Nonlocal half-ball vector operators on bounded domains: Poincar\'e inequality and its applications

This work contributes to nonlocal vector calculus as an indispensable mathematical tool for the study of nonlocal models that arises in a variety of applications. We define the nonlocal half-ball gradient, divergence and curl operators with general kernel functions (integrable or fractional type with finite or infinite supports) and study the associated nonlocal vector identities. We study the nonlocal function space on bounded domains associated with zero Dirichlet boundary conditions and the half-ball gradient operator and show it is a separable Hilbert space with smooth functions dense in it. A major result is the nonlocal Poincar\'e inequality, based on which a few applications are discussed, and these include applications to nonlocal convection-diffusion, nonlocal correspondence model of linear elasticity, and nonlocal Helmholtz decomposition on bounded domains

An optimization framework for wind farm layout design using CFD-based Kriging model

Wind farm layout optimization (WFLO) seeks to alleviate the wake loss and maximize wind farm power output efficiency, and is a crucial process in the design of wind energy projects.Since the optimization algorithms typically require thousands of numerical evaluations of the wake effects, conventional WFLO studies are usually carried out with the low-fidelity analytical wake models.In this paper, we develop an optimization framework for wind farm layout design using CFD-based Kriging model to maximize the annual energy production (AEP) of wind farms. This surrogate-based optimization (SBO) framework uses latin hypercube sampling to generate a group of wind farm layout samples, based on which CFD simulations are carried out to obtain the corresponding AEPs.This wind farm layout dataset is used to train the Kriging model, which is then integrated with an optimizer based on genetic algorithm (GA). As the optimization progresses, the intermediate optimal layout designs are again fed into the dataset.Such adaptive update of wind farm layout dataset continues until the algorithm converges.To evaluate the performance of the proposed SBO framework, we apply it to three representative wind farm cases.Compared to the conventional staggered layout, the optimized wind farm produces significantly higher total AEP.In particular, the SBO framework requires significantly smaller number of CFD calls to yield the optimal layouts that generates almost the same AEP with the direct CFD-GA method.Further analysis on the velocity fields show that the optimization framework attempts to locate the downstream turbines away from the the wakes of upstream ones.The proposed CFD-based surrogate model provides a more accurate and flexible alternative to the conventional analytical-wake-model-based methods in WFLO tasks, and has the potential to be used for designing efficient wind farm projects

Ultra-high speed OCT allows measurement of intraocular pressure, corneal geometry, and corneal stiffness using a single instrument

Screening for ocular diseases, such as glaucoma and keratoconus, includes measuring the eye-globe intraocular pressure (IOP) and corneal biomechanical properties. However, currently available clinical tools cannot quantify corneal tissue material parameters, which can provide critical information for detecting diseases and evaluating therapeutic outcomes. Here, we demonstrate measurement of eye-globe IOP, corneal elasticity, and corneal geometry of in situ porcine corneas with a technique termed applanation optical coherence elastography (Appl-OCE) with single instrument. We utilize an ultrafast phase-sensitive optical coherence tomography system comprised of a 4X buffered Fourier domain mode-locked swept source laser with an Ascan rate of ~1.5 MHz and a 7.3 kHz resonant scanner. The IOP was measured by imaging the response of in situ porcine corneas to a large force air-puff. As with other noncontact tonometers, the time when the cornea was applanated during the inwards and outwards motion was correlated to a measure air-pressure temporal profile. The IOP was also measured with a commercially available rebound tonometer for comparison. The stiffness of the corneas was assessed by directly imaging and analyzing the propagation of a focused micro air-pulse induced elastic wave, and the corneal geometry was obtained from the OCT structural image. Our results show that corneal thickness decreased as IOP increased, and that corneal stiffness increased with IOP. Moreover, the IOP measurements made by Appl-OCE were more closely correlated with the artificially set IOP than the rebound tonometer, demonstrating the capabilities of Appl-OCE to measure corneal stiffness, eye-globe IOP, and corneal geometry with a single instrument

Applanation optical coherence elastography: noncontact measurement of intraocular pressure, corneal biomechanical properties, and corneal geometry with a single instrument

Current clinical tools provide critical information about ocular health such as intraocular pressure (IOP). However, they lack the ability to quantify tissue material properties, which are potent markers for ocular tissue health and integrity. We describe a single instrument to measure the eye-globe IOP, quantify corneal biomechanical properties, and measure corneal geometry with a technique termed applanation optical coherence elastography (Appl-OCE). An ultrafast OCT system enabled visualization of corneal dynamics during noncontact applanation tonometry and direct measurement of micro air-pulse induced elastic wave propagation. Our preliminary results show that the proposed Appl-OCE system can be used to quantify IOP, corneal biomechanical properties, and corneal geometry, which builds a solid foundation for a unique device that can provide a more complete picture of ocular health

Fatigue assessment on local components of a semi-submersible platform subjected to wind and wave loads

The objective in this work is to assess fatigue damages on local components of a semi-submersible platform under combined actions of wind and wave loads in time domain. Some improvements are provided in the present study to improve the efficiency and accuracy of the whole evaluating process. Firstly, a combined wind and wave relationship as well as an innovative mixture simulation method are used to generate time series of random wind and waves. Moreover, an m-block division method is proposed to compress the number of the whole short-term sea states in the wind-wave scatter diagram. Then, with an improved multiple interpolation sub-model method, the structural stress responses of the local structural components are calculated as is in the whole model analysis. Finally, a modified rain-flow counting method is provided and validated to count the stress cycles efficiently and accurately. Thus, the short- and long-term fatigue damages are computed based on the S-N curve approach and the cumulative fatigue damage rule. In relative agreement with the numerical results by the traditional time-domain method and existing experimental data, these proposed improved methods are demonstrated to be applicable and efficient methods for fatigue damage analyses. All the fatigue damages on local components satisfy the specification requirements and the minimum value appears under the up wind-wave state, which is the proper working condition for a semi-submersible platform

Flow characteristics and dynamic responses of a rear circular cylinder behind the square cylinder with different side lengths

Wake-induced vibrations of a 2-DOF circular cylinder which is placed behind a stationary square cylinder with tandem arrangement are numerically investigated at low Reynolds numbers by using semi-implicit Characteristics-based split (CBS) finite element algorithm in this study. Numerical results demonstrate that the side length of the upstream square cylinder can significantly affect the characteristics of flow patterns, oscillation frequency, maximum amplitudes, X-Y trajectories, and hydrodynamic coefficients of the rear circular cylinder. The predominant vortex shedding patterns are 2S, 2P and 2T mode. In addition to the figure “8”, “raindrop” and figure “dual-8” are observed in the X-Y vibrating trajectories for the circular cylinder. Finally, the interactions between cylinders are revealed according to the phase portrait of fluid force to displacement and the power spectral densities (PSD) features of the vibration amplitude on the rear circular cylinder and the instantaneous flow field, together with the wake-induced vibration (WIV) mechanism underlying the oscillation characteristics of the circular cylinder behind a stationary square cylinder with different sizes

Flow characteristics and dynamic responses of a parked straight‐bladed vertical axis wind turbine

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Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography

Wave models that have been used to extract the biomechanical properties of the cornea from the propagation of an elastic wave are based on an assumption of thin-plate geometry. However, this assumption does not account for the effects of corneal curvature and thickness. This study conducts finite element (FE) simulations on four types of cornea-like structures as well as optical coherence elastography (OCE) experiments on contact lenses and tissue-mimicking phantoms to investigate the effects of curvature and thickness on the group velocity of an elastic wave. The elastic wave velocity as determined by FE simulations and OCE of a spherical shell section decreased from ∼2.8 m/s to ∼2.2 m/s as the radius of curvature increased from 19.1 mm to 47.7 mm and increased from ∼3.0 m/s to ∼4.1 m/s as the thickness of the agar phantom increased from 1.9 mm to 5.6 mm. Both the FE simulation and OCE results confirm that the group velocity of the elastic wave decreases with radius of curvature but increases with thickness. These results demonstrate that the effects of the curvature and thickness must be considered in the further development of accurate wave models for reconstructing biomechanical properties of the cornea

Quantifying the effects of hydration on corneal stiffness with optical coherence elastography

Several methods have been proposed to assess changes in corneal biomechanical properties due to various factors, such as degenerative diseases, intraocular pressure, and therapeutic interventions (e.g. corneal collagen crosslinking). However, the effect of the corneal tissue hydration state on corneal stiffness is not well understood. In this work, we induce low amplitude (< 10 μm) elastic waves with a focused micro air-pulse in fresh in situ rabbit corneas (n = 10) in the whole eye-globe configuration at an artificially controlled intraocular pressure. The waves were then detected with a phase-stabilized swept source optical coherence elastography system. Baseline measurements were taken every 20 minutes for an hour while the corneas were hydrated with 1X PBS. After the measurement at 60 minutes, a 20% dextran solution was topically instilled to dehydrate the corneas. The measurements were repeated every 20 minutes again for an hour. The results showed that the elastic wave velocity decreased as the corneal thickness decreased. Finite element modeling (FEM) was performed using the corneal geometry and elastic wave propagation speed to assess the stiffness of the samples. The results show that the stiffness increased from ~430 kPa during hydration with PBS to ~500 kPa after dehydration with dextran, demonstrating that corneal hydration state, apart from geometry and intraocular pressure, can change the stiffness of the cornea