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Partial Differential Equations (PDEs) are widely used for modeling the physical phenomena and analyzing the dynamical behavior of many engineering and physical systems. The heat equation is one of the most well-known PDEs that captures the…
The paper describes a numerical method for solving acoustic multibody scattering problems in two and three dimensions. The idea is to compute a highly accurate approximation to the scattering operator for each body through a local…
A numerically exact path integral treatment of the absorption and emission spectra of open quantum systems is presented that requires only the straightforward solution of a stochastic differential equation. The approach converges rapidly…
We outline the theory and practice of measuring the four Stokes parameters of spectral lines in emission/absorption observations. We apply these concepts to our Arecibo HI absorption line data and present the results. We include a detailed…
A new score function is proposed for stack decoding of polar codes, which enables one to accurately compare paths of different lengths. The proposed score function includes bias, which reflects the average behaviour of the correct path.…
Spectral representations have been shown to provide an efficient way to represent the poorly understood high-density portion of the neutron-star equation of state. This paper shows how the efficiency and accuracy of those representations…
This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…
Parameterized representations of the equation of state play an important role in efforts to measure the properties of the matter in the cores of neutron stars using astronomical observations. New representations are presented here that are…
We present the first numerical radiative transfer simulation of multiple light scattering in dust configurations containing aligned non-spherical (spheroidal) dust grains. Such models are especially important if one wants to explain the…
Multiple scalar integral representations for traces of operator derivatives are obtained and applied in the proof of existence of the higher order spectral shift functions.
Emission spectroscopy is an invaluable tool for probing the atmospheres of brown dwarfs and exoplanets, but interpretations based on flux spectra alone often suffer from degeneracies among temperature structure, chemical composition, and…
Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We…
The technique of polarized neutron scattering is reviewed with emphasis on applications. Many examples of the usefulness of the method in various fields of physics are given like the determination of spin density maps, measurement of…
Optics labs are an integral part of the advanced curriculum for physics majors. Students majoring in other disciplines, like chemistry, biology or engineering rarely have the opportunity to learn about the most recent optical techniques and…
The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier-Stokes equations. We develop a separation of variables representation for this equation in polar…
The main goals of `spin physics' are recalled, and some theoretical and phenomenological aspects of longitudinally polarized deep inelastic scattering and other hard processes are reviewed. The spin dependent parton densities of protons and…
Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…
We present the components of a high-order accurate Navier-Stokes solver designed to simulate high-Reynolds-number stratified flows. The proposed numerical model addresses some of the numerical and computational challenges that…
Higher resolution telescopes as well as 3D numerical simulations will require the development of detailed 3D radiative transfer calculations. Building upon our previous work we extend our method to include both continuum and line transfer.…
We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity. For this problem, the classical finite elements method of degree one converges only to order one-half for the L2 norm of the vorticity. We…