THE UPWARD CONTINUATION OF ANOMALIES IN TOTAL MAGNETIC INTENSITY FIELDS

Geophysics ◽  
1949 ◽  
Vol 14 (4) ◽  
pp. 517-534 ◽  
Author(s):  
Roland G. Henderson ◽  
Isidore Zietz
Keyword(s):  
Three Dimensional ◽  
Magnetic Intensity ◽  
Mathematical Basis ◽  
Upward Continuation ◽  
Multi Level

In airborne magnetometry consideration must be given to the necessity of multi‐level observations. The problem of computing total intensity anomalies from data observed on lower levels is investigated in the case of contours exhibiting both two‐ and three‐dimensional features. It is found that even fairly complex anomalies can be extended, with results differing but slightly from observations at the higher level. Maps for comparing computed and observed anomalies are presented. The mathematical basis is given together with numerical formulas and procedures for affecting the computations.

scholarly journals Automatic Reconstruction of Multi-Level Indoor Spaces from Point Cloud and Trajectory

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3493
Author(s):  
Gahyeon Lim ◽  
Nakju Doh
Keyword(s):  
Point Cloud ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Reconstruction Method ◽  
Complex Environments ◽  
Indoor Space ◽  
Multi Level ◽  
Level Building ◽  
Indoor Spaces ◽  
Data Term

Remarkable progress in the development of modeling methods for indoor spaces has been made in recent years with a focus on the reconstruction of complex environments, such as multi-room and multi-level buildings. Existing methods represent indoor structure models as a combination of several sub-spaces, which are constructed by room segmentation or horizontal slicing approach that divide the multi-room or multi-level building environments into several segments. In this study, we propose an automatic reconstruction method of multi-level indoor spaces with unique models, including inter-room and inter-floor connections from point cloud and trajectory. We construct structural points from registered point cloud and extract piece-wise planar segments from the structural points. Then, a three-dimensional space decomposition is conducted and water-tight meshes are generated with energy minimization using graph cut algorithm. The data term of the energy function is expressed as a difference in visibility between each decomposed space and trajectory. The proposed method allows modeling of indoor spaces in complex environments, such as multi-room, room-less, and multi-level buildings. The performance of the proposed approach is evaluated for seven indoor space datasets.

scholarly journals A Collision Dynamics Model of a Multi-Level Train

2006 ◽  
Author(s):  
Michelle Priante ◽  
David Tyrell ◽  
Benjamin Perlman
Keyword(s):  
Three Dimensional ◽  
Design Parameters ◽  
Collision Dynamics ◽  
Dynamics Model ◽  
Single Level ◽  
High Speeds ◽  
Front End ◽  
Multi Level ◽  
Low Speeds ◽  
Vertical Accelerations

In train collisions, multi-level rail passenger vehicles can deform in modes that are different from the behavior of single level cars. The deformation in single level cars usually occurs at the front end during a collision. In one particular incident, a cab car buckled laterally near the back end of the car. The buckling of the car caused both lateral and vertical accelerations, which led to unanticipated injuries to the occupants. A three-dimensional collision dynamics model of a multi-level passenger train has been developed to study the influence of multi-level design parameters and possible train configuration variations on the reactions of a multi-level car in a collision. This model can run multiple scenarios of a train collision. This paper investigates two hypotheses that could account for the unexpected mode of deformation. The first hypothesis emphasizes the non-symmetric resistance of a multi-level car to longitudinal loads. The structure is irregular since the stairwells, supports for tanks, and draglinks vary from side to side and end to end. Since one side is less strong, that side can crush more during a collision. The second hypothesis uses characteristics that are nearly symmetric on each side. Initial imperfections in train geometry induce eccentric loads on the vehicles. For both hypotheses, the deformation modes depend on the closing speed of the collision. When the characteristics are non-symmetric, and the load is applied in-line, two modes of deformation are seen. At low speeds, the couplers crush, and the cars saw-tooth buckle. At high speeds, the front end of the cab car crushes, and the cars remain in-line. If an offset load is applied, the back stairwell of the first coach car crushes unevenly, and the cars saw-tooth buckle. For the second hypothesis, the characteristics are symmetric. At low speeds, the couplers crush, and the cars remain in-line. At higher speeds, the front end crushes, and the cars remain in-line. If an offset load is applied to a car with symmetric characteristics, the cars will saw-tooth buckle.

AEROMAGNETIC FIELD TEST OF TOTAL INTENSITY UPWARD CONTINUATION

Geophysics ◽  
1971 ◽  
Vol 36 (2) ◽  
pp. 418-425 ◽  
Author(s):  
Angelo L. Kontis
Keyword(s):  
Dirichlet Problem ◽  
Field Test ◽  
Theoretical Basis ◽  
Numerical Evaluation ◽  
Integral Formula ◽  
Intensity Data ◽  
Magnetic Intensity ◽  
Normal Field ◽  
Area Of Interest ◽  
Upward Continuation

The theoretical basis for applying the upward‐continuation integral, [Formula: see text]z⩽0, (1) to total magnetic intensity data T(α, β) measured on the plane z=0 has been recently reviewed by Henderson (1970). To perform upward continuation in the spatial domain, weights or coefficients obtained by numerical evaluation of equation (1) (Peters, 1949; Henderson, 1960; Fuller, 1967) may be convolved with the total intensity anomaly T(α, β) to produce T(x, y, z) at heights z<0 (for z positive downward). The accuracy of upward continuation is, therefore, dependent on the validity of the numerical coefficients and of the assumptions required to show that T(α, β) satisfies the conditions of the Dirichlet problem for a plane. These assumptions are that the quantity sensed by a total‐intensity magnetometer is in the direction of the earth’s normal field and that this direction is invariant over the area of interest.

The Helium Stockpile: A Collaboration in Mathematical Folding Sculpture

Leonardo ◽  
2006 ◽  
Vol 39 (3) ◽  
pp. 233-235 ◽  
Author(s):  
Eric D. Demaine ◽  
Martin L. Demaine ◽  
A. Laurie Palmer
Keyword(s):  
Three Dimensional ◽  
Dimensional Chain ◽  
Mathematical Basis ◽  
One Dimensional ◽  
Dimensional Shape ◽  
Folding Structure ◽  
Three Dimensional Shape

The Helium Stockpile is a manipulable folding structure of hundreds of wooden blocks, representing the transformation between surface and solid through a foldable one-dimensional chain. The sculpture grew out of an unexpected collaboration between a sculptor and two mathematicians, giving the structure a mathematical basis through which it is guaranteed to be foldable into essentially any three-dimensional shape.

scholarly journals UAV Path Planning Based on Multi-Stage Constraint Optimization

Drones ◽  
2021 ◽  
Vol 5 (4) ◽  
pp. 144
Author(s):  
Yong Shen ◽  
Yunlou Zhu ◽  
Hongwei Kang ◽  
Xingping Sun ◽  
Qingyi Chen ◽  
...  
Keyword(s):  
Path Planning ◽  
Three Dimensional ◽  
Evolutionary Process ◽  
Constraint Processing ◽  
Multi Stage ◽  
Planning Ability ◽  
Path Constraints ◽  
Aerial Vehicle ◽  
Multi Level ◽  
Processing Mechanism

Evolutionary Algorithms (EAs) based Unmanned Aerial Vehicle (UAV) path planners have been extensively studied for their effectiveness and high concurrency. However, when there are many obstacles, the path can easily violate constraints during the evolutionary process. Even if a single waypoint causes a few constraint violations, the algorithm will discard these solutions. In this paper, path planning is constructed as a multi-objective optimization problem with constraints in a three-dimensional terrain scenario. To solve this problem in an effective way, this paper proposes an evolutionary algorithm based on multi-level constraint processing (ANSGA-III-PPS) to plan the shortest collision-free flight path of a gliding UAV. The proposed algorithm uses an adaptive constraint processing mechanism to improve different path constraints in a three-dimensional environment and uses an improved adaptive non-dominated sorting genetic algorithm (third edition—ANSGA-III) to enhance the algorithm’s path planning ability in a complex environment. The experimental results show that compared with the other four algorithms, ANSGA-III-PPS achieves the best solution performance. This not only validates the effect of the proposed algorithm, but also enriches and improves the research results of UAV path planning.

Three dimensional numerical modeling using a multi-level nesting system for identifying a Water layer suitable for scallop farming in Tongyeong, Korea

2020 ◽  
Vol 89 ◽  
pp. 102058
Author(s):  
Yeon S. Chang ◽  
Jae-Youll Jin ◽  
Jin Yong Choi ◽  
Weon Mu Jeong ◽  
Sang Kwon Hyun ◽  
...  
Keyword(s):  
Numerical Modeling ◽  
Three Dimensional ◽  
Water Layer ◽  
Multi Level

Comparative Frequency Domain Seakeeping Analysis of a Fast Monohull in Regular Head Waves

2002 ◽  
Author(s):  
Thomas E. Schellin ◽  
Christian Beiersdorf ◽  
Xiao-Bo Chen ◽  
Adolfo Maron
Keyword(s):  
Green Function ◽  
Frequency Domain ◽  
Three Dimensional ◽  
Forward Speed ◽  
Software Module ◽  
Mathematical Basis ◽  
Numerical Predictions ◽  
Head Waves ◽  
Seakeeping Analysis ◽  
Function Code

Two sets of seakeeping computations and comparative model teats were performed for a fast monohull in regular waves. The first set of computations used an existing three-dimensional frequency domain panel code that formulates the potential flow problem by means of the zero-speed Green function. The second set used a modified version of this code that implemented an advanced software module, newly developed within the European research project WAVELOADS, where the free-surface forward-speed Green function method based on the Fourier-Kochin formulation accounts for forward speed effects. Although this formulation provided a solid mathematical basis for obtaining robust and accurate numerical predictions, numerical inaccuracies prevented obtaining satisfactory results. For nearly all cases investigated, predictions from the original (zero-speed Green function) code correlated more favorably with test data than those from the modified (forward-speed Green function) code. For the fast monohull investigated here, practically relevant global load predictions based on the zero-speed Green function correlated favorably with measurements.

Bayesian Multi-Level Modelling for Improved Prediction of Corrosion Growth Rate

2020 ◽  
Author(s):  
Domenic Di Francesco ◽  
Marios Chryssanthopoulos ◽  
Michael Havbro Faber ◽  
Ujjwal Bharadwaj
Keyword(s):  
Epistemic Uncertainty ◽  
Simulated Data ◽  
Steel Structures ◽  
Pressure Vessels ◽  
Mathematical Basis ◽  
Management Planning ◽  
Integrity Management ◽  
Level Model ◽  
Multi Level ◽  
Inspection Data

Abstract In pipelines, pressure vessels and various other steel structures, the remaining thickness of a corroding ligament can be measured directly and repeatedly over time. Statistical analysis of these measurements is a common approach for estimating the rate of corrosion growth, where the uncertainties associated with the inspection activity are taken into account. An additional source of variability in such calculations is the epistemic uncertainty associated with the limited number of measurements that are available to engineers at any point in time. Traditional methods face challenges in fitting models to limited or missing datasets. In such cases, deterministic upper bound values, as recommended in industrial guidance, are sometimes assumed for the purpose of integrity management planning. In this paper, Bayesian inference is proposed as a means for representing available information in consistency with evidence. This, in turn, facilitates decision support in the context of risk-informed integrity management. Aggregating inspection data from multiple locations does not account for the possible variability between the locations, and creating fully independent models can result in excessive levels of uncertainty at locations with limited data. Engineers intuitively acknowledge that the areas with more sites of corrosion should, to some extent, inform estimates of growth rates in other locations. Bayesian multi-level (hierarchical) models provide a mathematical basis for achieving this by means of the appropriate pooling of information, based on the homogeneity of the data. Included in this paper is an outline of the process of fitting a Bayesian multi-level model and a discussion of the benefits and challenges of pooling inspection data between distinct locations, using example calculations and simulated data.

Image Based Simulation of Pulmonary Airflow Using Multi-Level Voxel Modeling

2007 ◽  
Author(s):  
Yohsuke Imai ◽  
Takahito Miki ◽  
Masanori Nakamura ◽  
Takuji Ishikawa ◽  
Shigeo Wada ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Airflow Obstruction ◽  
Three Dimensional ◽  
Patient Specific ◽  
Chronic Obstructive ◽  
Local Domain ◽  
Local Flow ◽  
Obstructive Pulmonary Disease ◽  
Multi Level ◽  
Cfd Method

Chronic Obstructive Pulmonary Disease (COPD) refers to a group of diseases that are characterized by airflow obstruction. Currently, COPD is the fourth leading cause of death worldwide, but fluid dynamics in airways of COPD patients has not been well understood. Multi-slice Computer Tomography (CT) images provide three-dimensional realistic geometry of patient airways. Computational Fluid Dynamics (CFD) analysis using the patient-specific geometry will greatly help the understanding of the mechanism of COPD. However, few studies have performed such a patient-specific pulmonary airflow simulation. Our aim is to develop a patient-specific CFD method applicable to multi-scale airways, involving trachea, bronchi, bronchioles, and alveoli. We propose a CFD method using multi-level voxel modeling of airway geometry, in which voxel size in a local domain is adaptively refined or coarsened to the local flow scale.

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