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Inertial modes in a rotating triaxial ellipsoid.

ABSTRACT: In this work, we present an algorithm that enables computation of inertial modes and their corresponding frequencies in a rotating triaxial ellipsoid. The method consists of projecting the inertial mode equation onto finite-dimensional bases of polynomial vector fields. It is shown that this leads to a well-posed eigenvalue problem, and hence, that eigenmodes are of polynomial form. Furthermore, these results shed new light onto the question whether the eigenmodes form a complete basis, i.e. whether any arbitrary velocity field can be expanded in a sum of inertial modes. Finally, we prove that two intriguing integral properties of inertial modes in rotating spheres and spheroids also extend to triaxial ellipsoids.

SUBMITTER: Vantieghem S

PROVIDER: S-EPMC4075787 | biostudies-literature | 2014 Aug

REPOSITORIES: biostudies-literature

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Inertial modes in a rotating triaxial ellipsoid.

Vantieghem S S

Proceedings. Mathematical, physical, and engineering sciences 20140801 2168

In this work, we present an algorithm that enables computation of inertial modes and their corresponding frequencies in a rotating triaxial ellipsoid. The method consists of projecting the inertial mode equation onto finite-dimensional bases of polynomial vector fields. It is shown that this leads to a well-posed eigenvalue problem, and hence, that eigenmodes are of polynomial form. Furthermore, these results shed new light onto the question whether the eigenmodes form a complete basis, i.e. whe ...[more]

PMID: 25104908

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Project description:PurposeTo adapt and validate a previously developed decision tree for youth to identify bedrest for use in preschool children.MethodsParents of healthy preschool (3-6-year-old) children (n = 610; 294 males) were asked to help them to wear an accelerometer for 7 to 10 days and 24 hours/day on their waist. Children with ≥3 nights of valid recordings were randomly allocated to the development (n = 200) and validation (n = 200) groups. Wear periods from accelerometer recordings were identified minute-by-minute as bedrest or wake using visual identification by two independent raters. To automate visual identification, chosen decision tree (DT) parameters (block length, threshold, bedrest-start trigger, and bedrest-end trigger) were optimized in the development group using a Nelder-Mead simplex optimization method, which maximized the accuracy of DT-identified bedrest in 1-min epochs against synchronized visually identified bedrest (n = 4,730,734). DT's performance with optimized parameters was compared with the visual identification, commonly used Sadeh's sleep detection algorithm, DT for youth (10-18-years-old), and parental survey of sleep duration in the validation group.ResultsOn average, children wore an accelerometer for 8.3 days and 20.8 hours/day. Comparing the DT-identified bedrest with visual identification in the validation group yielded sensitivity = 0.941, specificity = 0.974, and accuracy = 0.956. The optimal block length was 36 min, the threshold 230 counts/min, the bedrest-start trigger 305 counts/min, and the bedrest-end trigger 1,129 counts/min. In the validation group, DT identified bedrest with greater accuracy than Sadeh's algorithm (0.956 and 0.902) and DT for youth (0.956 and 0.861) (both P<0.001). Both DT (564±77 min/day) and Sadeh's algorithm (604±80 min/day) identified significantly less bedrest/sleep than parental survey (650±81 min/day) (both P<0.001).ConclusionsThe DT-based algorithm initially developed for youth was adapted for preschool children to identify time spent in bedrest with high accuracy. The DT is available as a package for the R open-source software environment ("PhysActBedRest").

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Inertial modes in a rotating triaxial ellipsoid.

Publications

Inertial modes in a rotating triaxial ellipsoid.

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