The Mean Shape of the Human Cornea

P.M. Kiely; G. Smith; L.G. Carney

doi:10.1080/713820960

GEOMETRY OF CONTACT BETWEEN SELF-AFFINE SURFACES

Fractals ◽

10.1142/s0218348x95000114 ◽

1995 ◽

Vol 03 (01) ◽

pp. 113-122 ◽

Cited By ~ 1

Author(s):

FRANCK PLOURABOUÉ ◽

STÉPHANE ROUX ◽

JEAN SCHMITTBUHL ◽

JEAN-PIERRE VILOTTE

Keyword(s):

Probability Distribution ◽

Contact Point ◽

Relative Shift ◽

Lévy Walk ◽

Contact Points ◽

Roughness Exponent ◽

Mean Shape ◽

Before And After ◽

Levy Walk ◽

The Mean

We study the geometry of the contact between two rigid self-affine surfaces. We investigate the mean shape of the surface in the vicinity of the contact point as well as the probability distribution of apertures a as a function of the distance to the contact point. The latter reveals two distinct scaling regimes which are characterized. We show that as the two surfaces are shifted with respect to each other, the contact point on one surface undergoes a “Levy walk”. If u is the relative shift of the surfaces, the distance d between the two contact points (before and after the shift), scales as d ∝ uα where the exponent α is shown to be equal to the roughness exponent of the surfaces.

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Drop Shapes and Axis Ratio Distributions: Comparison between 2D Video Disdrometer and Wind-Tunnel Measurements

Journal of Atmospheric and Oceanic Technology ◽

10.1175/2009jtecha1244.1 ◽

2009 ◽

Vol 26 (7) ◽

pp. 1427-1432 ◽

Cited By ~ 47

Author(s):

M. Thurai ◽

V. N. Bringi ◽

M. Szakáll ◽

S. K. Mitra ◽

K. V. Beard ◽

...

Keyword(s):

Wind Tunnel ◽

Close Agreement ◽

Drop Diameter ◽

Wind Tunnel Experiments ◽

Axis Ratio ◽

Wind Tunnel Measurements ◽

Mean Shape ◽

The Mean ◽

Ratio Versus ◽

Made In

Abstract Comparisons of drop shapes between measurements made using 2D video disdrometer (2DVD) and wind-tunnel experiments are presented. Comparisons are made in terms of the mean drop shapes and the axis ratio distributions. Very close agreement of the mean shapes is seen between the two sets of measurements; the same applies to the mean axis ratio versus drop diameter. Also, in both sets of measurements, an increase in the oscillation amplitudes with increasing drop diameter is observed. In the case of the 2DVD, a small increase in the skewness was also detected. Given that the two sets of measurements were conducted in very different conditions, the agreement between the two sets of data implies a certain “robustness” in the mean shape of oscillating drops that may be extended to natural raindrop oscillations, at least in steady rainfall and above the surface layer.

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On the mean normal measures of a particle process

Advances in Applied Probability ◽

10.1017/s0001867800010612 ◽

2001 ◽

Vol 33 (1) ◽

pp. 25-38 ◽

Cited By ~ 5

Author(s):

Rolf Schneider

Keyword(s):

Stationary Process ◽

Normal Measure ◽

Mean Shape ◽

The Mean ◽

Particle Process

The (unoriented or oriented) mean normal measure of a stationary process of convex particles carries information on the mean shape of the particles and may, in particular, be useful for describing and detecting anisotropy of the particle process. This paper investigates the mean normal measure under the aspect of its determination from intersections, especially with lines or hyperplanes.

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On the fuzziness of circulation types derived from the application of obliquely rotated principal component analysis to a T-mode climatic field

10.21203/rs.3.rs-530514/v1 ◽

2021 ◽

Author(s):

Chibuike Chiedozie Ibebuchi

Keyword(s):

Principal Component Analysis ◽

Frequency Distribution ◽

Principal Component ◽

Component Analysis ◽

Threshold Values ◽

Study Region ◽

Probability Of Occurrence ◽

Circulation Types ◽

Mean Shape ◽

The Mean

Abstract This study examined the separability of circulation types (CTs) classified from the application of principal component analysis (PCA) to the T-mode matrix (variable is time series and observation is grid points) of a climatic field that explains atmospheric circulation; in addition to the uncertainty introduced on (i) the probability of occurrence, (ii) the mean shape of the CTs, (iii) the trend in the annual frequency of occurrence, (iv) the frequency distribution of the CTs, by using varying threshold values within the range of 0.2–0.35 to assign days to a given CT. The study region is Africa, south of the equator. Some large clusters were classified with most days in the analysis period assigned to them; these classes are interpreted as the dominant states of the atmosphere and generally, their existence results in the poor separability of the CTs since their features overlap with other CTs. Qualitatively, the choice of the threshold values within the defined range has little or no influence on the overall structure of the probability of occurrence of the CTs, the mean shape of the CTs, and the year-to-year variations in the annual occurrence of the CTs. However, it significantly impacts the frequency distribution of the CTs and the statistical significance of the trend in the annual occurrence of the CTs. Stringent threshold values within the defined range might benefit studies that aim to isolate days when specific CTs are most expressed and analyze their mechanism using composite maps, without focus on the frequency distribution and annual occurrence of the CTs. Overall, for the study region, lower threshold values within the defined range might be recommended since relatively, they do not tend to further constrain the probability of group membership, and equally seem to reveal the mechanisms that might be consistent when a given CT occurred regardless of the strength of its signal at a given time.

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WAVE PERIOD AND THE SWASH ZONE ENERGY BALANCE

Coastal Engineering Proceedings ◽

10.9753/icce.v11.25 ◽

1968 ◽

Vol 1 (11) ◽

pp. 25

Author(s):

Graham S. Giese

Keyword(s):

Energy Balance ◽

Infiltration Rate ◽

Sandy Beaches ◽

Wave Period ◽

Swash Zone ◽

Approach Angle ◽

Mean Shape ◽

The Mean

The shape sorting of pebbles in the swash zone was studied in an effort to determine the effect of the amount of foreshore infiltration per wave on the swash zone energy balance. Measurements were made of pebbles collected from the swash limit and from the step of selected sandy beaches. The pebbles were sampled on occasions when, and at locations where, the conditions of breaker height, breaker approach angle and foreshore slope fell within predetermined limits. The wave period and the foreshore infiltration rate varied among the beaches and were measured. The results of these measurements indicate that the mean shape of swash limit pebbles, and presumably, therefore, the swash zone energy balance depends upon the amount of foreshore infiltration per wave. This finding leads to the conclusion that in the study of the dynamics of the swash zone the effect of wave period and the effect of foreshore permeability must be considered together.

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A Taylor Expansion Approach for Computing Structural Performance Variation Over a Shape Population

Volume 1A: 36th Computers and Information in Engineering Conference ◽

10.1115/detc2016-59561 ◽

2016 ◽

Author(s):

Xilu Wang ◽

Xiaoping Qian

Keyword(s):

Numerical Study ◽

Principal Component ◽

Taylor Series Expansion ◽

Structural Performance ◽

Shape Variation ◽

Element Analysis ◽

Plate Deformation ◽

Performance Variation ◽

Mean Shape ◽

The Mean

In this paper, we present a formal and efficient method for computing structural performance variation over its shape population. Each shape in the population is represented as discrete points. These shapes are then aligned together and principal component analysis is conducted to obtain the shape variation, which is represented as a sum of variations in multiple principal modes. Finite element analysis is conducted on the mean shape. For each shape specified by the shape parameters, we then invoke a thin-plate deformation based scheme to automatically deform the mesh nodes. The performance of the shapes is approximated via Taylor series expansion of the FE solution of the mean shape. Numerical study illustrates the accuracy and efficiency of this method.

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Optical Timing of the Crab Nebula Pulsar NP 0532

Symposium - International Astronomical Union ◽

10.1017/s0074180900007361 ◽

1971 ◽

Vol 46 ◽

pp. 151-151

Author(s):

Jerry Nelson ◽

Richard Hills ◽

David Cudaback ◽

Joseph Wampler

Keyword(s):

Time Scale ◽

Crab Nebula ◽

Rate Of Change ◽

Arrival Times ◽

Average Value ◽

Mean Shape ◽

The Mean ◽

The Difference ◽

The Crab Nebula ◽

Pulse Arrival

Accurate pulse arrival times have been measured for NP 0532 during the period 15 December 1969 to 3 May 1970, and have been fitted to simple models of the pulsar braking mechanism. A good fit could not be obtained to all the data at once, because of deviations on a time scale of several days. However it was possible to divide the observing period into four shorter intervals in such a way that the data within each deviated only slightly from smoothly varying functions. The difference in the parameters of these four functions may indicate sudden events in the pulsar producing changes of order of 1 part in 109 in the pulsar frequency and 4 parts in 105 in the rate of change of frequency. In each case the difference in frequency from one interval to the next implies a slowdown of the pulsar.We found that the average value of the ‘braking parameter’ n in the equation dE/dt = -Aωn was 3.63, but dividing the data into shorter intervals gave values between 0 and 5. We found no changes in the mean shape of the pulses, or the phase of the interpulse relative to the main pulse.

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The occasional perils of reflection (across the midline; in geometric morphometrics)

10.1101/770677 ◽

2019 ◽

Author(s):

David C. Katz

Keyword(s):

Data Collection ◽

Biological Sample ◽

Mirror Reflection ◽

Mean Shape ◽

Landmark Data ◽

Long Time ◽

The Mean ◽

Symmetric Structures ◽

Shape And Size ◽

Do So

AbstractManually collecting landmark data on a large biological sample takes a long time. Several options exist to speed data collection, though each strategy introduces problems or raises concerns of its own. For bilaterally symmetric structures (e.g., crania), some recent papers recommend limiting landmark collection to one side and the midline, then “mirror-reflecting” landmarks across the midline to produce an approximation of the true bilateral configuration. However, where the midline is narrow relative to the bilateral anatomy, net midline landmark deviations from the mid-sagittal axis or plane will distort the mirror-reflected configuration. Here, I test whether this is a substantive concern at the scale of real biology. To do so, I simulate small amounts of mediolateral error on the mean shape from a sample of human mandibles (n = 178), then compare the distribution of simulated forms to variation in the data. I also test how faithfully mirror-reflected configurations replicate bilateral shape and size relationships. In both analyses, midline deviations from symmetry create striking distortions. I go on to show that incorporating a small number of landmarks from the opposite side of the mandible produces far more accurate estimates of bilateral shape than does mirror reflection. Mirror reflection is clearly inappropriate for these data and is likely suspect in all cases of narrow midline morphology.

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