The Numerical Evaluation of Curvilinear Integrals and Areas

We envisage here that it is desired to evaluate (using a digital computer) the integral of a function f (x, y) with respect to x (say), along a curve γ in the xy-plane; the value of the function and of the co-ordinates of the curve being known only at discrete, and possibly irregularly spaced, points of γ. Such a problem frequently arises, especially where γ is a closed curve: as for instance in aerodynamics when it is desired to estimate the force components and pitching moment inferred from an experimentally determined set of pressures taken over an aerofoil; here the function values are related to the pressure measurements and γ is the aerofoil contour.

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Transient Heat Conduction in Elliptical Plates and Cylinders

Journal of Heat Transfer ◽

10.1115/1.4008132 ◽

1959 ◽

Vol 81 (1) ◽

pp. 54-58 ◽

Cited By ~ 9

Author(s):

E. T. Kirkpatrick ◽

W. F. Stokey

Keyword(s):

Heat Conduction ◽

Temperature Change ◽

Outer Surface ◽

Digital Computer ◽

Numerical Evaluation ◽

Initial Temperature ◽

Transient Heat Conduction ◽

Elliptical Cylinder ◽

Mathieu Functions ◽

Sudden Temperature Change

In 1945, N. W. McLachlan published the equations governing the problem of heat conduction in a long elliptical cylinder, including the solution for the case of a cylinder with a uniform initial temperature, subject to a sudden temperature change at the outer surface of the cylinder. This paper describes the numerical evaluation of McLachlan’s solution by the use of a digital computer and includes a table of the necessary zeros of the modified Mathieu functions. Tables of the temperatures in cylinders with eccentricities of 0.6, 0.7, 0.8, and 0.9 are given.

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Signal Interpretation Considerations When Estimating Subglottal Pressure From Oral Air Pressure

Journal of Speech Language and Hearing Research ◽

10.1044/2018_jslhr-s-17-0432 ◽

2019 ◽

Vol 62 (5) ◽

pp. 1326-1337 ◽

Cited By ~ 2

Author(s):

Brittany L. Perrine ◽

Ronald C. Scherer ◽

Jason A. Whitfield

Keyword(s):

Standard Condition ◽

Word Production ◽

Air Pressure ◽

Pressure Waveform ◽

Pressure Measurements ◽

Air Leak ◽

Pressure Signal ◽

Adult Participants ◽

Syllable Repetition ◽

Subglottal Pressure

Purpose Oral air pressure measurements during lip occlusion for /pVpV/ syllable strings are used to estimate subglottal pressure during the vowel. Accuracy of this method relies on smoothly produced syllable repetitions. The purpose of this study was to investigate the oral air pressure waveform during the /p/ lip occlusions and propose physiological explanations for nonflat shapes. Method Ten adult participants were trained to produce the “standard condition” and were instructed to produce nonstandard tasks. Results from 8 participants are included. The standard condition required participants to produce /pːiːpːiː.../ syllables smoothly at approximately 1.5 syllables/s. The nonstandard tasks included an air leak between the lips, faster syllable repetition rates, an initial voiced consonant, and 2-syllable word productions. Results Eleven oral air pressure waveform shapes were identified during the lip occlusions, and plausible physiological explanations for each shape are provided based on the tasks in which they occurred. Training the use of the standard condition, the initial voice consonant condition, and the 2-syllable word production increased the likelihood of rectangular oral air pressure waveform shapes. Increasing the rate beyond 1.5 syllables/s improved the probability of producing rectangular oral air pressure signal shapes in some participants. Conclusions Visual and verbal feedback improved the likelihood of producing rectangular oral air pressure signal shapes. The physiological explanations of variations in the oral air pressure waveform shape may provide direction to the clinician or researcher when providing feedback to increase the accuracy of estimating subglottal pressure from oral air pressure.

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