相关论文: Generalized Paraxial Ray Trace Procedure Derived f…
We derive the beam tracing and profile evolution for the propagation of any localised beam with arbitrary profile through an inhomogeneous cold plasma. We recover standard Gaussian beam-tracing, with an additional PDE describing the…
The detection of gravitational waves based on the geodesic deviation equation is discussed. In particular, it is shown that the only non-vanishing components of the wave field in the conventional traceless-transverse gauge in linearized…
Geometric acoustics is an efficient framework for room acoustics modeling, governed by the canonical time-dependent rendering equation. Acoustic radiance transfer (ART) solves the equation by discretization, modeling time- and…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
Recently, Differentiable Ray Tracing has been successfully applied in the field of wireless communications for learning radio materials or optimizing the transmitter orientation. However, in the frame of gradient based optimization,…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
Random fields are mathematical structures used to model the spatial interaction of random variables along time, with applications ranging from statistical physics and thermodynamics to system's biology and the simulation of complex systems.…
Regularity theory for diffusive operators is among the finest treasures of the modern mathematical sciences. It appears in several different fields, such as, differential geometry, topology, numerical analysis, dynamical systems,…
We show that Gaussian process regression (GPR) can be used to infer the electromagnetic (EM) duct height within the marine atmospheric boundary layer (MABL) from sparsely sampled propagation factors within the context of bistatic radars. We…
Linear structural equation models, which relate random variables via linear interdependencies and Gaussian noise, are a popular tool for modeling multivariate joint distributions. These models correspond to mixed graphs that include both…
Paraxial fluids of light are a promising platform for exploring collective phenomena in a highly tunable environment. These systems, which map the propagation of light through nonlinear media onto the wavefunction of effective 2D quantum…
We consider a generalised Webster's equation for describing wave propagation in curved tubular structures such as variable diameter acoustic wave guides. Webster's equation in generalised form has been rigorously derived in a previous…
Paraxial diffraction of monochromatic Gaussian beams by arbitrarily shaped polygonal apertures is analytically explored within the boundary diffraction wave theory framework. Exact closed-form expressions of the diffracted wavefield are…
We study the paraxial wave equation with a randomly perturbed index of refraction, which can model the propagation of a wave beam in a turbulent medium. The random perturbation is a stationary and isotropic process with a general form of…
In this paper, a new exact solution of general Degasperis-Procesi (gDP) equation, a nonlinear equation in plasma, will be constructed by using PPA method, extended trigonometry and extended hyperbolic method. gDP equation is a good…
We report the development of a new ray-tracing simulation tool having the potential of the full characterization of a radio link through the accurate study of the propagation path of the signal from the transmitting to the receiving…
We construct a frame of complex Gaussians for the space of $L^2(\mathbb{R}^n)$ functions. When propagated along bicharacteristics for the wave equation, the frame can be used to build a parametrix with suitable error terms. When the…
The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…
The Gaussian process is a powerful and flexible technique for interpolating spatiotemporal data, especially with its ability to capture complex trends and uncertainty from the input signal. This chapter describes Gaussian processes as an…
Irregular terrain has a pronounced effect on the propagation of seismic and acoustic wavefields but is not straightforwardly reconciled with structured finite-difference (FD) methods used to model such phenomena. Methods currently detailed…