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Abstract High-resolution profiles of vertical velocity obtained from two different surface-following autonomous platforms, Surface Wave Instrument Floats with Tracking (SWIFTs) and a Liquid Robotics SV3 Wave Glider, are used to compute dissipation rate profilesϵ(z) between 0.5 and 5 m depth via the structure function method. The main contribution of this work is to update previous SWIFT methods to account for bias due to surface gravity waves, which are ubiquitous in the near-surface region. We present a technique where the data are prefiltered by removing profiles of wave orbital velocities obtained via empirical orthogonal function (EOF) analysis of the data prior to computing the structure function. Our analysis builds on previous work to remove wave bias in which analytic modifications are made to the structure function model. However, we find the analytic approach less able to resolve the strong vertical gradients inϵ(z) near the surface. The strength of the EOF filtering technique is that it does not require any assumptions about the structure of nonturbulent shear, and does not add any additional degrees of freedom in the least squares fit to the model of the structure function. In comparison to the analytic method,ϵ(z) estimates obtained via empirical filtering have substantially reduced noise and a clearer dependence on near-surface wind speed.
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Accurate Quantum States for a 2D-Dipole
Edge dislocations are crucial in understanding both mechanical and electrical transport in solid and are modeled as line distributions of dipole moments. The calculation of the electronic spectrum for the two dimensional dipole, represented by the potential energy V(r,θ)=pcosθ/r, has been the topic of several studies that show significant difficulties in obtaining accurate results. In this work, we demonstrate that the source of these difficulties is a logarithmic contribution to the behavior of the wave function at the origin that was neglected by previous authors. By taking into account this non-analytic deviation of the solution of Schrödinger’s equation, superior results, with the expected rate of convergence, are obtained. This goal is accomplished by “adapting” general algorithms for solving partial derivative differential equations to include the desired asymptotic behavior. We illustrate this principle for the variational principle and finite difference methods. Accurate energies and wave functions are obtained not only for the ground state but also for the first eleven excited states and are useful for designing nanoelectronic devices. This paper demonstrates that augmentary knowledge about analytic properties of the solutions leads to the improved convergence and stability of numerical methods.
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- PAR ID:
- 10491839
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Nanomaterials
- Volume:
- 14
- Issue:
- 2
- ISSN:
- 2079-4991
- Page Range / eLocation ID:
- 206
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/nano14020206
