Related papers: Generalized Paraxial Ray Trace Procedure Derived f…
A hidden symmetry of the nonlinear wave equation is exploited to analyse the propagation of paraxial and uniform atom-laser beams in time-independent, quadratic and cylindrical potentials varying smoothly along the propagation axis. The…
We study the performance of nonparametric Bayes procedures for one-dimensional diffusions with periodic drift. We improve existing convergence rate results for Gaussian process (GP) priors with fixed hyper parameters. Moreover, we exhibit…
This paper proposes an efficient general alternating-direction implicit (GADI) framework for solving large sparse linear systems. The convergence property of the GADI framework is discussed. Most of the existing ADI methods can be viewed as…
Propagation of sound beam diffracted from a circular aperture in far-field region has been studied in this paper by the method of angular spectrum representation and stationary phase method. This nonparaxial theory is useful when beam angle…
The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this note we point out some subtleties in the…
General properties of linear propagation of discretized light in homogeneous and curved waveguide arrays are comprehensively investigated and compared to those of paraxial diffraction in continuous media. In particular, general laws…
The non-linear transformations incurred by the rays in an optical system can be suitably described by matrices to any desired order of approximation. In systems composed of uniform refractive index elements, each individual ray refraction…
We present a Bayesian estimation analysis for a particular trace gas detection technique with species separation provided by differential diffusion. The proposed method collects a sample containing multiple gas species into a common volume,…
An approximate analytical approach to describe the stochastic motion of sound rays in deep ocean is developed. This is done for a realistic propagation model with an internal wave induced perturbation imposed on the smooth background sound…
This article firstly develops a proximal explicit approach for the generalized method of lines. In such a method, the domain of the PDE in question is discretized in lines and the equation solution is written on these lines as functions of…
Ray tracing (RT) is instrumental in 6G research in order to generate spatially-consistent and environment-specific channel impulse responses (CIRs). While acquiring accurate scene geometries is now relatively straightforward, determining…
For metrology, geodesy and gravimetry in space, satellite based instruments and measurement techniques are used and the orbits of the satellites as well as possible deviations between nearby ones are of central interest. The measurement of…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
Fractional Gaussian fields provide a rich class of spatial models and have a long history of applications in multiple branches of science. However, estimation and inference for fractional Gaussian fields present significant challenges. This…
We describe a novel adaptive ray tracing scheme to solve the equation of radiative transfer around point sources in hydrodynamical simulations. The angular resolution adapts to the local hydrodynamical resolution and hence is of use for…
Many real world problems exhibit patterns that have periodic behavior. For example, in astrophysics, periodic variable stars play a pivotal role in understanding our universe. An important step when analyzing data from such processes is the…
In seismic imaging, understanding the relationship between wavefront-propagation velocity and time-interval velocity is crucial for achieving optimal resolution. However, this task becomes even more challenging when considering anisotropic…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
The perturbation equation for aeroacoustics has been derived in a dissipative medium from the linearized compressible Navier-Stokes equation without any assumption, by expressing the same in spectral plane as in Continuum perturbation field…
Seismic tomography solves high-dimensional optimization problems to image subsurface structures of Earth. In this paper, we propose to use random batch methods to construct the gradient used for iterations in seismic tomography.…