be refracted and reflected across boundaries. In order to calculate the speed along the wave's ray path, the time it takes for a seismic wave to arrive at a seismic station from an earthquake needs to be determined. Arrival times of different seismic waves allow scientists to define slower or faster regions deep in the Earth. The chapter first presents the relevant equations for seismic rays before discussing how rays are propagated in a spherical Earth. The Wiechert-Herglotz inverse problem is considered, along with the properties of X in a horizontally stratified Earth.

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