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We study here the water-waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known, that for such regimes, a generalization of the KdV…
We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the nonlinear wave system. This shock diffraction problem can be formulated as a…
We present a volume rendering-based neural surface reconstruction method that takes as few as three disparate RGB images as input. Our key idea is to regularize the reconstruction, which is severely ill-posed and leaving significant gaps…
We study the unique recovery of time-independent lower order terms appearing in the symmetric first order perturbation of the Riemannian wave equation by sending and measuring waves in disjoint open sets of \textit{a priori} known closed…
It is well known that a band-limited signal can be reconstructed from its uniformly spaced samples if the sampling rate is sufficiently high. More recently, it has been proved that one can reconstruct a 1D band-limited signal even if the…
From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, new theories state that transitions between extreme waves are allowed. However, these have never been experimentally observed…
We present a data-driven generative framework for synthesizing blood vessel 3D geometry. This is a challenging task due to the complexity of vascular systems, which are highly variating in shape, size, and structure. Existing model-based…
In the past 30 years, subwavelength gratings have been developed and produced as highly secured Diffractive Optical Variable Image Devices (DOVIDs). They allowed new distinct optical effects and dramatically lowered DOVIDs counterfeiting.…
Consider a two-dimensional stratified solitary wave propagating through a body of water that is bounded below by an impermeable ocean bed. In this work, we study how such a wave can be reconstructed from data consisting of the wave speed,…
We propose Dirichlet Winding Reconstruction (DiWR), a robust method for reconstructing watertight surfaces from unoriented point clouds with non-uniform sampling, noise, and outliers. Our method uses the generalized winding number (GWN)…
When constructing high-order schemes for solving hyperbolic conservation laws, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For…
Conductance-voltage characteristics (CVCs) for non-symmetric tunnel junctions between $d$-wave superconductors with charge-density waves (CDWs) and normal metals were calculated. It was shown that they have a V-like form at small voltages…
We introduce a new methodology for adding localized, space-time smooth, artificial viscosity to nonlinear systems of conservation laws which propagate shock waves, rarefactions, and contact discontinuities, which we call the $C$-method. We…
Using weak wave turbulence theory analysis, we distinguish three main regimes for 2D stratified fluids in the dimensionless parameter space defined by the Froude number and the Reynolds number: discrete wave turbulence, weak wave…
Using the variable phase method, we reformulate the Dirac equation governing the charge carriers in graphene into a nonlinear first-order differential equation from which we can treat both confined-state problems in electron waveguides and…
Starting from a realistic extended Hubbard model for a $p_{x,y}$-orbital tight-binding model on the Honeycomb lattice, we perform a thorough investigation on the possible electron instabilities in the MA-TBG near the van Hove (VH) dopings.…
The unique reconstruction of a spherically-symmetric wave speed $v$ is considered in a bounded spherical region of radius $b$ from the set of corresponding transmission eigenvalues for which the corresponding eigenfunctions are also…
Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the Singular Value…
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on…
A two-step shape reconstruction method for diffuse optical tomography (DOT) is presented which uses adjoint fields and level sets. The propagation of near-infrared photons in tissue is modeled by the time-dependent linear transport…