Torsional pendulum with small time constant

When the input to a sensor is changing rapidly, we observe performance characteristics that are due to the change in input and are not related to static performance characteristics. In this chapter we will assume that a static calibration has been applied so that we can consider dynamic performance independently of static characteristics. The terms “linear” and “nonlinear” have been used in chap. 3 in the static sense. Now they are being used in the dynamic sense where “linear” connotes the applicability of the superposition property. A given sensor could be nonlinear in the static sense (e.g., a PRT is nonlinear in that is static sensitivity is not constant over the range) but could be linear in the dynamic sense (modeled by a linear differential equation). We use differential equations to model this dynamic performance while realizing the models can never be exact. If the dynamic behavior of physical systems can be described by linear differential equations with constant coefficients, the analysis is relatively easy because the solutions are well known. Such equations are always approximations to the actual performance of physical systems that are often nonlinear, vary with time, and have distributed parameters. The justification for the use of simple, readily solved models must be the quality of the fit of the solution to the actual system output and the usefulness of the resulting analysis. Dynamic performance characteristics define the way instruments react to measurand fluctuations. When a temperature sensor is mounted on an airplane these characteristics will indicate what the sensor “sees.” If the airplane flies through a cloud with a slow sensor (where time constant is large) it may not register change of temperature or humidity. That would not be tolerable if we wanted to measure the cloud. Similarly, if the airplane flies through turbulence we would like to measure changes in air speed. Variations in temperature and humidity would be vital in the flight of a radiosonde, so again the time constant of the sensors would be considered. Fluxes of heat, water vapor, and momentum near the ground require fast sensors (with small time constants).

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Inversions of time-domain spectral induced polarization data using stretched exponential

Geophysical Journal International ◽

10.1093/gji/ggz401 ◽

2019 ◽

Vol 219 (3) ◽

pp. 1851-1865

Author(s):

Seogi Kang ◽

Douglas W Oldenburg

Keyword(s):

Time Constant ◽

Time Domain ◽

Induced Polarization ◽

Small Time ◽

Mineral Deposit ◽

The Body ◽

Stretched Exponential ◽

Simultaneous Inversion ◽

Spectral Induced Polarization ◽

Alteration Halo

SUMMARY We provide a two-stage approach to extract spectral induced polarization (SIP) information from time-domain IP data. In the first stage we invert dc data to recover the background conductivity. In the second, we solve a linear inverse problem and invert all time channels simultaneously to recover the IP parameters. The IP decay curves are represented by a stretched exponential (SE) rather than the traditional Cole–Cole model, and we find that defining the parameters in terms of their logarithmic values is advantageous. To demonstrate the capability of our simultaneous SIP inversion we use synthetic data simulating a porphyry mineral deposit. The challenge is to image a mineral body that is hosted within an alteration halo having the same chargeability but a different time constant. For a 2-D problem, we were able to distinguish the body using our simultaneous inversion but we were not successful in using a sequential (or conventional) SIP inversion approach. For the 3-D problem we recovered 3-D distributions of the SIP parameters and used those to construct a 3-D rock model having four rock units. Three chargeable units were distinguished. The compact mineralization zone, having a large time constant, was distinguished from the circular alteration halo that had a small time constant. Finally, to promote the use of the SIP technique, and to have further development of SIP inversion, all examples presented in this paper are available in our open source resources (https://github.com/simpeg-research/kang-2018-spectral-inducedpolarization).

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The Measurement of Inductances with very small Time Constant

Physical Review ◽

10.1103/physrevseriesi.32.609 ◽

1911 ◽

Vol 32 (6) ◽

pp. 609-611

Author(s):

F. W. Grover ◽

H. L. Curtis

Keyword(s):

Time Constant ◽

Small Time

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Pulsed Electrochemical Mass Spectrometry for Operando Tracking of Interfacial Processes in Small-Time-Constant Electrochemical Devices such as Supercapacitors

ACS Applied Materials & Interfaces ◽

10.1021/acsami.7b12068 ◽

2017 ◽

Vol 9 (47) ◽

pp. 41224-41232 ◽

Cited By ~ 9

Author(s):

Nicolas Batisse ◽

Encarnación Raymundo-Piñero

Keyword(s):

Mass Spectrometry ◽

Time Constant ◽

Small Time ◽

Interfacial Processes ◽

Electrochemical Devices

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The Effect of Sensori-Neural Hearing Loss on Threshold-Duration Functions

Journal of Speech and Hearing Research ◽

10.1044/jshr.1104.842 ◽

1968 ◽

Vol 11 (4) ◽

pp. 842-852 ◽

Cited By ~ 26

Author(s):

H. N. Wright

Keyword(s):

Hearing Loss ◽

Differential Diagnosis ◽

Time Constant ◽

Present Series ◽

Auditory Disorders ◽

Threshold Duration

Previous findings on the threshold for tones as a function of their duration have suggested that such functions may be systematically affected by sensori-neural hearing losses of cochlear origin. The present series of investigations was designed to explore this relation further and to determine also whether the amount of hearing loss present has any effect upon the results which are obtained. Preliminary studies were also carried out on a conductively impaired listener to indicate whether hearing losses of this type affect the threshold-duration function. The results indicate that the threshold-duration function is systematically affected by sensori-neural hearing losses of cochlear origin. This effect is manifested by a progressive shortening of the time constant relating threshold to duration and is not uniquely related to the amount of hearing loss present. The results obtained from the conductively impaired listener suggested that this type of hearing loss has no effect on the threshold-duration function, thereby implying that such functions may contribute significantly to the differential diagnosis of auditory disorders.

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