A three-dimensional multi-block Newton-Krylov flow solver for the Euler equations has been developed for steady aerodynamic flows. The solution is computed through a Jacobian-free inexact-Newton method with an approximate-Newton method for startup. The linear system at each outer iteration is solved using a Generalized Minimal Residual (GMRES) Krylov subspace algorithm. An incomplete lower/uppe...

In his 2007 monograph, D. Christodoulou proved a breakthrough result giving a complete description of the formation of shock waves, starting from small, regular initial conditions, in solutions to the relativistic Euler equations. In 2014, Christodoulou–Miao extended the result to the nonrelativistic compressible Euler equations. In both works, the assumptions on the initial conditions caused t...

the studies in aerial vehicles modeling and control have been increased rapidly recently. in this paper , a coordination of two types of heterogeneous robots , namely unmanned aerial vehicle (uav) and unmanned ground vehicle (ugv) is considered. in this paper the uav plays the role of a virtual leader for the ugvs. the system consists of a vision- based target detection algorithm that uses the ...

A new formulation of the equations of motion of constrained multibody systems is presented using a coordinate-splitting (CS) technique. In contrast to the conventional index reduction techniques which apply diierentiation to the Lagrange formulation, this approach applies the coordinate-split operator to the variational form of constrained dynamics, yielding consistent dynamic equations of mult...

We propose new construction of dependent variables for equations of an ideal barotropic fluid. This construction is based on a direct generalization of the known connection between Schroedinger equation and a system of Euler-type equations. The system for two complexvalued functions is derived that is equivalent to Euler equations. Possible advantages of the proposed formulation are discussed.

Let φ(·) denote the Euler function, and let a > 1 be a fixed integer. We study several divisibility conditions which exhibit typographical similarity with the standard formulation of the Euler theorem, such as an ≡ 1 (mod φ(n)), and we estimate the number of positive integers n ≤ x satisfying these conditions. 2000 Mathematics Subject Classification. 11A07, 11N37.

The problem of recovering a parameter function based on measurements of solutions of a system of partial diierential equations in several space variables leads to a number of computational challenges. Upon discretization of a regularized formulation a large, sparse constrained optimization problem is obtained. Typically in the literature , the constraints are eliminated and the resulting uncons...

A transfer matrix formalism applicable to certain reparametrization invariant theories , including quantum gravity, is proposed. In this formulation it is found that every stationary state in quantum gravity satisfies a Wheeler-DeWitt equation, but each with a different value of the Planck mass; the value m 4 P lanck turns out to be proportional to the eigenvalue of the evolution operator. As a...

Recent theoretical work has developed the Hamilton’s-principle analog of Lie-Poisson Hamiltonian systems defined on semidirect products. The main theoretical results are twofold: 1. Euler–Poincaré equations (the Lagrangian analog of Lie-Poisson Hamiltonian equations) are derived for a parameter dependent Lagrangian from a general variational principle of Lagrange d’Alembert type in which variat...