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A formulation is developed to assimilate ocean-wave data into the Numerical Flow Analysis (NFA) code. NFA is a Cartesian-based implicit Large-Eddy Simulation (LES) code with Volume of Fluid (VOF) interface capturing. The sequential…
A question of global concern regarding the sustainable future of humankind stems from the effect due to aerosols on the global climate. The quantification of atmospheric aerosols and their relationship to climatic impacts are key to…
Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations…
This study focuses on solving the numerical challenges of imposing absorbing boundary conditions for dynamic simulations in the material point method (MPM). To attenuate elastic waves leaving the computational domain, the current work…
The spatiotemporal dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate and stable reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear…
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…
The quantitative formulation of evolution equations is the backbone for prediction, control, and understanding of dynamical systems across diverse scientific fields. Besides deriving differential equations for dynamical systems based on…
This paper presents a novel quantification of the fraction of broken waves (Qb) in natural surf zones using data from seven wave-dominated Australian beaches. Qb is a critical, but rarely quantified, parameter for parametric surf zone…
In the study of high-dimensional data, it is often assumed that the data set possesses an underlying lower-dimensional structure. A practical model for this structure is an embedded compact manifold with boundary. Since the underlying…
Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…
We formulate a depth-averaged non-hydrostatic model to solve wave equations with generation by a moving bottom. This model is built upon the shallow water equations, which are widely used in tsunami wave modelling. An extension leads to two…
The development of novel autonomous underwater gliders has been hindered by limited shape diversity, primarily due to the reliance on traditional design tools that depend heavily on manual trial and error. Building an automated design…
Global climate change plays an essential role in our daily life. Mesoscale ocean eddies have a significant impact on global warming, since they affect the ocean dynamics, the energy as well as the mass transports of ocean circulation. From…
In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…
Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…
All metamaterial applications are based upon the idea that extreme material properties can be achieved through appropriate dynamic homogenization of composites. This homogenization is almost always done for infinite domains and the results…
We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope…
Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty…
Time series classification is of significant importance in monitoring structural systems. In this work, we investigate the use of supervised machine learning classification algorithms on simulated data based on a physical system with two…
Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…