An exact analytic solution is presented to the problem of scattering of a plane wave from a perfect electromagnetic conducting (PEMC) elliptic cylinder, using the method of separation of variables. The formulation is carried out by expanding the incident as well as the scattered electromagnetic fields in terms of appropriate angular and radial Mathieu functions and a set of expansion coefficien...

| Gear theory is reexamined and we nd optimal shapes for gears. As optimality criteria, we allow: (1) minimal frictional losses (highest eeciency) assuming linear law of friction or (2) uniform maximum stress (it will wear out slowly and last the longest) assuming Hertzian contacts or (3) uniform maximal temperature, assuming we are in a high power limit in which all heat is removed by the lubr...

The flow over a pair of counter-rotating cylinders is investigated numerically and experimentally. It is demonstrated that it is possible to suppress unsteady vortex shedding for gap sizes from one to five cylinder diameters, at Reynolds numbers from 100 to 200, expanding on the more limited work by Chan & Jameson (Intl J. Numer. Meth. Fluids, vol. 63, 2010, p. 22). The degree of unsteady wake ...

We prove the W 1,2 p -solvability of second order parabolic equations in nondivergence form in the whole space for p ∈ (1,∞). The leading coefficients are assumed to be measurable in one spatial direction and have vanishing mean oscillation (VMO) in the orthogonal directions and the time variable in each small parabolic cylinder with the direction depending on the cylinder. This extends a recen...

A 2+1-dimensional anisentropic magnetogasdynamic system with a polytropic gas law is shown to admit an integrable elliptic vortex reduction when γ = 2 to a nonlinear dynamical subsystem with underlying integrable Hamiltonian–Ermakov structure. Exact solutions of the magnetogasdynamic system are thereby obtained which describe a rotating elliptic plasma cylinder. The semi-axes of the elliptical ...

New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet’s solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is related to the solution of a Mathieu equation of odd characteristic exponent. The number of notches of these analysing filters can be easily designed. Wavelet...

New direct spectral solvers for the 3D Helmholtz equation in a finite cylindrical region are presented. A purely variational (no collocation) formulation of the problem is adopted, based on Fourier series expansion of the angular dependence and Legendre polynomials for the axial dependence. A new Jacobi basis is proposed for the radial direction overcoming the main disadvantages of previously d...

Electro hydraulic actuator (EHA) system has inner and outer loops like a cascade system. The inner loop consists of an electric motor, a gear pump, and an angular velocity controller, and the outer loop consists of a hydro-actuator and a position controller. Especially, dead-band nonlinearity that exists between the electric motor and the gear pump and friction that occurs between the cylinder ...