The objective of this paper is to construct and investigate smooth orientable surfaces in RN −1 by analytical methods. The structural equations of surfaces in connection with CPN−1 sigma models on Minkowski spacetime are studied in detail. This is carried out using a moving frame adapted to the surface immersed in su(N) algebra. The first and second fundamental forms of the surface as well as t...

Introduction In this paper we present a modification of Gauss-Huard's method for solving dense linear systems that allows an efficient implementation on machines with a hierarchical memory structure. GaussHuard's method resembles Gauss-Jordan's method in the fact that it reduces the given system by elementary transformations to a diagonal system and it resembles regular Gaussian elimination in ...

A novel time domain solver of Maxwell’s equations in passive (dispersive and absorbing) media is proposed. The method is based on the path integral formalism of quantum theory and entails the use of (i) the Hamiltonian formalism and (ii) pseudospectral methods (the fast Fourier transform, in particular) of solving differential equations. In contrast to finite differencing schemes, the path inte...

A stair Laguerre pseudospectral method is proposed for numerical solutions of differential equations on the half line. Some approximation results are established. A stair Laguerre pseudospcetral scheme is constructed for a model problem. The convergence is proved. The numerical results show that this new method provides much more accurate numerical results than the standard Laguerre spectral me...

A novel time domain solver of Maxwell’s equations in passive (dispersive and absorbing) media is proposed. The method is based on the path integral formalism of quantum theory and entails the use of (i) the Hamiltonian formalism and (ii) pseudospectral methods (the fast Fourier transform, in particular) of solving differential equations. In contrast to finite differencing schemes, the path inte...

Poisson equation is frequently encountered in mathematical modeling for scientific and engineering applications. Fast Poisson numerical solvers for 2D and 3D problems are, thus, highly requested. In this paper, we consider solving the Poisson equation ∇2u = f(x, y) in the Cartesian domain Ω = [−1, 1] × [−1, 1], subject to all types of boundary conditions, discretized with the Chebyshev pseudosp...

We describe Fourier pseudospectral time-domain simulations, carried out in order to study light interacting with a metallic nanoscale object. The difficulty of using Fourier methods to accurately predict the electromagnetic scattering in such problems arises from the discontinuity in the dielectric function along the surface of the metallic object. Standard Fourier methods lead to oscillatory b...

Transcription for Optimal Control Problems by Geoffrey Todd Huntington B. S. Aerospace Engineering, University of California, Los Angeles, 2001 S. M. Aerospace Engineering, Massachusetts Institute of Technology, 2003 Submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Aeronautics and Astronautics at the...

By systematically altering the in-plane flight path and velocity of an aircraft and the rate at which the cable is deployed, the tip of a cable being towed behind an aircraft is shown to rendezvous with a ground-based surface location in minimum time, with minimum control effort required. This is achieved through optimal control, formulated as a nonlinear programming problem using the Legendre-...

In our previous work, we have shown that the pseudospectral method is an effective and flexible computation scheme for deriving pulses for optimal control of quantum systems. In practice, however, quantum systems often exhibit variation in the parameters that characterize the system dynamics. This leads us to consider the control of an ensemble (or continuum) of quantum systems indexed by the s...