scholarly journals Interference Identification for Time-Varying Polyhedra

2021 ◽  
Author(s):  
Adam Bienkowski
Keyword(s):  
Traffic Control ◽  
Potential Conflict ◽  
Linear Projection ◽  
The Earth ◽  
Large Numbers ◽  
Mercator Projection ◽  
Maritime Operations ◽  
Conflict Identification ◽  
Polygon Intersection ◽  
Straight Lines

Identification of when and where moving areas intersect is an important problem in maritime operations and air traffic control. This problem can become particularly complicated when considering large numbers of objects, and when taking into account the curvature of the earth. In this paper, we present an approach to conflict identification as a series of stages where the earlier stages are fast, but may result in a false detection of a conflict. These early stages are used to reduce the number of potential conflict pairs for the later stages, which are slower, but more precise. The stages use R-trees, polygon intersection, linear projection and nonlinear programming. Our approach is generally applicable to objects moving in piece-wise straight lines on a 2D plane, and we present a specific case where the Mercator Projection is used to transform objects moving along rhumb lines on the earth into straight lines to fit in our approach. We present several examples to demonstrate our methods, as well as to quantify the empirical time complexity by using randomly generated areas.

scholarly journals Interference Identification for Time-Varying Polyhedra

2021 ◽  
Author(s):  
Adam Bienkowski
Keyword(s):  
Traffic Control ◽  
Potential Conflict ◽  
Linear Projection ◽  
The Earth ◽  
Large Numbers ◽  
Mercator Projection ◽  
Maritime Operations ◽  
Conflict Identification ◽  
Polygon Intersection ◽  
Straight Lines

Identification of when and where moving areas intersect is an important problem in maritime operations and air traffic control. This problem can become particularly complicated when considering large numbers of objects, and when taking into account the curvature of the earth. In this paper, we present an approach to conflict identification as a series of stages where the earlier stages are fast, but may result in a false detection of a conflict. These early stages are used to reduce the number of potential conflict pairs for the later stages, which are slower, but more precise. The stages use R-trees, polygon intersection, linear projection and nonlinear programming. Our approach is generally applicable to objects moving in piece-wise straight lines on a 2D plane, and we present a specific case where the Mercator Projection is used to transform objects moving along rhumb lines on the earth into straight lines to fit in our approach. We present several examples to demonstrate our methods, as well as to quantify the empirical time complexity by using randomly generated areas.

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.

Sonchus oleraceus (common sowthistle).

2021 ◽  
Author(s):  
Julissa Rojas-Sandoval ◽  
Pedro Acevedo-Rodríguez ◽  
A. I. Popay
Keyword(s):  
Sand Dunes ◽  
Cultivated Land ◽  
Construction Sites ◽  
Burned Areas ◽  
Sonchus Oleraceus ◽  
The Earth ◽  
Large Numbers ◽  
Disturbed Areas ◽  
Wide Range ◽  
Winter Crops

Abstract S. oleraceus is a common seed crop contaminant and has been carried either deliberately or accidentally by humans to almost every corner of the earth, where it invades mainly open and disturbed areas. It grows in a wide variety of environments on a wide range of substrates - roadsides, cultivated land, gardens, construction sites, sand dunes, logged or burned areas, on walls, mountain slopes, and near water. Once introduced to a new area the plants spread quickly because they grow and flower quickly and produce copious wind- and bird-dispersed seeds that germinate quickly in large numbers. They invade many cropped areas, especially among vegetable and winter crops. They are almost perfect 'designer weeds'. Additionally, this species has small light seeds which are easily dispersed by wind and water.

Introduction

Catastrophe ◽  
2004 ◽  
Author(s):  
Richard A. Posner
Keyword(s):  
Forest Fires ◽  
High Energy ◽  
Particle Accelerator ◽  
High Energy Particle ◽  
Strange Matter ◽  
Strange Quarks ◽  
Tidal Waves ◽  
The Earth ◽  
Large Numbers ◽  
Protons And Neutrons

You wouldn’t see the asteroid, even though it was several miles in diameter, because it would be hurtling toward you at 15 to 25 miles a second. At that speed, the column of air between the asteroid and the earth’s surface would be compressed with such force that the column’s temperature would soar to several times that of the sun, incinerating everything in its path. When the asteroid struck, it would penetrate deep into the ground and explode, creating an enormous crater and ejecting burning rocks and dense clouds of soot into the atmosphere, wrapping the globe in a mantle of fiery debris that would raise surface temperatures by as much as 100 degrees Fahrenheit and shut down photosynthesis for years. The shock waves from the collision would have precipitated earthquakes and volcanic eruptions, gargantuan tidal waves, and huge forest fires. A quarter of the earth’s human population might be dead within 24 hours of the strike, and the rest soon after. But there might no longer be an earth for an asteroid to strike. In a high-energy particle accelerator, physicists bent on re-creating conditions at the birth of the universe collide the nuclei of heavy atoms, containing large numbers of protons and neutrons, at speeds near that of light, shattering these particles into their constituent quarks. Because some of these quarks, called strange quarks, are hyperdense, here is what might happen: A shower of strange quarks clumps, forming a tiny bit of strange matter that has a negative electric charge. Because of its charge, the strange matter attracts the nuclei in the vicinity (nuclei have a positive charge), fusing with them to form a larger mass of strange matter that expands exponentially. Within a fraction of a second the earth is compressed to a hyperdense sphere 100 meters in diameter, explodes in the manner of a supernova, and vanishes. By then, however, the earth might have been made uninhabitable for human beings and most other creatures by abrupt climate changes.

Surface Lunar Soil Excavation Simulation Based on Three-Dimensional Discrete Element Method

2013 ◽  
Vol 376 ◽  
pp. 366-370
Author(s):  
Hui Gao ◽  
Da Wei Zhang ◽  
Bin Liu ◽  
Long Chen Duan
Keyword(s):  
Discrete Element Method ◽  
Three Dimensional ◽  
Lunar Soil ◽  
Discrete Element ◽  
Spherical Particles ◽  
Lunar Exploration ◽  
The Earth ◽  
Large Numbers ◽  
Soil Excavation ◽  
Element Method

One of the important objectives of lunar exploration is to obtain the lunar soil samples. However, the sampling process is very different from that on the Earth due to special characteristics of the lunar soil and surface environment. In order to ensure that the lunar exploration and sampling are successful, large numbers of ground experiments and computer simulations must be taken. In this paper, the surface lunar soil excavation simulation is investigated by three-dimensional discrete element method (DEM). It is implemented based on the open source LIGGGHTS, which takes the lunar soil as spherical particles. The interaction between the excavation tool and lunar soil is demonstrated. The excavation force and torque have also been calculated in real time. Moreover, the comparison of the excavation in different environments between the Earth and Moon corresponding to their different gravity accelerations was done. This paper shows that three-dimensional discrete element method can be used for the surface lunar soil excavation simulation and can provide important reference results for actual operations.

scholarly journals Calculation of Charts on an Oblique Gnomonic Projection by Electronic Computer

1960 ◽  
Vol 13 (3) ◽  
pp. 345-347
Author(s):  
P. B. Sarson
Keyword(s):  
Electronic Computer ◽  
Great Accuracy ◽  
Lightning Flash ◽  
Projection Plane ◽  
Mercator Projection ◽  
Straight Lines

IN the Meteorological Office, great accuracy is not usually attainable in determining or forecasting the position of significant weather features. Special projections of charts are therefore not often required; the normal conic projection with two standard parallels or (near the equator) the mercator projection is quite adequate. However, in the radiolocation of thunderstorms a chart drawn on a gnomonic projection is required. The bearings of each lightning flash within one or two thousand miles are recorded from a small number of special stations (SFERICS stations). When these bearings are plotted on a gnomonic chart by straight lines drawn from the appropriate observing station the coordinates of the source of the lightning can be quickly determined and reported through normal meteorological channels. Speed is essential and therefore the charts on which the bearings are drawn are specially designed with the SFERICS stations grouped more or less evenly about the tangential point of the projection plane of the gnomonic chart.

Longitudinal bending strength of corrugated steel pipe

1980 ◽  
Vol 7 (3) ◽  
pp. 547-551
Author(s):  
C. D. Smith
Keyword(s):  
Bending Strength ◽  
Steel Pipe ◽  
Buried Pipe ◽  
Highway Engineering ◽  
The Earth ◽  
Large Numbers ◽  
Wall Stiffness ◽  
Cantilever Length ◽  
Strength Tests ◽  
Longitudinal Bending

Corrugated steel pipe (CSP) is used in large numbers for drainage structures, particularly in highway engineering. The corrugations increase the wall stiffness of the pipe by a factor of about 100, so relatively light-gauge material can be used to resist the earth loading on the buried pipe. These same corrugations, however, result in a decrease in longitudinal bending strength. This can be an important consideration in situations where the culvert may be undermined at the outlet, or is deliberately cantilevered beyond its imbedment. Strength tests were carried out on three sizes of standard 16 gauge (0.001676 m) rivetted CSP. From this it was determined that the safe cantilever length for a flowing full culvert is about 2 m for pipes of 0.61 m diameter and larger.

A Discussion on the evolution of the Precambrian crust - Introductory remarks

1973 ◽  
Vol 273 (1235) ◽  
pp. 316-316 ◽  
Keyword(s):  
Early History ◽  
Geological Time ◽  
Precambrian Rocks ◽  
The Past ◽  
Geological Processes ◽  
The Earth ◽  
Large Numbers ◽  
The World ◽  
History Of

The realization that the behaviour of the Earth has changed radically during geological time has come about largely in the last decade. This development, which constitutes one of the major advances in geological thinking, results from the study of Precambrian phenomena in many parts of the world and in particular from the work of a small number of geochronologists. In the last ten years as large numbers of unfossiliferous Precambrian rocks have been dated, it has become clear that the nature of geological processes has varied throughout geological time and that one of the cardinal doctrines of geology - the concept that the present is the key to the past — could not be applied to the study of the early history of the Earth.

UNIVERSAL METRIC BASE (RUMB), UNITS OF ANGLE MEASUREMENT IN GEODESY AND CARTOGRAPHY

2020 ◽  
pp. 53-63
Author(s):  
Nikola Ryazantsev ◽  
◽  
Alexander Nosach
Keyword(s):  
Angle Measurement ◽  
The Earth ◽  
Units Of Measurement ◽  
Mercator Projection ◽  
Rectangular Coordinates ◽  
Measurement Metric ◽  
First Time ◽  
Cylindrical Axis ◽  
Practical Implications ◽  
Objective Study

Objective. Study of ancient cartographic documents in order to clarify the principle of working with a portolan map based on the RUMB metric base. Methodology. Analytical, graphic, mathematical, geodesic. Scientific novelty. For the first time, a table of interrelation of units of measurement of time, angles and distances in the metric base of RUMB is shown. It was found that the so-called portolan maps were built on the basis of RUMB, and their projection is similar to the oblique Mercator projection with a cylindrical axis oriented along the earth’s magnetic axis, with an additional network of rhomb rectangular coordinates, which allows the map to be used at any position of the poles. The Mercator projection is a simplified version of it with one coordinate system. Practical implications. It is shown that dividing the clock face, equator and meridians of the Earth into the same number of parts allows determining the coordinates of points on the Earth’s surface using any of the known parameters, which greatly simplifies the solution of geodetic and navigation problems. Key words: units of measurement, metric base, degree, bearing, portolan map, rose card, projection, coordinate.

Oresme, Nicole (c.1325–82)

2018 ◽  
Author(s):  
George Molland
Keyword(s):  
Natural Philosophy ◽  
Mathematical Language ◽  
Mathematical Approach ◽  
Late Medieval ◽  
Empirical Basis ◽  
The Third ◽  
The Earth ◽  
Rotation Of The Earth ◽  
Important Position ◽  
Straight Lines

Nicole Oresme, a French thinker active in the third quarter of the fourteenth century, occupies an important position in late medieval natural philosophy. He was especially notable for his mathematical approach, in which he represented the intensities of qualities and of speeds by geometrical straight lines, which allowed them to be ‘plotted’ in principle against both distance and time. He held that the shapes of the resulting graphs would then have explanatory force in the manner of ancient atomism, but, like the latter, his doctrine had a weak empirical basis. His graphical representations of speed have been compared to those later given by Galileo, but there are no grounds for positing influence. He was prominent in developing a particular mathematical language of ratios, which had earlier been used by Thomas Bradwardine to propose a ‘law’ relating speeds to forces and resistances, and Oresme likewise applied the language to cosmological and physical questions. He was a firm opponent of much of astrology and of magic, and to this end he employed both naturalistic and sceptical arguments. He gave many strong arguments in favour of a daily rotation of the earth, but finally concluded that it was at rest: his gambit had primarily a sceptical and fideistic purpose.

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