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Maxwell's equations resemble Schr\"odinger's equation in that an exact solution for a well-defined model delivers all physically relevant details. Solvable microscopic electrodynamic models, however, are rare. An exception is the discrete…
The scattering of electromagnetic waves by three--dimensional periodic structures is important for many problems of crucial scientific and engineering interest. Due to the complexity and three-dimensional nature of these waves, the fast,…
The radiative transfer equation (RTE) is a cornerstone for describing the propagation of electromagnetic radiation in a medium, with applications spanning atmospheric science, astrophysics, remote sensing, and biomedical optics. Despite its…
We present a numerical method which is able to approximate traveling waves (e.g. viscous profiles) in systems with hyperbolic and parabolic parts by a direct long-time forward simulation. A difficulty with long-time simulations of traveling…
We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral…
An eigenmode projection technique (EPT) is developed and employed to solve problems of electromagnetic resonance in closed cavities and scattering from discontinuities in guided-wave structures. The EPT invokes the eigenmodes of a canonical…
A Maxwell solver derived from finite element method with \mathcal{O}(N) computing cost is developed to improve the numerical dispersion properties in relativistic particle-in-cell (PIC) simulations. The correction of the dispersion relation…
Positron Emission Tomography using 2-[18F]-2deoxy-D-glucose as radiotracer (FDG-PET) is currently one of the most frequently applied functional imaging methods in clinical applications. The interpretation of FDG-PET data requires…
Many new applications of ferroelastic materials require a better understanding of their dynamics that often involve phase transformations. In such cases, an important prerequisite is the understanding of wave propagation caused by…
A k-space method for nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme [Mast et al.,…
The problem of light propagation of frequency corresponding to half of the energy difference between a metastable excited state and the ground state of atoms is examined, and solved for coherent medium by analytic means. We demonstrate that…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…
I present an overview of pulse propagation methods used in nonlinear optics, covering both full-field and envelope-and-carrier methods. Both wideband and narrowband cases are discussed. Three basic forms are considered -- those based on (a)…
Magnetic guiding fields in combination with energy dispersive semiconductor detectors have been employed already more than 50 years ago for in-beam internal conversion electron spectroscopy. Even then it was recognized that efficiency…
We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…
We describe and evaluate a numerical solution strategy for simulating surface acoustic waves through semiconductor devices with complex geometries. This multi-physics problem is of particular relevance to the design of quantum electronic…
Thermal radiative transfer (TRT) is an essential piece of physics in inertial confinement fusion, high-energy density physics, astrophysics etc. The physical models of this type of problem are defined by strongly coupled differential…
There is great interest in the development of novel nanomachines that use charge, spin, or energy transport, to enable new sensors with unprecedented measurement capabilities. Electrical and thermal transport in these mesoscopic systems…
Boltzmann transport equation (BTE) is an ideal tool to describe the multiscale phonon transport phenomena, which are critical to applications like microelectronics cooling. Numerically solving phonon BTE is extremely computationally…
A new spectral particle-in-cell (PIC) method for plasma modeling is presented and discussed. In the proposed scheme, the Fourier-Bessel transform is used to translate the Maxwell equations to the quasi-cylindrical spectral domain. In this…