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In this paper we describe a method for modeling the dynamic behavior of splashing fluids. The model simulates the behavior of a fluid when objects impact or float on its surface. The forces generated by the objects create waves and splashes…
Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly…
We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…
Structured light illumination is an active 3-D scanning technique based on projecting/capturing a set of striped patterns and measuring the warping of the patterns as they reflect off a target object's surface. In the case of phase…
Metasurfaces are extremely useful for controlling and manipulating electromagnetic waves. Full-wave numerical simulation is highly desired for their design and optimization, but it is notoriously difficult, even for two-dimensional…
Estimating three-dimensional conformations of a molecular graph allows insight into the molecule's biological and chemical functions. Fast generation of valid conformations is thus central to molecular modeling. Recent advances in…
Wave groups can be detected and studied by using the wave envelope. So far, the method used to compute the wave envelope employs the Riesz transform. However, such a technique always produces symmetric envelopes, which is only realistic in…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
The flow field generated by a transom-stern hullform is a complex, broad-banded, three-dimensional phenomenon marked by a large breaking wave. This unsteady multiphase turbulent flow feature is difficult to study experimentally and simulate…
Effective spatio-temporal measurements of water surface elevation (water waves) in laboratory experiments are essential for scientific and engineering research. Existing techniques are often cumbersome, computationally heavy and generally…
The dimer model is the study of random dimer covers (perfect matchings) of a graph. A double-dimer configuration on a graph $G$ is a union of two dimer covers of $G$. We introduce quaternion weights in the dimer model and show how they can…
We study the coupled small-amplitude motion of the mechanical system consisting of infinitely deep water and a structure immersed in it. The former is bounded above by a free surface, whereas the latter is formed by an arbitrary finite…
Elastic wave propagation is studied in a heterogeneous 2-D medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident…
This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic composite membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The model and the method…
Existing conformal prediction algorithms estimate prediction intervals at target confidence levels to characterize the performance of a regression model on new test samples. However, considering an autonomous system consisting of multiple…
A comprehensive study of the problem of modelling vaporous cavitation in transmission lines is presented. The two-phase homogeneous equilibrium vaporous cavitation model which has been developed is compared with the conventional column…
Structures such as waves, jets, and vortices have a dramatic impact on the transport properties of a flow. Passive tracer transport in incompressible two-dimensional flows is described by Hamiltonian dynamics, and, for idealized structures,…
We propose conformal hyperrectangular prediction regions for multi-target regression. We propose split conformal prediction algorithms for both point and quantile regression to form hyperrectangular prediction regions, which allow for easy…
A new approach for analyzing waveguide junctions containing conductive cylindrical objects is proposed. The algorithm is based on mode matching technique using local projection functions, which improves the numerical conditioning of the…
A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a formulation of a fully nonlinear and dispersive potential flow water wave…