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Wind-generated waves are often treated as stochastic processes. There is particular interest in their spectral density functions, which are often expressed in some parametric form. Such spectral density functions are used as inputs when…

We present methods for analyzing and designing cylindrical electromagnetic metasurfaces with non-circular cross sections based on conformal transformations. It can be difficult to treat surfaces with non-canonical geometries since they…

Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows…

Wind-wave and ocean current interactions affect critical coastal and oceanic processes, yet modeling these interactions presents significant challenges. The western North Atlantic Ocean provides an ideal test environment for coupled…

Spatial sound field interpolation relies on suitable models to both conform to available measurements and predict the sound field in the domain of interest. A suitable model can be difficult to determine when the spatial domain of interest…

A computational fluid model is developed to study waves and instabilities. A new technique involving initial perturbations in configuration space have been implemented to excite the plasma waves; i.e. the perturbations acting similar to a…

Errors in applying regression models and wavelet filters used to analyze geophysical signals are discussed: (1) multidecadal natural oscillations (e.g. the quasi 60-year Atlantic Multidecadal Oscillation (AMO), North Atlantic Oscillation…

This paper presents and investigates a novel methodology for validating high-resolution ocean models using satellite imagery. High-resolution ocean models provide detailed information in coastal areas where other available data products are…

We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.

Given multi-model ensemble climate projections, the goal is to accurately and reliably predict future sea-level rise while lowering the uncertainty. This problem is important because sea-level rise affects millions of people in coastal…

Light Detection and Ranging (LiDAR) are fast emerging sensors in the field of Earth Observation. It is a remote sensing technology that utilizes laser beams to measure distances and create detailed three-dimensional representations of…

In situ and remotely sensed observations have potential to facilitate data-driven predictive models for oceanography. A suite of machine learning models, including regression, decision tree and deep learning approaches were developed to…

Fourier-based wavefront sensors, such as the Pyramid Wavefront Sensor (PWFS), are the current preference for high contrast imaging due to their high sensitivity. However, these wavefront sensors have intrinsic nonlinearities that constrain…

In this article, we introduce a moving-frame approach to the geophysical equation of two-dimensional uniformly stratified rotational fluid in oceans and find a family of exact solutions containing ten arbitrary parameter functions.

We study the two dimensional water waves problem with surface tension in the case when there is a non-zero contact angle between the free surface and the bottom. In the presence of surface tension, dissipations take place at the contact…

We prove decay estimates for solutions to non-isotropic linear systems of wave equations. The defining feature of these estimates is that they depend only on the commutation properties of the system with the scaling vector field. As…

A general algorithm for calculating the reflection and refraction of nonuniform plane waves from an arbitrarily oriented and charged planar interface between two lossy isotropic media is proposed based on the decomposition of the complex…

We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…

The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly-used deep learning approaches suffer from a lack of interpretability of the trained models. Here we present an interpretable machine learning…

In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images on surfaces. The evolving curves on the surfaces are…