相关论文: Derivation of the Paraxial Ray Equations in Three …
Paraxial ray tracing procedures have become widely accepted techniques for acoustic models in seismology and underwater acoustics. To date a generic form of these procedures including fluid motion and time dependence has not appeared in the…
Caustic formation occurs within a ray skeleton as optical or acoustic fields propagate in a medium with variable refractive properties and are unphysical, their presence being an artifact of the ray approximation of the field, and methods…
"Acoustic spacetimes", in which techniques of differential geometry are used to investigate sound propagation in moving fluids, have attracted considerable attention over the last few decades. Most of the models currently considered in the…
Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics…
Geodesics become an essential element of the geometry of a semi-Riemannian manifold. In fact, their differences and similarities with the (positive definite) Riemannian case, constitute the first step to understand semi-Riemannian Geometry.…
Parts V, VI and VII of this study are dedicated to the computation of paraxial rays and dynamic characteristics along the stationary rays obtained numerically in Part III. In this part (Part V), we formulate the linear, second-order, Jacobi…
In this work, the paraxial approximation of the free Dirac equation is examined. The results are first obtained by constructing superpositions of exact solutions with suitable profiles, which are borrowed from paraxial optics. In this…
A concise method of deriving expressions for Gaussian-like solutions of the paraxial and d'Alembert equations is presented. This method is based on the Hankel transform. Choosing some Gaussian base functions with slight modifications of the…
Sound wave propagation in a relativistic perfect fluid with a non-homogeneous isentropic flow is studied in terms of acoustic geometry. The sound wave equation turns out to be equivalent to the equation of motion for a massless scalar field…
We first derive the relation between the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold using a method which identifies the…
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.…
In Part V of this study, we presented an original Lagrangian approach for computing the dynamic characteristics along stationary rays, by solving the linear, second-order Jacobi differential equation, considering four sets of initial…
In this paper, we present an adaptive gradient descent method for geodesically convex optimization on a Riemannian manifold with nonnegative sectional curvature. The method automatically adapts to the local geometry of the function and does…
In this work, the paraxial version of Maxwell equations is derived with the use of two Riemann-Silberstein vectors. Exact solutions of these equations are then obtained representing the paraxial electromagnetic fields. These fields satisfy…
Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on…
We define the notion of a smooth pseudo-Riemannian algebraic variety $(X,g)$ over a field $k$ of characteristic $0$, which is an algebraic analogue of the notion of Riemannian manifold and we study, from a model-theoretic perspective, the…
The paper is a study of geodesic in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investigated. The equation of the geodesic flow has singularities at…
We derive system of equations describing fluidity of the medium consisting of non-relativistic particles with finite mass-widths. For that we use expressions for the kinetic Noether 4-current and the Noether energy-momentum tensor being…
We present the Eulerian Gaussian beam method in anisotropic media. We derive kinematic and dynamic ray tracing equations based on the level set theory and Eulerian theory using the anisotropic eikonal equation. Compared with the traditional…
In this paper a new formalism based on exterior differential systems is derived for perfect-fluid spacetimes endowed with an abelian orthogonally transitive G2 group of motions acting on spacelike surfaces. This formulation allows…