We propose an improved adjoint-based method for the reconstruction and prediction of the nonlinear wave field from coarse-resolution measurement data. We adopt the data assimilation framework using an adjoint equation to search for the optimal initial wave field to match the wave field simulation result at later times with the given measurement data. Compared with the conventional approach where the optimised initial surface elevation and velocity potential are independent of each other, our method features an additional constraint to dynamically connect these two control variables based on the dispersion relation of waves. The performance of our new method and the conventional method is assessed with the nonlinear wave data generated from phase-resolved nonlinear wave simulations using the high-order spectral method. We consider a variety of wave steepness and noise levels for the nonlinear irregular waves. It is found that the conventional method tends to overestimate the surface elevation in the high-frequency region and underestimate the velocity potential. In comparison, our new method shows significantly improved performance in the reconstruction and prediction of instantaneous surface elevation, surface velocity potential and high-order wave statistics, including the skewness and kurtosis.
Bathymetry is an important factor affecting wave propagation in coastal environments but is often challenging to measure in practice. We propose a method for inferring coastal bathymetry from spatial variations in surface waves by combining a high-order spectral method for wave simulation and an adjoint-based variational data assimilation method. Recursion-formed adjoint equations are derived to obtain the sensitivity of the wave surface elevation to the underlying bottom topography to any desired order of nonlinear perturbation. We also develop a multiscale optimisation method to eliminate spurious high-wavenumber fluctuations in the reconstructed bathymetry data caused by sensitivity variations over the different length scales of surface waves. The proposed bottom detection method is validated with a realistic coastal wave environment involving complex two-dimensional bathymetry features, non-periodic incident waves and nonlinear broadband multidirectional waves. In numerical experiments at both laboratory and field scales, the bathymetry reconstructed from our method agrees well with the ground truth. We also show that our method is robust against imperfect surface wave data in the presence of limited sampling frequency and noise.
When the edge which is under the multi-film is more steep or angular, the stress in the multilayer film near the edge is concentrated, this situation will greatly reduce the reliability of electronic components. And sometimes, we need some special structure such as a slope with a specific angle in the MEMS, so that the metal line can take the signal to the output pad through the slope instead of deep step. To cover these problems, the lithography method of preparing the structure with edge slope is studied. In this paper, based on the Kirchhoff scalar diffraction theory we try to change the contact exposure gap and the post-baking time at the specific temperature to find out the effect about the edge angle of the photoresist. After test by SEM, the results were presented by using AZP4330 photoresist, we can get the PR Pattern with edge slope 40° of the process and the specific process parameters.
Abstract Nonlinear internal waves are an upper ocean phenomenon that drives horizontal surface current gradients, which in turn modulate ocean surface waves. Under certain conditions, this wave‐current interaction creates ocean surface roughness heterogeneity, in the form of alternating rough/smooth bands. In this study, we investigate the sensitivity of the modulation effect to internal wave properties and develop sea states using simulations of individual internal wave solitons. We utilize a phased‐resolved two‐layer fluid model to capture the evolution of surface waves deterministically. We conduct extensive simulations with a wide range of parameters, including fluid layer density ratio, internal wave amplitude, and parametric wind speed. We use the ratio of the mean surface slope between the rough and smooth bands, which are identified in the simulated surface wave field, to systematically investigate their response to the internal wave forcing across all our simulation cases. Our results show that, among the internal wave parameters, the upper‐lower layer density ratio causes the strongest surface heterogeneity. Spectral analysis of the surface wave elevation and slope variance reveals that the wavenumbers above the peak are most impacted. We demonstrate that accounting for the internal wave‐induced modulation requires including wave steepness statistics, for example, when modeling air‐sea exchange using a surface roughness, z 0 , parameter. Currently, these statistics are not included in typically coupled modeling schemes, and these systems cannot account for the impact of internal waves, even if the solitary wave phenomena are resolved.
This paper considers the problem of real-time reconstruction of ocean wave field with a network of discrete wave height sensors. Being able to predict incoming wave characteristics helps individual or collections of wave energy converters to increase the amount of energy that they can capture. In this paper, the wave field is modeled to consist of a frequency spectrum of monotone Airy waves with unknown strengths and phases. Kalman filter based observers are then designed to estimate the wave fields. The observers' performance in reconstructing the wave field accurately is validated in simulation for 1-D and 2-D linear and nonlinear waves. Wave tank experiments have also been performed to validate its ability to reconstruct a wave field in real-time using noisy data obtained from a vision-based wave height sensor.
Through a case of glass plate cutting, two-dimensional cutting pattern problem of rectangular blanks is discussed. The raw material is cut and layout by applying the method of grouping and two-stage cutting pattern types. Here first all the blanks are divided into different groups based on certain requirement, and then two-dimensional cutting pattern problem is transformed into two one-dimensional cutting problems. Through constructing an integer programming model, the cutting program of the raw material can be obtained step by step by calculating in LINGO. Because here the precise algorithm of integer programming is applied, which is not the time algorithm of polynomial, in the specific implementation, there shouldn’t be more variables, so all the data should be divided into different groups to calculate. In each group, there should be no more than 6 blanks, which are grouped according to their size. This algorithm is simple and easy to operate with a high material usage.
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