Related papers: A More General Linear Projectile Problem
The problem of three-dimensional (3-D) wind profile prediction is addressed based a trinion wind model, which inherently reckons the coupling of the three perpendicular components of a wind field. The augmented trinion statistics are…
This paper analyzes the nonlinear correspondence between the reflectivity profile (model) and the plane wave impulse response at the boundary (data) for a three-dimensional half space consisting of a sequence of homogeneous horizontal…
Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent…
The problem of de-projection of radio line observations of axi-symmetric expanding circumstellar envelopes is studied with the aim of easing their analysis in terms of physics models. The arguments developed rest on the remark that, in…
The complete solutions of the Schr\"odinger equation for a particle with time-dependent mass moving in a time-dependent linear potential are presented. One solution is based on the wave function of the plane wave, and the other is with the…
The problem of determining three-dimensional density fields from single two-dimensional projections is hopelessly underdetermined without additional assumptions. While parameterized inversions are typically used to solve this problem, we…
The metric for plane gravitational waves is quantized using the Ashtekar field variables. The z axis (direction of travel of the waves) is taken to be the entire real line. Solutions to the constraints are proposed; they involve open-ended…
This paper describes the extensive Wind Tunnel (WT) linear cascade testing campaign carried out on a constant section turbine blade developed for low subsonic applications. Comprehensive experimental program was designed to determine the…
In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture…
We present the problem stated in intuitive language as problem 2 at the 52nd International Mathematical Olympiad as a formal statement, and prove that it is valid in ordered regular incidence planes, the weakest ordered geometry whose…
Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…
While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…
In this paper, we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weighted $\ell_1$ (OWL1) norm ball. In particular, an efficient semismooth Newton method is proposed for solving the…
Several N-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (``acceleration equal force;'' in most cases, the forces are velocity-dependent) and are amenable to exact…
We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed…
For nonlinear wave equations with a potential term we prove pointwise space-time decay estimates and develop a perturbation theory for small initial data. We show that the perturbation series has a positive convergence radius by a method…
We study the Dirichlet problem for semilinear equations on general open sets with measure data on the right-hand side and irregular boundary data. For this purpose we develop the classical method of orthogonal projection. We treat in a…
As a follow up to \cite{Causley2013}, we provide a detailed description of the numerical implementation of an O(N), A-stable, second order accurate solution of the wave equation, constructed from semi-discrete boundary value problems. We…
Both null and timelike rays experience trajectory bending in a gravitational field. In this work, we systematically develop a perturbative method to compute the deflection angle of rays with general velocity $v$ in arbitrary static and…
In this paper, we construct exact solutions that character three-dimensional, nonlinear trapped lee waves propagation superimposed on longitudinal atmospheric currents in the $\beta$-plane approximation. The solutions obtained are presented…