Related papers: Discovery of physically interpretable wave equatio…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
This paper presents a computational framework that generates ensemble predictive mechanics models with uncertainty quantification (UQ). We first develop a causal discovery algorithm to infer causal relations among time-history data measured…
In this article, we consider the stochastic wave equation on $\mathbb{R}_{+} \times \mathbb{R}$, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structures are given by locally…
A two-dimensional generalized hydrodynamics (GH) model is developed to study the full spectrum of both longitudinal and transverse dust acoustic waves (DAW) in strongly coupled complex (dusty) plasmas, with memory-function-formalism being…
Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques…
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…
Data from gravitational wave detectors are recorded as time series that include contributions from myriad noise sources in addition to any gravitational wave signals. When regularly sampled data are available, such as for ground based and…
In the identification of differential equations from data, significant progresses have been made with the weak/integral formulation. In this paper, we explore the direction of finding more efficient and robust test functions adaptively…
In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements,…
Data-driven methods have recently made great progress in the discovery of partial differential equations (PDEs) from spatial-temporal data. However, several challenges remain to be solved, including sparse noisy data, incomplete candidate…
We describe here an experimental technique based on the acoustic scattering phenomenon allowing the direct probing of the vorticity field in a turbulent flow. Using time-frequency distributions, recently introduced in signal analysis…
This paper presents a novel method for evaluating second-order consistent hydrodynamic loads, which employs nonlinear wave and body kinematics. The pseudo-spectral formulation of nonlinear potential flow wave solvers is exploited,…
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…
The assimilation and prediction of phase-resolved surface gravity waves are critical challenges in ocean science and engineering. Potential flow theory (PFT) has been widely employed to develop wave models and numerical techniques for wave…
Rapid evolution of sensor technology, advances in instrumentation, and progress in devising data-acquisition softwares/hardwares are providing vast amounts of data for various complex phenomena, ranging from those in atomospheric…
In this short note, we derive a system of two nonlocal equations for the water-wave problem following the work of [AFM06]. Specifically, we consider a fluid with a one-dimensional free surface for an irrotational fluid both with, and…
A unidirectional reduction of the deep-water surface gravity wave problem is derived in physical space using real variables. By employing a near-identity canonical transformation, cubic interactions are eliminated from the Hamiltonian, with…
Computational modeling is a key resource to gather insight into physical systems in modern scientific research and engineering. While access to large amount of data has fueled the use of Machine Learning (ML) to recover physical models from…
Gravitational waves (GWs) generated by a first-order phase transition at the electroweak scale are detectable by future space-based detectors like LISA. The lifetime of the resulting shock waves plays an important role in determining the…
We explore the relation between fast waves, damping and imposed noise for different scalings by considering the singularly perturbed stochastic nonlinear wave equations \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on a bounded spatial domain.…