Related papers: Ray Theory of Waves
Under ray-optical light transport, the classical ray serves as a linear and local "point query" of light's behaviour. Linearity and locality are crucial to the formulation of sophisticated path tracing and sampling techniques, that enable…
Diffraction tomography is an inverse scattering technique used to reconstruct the spatial distribution of the material properties of a weakly scattering object. The object is exposed to radiation, typically light or ultrasound, and the…
In this article, we review different studies based on advanced x-ray diffraction techniques - especially coherent x-ray diffraction - that allowed us to reveal the behaviour of such symmetry-breaking systems as Charge Density Wave (CDW) and…
Waves play an essential role in many aspects of plasma science, such as plasma manipulation and diagnostics. Due to the complexity of the governing equations, approximate models are often necessary to describe wave dynamics. In this…
Modeling 4D scenes requires capturing both spatial structure and temporal motion, which is challenging due to the need for physically consistent representations of complex rigid and non-rigid motions. Existing approaches mainly rely on…
Time series data analytics has been a problem of substantial interests for decades, and Dynamic Time Warping (DTW) has been the most widely adopted technique to measure dissimilarity between time series. A number of global-alignment kernels…
We study the propagation in three dimensions of internal waves using ray tracing methods and traditional dynamical systems theory. The wave propagation on a cone that generalizes the Saint Andrew's cross justifies the introduction of an…
In this paper, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the…
The well-known diffusion theory describes propagation of light and electromagnetic waves in complex media. While diffusion theory is known to fail both for predominant forward scattering or strong absorption, its precise range of validity…
3D shape completion has broad applications in robotics, digital twin reconstruction, and extended reality (XR). Although recent advances in 3D object and scene completion have achieved impressive results, existing methods lack 3D…
Detecting water-surface targets for Unmanned Surface Vehicles (USVs) is challenging due to wave clutter, specular reflections, and weak appearance cues in long-range observations. Although 4D millimeter-wave radar complements cameras under…
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…
We propose a novel method for establishing the convergence rates of solutions to reaction-diffusion equations to traveling waves. The analysis is based on the study of the traveling wave shape defect function introduced in [2]. It turns out…
We study dispersion properties of linear surface gravity waves propagating in an arbitrary direction atop a current profile of depth-varying magnitude using a piecewise linear approximation, and develop a robust numerical framework for…
Wireless Technology Recognition (WTR) and localization are essential in modern communication systems, enabling efficient spectrum management, seamless coexistence of diverse technologies, and accurate positioning in dynamic environments. In…
We study the convergence properties of the two-dimensional Rigorous Coupled Wave Approach (RCWA) for p-polarized monochromatic incident light. The RCWA is a semi-analytical numerical method that is widely used to solve the boundary-value…
A transformation method based on elastic ray theory is proposed to control high frequency elastic waves. We show that ray path can be controlled in an exact manner, however energy distribution along the ray is only approximately controlled.…
Solving the wave equation is one of the most (if not the most) fundamental problems we face as we try to illuminate the Earth using recorded seismic data. The Helmholtz equation provides wavefield solutions that are dimensionally reduced,…
Full waveform inversion (FWI) has the potential to provide high-resolution subsurface model estimations. However, due to limitations in observation, e.g., regional noise, limited shots or receivers, and band-limited data, it is hard to…
Understanding atomic structures is crucial, yet amorphous materials remain challenging due to their irregular and non-periodic nature. The Wavelet Transform Radial Distribution Function (WT-RDF) offers a physics-based framework for…