scholarly journals Nets Composed of Parts of Circles for the Approximate Solution of Field Problems

1955 ◽  
Vol 8 (1) ◽  
pp. 8 ◽  
Author(s):  
L Tasny-Tschiassny
Keyword(s):  
Electrical Potential ◽  
Mesh Size ◽  
Electrical Network ◽  
Two Dimensional ◽  
Transverse Current ◽  
Straight Line ◽  
Potential Gradients ◽  
The Individual ◽  
Straight Lines ◽  
Sharp Corners

The two� dimensional differential equation describes the current flow in a sheet of conductivity cr loaded by a transverse current density , cp being the electrical potential. It is known that equation (1) can be solved approximately by a procedure in which the two� dimensional continuum is replaced by a net of straight-line bounded meshes, leading to an electrical network of conductances. The author shows that meshes bounded by "curvilinear rectangles" can be equally well dealt with and, on� the basis of different conformal transformation functimls for the individual meshes, derives the formulae required for a solution, if the mesh boundaries are circle arcs or circle arcs and straight lines. A good fit of the contours of the boundaries and equipotentials and their orthogonal trajectories can be obtained. This reduces the number of meshes without impairing the accuracy. Sharp corners at boundaries can be dealt with in a similar way. Formulae for a good accuracy computation of potential gradients and a method for changing th.e mesh size abruptly are given. Two examples using nets of only four meshes demonstrate the power of the method, the maximum errors being of the order of a few per cent.

Thermal Deformation of Base Sheet and Local Deformation Around Laser Cutting Edge

2008 ◽  
Vol 389-390 ◽  
pp. 404-409
Author(s):  
Masayuki Nunobiki ◽  
Koichi Okuda ◽  
Shogo Morino
Keyword(s):  
Laser Cutting ◽  
Thermal Deformation ◽  
Local Deformation ◽  
Cutting Edge ◽  
Terminal Point ◽  
Straight Line ◽  
The Individual ◽  
Global Deformation ◽  
Straight Lines ◽  
Cutting Path

When many products were cut out from a wide base sheet by laser cutting in some conditions, an error occurred in a height regulator by the sheet's greatly bending. It is necessary to avoid occurring the error at unmanned processing. We paper investigated local deformation around cutting edge. The cutting path consists of piercing point, terminal point, straight lines, cranks and curves. We measured local deformation around terminal point, crank and straight line. It was clarified that base sheet bent greatly around terminal points and crank and the sheet curved gradually along the straight line. We investigated relationship between global deformation of the base sheet and the local deformation. It was able to presume the entire deformation of base sheet by overlapping the individual deformations around cutting edge.

scholarly journals On the displacements of the particles and their paths in some cases of two-dimensional motion of a frictionless liquid

1913 ◽  
Vol 89 (608) ◽  
pp. 106-124 ◽  
Keyword(s):  
Circular Cylinder ◽  
The Other ◽  
Two Dimensional ◽  
Ellipsoidal Shell ◽  
Straight Line ◽  
The Individual ◽  
Lord Kelvin ◽  
Stream Lines ◽  
Individual Particles

The paths described by the individual particles of a liquid have been investigated only in a few cases, excluding those in which the motion is steady, so that the particles follow the stream-lines. Clerk Maxwell, in 1870, published drawings for the paths in an unbounded liquid disturbed by the passage of a circular cylinder. The curves for particles in contact with the cylinder were plotted by calculation; the other paths were drawn by eye from a knowledge of their terminal points and curvature. From these curves were derived others, showing the successive stages in the deformation of a row of particles which, before the approach of the cylinder, lay in a straight line perpendicular to its motion. In 1885, Lord Kelvin investigated the paths of particles of a liquid enclosed in a rotating ellipsoidal shell. He showed that they moved, relatively to the shell, along a set of similar ellipses in parallel planes, the period of this motion being the same for all the particles, so that after this period the configuration comes back to the initial one rotated through an angle.

scholarly journals Evaluation of Two-Dimensional Angular Orientation of a Mobile Robot by a Modified Algorithm Based on Hough Transform

2018 ◽  
Vol 18 (2) ◽  
pp. 112-122
Author(s):  
Dmitry N. Aldoshkin ◽  
Roman Y. Tsarev
Keyword(s):  
Mobile Robot ◽  
Hough Transform ◽  
Dimensional Space ◽  
Two Dimensional ◽  
Angular Orientation ◽  
Polygonal Chain ◽  
Straight Line ◽  
Robustness To Noise ◽  
Surrounding Space ◽  
Straight Lines

Abstract This paper proposes an algorithm that assesses the angular orientation of a mobile robot with respect to its referential position or a map of the surrounding space. In the framework of the suggested method, the orientation problem is converted to evaluating a dimensional rotation of the object that is abstracted as a polygon (or a closed polygonal chain). The method is based on Hough transform, which transforms the measurement space to a parametric space (in this case, a two-dimensional space [θ, r] of straight-line parameters). The Hough transform preserves the angles between the straight lines during rotation, translation, and isotropic scaling transformations. The problem of rotation assessment then becomes a one-dimensional optimization problem. The suggested algorithm inherits the Hough method’s robustness to noise.

Automatic Tread Gaging Machine

1979 ◽  
Vol 7 (1) ◽  
pp. 31-39
Author(s):  
G. S. Ludwig ◽  
F. C. Brenner
Keyword(s):  
Experimental Tests ◽  
Automatic Machine ◽  
Wear Rates ◽  
Handling Device ◽  
Straight Line ◽  
Component Systems ◽  
Before And After ◽  
Good Repeatability ◽  
The Difference ◽  
Straight Lines

Abstract An automatic tread gaging machine has been developed. It consists of three component systems: (1) a laser gaging head, (2) a tire handling device, and (3) a computer that controls the movement of the tire handling machine, processes the data, and computes the least-squares straight line from which a wear rate may be estimated. Experimental tests show that the machine has good repeatability. In comparisons with measurements obtained by a hand gage, the automatic machine gives smaller average groove depths. The difference before and after a period of wear for both methods of measurement are the same. Wear rates estimated from the slopes of straight lines fitted to both sets of data are not significantly different.

A comparison of the compressibilities of some gases with that of nitrogen at pressures below one atmosphere

1950 ◽  
Vol 200 (1061) ◽  
pp. 201-218 ◽  
Keyword(s):  
Carbon Dioxide ◽  
Differential Method ◽  
Linear Extrapolation ◽  
Volume Changes ◽  
Pure Nitrogen ◽  
Molecular Weights ◽  
Nitrous Oxide Oxygen ◽  
The Individual ◽  
Straight Lines ◽  
High Degree

A differential method for comparing the compressibilities of gases at pressures below 1 atm. has been developed in which many of the errors inherent in methods employed previously have been to a large extent eliminated, especially those due to meniscus volume changes and capillary depression. Using pure nitrogen as a standard the low-pressure isothermals of carbon monoxide, carbon dioxide, nitrous oxide, oxygen, ethylene and propane have been determined at a temperature of 22-05° C. The deviations of the individual points from straight lines do not in most cases exceed 2 parts in 100,000. In no case, even with propane, was any curvature in the isotherms detectable. The contention of Moles and other recent workers that the molecular weights of liquefiable gases can be determined to a high degree of accuracy by linear extrapolation is rendered highly probable by this fresh evidence.

A modified tangent-gas approximation for two-dimensional steady flow

1958 ◽  
Vol 4 (6) ◽  
pp. 600-606 ◽  
Author(s):  
G. Power ◽  
P. Smith
Keyword(s):  
Least Squares ◽  
Steady Flow ◽  
Variational Approach ◽  
Least Squares Method ◽  
Two Dimensional ◽  
Subsonic Flows ◽  
Von Karman ◽  
Straight Line ◽  
Volume Relationship ◽  
Pressure Volume Relationship

A set of two-dimensional subsonic flows past certain cylinders is obtained using hodograph methods, in which the true pressure-volume relationship is replaced by various straight-line approximations. It is found that the approximation obtained by a least-squares method possibly gives best results. Comparison is made with values obtained by using the von Kármán-Tsien approximation and also with results obtained by the variational approach of Lush & Cherry (1956).

scholarly journals An Improved Path-Generating Regulator for Two-Wheeled Robots to Track the Circle/Arc Passage

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Jun Dai ◽  
Naohiko Hanajima ◽  
Toshiharu Kazama ◽  
Akihiko Takashima
Keyword(s):  
Control Method ◽  
Convergence Property ◽  
Tangential Direction ◽  
Navigation Problem ◽  
Wheeled Robots ◽  
Robot Trajectory ◽  
Look Ahead ◽  
Straight Line ◽  
The Family ◽  
Straight Lines

The improved path-generating regulator (PGR) is proposed to path track the circle/arc passage for two-wheeled robots. The PGR, which is a control method for robots so as to orient its heading toward the tangential direction of one of the curves belonging to the family of path functions, is applied to navigation problem originally. Driving environments for robots are usually roads, streets, paths, passages, and ridges. These tracks can be seen as they consist of straight lines and arcs. In the case of small interval, arc can be regarded as straight line approximately; therefore we extended the PGR to drive the robot move along circle/arc passage based on the theory that PGR to track the straight passage. In addition, the adjustable look-ahead method is proposed to improve the robot trajectory convergence property to the target circle/arc. The effectiveness is proved through MATLAB simulations on both the comparisons with the PGR and the improved PGR with adjustable look-ahead method. The results of numerical simulations show that the adjustable look-ahead method has better convergence property and stronger capacity of resisting disturbance.

KNOT POINTS IN TWO-DIMENSIONAL MAPS AND RELATED PROPERTIES

2009 ◽  
Vol 19 (02) ◽  
pp. 545-555 ◽  
Author(s):  
F. TRAMONTANA ◽  
L. GARDINI ◽  
D. FOURNIER-PRUNARET ◽  
P. CHARGE
Keyword(s):  
Focal Point ◽  
Singular Line ◽  
Two Dimensional ◽  
Focal Points ◽  
Singular Set ◽  
One Dimensional ◽  
Attracting Set ◽  
Straight Line ◽  
Special Character ◽  
Stable And Unstable Sets

We consider the class of two-dimensional maps of the plane for which there exists a whole one-dimensional singular set (for example, a straight line) that is mapped into one point, called a "knot point" of the map. The special character of this kind of point has been already observed in maps of this class with at least one of the inverses having a vanishing denominator. In that framework, a knot is the so-called focal point of the inverse map (it is the same point). In this paper, we show that knots may also exist in other families of maps, not related to an inverse having values going to infinity. Some particular properties related to focal points persist, such as the existence of a "point to slope" correspondence between the points of the singular line and the slopes in the knot, lobes issuing from the knot point and loops in infinitely many points of an attracting set or in invariant stable and unstable sets.

scholarly journals EXPRESS: Sources of Variation In Search and Foraging A Theoretical Perspective

2021 ◽  
pp. 174702182110503
Author(s):  
Alastair David Smith ◽  
Carlo De Lillo
Keyword(s):  
Spatial Scales ◽  
Theoretical Perspective ◽  
Search Space ◽  
Visual Exploration ◽  
Two Dimensional ◽  
Search Behaviour ◽  
Wide Range ◽  
Search Processes ◽  
Sources Of Variation ◽  
The Individual

Search – the problem of exploring a space of alternatives in order to identify target goals – is a fundamental behaviour for many species. Although its foundation lies in foraging, most studies of human search behaviour have been directed towards understanding the attentional mechanisms that underlie the efficient visual exploration of two-dimensional scenes. With this review, we aim to characterise how search behaviour can be explained across a wide range of contexts, environments, spatial scales, and populations, both typical and atypical. We first consider the generality of search processes across psychological domains. We then review studies of interspecies differences in search. Finally, we explore in detail the individual and contextual variables that affect visual search and related behaviours in established experimental psychology paradigms. Despite the heterogeneity of the findings discussed, we identify that variations in control processes, along with the ability to regulate behaviour as a function of the structure of search space and the sampling processes adopted, to be central to explanations of variations in search behaviour. We propose a tentative theoretical model aimed at integrating these notions and close by exploring questions that remain unaddressed.

Sign in / Sign up

Export Citation Format

Share Document