Straight Line Geometric Path Lengths – Examples and Distributions

2021 ◽  
Author(s):  
Brian Larsen ◽  
Caleb Roecker ◽  
Daniel Coupland
Keyword(s):  
Straight Line ◽  
Path Lengths

scholarly journals BALANCING TRAFFIC LOAD USING ONE-TURN RECTILINEAR ROUTING

2009 ◽  
Vol 10 (01n02) ◽  
pp. 93-120 ◽  
Author(s):  
STEPHANE DUROCHER ◽  
EVANGELOS KRANAKIS ◽  
DANNY KRIZANC ◽  
LATA NARAYANAN
Keyword(s):  
Single Point ◽  
Maximum Load ◽  
Traffic Load ◽  
Destination Node ◽  
Continuous Path ◽  
Dense Network ◽  
Routing Policy ◽  
Straight Line ◽  
Routing Policies ◽  
Path Lengths

We consider the problem of load-balanced routing, where a dense network is modelled by a continuous square region, and origin-destination node pairs correspond to pairs of points in that region. The objective is to define a routing policy that assigns a continuous path to each origin-destination pair while minimizing the traffic, or load, passing through any single point. While the average load is minimized by straight-line routing, such a routing policy distributes the load non-uniformly, resulting in higher load near the center of the region. We consider one-turn rectilinear routing policies that divert traffic away from regions of heavier load, resulting in up to a 33% reduction in the maximum load while simultaneously increasing the path lengths by an average of less than 28%. Our policies are simple to implement, being both local and oblivious. We provide a lower bound that shows that no one-turn rectilinear routing policy can reduce the maximum load by more than 39% and we give a polynomial-time procedure for approximating the optimal randomized policy.

Microdensitometer—computer correlation analysis of ultrastructural periodicity

1978 ◽  
Vol 36 (2) ◽  
pp. 32-33
Author(s):  
D.R. Ensor ◽  
C.G. Jensen ◽  
J.A. Fillery ◽  
R.J.K. Baker
Keyword(s):  
Correlation Analysis ◽  
Background Noise ◽  
Computer Control ◽  
Optical Diffraction ◽  
Screw Thread ◽  
Straight Line ◽  
Computer Storage ◽  
Correlation Process ◽  
Electron Microscope Image ◽  
Fixed Beam

Because periodicity is a major indicator of structural organisation numerous methods have been devised to demonstrate periodicity masked by background “noise” in the electron microscope image (e.g. photographic image reinforcement, Markham et al, 1964; optical diffraction techniques, Horne, 1977; McIntosh,1974). Computer correlation analysis of a densitometer tracing provides another means of minimising "noise". The correlation process uncovers periodic information by cancelling random elements. The technique is easily executed, the results are readily interpreted and the computer removes tedium, lends accuracy and assists in impartiality.A scanning densitometer was adapted to allow computer control of the scan and to give direct computer storage of the data. A photographic transparency of the image to be scanned is mounted on a stage coupled directly to an accurate screw thread driven by a stepping motor. The stage is moved so that the fixed beam of the densitometer (which is directed normal to the transparency) traces a straight line along the structure of interest in the image.

Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

1983 ◽  
Vol 41 ◽  
pp. 646-647
Author(s):  
Joseph A. Zasadzinski
Keyword(s):  
Liquid Crystalline ◽  
Freeze Fracture ◽  
Continuum Theory ◽  
Closed Surfaces ◽  
Straight Line ◽  
Low Weight ◽  
Concentric Spheres ◽  
Membrane Geometry ◽  
Dupin Cyclides ◽  
Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

Human Enamel Replication

1976 ◽  
Vol 34 ◽  
pp. 180-181
Author(s):  
Norman L. Dockum ◽  
John G. Dockum
Keyword(s):  
Organic Matrix ◽  
Human Teeth ◽  
Human Enamel ◽  
Straight Line ◽  
Ultrastructural Characteristics

Ultrastructural characteristics of fractured human enamel and acid-etched enamel were compared using acetate replicas shadowed with platinum and palladium. Shadowed replications of acid-etched surfaces were also obtained by the same method.Enamel from human teeth has a rod structure within which there are crystals of hydroxyapatite contained within a structureless organic matrix composed of keratin. The rods which run at right angles from the dentino-enamel junction are considered to run in a straight line perpendicular to the perimeter of the enamel, however, in many areas these enamel rods overlap, interlacing and intertwining with one another.

An improved magnetic prism design for a transmission electron microscope energy filter

1978 ◽  
Vol 36 (1) ◽  
pp. 40-41 ◽  
Author(s):  
John W. Andrew ◽  
F.P. Ottensmeyer ◽  
E. Martell
Keyword(s):  
Energy Resolution ◽  
Symmetry Plane ◽  
Fringe Field ◽  
Focal Distance ◽  
Electron Trajectories ◽  
Focusing Effect ◽  
Transmission Electron ◽  
Path Lengths ◽  
Electron Microscopes ◽  
Focusing Properties

Energy selecting electron microscopes of the Castaing-Henry prism-mirror-prism design suffer from a loss of image and energy resolution with increasing field of view. These effects can be qualitatively understood by examining the focusing properties of the prism shown in Fig. 1. A cone of electrons emerges from the entrance lens crossover A and impinges on the planar face of the prism. The task of the prism is to focus these electrons to a point B at a focal distance f2 from the side of the prism. Electrons traveling in the plane of the diagram (i.e., the symmetry plane of the prism) are focused toward point B due to the different path lengths of different electron trajectories in the triangularly shaped magnetic field. This is referred to as horizontal focusing; the better this focusing effect the better the energy resolution of the spectrometer. Electrons in a plane perpendicular to the diagram and containing the central ray of the incident cone are focused toward B by the curved fringe field of the prism.

Problems in Thin-Film X-ray Quantification

1990 ◽  
Vol 48 (2) ◽  
pp. 458-459
Author(s):  
J N Chapman ◽  
W A P Nicholson
Keyword(s):  
Thin Film ◽  
Specimen Thickness ◽  
X Rays ◽  
Characteristic Peak ◽  
Local Composition ◽  
X Ray ◽  
Measured Ratio ◽  
Path Lengths ◽  
Composition Changes

Energy dispersive x-ray microanalysis (EDX) is widely used for the quantitative determination of local composition in thin film specimens. Extraction of quantitative data is usually accomplished by relating the ratio of the number of atoms of two species A and B in the volume excited by the electron beam (nA/nB) to the corresponding ratio of detected characteristic photons (NA/NB) through the use of a k-factor. This leads to an expression of the form nA/nB = kAB NA/NB where kAB is a measure of the relative efficiency with which x-rays are generated and detected from the two species.Errors in thin film x-ray quantification can arise from uncertainties in both NA/NB and kAB. In addition to the inevitable statistical errors, particularly severe problems arise in accurately determining the former if (i) mass loss occurs during spectrum acquisition so that the composition changes as irradiation proceeds, (ii) the characteristic peak from one of the minority components of interest is overlapped by the much larger peak from a majority component, (iii) the measured ratio varies significantly with specimen thickness as a result of electron channeling, or (iv) varying absorption corrections are required due to photons generated at different points having to traverse different path lengths through specimens of irregular and unknown topography on their way to the detector.

Acute Constraints in Straight-Line Drawings of Planar Graphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 994-1001
Author(s):  
Akane SETO ◽  
Aleksandar SHURBEVSKI ◽  
Hiroshi NAGAMOCHI ◽  
Peter EADES
Keyword(s):  
Planar Graphs ◽  
Line Drawings ◽  
Straight Line

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.

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