Two‐point ray tracing in a three‐dimensional medium consisting of homogeneous nonisotropic layers separated by plane interfaces

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 767-770 ◽  
Author(s):  
R. F. Stöckli
Keyword(s):  
Point Source ◽  
Travel Time ◽  
Ray Tracing ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Point Of View ◽  
Wave Surface ◽  
Computational Point ◽  
Time Problem

The ray‐tracing problem is considered the solution to a minimum travel time problem for media where each layer may be regarded as a transversely isotropic homogeneous solid. The wave surface‐wavefront at t = 1 s, corresponding to a wave generated at the point source, associated with each layer’s anisotropy is approximated by surfaces which are not more difficult to handle, from a computational point of view, than ellipsoidal surfaces. These approximating surfaces are those used in ray‐tracing computation; a ray being a true ray approximation is thus obtained.

Construction of Dynamic Fundamental Solutions for Piezoelectric Solids

1995 ◽  
Vol 48 (11S) ◽  
pp. S222-S229 ◽  
Author(s):  
Naum Khutoryansky ◽  
Horacio Sosa
Keyword(s):  
Three Dimensional ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Point Of View ◽  
Integral Representations ◽  
Computational Point ◽  
Plane Wave Decomposition ◽  
Piezoelectric Solid ◽  
Piezoelectric Solids ◽  
Wave Decomposition

Fundamental solutions are derived within the framework of transient dynamic, three-dimensional piezoelectricity. The purpose of the article is to show alternate integral representations for such solutions. Thus, a representation over the unit sphere in accordance to a methodology based on the plane wave decomposition is provided. It is shown, however, that more efficient representations from a computational point of view can be achieved through appropriate coordinate transformations. Hence, representations of the fundamental solutions over surfaces of slowness are provided as novel alternatives to more classical approaches. The computational benefits of these new representations are displayed through a numerical example involving a transversely isotropic piezoelectric solid.

Vibration Analysis of Thin/Thick, Composites/Metallic Spinning Cylindrical Shells by Refined Beam Models

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
E. Carrera ◽  
M. Filippi
Keyword(s):  
Composite Materials ◽  
Initial Stress ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Point Of View ◽  
Displacement Fields ◽  
Previous Theory ◽  
Cross Sectional ◽  
Computational Point ◽  
Thick Composites

This paper evaluates the vibration characteristics of thin/thick rotating cylindrical shells made of metallic and composite materials. A previous theory of the authors is extended here to include the effects of geometrical stiffness due to rotation. To this end, variable kinematic one-dimensional (1D) models obtained by applying the Carrera Unified Formulation (CUF) were used. The components of the displacement fields are x, z polynomials of arbitrary order N, making it possible to go beyond the rigid cross section assumptions of the classical beam theories. A significant contribution of this formulation consists in the possibility to include the in-plane cross-sectional deformations allowing the introduction of the in-plane initial stress effects, e.g., the effect of the geometrical stiffness. Equations of motions, including both Coriolis and in-plane initial stress contributions, were solved through the finite element method. Several analyses were carried out on both thin and thick cylinders made of either metallic or composite materials with different boundary conditions. The results are compared with analytical and numerical shell formulations and three-dimensional solutions available in the literature. Various laminate lay-up have been considered in the case of composites shells. Numerical evaluations of the effect of geometric stiffness are provided, demonstrating its importance in the analyses presented. The 1D models appear very effective to investigate the dynamics of spinning shells and, contrary to shell theories, they do not require any amendments with thick shell geometry. From the computational point of view, the present refined beam models are less expensive than the shell and solid counterparts.

An enhancement of the warping shear functions of Refined Zigzag Theory

2021 ◽  
pp. 1-15
Author(s):  
Matteo Sorrenti ◽  
Marco Di Sciuva
Keyword(s):  
Coupling Effect ◽  
Three Dimensional ◽  
Composite Plates ◽  
Laminated Plates ◽  
Point Of View ◽  
Multilayered Structures ◽  
Computational Point ◽  
Multilayered Plates ◽  
Elasticity Solutions ◽  
Zigzag Theory

Abstract The paper presents an enhancement in Refined Zigzag Theory (RZT) for the analysis of multilayered composite plates. In standard RZT, the zigzag functions cannot predict the coupling effect of in-plane displacements for anisotropic multilayered plates, such as angle-ply laminates. From a computational point of view, this undesirable effect leads to a singular stiffness matrix. In this work, the local kinematic field of RZT is enhanced with the other two zigzag functions that allow the coupling effect. In order to assess the accuracy of these new zigzag functions for RZT, results obtained from bending of angle-ply laminated plates are compared to the three-dimensional exact elasticity solutions and other plate models used in the open literature. The numerical results highlight that the enhanced zigzag functions extend the range of applicability of RZT to the study of general angle-ply multilayered structures, maintaining the same seven kinematic unknowns of standard RZT.

A fast algorithm for two-point seismic ray tracing

1987 ◽  
Vol 77 (3) ◽  
pp. 972-986
Author(s):  
Junho Um ◽  
Clifford Thurber
Keyword(s):  
Travel Time ◽  
Ray Tracing ◽  
Three Dimensional ◽  
Linear Interpolation ◽  
Geometric Interpretation ◽  
Approximate Algorithm ◽  
Velocity Models ◽  
Limit Test ◽  
Ray Path ◽  
Lateral Variations

Abstract A new approximate algorithm for two-point ray tracing is proposed and tested in a variety of laterally heterogeneous velocity models. An initial path estimate is perturbed using a geometric interpretation of the ray equations, and the travel time along the path is minimized in a piecewise fashion. This perturbation is iteratively performed until the travel time converges within a specified limit. Test results show that this algorithm successfully finds the correct travel time within typical observational error much faster than existing three-dimensional ray tracing programs. The method finds an accurate ray path in a fully three-dimensional form even where lateral variations in velocity are severe. Because our algorithm utilizes direct minimization of the travel time instead of solving the ray equations, a simple linear interpolation scheme can be employed to compute velocity as a function of position, providing an added computational advantage.

scholarly journals Effects of the Inlet Endwall Boundary Layer on 3-D Flows and Loss Evolution in a Linear Turbine Cascade

1995 ◽  
Author(s):  
J. Tominaga ◽  
E. Outa ◽  
Atsumasa Yamamoto
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Test Data ◽  
Three Dimensional ◽  
Internal Flow ◽  
Point Of View ◽  
Navier Stokes ◽  
Turbine Cascade ◽  
Computational Point ◽  
Flow Phenomena

A three-dimensional Navier-Stokes computation was made for investigating internal flow phenomena of a linear turbine cascade, and the results were compared with the test data obtained inside the cascade passage. The present code was found to fairly well simulate the experimental data, as well as various vortices being generated in the cascade passage. In this paper, detailed mechanisms of the loss generation are discussed mainly from the computational point of view.

Nonlinear teleseismic tomography at Long Valley Caldera, using three-dimensional minimum travel time ray tracing

1995 ◽  
Vol 100 (B10) ◽  
pp. 20379-20390 ◽  
Author(s):  
Charles M. Weiland ◽  
Lee K. Steck ◽  
Phillip B. Dawson ◽  
Valeri A. Korneev
Keyword(s):  
Travel Time ◽  
Ray Tracing ◽  
Three Dimensional ◽  
Long Valley Caldera ◽  
Teleseismic Tomography ◽  
Long Valley

COMBINATORIAL POLYNOMIALLY COMPUTABLE CHARACTERISTICS OF SUBSTITUTIONS AND THEIR PROPERTIES

2020 ◽  
Vol 7 (2) ◽  
pp. 34-41
Author(s):  
VLADIMIR NIKONOV ◽  
◽  
ANTON ZOBOV ◽  
Keyword(s):  
Mathematical Expectation ◽  
Point Of View ◽  
Small Range ◽  
Computational Point ◽  
Wide Range ◽  
Bijective Function ◽  
The Difference ◽  
Element Base ◽  
Selection Of

The construction and selection of a suitable bijective function, that is, substitution, is now becoming an important applied task, particularly for building block encryption systems. Many articles have suggested using different approaches to determining the quality of substitution, but most of them are highly computationally complex. The solution of this problem will significantly expand the range of methods for constructing and analyzing scheme in information protection systems. The purpose of research is to find easily measurable characteristics of substitutions, allowing to evaluate their quality, and also measures of the proximity of a particular substitutions to a random one, or its distance from it. For this purpose, several characteristics were proposed in this work: difference and polynomial, and their mathematical expectation was found, as well as variance for the difference characteristic. This allows us to make a conclusion about its quality by comparing the result of calculating the characteristic for a particular substitution with the calculated mathematical expectation. From a computational point of view, the thesises of the article are of exceptional interest due to the simplicity of the algorithm for quantifying the quality of bijective function substitutions. By its nature, the operation of calculating the difference characteristic carries out a simple summation of integer terms in a fixed and small range. Such an operation, both in the modern and in the prospective element base, is embedded in the logic of a wide range of functional elements, especially when implementing computational actions in the optical range, or on other carriers related to the field of nanotechnology.

Incorporation of spatial variability in modeling non-point source groundwater nitrate pollution

1996 ◽  
Vol 33 (4-5) ◽  
pp. 233-240 ◽  
Author(s):  
F. S. Goderya ◽  
M. F. Dahab ◽  
W. E. Woldt ◽  
I. Bogardi
Keyword(s):  
Spatial Variability ◽  
Point Source ◽  
Three Dimensional ◽  
Nitrate Contamination ◽  
Geostatistical Simulation ◽  
Chemical Measurements ◽  
Spatially Distributed ◽  
Potential Benefits ◽  
Zone Modeling ◽  
Physical And Chemical

A methodology for incorporation of spatial variability in modeling non-point source groundwater nitrate contamination is presented. The methodology combines geostatistical simulation and unsaturated zone modeling for estimating the amount of nitrate loading to groundwater. Three dimensional soil nitrogen variability and 2-dimensional crop yield variability are used in quantifying potential benefits of spatially distributed nitrogen input. This technique, in combination with physical and chemical measurements, is utilized as a means of illustrating how the spatial statistical properties of nitrate leaching can be obtained for different scenarios of fixed and variable rate nitrogen applications.

Comparison of the reluctance laminated and solid rotor synchronous machine operating at high temperatures

2019 ◽  
Vol 38 (4) ◽  
pp. 1111-1119 ◽  
Author(s):  
Marcin Lefik ◽  
Krzysztof Komeza ◽  
Ewa Napieralska-Juszczak ◽  
Daniel Roger ◽  
Piotr Andrzej Napieralski
Keyword(s):  
High Speed ◽  
Design Methodology ◽  
Three Dimensional ◽  
Synchronous Machine ◽  
Point Of View ◽  
Heat Sources ◽  
Model Calculations ◽  
Content Type ◽  
Thermal Phenomenon ◽  
Practical Implications

Purpose The purpose of this paper is to present a comparison between reluctance synchronous machine-enabling work at high internal temperature (HT° machine) with laminated and solid rotor. Design/methodology/approach To obtain heat sources for the thermal model, calculations of the electromagnetic field were made using the Opera 3D program including effect of rotation and the resulting eddy current losses. To analyse the thermal phenomenon, the 3D coupled thermal-fluid (CFD) model is used. Findings The presented results show clearly that laminated construction is much better from a point of view of efficiency and temperature. However, solid construction can be interesting for high speed machines due to their mechanical robustness. Research limitations/implications The main problem, despite the use of parallel calculations, is the long calculation time. Practical implications The obtained simulation and experimental results show the possibility of building a machine operating at a much higher ambient temperature than it was previously produced for example in the vicinity of the aircraft turbines. Originality/value The paper presents the application of fully three-dimensional coupled electromagnetic and thermal analysis of new machine constructions designed for elevated temperature.

Cyclopean Vision, Size Estimation, and Presence in Orthostereoscopic Images

2001 ◽  
Vol 10 (3) ◽  
pp. 312-330 ◽  
Author(s):  
Bernard Harper ◽  
Richard Latto
Keyword(s):  
Visual System ◽  
Three Dimensional ◽  
Point Of View ◽  
Psychophysical Experiment ◽  
Size Estimation ◽  
Human Form ◽  
Image Capture ◽  
Series Of Experiments ◽  
Abstract Shapes ◽  
And Control

Stereo scene capture and generation is an important facet of presence research in that stereoscopic images have been linked to naturalness as a component of reported presence. Three-dimensional images can be captured and presented in many ways, but it is rare that the most simple and “natural” method is used: full orthostereoscopic image capture and projection. This technique mimics as closely as possible the geometry of the human visual system and uses convergent axis stereography with the cameras separated by the human interocular distance. It simulates human viewing angles, magnification, and convergences so that the point of zero disparity in the captured scene is reproduced without disparity in the display. In a series of experiments, we have used this technique to investigate body image distortion in photographic images. Three psychophysical experiments compared size, weight, or shape estimations (perceived waist-hip ratio) in 2-D and 3-D images for the human form and real or virtual abstract shapes. In all cases, there was a relative slimming effect of binocular disparity. A well-known photographic distortion is the perspective flattening effect of telephoto lenses. A fourth psychophysical experiment using photographic portraits taken at different distances found a fattening effect with telephoto lenses and a slimming effect with wide-angle lenses. We conclude that, where possible, photographic inputs to the visual system should allow it to generate the cyclopean point of view by which we normally see the world. This is best achieved by viewing images made with full orthostereoscopic capture and display geometry. The technique can result in more-accurate estimations of object shape or size and control of ocular suppression. These are assets that have particular utility in the generation of realistic virtual environments.

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