<i>Mathematical Methods in the Physical Sciences</i>

Boas, Mary L.; Romain, Jacques E.

doi:10.1063/1.3034374

Cited by 183 publications

(46 citation statements)

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“…The tortuosity of a fiber, which we denote τ hereafter, is defined as the integrated path length divided by the end to end distance (Boas, 2006). For a two dimensional image, the tortuosity is given by the relationship…”

Section: Resultsmentioning

confidence: 99%

The role of mode of delivery on elastic fiber architecture and vaginal vault elasticity: A rodent model study

Downing

Billah

Raparia

et al. 2014

Journal of the Mechanical Behavior of Biomedical Materials

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We report on an experimental study of the role of mode of delivery and pregnancy on the architecture of vaginal elastic fibers and vaginal vault elasticity in female Sprague-Dawley rats. In primiparous rats submitted to spontaneous or Cesarean delivery and virgin rats submitted to simulated delivery, the tortuosity of elastic fibers (defined as the ratio of length to end-to-end distance) was observed to decrease when measured two days to two weeks postpartum. In addition, the measured tortuosity of elastic fibers in multiparous rats was greater than that of virgin rats. The tortuosity of elastic fibers of all rats measured at two days postpartum were found to be similar to that of multiparous rats. At two weeks postpartum the measured tortuosity of vaginal elastic fibers was indistinguishable from virgin rats, regardless of the delivery method. Borrowing from the field of polymer physics, a model is suggested that connects elastic fiber tortuosity to the resulting tension under an applied stress; fibers having high tortuosity are expected to provide less structural support than more linear, low tortuosity fibers. To probe the macroscopic effects in elasticity due to architectural changes observed in elastic fibers, we have measured the stiffness of the vaginal vault in each cohort using a pressure-infusion system. The vaginal vault stiffness of all primiparous rats measured two weeks postpartum was greater than that measured two days postpartum. In addition, the vaginal vault of virgin rats was stiffer than that of multiparous rats. These observations confirmed that vaginal vault elastic fibers undergo significant remodeling due to pregnancy and parturition, and that the complex remodeling may be a significant contributor to tissue elasticity. Remarkably, regardless of the mode of delivery or simulated tissue trauma, elastic fiber tortuosity is observed to decrease from two days to two weeks postpartum indicating the onset of repair and recovery of tissue stiffness.

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Section: Resultsmentioning

confidence: 99%

The role of mode of delivery on elastic fiber architecture and vaginal vault elasticity: A rodent model study

Downing

Billah

Raparia

et al. 2014

Journal of the Mechanical Behavior of Biomedical Materials

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“…Assuming the noise has zero mean and known variance (which can be different from measurement to measurement), it follows thatThe goal is to find a linear combination of the datathat is optimal in the sense of being an unbiased, minimal variance estimator of a . Unbiased (i.e., ) implieswhile minimum variance impliesSince (6.4) is a constraint that must hold when we minimize the variance, we can use Lagrange’s method of undetermined multipliers (Boas 2006) and minimize insteadwith respect to both and . The final result is:so thatThus, the linear combination is a weighted average that gives less weight to the noiser measurements (i.e., those with large variance ).…”

Section: Optimal Filteringmentioning

confidence: 99%

Detection methods for stochastic gravitational-wave backgrounds: a unified treatment

2017

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We review detection methods that are currently in use or have been proposed to search for a stochastic background of gravitational radiation. We consider both Bayesian and frequentist searches using ground-based and space-based laser interferometers, spacecraft Doppler tracking, and pulsar timing arrays; and we allow for anisotropy, non-Gaussianity, and non-standard polarization states. Our focus is on relevant data analysis issues, and not on the particular astrophysical or early Universe sources that might give rise to such backgrounds. We provide a unified treatment of these searches at the level of detector response functions, detection sensitivity curves, and, more generally, at the level of the likelihood function, since the choice of signal and noise models and prior probability distributions are actually what define the search. Pedagogical examples are given whenever possible to compare and contrast different approaches. We have tried to make the article as self-contained and comprehensive as possible, targeting graduate students and new researchers looking to enter this field.Electronic supplementary materialThe online version of this article (doi:10.1007/s41114-017-0004-1) contains supplementary material, which is available to authorized users.

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“…The PCC software was used to determine the velocity of 10 consecutive ferrofluid droplets. Points in all graphs denote the mean of the measurements and the error bar represents the standard error of the mean79 for the corresponding data points.…”

Section: Discussionmentioning

confidence: 99%

Droplet Merging on a Lab-on-a-Chip Platform by Uniform Magnetic Fields

Varma

Ray

Wang

et al. 2016

Sci Rep

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Droplet microfluidics offers a range of Lab-on-a-chip (LoC) applications. However, wireless and programmable manipulation of such droplets is a challenge. We address this challenge by experimental and modelling studies of uniform magnetic field induced merging of ferrofluid based droplets. Control of droplet velocity and merging was achieved through uniform magnetic field and flow rate ratio. Conditions for droplet merging with respect to droplet velocity were studied. Merging and mixing of colour dye + magnetite composite droplets was demonstrated. Our experimental and numerical results are in good agreement. These studies are useful for wireless and programmable droplet merging as well as mixing relevant to biosensing, bioassay, microfluidic-based synthesis, reaction kinetics, and magnetochemistry.

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Mathematical Methods in the Physical Sciences

Cited by 183 publications

References 0 publications

The role of mode of delivery on elastic fiber architecture and vaginal vault elasticity: A rodent model study

The role of mode of delivery on elastic fiber architecture and vaginal vault elasticity: A rodent model study

Detection methods for stochastic gravitational-wave backgrounds: a unified treatment

Droplet Merging on a Lab-on-a-Chip Platform by Uniform Magnetic Fields

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